Dimitrios VAMVATSIKOS
Dimitrios was born in Nea Ionia Volou, Greece in 1974. Having an intense interest in math and physics he enrolled in NTU Athens and graduated with a Diploma in Civil Engineering (1997) and a desire to broaden his horizons. He then moved to California and Stanford University where he studied geomechanics (MSc 1998), probabilistic methods, hazard estimation and seismic performance of structures (PhD 2002). After graduating he participated in various research projects in Greece ranging from modal identification and Bayesian model updating for bridges to modeling older reinforced concrete buildings. On September 2005 he was appointed at the University of Cyprus as a Lecturer teaching design of steel structures and earthquake engineering. Since January 2011 he has joined the faculty of the Metal Structures Laboratory at the National Technical University of Athens specializing in the static and dynamic analysis of steel structures.
Research Interests
His research vision is focused on integrating structural modeling, computational techniques, probabilistic concepts and experimental results into a coherent framework for the performance evaluation of structures. Specifically, he is highly interested in the estimation of seismic hazard, the modeling, analysis and design of steel and monumental structures, the nonlinear static and dynamic analysis of structures, the seismic performance of buildings and bridges and the associated influence of uncertainties. The underlying ambition is to integrate elements of such procedures into future codes and design practices.
JOURNAL PAPERS
Now - 1999
Melissianos V.E., Karaferis N.D., Bakalis K., Kazantzi A.K., Vamvatsikos D. (2024). Operational status effect on the seismic risk assessment of oil refineries. International Journal of Disaster Risk Reduction, 113: 104842.
Abstract | The operational status of an oil refinery (type and scale of operations that take place at any time instance) largely determines the amount of fuel produced, circulated within the facility, and stored in tanks. This status is affected by seasonality, periods of peak or low demand, as well as periods of routine maintenance. However, it is an aspect that is typically neglected even though it stands out among the factors that determine the seismic performance of several critical industrial assets, such as the storage tanks, as well as the consequences of any potential failure. An open-source refinery testbed is employed herein to demonstrate the effect of the refinery’s operational status on the seismic risk estimates. Alternative realistic operational scenarios are developed following typical industry practices and are arranged over a time period between two refinery major maintenance shutdown events. The most probable damage state is selected for each asset to identify the most vulnerable ones. Based on the type and importance of the impacted assets, the potential consequences are determined at the facility level. Resulting estimates are very different if an earthquake strikes during a regular/high/low-demand period, or a maintenance period. The framework can be utilized to identify the locations within the refinery that may trigger cascading failures and secondary damages, should their assets be damaged by a seismic event. The outcomes can be exploited by stakeholders, risk engineers, and emergency action planners for developing customized and businesslike procedures to enhance the seismic resilience of the facility.
Melissianos V.E., Karaferis N.D., Bakalis K., Kazantzi A.K., Vamvatsikos D. (2024). Hazard, exposure, fragility, and damage state homogenization of a virtual oil refinery testbed for seismic risk assessment. Earthquake Spectra. 2024;0(0).
Abstract | A virtual mid-size oil refinery, located in a high-seismicity region of Greece, is offered as a testbed for developing and testing system-level assessment methods due to direct impact from seismic shaking and without considering geohazards, such as liquefaction and surface faulting. Its characterization is offered in a dedicated repository (https://doi.org/10.5281/zenodo.11419659) and it comprises (a) a comprehensive probabilistic treatment of seismic hazard tied to an open-source seismological model; (b) a hazard-consistent set of ground motion records; (c) a full geolocated exposure model with all pertinent critical assets, namely tanks, pressure vessels, process towers, chimneys, equipment-supporting buildings, and a flare; (d) the corresponding record-wise asset demands and summarized fragilities derived via nonlinear dynamic analyses on reduced-order numerical models. Background information is provided on all refinery assets to delineate their role in the refining process. Furthermore, an explicit homogenization of the damage states is proposed, translating them from the asset level to the refinery system level considering the importance of each asset on the overall operational and structural integrity of the refinery. The results can form the basis of any follow-up study that seeks to characterize the effects of cascading failures (fires, explosions), mitigation measures, seismic sequences, and operational constraints on the functionality, risk, and resilience of refining facilities.
Karaferis N.D., Melissianos V.E., Vamvatsikos D. (2024). Mechanical modeling, seismic fragility, and correlation issues for groups of spherical pressure vessels, Acta Mech, 235:1563-1582.
Abstract | A roadmap is outlined for determining comprehensive seismic fragility curves for (single or groups of) spherical pressure vessel structures commonly found in oil refineries. The developed modeling techniques aim to strike a balance between accuracy and computational efficiency, with a focus on capturing the most pertinent failure modes relevant to these structural types. First, a set of “partial” fragilities is determined based on each vessel’s fill ratio, as the response varies substantially depending on the amount of liquid content. Considering that a seismic assessment process invariably involves simultaneous consideration of such partial fragilities, a Monte Carlo-based approach is employed for their combination. The results naturally depend on the level of correlation employed, but can be almost perfectly matched by simpler analytical methods in the edge cases of full and zero correlation.
Melissianos V.E., Vamvatsikos D., Danciu L., Basili R. (2024). Design Fault Displacement for Lifelines at Fault Crossings: The Code-Based Approach for Europe. Bulletin of Earthquake Engineering, 22: 2677-2720.
Abstract | The earthquake-resistant design of lifelines, such as pipelines, tunnels and bridges, is based on the reliable representation and estimation of the seismic loading. In the case of lifeline–fault crossings, the design fault displacement is typically derived from estimates based on fault dimensions via empirical fault scaling relations for a given “design” scenario event. This approach comes with an unknown level of safety because the fault productivity and the actual distribution of earthquake events are essentially disregarded. To overcome this challenge, a simplified approach is proposed by statistically analyzing the outcome of probabilistic fault displacement hazard analyses (PFDHAs). A selection of faults from the 2020 European Fault-Source Model is used to build the logic tree and to set the range of parameters considered in the PFDHAs. The methodology allows the (mostly conservative) approximation of the fault displacement corresponding to any given return period based on readily available data, namely fault productivity, fault mechanism, fault length, and lifeline crossing location on the fault. The proposed methodology has been proposed and adopted as an informative Annex in prEN 1998-4:2022.
Kazantzi A.K., Karaferis N.D., Melissianos V.E., Vamvatsikos D. (2024). Acceleration-sensitive ancillary elements in industrial facilities: alternative seismic design approaches in the new Eurocode. Bulletin of Earthquake Engineering, 22: 109-132.
Abstract | The Eurocode 8—Part 4 approaches, per their December 2022 update, are presented for the design of acceleration-sensitive industrial ancillary components. The seismic performance of such nested and/or supported ancillary elements, namely mechanical and electrical equipment, machinery, vessels, etc. is critical for the safety and operability of an industrial facility in the aftermath of an earthquake. Of primary importance are the structural characteristics of the supporting structure and the supported component, pertaining to resonance, strength, and ductility, and whether these are known (and to what degree) during initial design and/or subsequent modifications and upgrades. Depending on the availability and reliability of information on the overall system, the Eurocode methods comprise (a) a detailed component/structure-specific design accounting for all pertinent component and building characteristics, equivalent to typical building design per Eurocode 8—Part 1–2, (b) a conservative approach where a blanket safety factor is applied when little or no such data is available, and (c) a ductile design founded on the novel concept of inserting a fuse of verified ductility and strength in the load path between the supporting structure and the ancillary element. All three methods are evaluated and compared on the basis of a case-study industrial structure, showing how an engineer can achieve economy without compromising safety under different levels of uncertainty.
Dasiou M-E., Lachanas C.G., Melissianos V.E., Vamvatsikos D. (2024). Seismic performance of the temple of Aphaia in Aegina island, Greece. Earthquake Engineering and Structural Dynamics, 53(2):573-592
Abstract | The seismic performance assessment of the ancient Temple of Aphaia in Aegina island, Greece, is presented. The Temple of Aphaia was erected around 500BC using porous limestone and is one of the most characteristic examples of Doric architecture. The assessment is performed within a performance-based framework using state-of-the-art tools of earthquake engineering. In the first part, the seismic hazard of the site was calculated using the European Seismic Hazard Model and hazard-consistent records were selected. Then, the Temple was scanned by drone and the point cloud was used to develop the numerical structural model. The Temple was analyzed using the discrete element method. Appropriate engineering demand parameters and limit state thresholds were defined. Fragility curves for the structural elements, namely, columns and architraves, of the Temple were computed via multi-stripe analysis. Finally, the seismic risk of the Temple was evaluated using long-term estimates in terms of return periods of exceeding limit states and total loss. The outcomes of the study offer valuable information to engineers, architects, and archaeologists regarding the current status of the monument in terms of identifying its most vulnerable elements and allowing the prioritization of short- and long-term restoration actions.
Melissianos V.E., Danciu L., Vamvatsikos D., Basili R. (2023). Fault displacement hazard estimation at lifeline–fault crossings: A simplified approach for engineering applications. Bulletin of Earthquake Engineering, 21: 4821–4849
Abstract | Lifelines, such as pipelines, roads, and tunnels, are critical infrastructure and when crossing active tectonic faults, a reliable estimation of the fault displacement in case of an earthquake is required. The first and simplest approach is to use empirical fault scaling relations to compute the design fault displacement, but this may result in an unknown level of safety. Thus, the probabilistic fault displacement hazard analysis (PFDHA) is the appropriate tool to assess the fault displacement hazard within a performance-based framework. Based upon an established PFDHA model, we present a simplified approach for engineering applications focusing on the lifeline–fault crossing along with appropriate simplifications and assumptions to extend its applicability to numerous faults. The aim is to provide a structure-independent approach of PFDHA that can be used when a site-specific study is not required, not possible (e.g., absence of recent sediments for dating past events), or too cumbersome, e.g., for lifeline route selection. Additionally, an in-depth investigation is presented on the key parameters, such as maximum earthquake magnitude, fault length, recurrence rate of all earthquakes above a minimum magnitude, and lifeline-fault crossing site, and how they affect the hazard level. This approach will be the basis for deriving hazard-consistent expressions to approximate fault displacement for use within the Eurocodes. The latter is intended to serve as a compromise between hazard-agnostic fault scaling relations and a comprehensive PFDHA, which requires detailed calculations and site-specific seismological data.
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G. (2023). Intensity measures as interfacing variables versus response proxies: The case of rigid rocking blocks. Earthquake Engineering and Structural Dynamics, 52(6):1722-1739.
Abstract |A comparative study of alternative Intensity Measures (IMs) for structures of rocking response is presented, focusing on the salient characteristics that define the selection of an optimal IM for the problem at hand. An IM may play the role of an interfacing variable, linking hazard with fragility/vulnerability for the risk assessment of structures, or it may only be employed as a proxy for predicting structural response under a given ground motion. In the first case, low conditional variability (high efficiency) and low conditional dependence on seismological parameters (high sufficiency) are needed. For response proxy usage, one may place more importance on the predictive capability of the IM within a simple regression model, favoring high correlation and low fitting errors over an extended range of response. The results showcased that (i) the peak ground acceleration and peak ground velocity, tend to be highly efficient and sufficient in specific regions of rocking response, that is, onset of rocking and overturning, respectively, but not necessarily everywhere; (ii) the average spectral acceleration shows a more consistent performance at the cost of requiring the definition of a proper period range; (iii) magnitude sufficiency is generally more difficult to achieve, compared to the distance from the rupture, and (iv) IMs that may be unsuitable for risk and vulnerability assessment, can still be highly effective as response predictors in statistical models.
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G. (2022). Statistical property parameterization of simple rocking block response. Earthquake Engineering and Structural Dynamics, 52(2):394-414.
Abstract | The parametric representation of rocking fragilities is statistically investigated. Initially, the potential normalization of the rocking parameters to reduce the problem’s dimensionality is tackled by undertaking comparisons both on a single-record and a sample-of-records basis. It is found that the slenderness angle can be normalized out when probabilistically considering the rocking response of simple rocking blocks with the same semi-diagonal length. Then, the robustness of the lognormal distribution for characterizing the rocking motion is investigated. Sets of pulse-like and ordinary ground motions are employed to test the lognormal fit for the full range of rocking response when the peak ground acceleration or the peak ground velocity are employed as intensity measures. In both cases, the lognormal distribution offers an adequate, but often imperfect, baseline model of the rocking fragility curves. Instead, a shifted lognormal that accounts for the absence of response below the rocking initiation intensity is an enhanced solution that can form the basis for offering simplified response model surrogates.
Bilionis D.V., Vlachakis K., Dasiou M.E., Vayas I., Vamvatsikos D., Lagouvardos K. (2022). Risk assessment of rehabilitation strategies for steel lattice telecommunication towers of Greece under extreme wind hazard. Engineering Structures, 267: 114625.
Abstract | The risk and losses associated with the wind-induced failure of existing steel lattice telecommunication towers are assessed for a number of upgrade/replace/redesign schemes. Specifically, a performance-based wind engineering framework is employed for assessing a typical tower topology used by EU telecommunication network operators over four different cases: a conventional design, its corroded version after 60 years, a strengthened version of the corroded tower by applying fibre-reinforced polymer plates, and a redesign with high-strength steel. Multiple potential sites of installation were considered throughout coastal and mainland Greece, comprising two different groups of design wind speed. Mischaracterization of the site-specific wind distribution is by far the most important risk factor, with corrosion coming right behind. Still, selecting a rehabilitation approach does not depend only on site and tower characteristics, but also on the projected direct and indirect losses. By considering service to different populations, even after 60 years of corrosion, the “Do Nothing” approach may still be competitive when serving few residents and for short projected lifetime, while an upgrade is considered optimal for larger towns, or wherever higher revenue is on the line.
Ruggieri S., Chatzidaki A., Vamvatsikos D., Uva G. (2022). Reduced-order models for the seismic assessment of plan-irregular low-rise frame buildings. Earthquake Engineering and Structural Dynamics, 51(14): 3327-3346.
Abstract | A procedure is presented for deriving low-complexity structural models to predict the global response of asymmetric-plan low-rise frame buildings for purposes of class-level assessment. As a compromise between employing a full-scale multi-degree-of-freedom structural model versus an equivalent single-degree-of-freedom one, the challenge is to create an idealized 3D structure with few degrees-of-freedom that can match the inelastic response of a building for which full knowledge of geometrical and mechanical properties is available. Such a 3D reduced-order model can offset the computational cost related to performing multiple nonlinear dynamic analyses within the framework of Performance-Based Earthquake Engineering. To this goal, rules and equations are proposed for achieving equivalence among the linear and nonlinear properties (e.g. mass, stiffness, strength) of the building analysed and the related 3D reduced-order model. The procedure is applied on a sample of 15 existing reinforced-concrete frame school buildings, from the province of Foggia in Southern Italy, for which the full numerical models are available. Both calibrated and uncalibrated reduced-order models are created, exploring the limitations of the proposed order-reduction in a real-life case study.
Kazantzi A.K., Karaferis N.D., Melissianos V.E., Bakalis K., Vamvatsikos D. (2022). Seismic fragility assessment of building-type structures in oil refineries. Bulletin of Earthquake Engineering, 20: 6853–6876.
Abstract | A seismic fragility assessment methodology is presented for equipment-supporting reinforced concrete and steel buildings that are typically encountered in oil refineries. Using a suite of hazard-consistent ground motions and reduced-order models, incremental dynamic analysis is performed to obtain the seismic demand of the structural systems examined. Appropriate drift- and floor acceleration-sensitive failure modes are considered to define the limit state capacities of the supporting structure and the nested non-structural process equipment. Special care is exercised on the demand and capacity representation of structural and non-structural components, offering a transparent roadmap for undertaking analytical fragility assessment for equipment-supporting buildings typical to an oil refinery. The findings and the proposed methodology can be exploited by designers and facility managers for mitigating the risk of failure prior to the occurrence of an earthquake event, for designing the pertinent structures and their non-structural components by means of a risk-aware performance-based methodology, or as feed data in early warning systems.
Karaferis N.D., Kazantzi A.K., Melissianos V.E., Bakalis K., Vamvatsikos D. (2022). Seismic fragility assessment of high-rise stacks in oil refineries. Bulletin of Earthquake Engineering. 20:6877–6900.
Abstract | The seismic fragility is assessed for typical high-rise stacks encountered in oil refineries, namely process towers, chimneys, and flares. Models of varying complexity were developed for the structures of interest, attempting to balance computational complexity and accuracy regarding the structural dynamic and strength properties. The models were utilized along with a set of hazard-consistent ground motions for evaluating the seismic demands through incremental dynamic analysis. Demand/capacity-related uncertainties were explicitly accounted for in the proposed framework. Damage states were defined for each of the examined structure considering characteristic serviceability and ultimate limit states. Τhe proposed resource-efficient roadmap for the analytical seismic fragility assessment of typical high-rise stacks, as well as the findings of the presented research work are available to be exploited in seismic risk assessment studies of oil refineries.
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2022). Seismic response distribution expressions for rocking building contents under ordinary ground motions. Bulletin of Earthquake Engineering, 20: 6659–6682.
Abstract | Analytical expressions are proposed for predicting the rocking response of rigid free-standing building contents subjected to seismic-induced floor excitations. The study considers a wide range of rigid block geometries and seismic floor acceleration histories that were recorded during actual earthquakes in instrumented Californian buildings, so as to cover, in a fully probabilistic manner, the entire spectrum of potential pure rocking responses, i.e. from the initiation of rocking up to the block overturning. Contrary to past observations on anchored building contents (prior to any failure in their anchorage system that could alter their response and mode of failure), it is shown that the response of free-standing blocks is not influenced by the predominant period of the supporting structure. The proposed set of equations can be utilised for estimating the response statistics and consequently for undertaking an analytical seismic fragility assessment on rocking building contents.
[pre-print version]
Van der Burg L., Kohrangi M., Vamvatsikos D., Bazzurro P. (2022). A risk-based evaluation of direct displacement-based design. Bulletin of Earthquake Engineering, 20: 6611–6633.
Abstract |
Reggiani Manzo N., Lachanas C.G., Vassiliou M.F., Vamvatsikos D. (2022). Uniform risk spectra for rocking structures. Earthquake Engineering and Structural Dynamics, 51(11): 2610–2626.
Abstract | This paper presents uniform risk spectra for zero stiffness bilinear elastic (ZSBE) systems. The ZSBE oscillator is a bilinear elastic system with zero post-“yield” stiffness that satisfactorily predicts the response of different systems with negative lateral stiffness (e.g., free-standing or restrained rocking blocks). It can be described by a single parameter; thus, it is simpler to produce its spectrum. Using the ZSBE proxy, this paper provides the uniform risk spectra for sites in six locations in Europe. The spectra are constructed using two distinct intensity measures (IMs): peak ground velocity (PGV) and peak ground acceleration (PGA). The efficiency of both IMs at different ranges of displacement demands is discussed and analytical approximations of the spectra are proposed.
Lachanas C.G., Vamvatsikos D., Vassiliou M.F. (2022). The influence of the vertical component of ground motion on the probabilistic treatment of the rocking response of free-standing blocks. Earthquake Engineering and Structural Dynamics. 51(8): 1874-1894.
Abstract | The influence of the vertical component of ground motion is investigated for assessing the distribution of the seismic response of unanchored rigid blocks. Multiple stripes of site-hazard-consistent ground motions are employed for calculating the seismic response of rigid rocking blocks with and without the inclusion of the vertical component. The comparison of the resulting response is being made both for single records and full suites, employing a paired record versus an ensemble-statistics comparison, respectively. It is shown that on a single record basis, the vertical component may have a non-negligible but highly variable influence on the rocking response, sometimes detrimental, sometimes beneficial. Still, when considering any large ensemble of records, the effect becomes statistically insignificant, except for the very specific case of rocking uplift for stocky blocks. To this end, for cases where the appearance of uplift is associated with damage, closed-form expressions are proposed to modify the lognormal fragility function of rocking initiation given the block slenderness and the ratio of the peak vertical over the peak horizontal ground acceleration.
[pre-print version]
Tsarpalis D., Vamvatsikos D., Delladonna F., Fabini M., Hermanek J., Margotan P. D., Sesana S., Vantusso E., Vayas I. (2022). Macro-characteristics and taxonomy of steel racking systems for seismic vulnerability assessment. Bulletin of Earthquake Engineering, 20: 2695–2718.
Abstract | Steel racking systems are civil engineering structures used to store goods and materials before their distribution to the public. In order to serve different logistic needs, a variety of rack typologies with different uses and salient characteristics has evolved over time. As a result, racks can range from large independent buildings in the form of the Automated Rack Supported Warehouses, down to compact sub-structures, or even smaller-scale shelves contained in warehousing units. Still, in all their incarnations they represent significant capital investment in terms of structure and stored goods in need of assessment. Despite their differences in terms of usability and functionality, racking structures share common macro-characteristics that can be summarized in a flexible and collapsible taxonomy, providing the risk analyst with sufficient identification to develop exposure and seismic vulnerability models. The proposed taxonomy adopts the same terminology as the Building Taxonomy of the Global Earthquake Model, comprising five basic classes or Attributes, capable of characterizing any existing, contemporary and upcoming rack typology.
Lachanas C.G., Vamvatsikos D. (2022). Rocking incremental dynamic analysis. Earthquake Engineering and Structural Dynamics, 51(3):688-703.
Abstract | The seismic response assessment of rocking systems via Incremental Dynamic Analysis (IDA) is investigated, focusing on the issues that arise in the analysis and postprocessing stages. Rocking IDA curves generally differ from those of hysteretic structural systems due to (i) the frequent appearance of resurrections; (ii) their highly weaving non-monotonic behavior; and (iii) their overall high variability. Hence, including or ignoring analysis results above the first resurrection level, deriving statistics given a response level versus an intensity measure level, as well as selecting an adequate number of ground motion records and runs per record, become challenging issues with non-trivial impact on the probabilistic characterization of rocking response. This necessitates a fresh view on analysis choices and post-processing techniques, aiming to assure the accuracy and fidelity of rocking IDA results. As an example, the effect of different choices and techniques are showcased on two-dimensional rigid blocks that are assumed to represent simplified models of monolithic ancient columns of different slenderness.
Hernández-Montes E., Chatzidaki A., Gill-Martin L.M., Aschheim M., Vamvatsikos D. (2022). A seismic design procedure for different performance objectives for post-tensioned walls. Journal of Earthquake Engineering, 26(1): 475-492.
Abstract | A method is presented for the design of unbonded post-tensioned concrete walls for seismic loading to satisfy multiple performance objectives. It takes advantage of the fact that the initial stiffness of the wall is nearly independent of the amount of post-tensioning reinforcement, and thus the fundamental period of the building can be considered to be a stable parameter in design of walls of a given cross section, independent of the degree of post-tensioning. The design spectra used to follow the specification provided in Eurocode 8 considering the probability of exceedance of the seismic action. A detailed example is provided.
Vargas-Alzate Y.F., Silva V., Vamvatsikos D., Pujades L.G. (2022). A simplified approach for including the incidence angle effect in seismic risk assessment. Earthquake Engineering and Structural Dynamics, 51(1): 191-212.
Abstract | A simplified procedure is developed to consider the azimuthal orientation of buildings when estimating seismic risk. Two square-plan reinforced concrete building models are considered as a testbed, one with similar and one with dissimilar properties along the two principal horizontal axes. The fragility of both structures is analysed using a set of ground motion records rotated to multiple incidence angles to develop orientation-dependent fragility functions. It has been observed that, re-orienting all records so that these structures have the same azimuth vis-à-vis the corresponding epicentre leads to significant differences compared to assuming random orientations. Additional results stemming from single-degree-of-freedom oscillators further confirm such findings, showing a dependence to the proximity to the faults and the level of dissimilarity in the principal horizontal axes of the structure. The end results point to a non-negligible bias in assessment studies when a structure’s orientation with respect to governing rupture scenarios is not taken into account. It is shown that the median of fragility curves calculated for un-rotated incidence angles can be bias-corrected through shifted by an amount that depends on the azimuthal orientation and level of axes-dissimilarity of structures.
Silva V., Bazzurro P., Vamvatsikos D. (2021). Preface to the Special Issue: The evolution of fragility and vulnerability. The origin story of a preface. Bulletin of Earthquake Engineering, 19(15): 6269-6270.
Abstract |
In the primordial soup of engineering creation something was a-churning. The elementary particles of structural life were combining and breaking apart, seeking equilibrium: stresses, forces, and moments; strains, displacements, and rotations; all mixing and matching until the two fundamental letters of safety emerged: C for capacity and D for demand. Let D be lower than C, said the Civil Engineer, and you will experience zero failures. But if D exceeds C, a failure will occur. Build structures from these verification zeros, and the world will be stable and safe. And, the Civil Engineer was happy.
For countless years it was all zeros and ones. Buildings and towers, bridges and domes were built and valiantly stood their ground, yet once in a while the earth shook and more than a few came down. “Maybe I forgot a 1 somewhere in those buildings,” tried to reason the Civil Engineer. But the seed of doubt had now been planted, and it kept digging its roots into the masonry/steel/concrete/wooden shell of the 0 and 1 creations. Through the cracks the little devil of uncertainty snuck in. He had been banging on that shell for a while, shouting to get in, but he was never noticed. Now he found the way, and his voice was heard. First as a whisper, then as loud as the howling wind, and the message was as simple and as devious as it gets: there is infinite space between 0 and 1. And, the Civil Engineer was not that happy anymore.
Henceforth, all cannot be black and white, but only different shades of grey, said the Engineer. One needs to pick a light enough shade of grey to call it a white, a zero, perfectly knowing that it is imperfectly so. And one needs to map this for multiple levels of a seismic intensity measure, or IM, seeing the darkness grow as the IM increases. You mean P(D > C | IM), said the little devil of uncertainty. Why not call this fragility, to always remind you of the futility of perfect safety in your 0 and 1 creation? And, the Civil Engineer was positively miffed.
And so it went for many years. The Civil Engineer building structures with zeros and ones, and the little devil keeping him on his toes with unholy fragilities, safety factors, reliability indices and other hellish concepts of probabilistic safety. Every time the Engineer tried to think hard about these, he became dizzy, but he grudgingly acknowledged that his creations no longer failed as frequently as before whenever the earth shook. Yet the Engineer’s troubles were not even close to being finished. The little devil of actuarial capitalism was soon heard banging on the door. He did not care about zeroes, ones or the more than fifty shades of grey between them. What about balance sheets? Losses? Insurance? “Show me the money!” he shouted through his business handset. Tell me how much I stand to lose if the earthquake happens. “You mean P(Loss | IM),” quipped the ever-present uncertainty devil. Let’s call it vulnerability to make sure that non-Latin languages will struggle to find a term to distinguish it from fragility. And, the Civil Engineer was downright miserable.
Yet, this only brings us to 2021 and it is not the end of this story—not by far. Little devils come in droves, and every time new seams pop open in the fabric of civil engineering—a few will always try to slip in. We actually seem to have attracted eighteen teams of such little devils in this Special Issue, each one with its own set of ideas on how to increase the Engineer’s woes. This issue presents novel fragility and vulnerability functions for global risk analyses, or for the assessment of the impact of earthquakes in specific building typologies in countries with significant risk such as high-rise RC structures in Romania, cast-in-place and precast RC buildings in Portugal, tall buildings in Turkey, light-frame wood houses in the United States, and unreinforced masonry in the Netherlands. It goes beyond the conventional assessment of damage in buildings, covering also the investigation of the collapse likelihood of bridges and the impact of corrosion in their seismic fragility. Understanding that fragility assessment is characterized by a wide spectrum of aleatory and epistemic uncertainties, this issue includes studies regarding the incorporation of directivity-induced pulse-like ground motions, consideration of ageing effects in the fragility assessment of RC structures, assessment of the impact of liquefaction effects and soil-structure interaction in the likelihood of damage, verification of the influence of the angle of seismic incidence in the resulting economic losses, and evaluation of the impact of limited ground motion records in seismic safety assessment. By proposing new fragility and vulnerability functions, advanced probabilistic methodologies, and detailed 3D numerical models, this issue contributes to the better understanding of the effects of earthquakes in the built environment, and ultimately how risk mitigation measures should be designed and implemented. Take a look at the contents, Dear Reader, and decide for yourself which one is destined to become the next thorn in our Engineer’s side.
Tsarpalis D., Vamvatsikos D., Vayas I. (2021). Seismic assessment approaches for mass‐dominant sliding contents: The case of storage racks. Earthquake Engineering & Structural Dynamics.
Abstract | The typical view of seismic performance of structure-content systems is one of segregation: Contents are assumed to be of low mass relative to the supporting structure, leading to a separate treatment of the two, whereby one first analyzes the structure and then subjects any contents to the resulting peak floor acceleration responses. Racking structures are of the exact opposite persuasion, having massive “palletized” contents that can slide on top of light cold-formed steel frames, with Content-Structure-Sliding Interaction (CSSI) governing global and local response. In support of assessment and design, three approaches are investigated to capture CSSI: (i) introducing friction sliders per pallet and running nonlinear response-history analysis, (ii) increasing the model viscous damping and using elastic response-history analysis, and (iii) reducing the horizontal seismic loads in tandem with modal response spectrum analysis. Each comes with its own challenges and modelling/analysis needs, offering different levels of accuracy (or no appreciable capability at all) when assessing the actual sliding displacement of contents. Three case studies are employed to calibrate empirical relationships for damping amplification and seismic load reduction, largely removing the bias of simpler alternatives (ii) and (iii), respectively, to level the ground for future code applications.
Tsarpalis D., Vayas I., Thanopoulos P., Vamvatsikos D. (2021). Rehabilitation of reinforced concrete building using the fuseis beam-link system. Structures, 34(12):3300-3314.
Abstract | A methodology is introduced for applying the FUSEIS beam-link steel lateral-load-resisting system for strengthening existing reinforced-concrete buildings. The purpose is to take advantage of the easy replaceability and architectural versatility of the FUSEIS systems to strengthen a deficient structure, while minimizing the economic impact of the rehabilitation works due to suspension of the operation of the building. Additionally, a case study is presented, where an existing building is upgraded by introducing FUSEIS beam-link systems, first by performing response spectra analysis using an initial behaviour factor, then refining the results via the INNOSEIS performance-based methodology. This necessitates the use of nonlinear dynamic analyses to quantify a risk-consistent behaviour factor that incorporates the effect of aleatory and epistemic uncertainty on the actual systems’ performance. Finally, a pre-normative assessment for the q-factor of FUSEIS-beam link systems is achieved, for use in existing reinforced concrete buildings within Eurocode 8.
Tsarpalis D., Vamvatsikos D., Vayas, I., Delladonna F. (2021). Simplified Modeling for the Seismic Performance Assessment of Automated Rack-Supported Warehouses. ASCE Journal of Structural Engineering, 147(11): 04021189.
Abstract | A reduced-order modeling approach is proposed for the linear and nonlinear analysis of automated rack-supported warehouse (ARSW) structures under seismic loads. Steel ARSWs are massive structures that employ traditional racking configurations to support both the stored pallets and the external cladding shell. Capturing all the structural details of an ARSW requires tens or hundreds of thousands of elements, leading to complex numerical models that are analyzed with difficulty even in the linear range and are clearly unsuitable for nonlinear analysis. Thus, despite being prolific in earthquake-prone areas, their true seismic behavior remains largely untested. As a viable compromise between fidelity and low computational cost, we offer instead a reduced-order model that relies on the substitution of the one or more built-up columns (i.e., upright frames) with equivalent Timoshenko beam-column elements and two-node link elements. The resulting model can support both two-dimensional (2D) and three-dimensional (3D) elastic and inelastic analyses, offering a powerful tool for the seismic assessment of ARSWs and of complex structures comprising built-up columns in general.
Fasoulakis Z., Vamvatsikos D., Papadopoulos V. (2021). Stability of single-bolted thin-walled steel angle beam-columns with stochastic imperfections. ASCE Journal of Structural Engineering, 147(8): 04021108, DOI: 10.1061/(ASCE)ST.1943-541X.0003061
Abstract | The focus of this paper is on the probabilistic estimation of the buckling capacity of single-bolted members from plain or lipped angle sections with stochastic geometric imperfections. A joint experimental-stochastic mechanics approach is adopted, employing in-house imperfection measurements of angle members in combination with detailed numerical models. Different slenderness values, plain and lipped angle sections, as well as single-brace or X-bracing diagonals are investigated in all cases accounting for the single-bolt connection. The member buckling loads are obtained via numerical analyses considering geometric and material nonlinearities with initial imperfections. The random variables are the geometric imperfections, the material properties, and the lateral load (wind pressure) on the member. Quatro-variate single-dimensional stochastic processes (the spectral representation method in connection with the method of separation) are used for the modeling of the geometric imperfections. It is shown that the influence of imperfections for typical lattice tower angle members is 3–6 times lower than the influence of material properties and lateral loading. All in all, current EU and US design provisions are found to be mostly conservative for the design of such members, while the use of equivalent imperfections in a numerical model can provide a more rational safety margin.
Chatzidaki A., Vamvatsikos D. (2021). Mixed probabilistic seismic demand models for fragility assessment. Bulletin of Earthquake Engineering, 19: 6397–6421.
Abstract | A mixture model approach is presented for combining the results of different models or analysis methods into a single probabilistic demand model for seismic assessment. In general, a structure can be represented using models of different type or different number of degrees of freedom, each offering a distinct compromise in computational load versus accuracy; it may also be analysed via methods of different complexity, most notably static versus dynamic nonlinear approaches. Employing the highest fidelity options is theoretically desirable but practically infeasible, at best limiting their use to calibrating or validating lower fidelity approaches. Instead, a large sample of low fidelity results can be selectively combined with sparse results from higher fidelity models or methods to simultaneously capitalize on the frugal nature of the former and the low bias of the latter to deliver fidelity at an acceptable cost. By employing a minimal 5 parameter power-law-based surrogate model we offer two options for forming mixed probabilistic seismic demand models that (i) can combine different models with varying degree of fidelity at different ranges of structural response, or (ii) nonlinear static and dynamic results into a single output suitable for fragility assessment.
Lachanas C.G., Vamvatsikos D. (2021). Model type effects on the estimated seismic response of a 20-story steel moment resisting frame. ASCE Journal of Structural Engineering, 147(6): 04021078.
Abstract | Finite-element models of varying sophistication may be employed to determine a building’s seismic response with increasing complexity, potentially offering a higher fidelity at the cost of the computational load. To account for this effect on the reliability of performance assessment, model-type uncertainty needs to be incorporated as distinct to the uncertainty related to a given model’s parameters. At present, only placeholder values are available in seismic guidelines. Instead, we attempt to quantify them accurately for a modern 20-story steel moment-resisting frame. Different types of three-dimensional (3D), two-dimensional (2D) multibay, and 2D single-bay multidegree-of-freedom models are investigated, together with their equivalent single-degree-of-freedom ones, to evaluate the model dependency of the response both within each broad model category, as well as among different categories. In conclusion, ensemble values are recommended for the uncertainty in each model category showing that for the perfectly-symmetric perimeter-frame P–ΔP-Δ sensitive building under investigation, the uncertainty stemming from 3D versus 2D or distributed versus lumped plasticity models is lower than the governing record-to-record variability.
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2021). Seismic response distribution expressions for on-ground rigid rocking blocks under ordinary ground motions. Earthquake Engineering and Structural Dynamics, 50(12):3311-3331.
Abstract | Predictive relationships are offered for the response of on-ground 2D rigid blocks undergoing rocking. Among others, this is pertinent to (1) modern or classical antiquity structures that utilize rocking as a seismic protection mechanism and (2) freestanding contents (e.g., cabinets, bookcases, and museum artifacts) located on the ground or lower floors of stiff buildings. Blocks of varying dimensions were subjected to a full range assessment of seismic response under increasing intensity levels of ordinary (no-pulse and no-long-duration) ground motions, parameterized by peak ground acceleration or velocity. Both response and intensity were normalized, allowing the fitting of general-purpose parametric expressions to determine the mean and dispersion of response for an arbitrary block of interest. These can be utilized in the same way as conventional strength-ratio/ductility/period relationships of yielding oscillators, to enable the rapid assessment or design of simple rocking systems.
Spillatura A., Kohrangi M., Bazzurro P., Vamvatsikos D. (2021). Conditional spectrum record selection faithful to causative earthquake parameter distributions. Earthquake Engineering and Structural Dynamics, 50(10):2653-2671.
Abstract | In performance‐based earthquake wngineering, record selection comes into play at the interface of seismic hazard and structural analysis aiming to repair any loss of essential seismological dependencies caused by the choice of an insufficient intensity measure to be used for structural response prediction. Site‐specific selection is best exemplified by the prominent conditional spectrum (CS) approach that attempts to ensure a hazard‐consistent response prediction by involving site hazard disaggregation. Specifically, CS utilizes a target spectrum (with mean and dispersion) that, in its latest formulation, accounts for all the scenarios (in terms of magnitude, M, and closest to rupture distance, R) contributing to the hazard of the site at a given intensity level. The ground motion records, however, are selected to match this target spectrum–based solely on their spectral shape but with no explicit consideration to their underlying M‐R characteristics. The main focus of this study is to explore whether the reintroduction of M‐R criteria in the selection process preserves hidden dependencies that may otherwise be lost through a spectral‐shape‐only proxy. The proposed record selection method, termed CS‐MR, offers a simple approach to maintain a higher order of hazard consistency able to indirectly account for metrics that depend on M‐R (e.g., duration, Arias intensity) but are not captured in the response spectra. Herein the CS‐MR response prediction is favorably compared to CS and to the generalized conditional intensity measure methods that select records according to, respectively, spectral shape only and, for the case at hand, to spectral shape plus duration.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2021). Seismic risk and loss estimation for the building stock in Isfahan. Part II: Hazard analysis and risk assessment. Bulletin of Earthquake Engineering, 19: 1739-1763.
Abstract | The second part of a seismic risk assessment study for the Iranian city of Isfahan is presented, focusing on the description of the hazard, the risk analysis, and the discussion of the results. This study utilizes the building exposure model, the fragility and the vulnerability curves illustrated in the companion paper. The earthquake occurrence source model adopted is based on the EMME14 hazard study. The site effects accounting for the soil nonlinear behavior are modeled by means of a Vs30 map derived from the topographical slope. The validity of this map is tested based on the local surface geology and geotechnical reports. The probabilistic seismic hazard maps for different return periods that account for site effects are generated and compared with the design spectra mandated by the Iranian national seismic design code. In addition, direct seismic monetary and human losses are estimated for two earthquake scenarios and also for 100- and 475-year return periods. We show loss maps and loss curves, offering insights on the most vulnerable building classes and the spatial distribution of the estimated losses. The results provide a basis for pre- and post-disaster emergency planning, for global and local urban planning, as well as for conceiving adequate risk mitigation strategies including devising fair earthquake insurance policies. This study may also serve as a blueprint for carrying out similar work in other urban areas of the Middle East.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2021). Seismic risk and loss estimation for the building stock in Isfahan. Part I: Exposure and vulnerability. Bulletin of Earthquake Engineering, 19: 1709-1737.
Abstract | This paper focuses on the exposure and fragility/vulnerability of the residential, mixed residential/commercial, and public building stock of the city of Isfahan, in Central Iran, and constitutes the first part of a seismic risk assessment study for that city. To determine the assets at risk, we first summarize the details of the building stock and population from the available georeferenced 2011 Census data. From this dataset and from a local survey of the city, we categorize the building taxonomy in 27 construction classes characterized by age, height, and material/lateral-load-resisting system. A building exposure model is then assembled by first dividing Isfahan in city blocks and then by assigning the appropriate statistical properties to the buildings, such as construction class, built area, and replacement cost. The population of each city block is also estimated and accounted for. To assess the fragility and vulnerability to earthquake ground motion, for each building class we performed nonlinear dynamic analysis of multiple equivalent single-degree-of-freedom systems. This process generated a set of class- and region-specific fragility and vulnerability functions that considered both record-to-record and building-to-building response variability. In the companion paper we used the exposure model and the fragility and vulnerability curves generated for all these asset classes to probabilistically assess the seismic risk of Isfahan.
Ruggieri S., Porco F., Uva G., Vamvatsikos D. (2021). Two frugal options to assess class fragility and seismic safety for low-rise reinforced concrete school buildings in Southern Italy. Bulletin of Earthquake Engineering, 19: 1415-1439.
Abstract | A study is presented on the seismic fragility of a sample of 15 reinforced-concrete school buildings built between 1960 and 1980s in the province of Foggia, Southern Italy, for which near-perfect information is provided on geometrical and mechanical parameters. In particular, the focus is on the application of two probabilistic methods, employing different compromises in terms of complexity versus accuracy. First, a Eurocode 8 compatible nonlinear static approach is employed, which is augmented via the use of the regression expressions of the SPO2FRAG tool to incorporate record-to-record variability. Second, a nonlinear dynamic approach is used to directly account for record-to-record variability via a constrained multi-stripe analysis. In particular, in view of practitioners’ needs (analysis time, computational efforts, software used), a practical mode for application of the multi-stripe analyses is proposed, based on conducting few stripe analyses, in order to predict the behavior of structures in both the elastic and inelastic ranges of response. Both the static and the dynamic approaches are shown to be viable alternatives, offering fairly matching results at the individual building-level and even closer predictions at the level of ensemble regional fragility curves that incorporate both inter-building and intra-building uncertainties.
Kazantzi A. K., Vamvatsikos D. (2021). Practical performance-based design of friction pendulum bearings for a seismically isolated steel top story spanning two RC towers. Bulletin of Earthquake Engineering, 19: 1231-1248.
Abstract | A case study of performance-based design is presented for a seismically isolated steel structure that rests on top of two adjacent high-rise reinforced concrete towers, the latter separated by means of an expansion joint. The isolation system comprises Friction Pendulum Bearings (FPBs) that are designed to accommodate two salient characteristics of the system. First, the isolated top floor is subjected to narrow-band floor acceleration histories as the ground motion excitation is filtered by the dynamic response of the supporting towers. Second, the displacement demands imposed to the FPBs are affected by the in-phase or out-of-phase movement of the supporting structures, with the latter case potentially giving rise to higher displacement capacity requirements for the bearings. In a search for a solution beyond conventional design norms, the probability of bearing failure associated with a wide range of FPB displacement capacities was determined via an explicitly risk-consistent performance-based seismic design. Overall, the case-specific design approach is shown to be able to meet any desired performance objective, consistently determining the final compromise between safety, cost-efficiency and practicability.
Melissianos V., Vamvatsikos D., Gantes C.J. (2020). Methodology for failure mode prediction of onshore buried steel pipelines subjected to reverse fault rupture. Soil Dynamics and Earthquake Engineering, 135: 106116
Abstract | Oil and gas buried steel pipelines are vulnerable to permanent ground displacements, such as those resulting from tectonic fault activation. The dominant failure mechanism is strongly dependent on the type of faulting. The more complex case is the reverse fault type because the crossing pipeline is significantly compressed and bent and consequently, it may fail due to local buckling, upheaval buckling or tensile weld fracture. Which among those failure modes will be critical, depends on a set of parameters, comprising fault crossing geometry, diameter to thickness ratio (D/t) of the pipeline, pipeline steel grade, and backfill soil properties. An extensive parametric study is carried out, followed by statistical processing of the results in order to formulate simplified statistical models for the prediction of the predominant failure mode according to criteria set by the American Lifelines Alliance and EN 1998-4 standards. The study thus offers the first comprehensive attempt to quantify the qualitative criterion that deeply buried pipes with high D/t ratio tend to buckle locally, while shallowly buried pipes with low D/t ratio tend to buckle globally. Pipe designers may use the provided expressions to predict the predominant failure mode in order to either apply the necessary seismic countermeasures or re-design the pipeline if necessary.
Kazantzi A.K., Miranda E., Vamvatsikos D. (2020). Strength-reduction factors for the design of light nonstructural elements in buildings. Earthquake Engineering and Structural Dynamics, 49: 1329–1343
Summary | Strength‐reduction factors that reduce ordinates of floor spectra acceleration due to nonlinearity in the secondary system are investigated. In exchange for permitting some inelastic deformation to occur in the secondary system or its supports, these strength reduction factors allow to design the nonstructural elements or their supports for lateral forces that are smaller than those that would be required to maintain them elastically during earthquakes. This paper presents the results of a statistical analysis on component strength‐reduction factors that were computed considering floor motions recorded on instrumented buildings in California during various earthquakes. The effect of yielding in the component or its anchorage/bracing in offering protection against excessive component acceleration demands is investigated. It is shown that strength‐reduction factors computed from floor motions are significantly different from those computed from ground motions recorded on rock or on firm soils. In particular, they exhibit much larger reductions for periods tuned or nearly tuned to the dominant modal periods of the building response. This is due to the large differences in frequency content of ground motions and floor motions, with the former typically characterized by wide‐band spectra whereas the latter are characterized by narrow‐band spectra near periods of dominant modes in the response of the building. Finally, the study provides approximate equations to estimate component strength‐reduction factors computed through nonlinear regression analyses.
Kohrangi M., Vamvatsikos D., Bazzurro P. (2020). Multi-level conditional spectrum-based record selection for IDA. Earthquake Spectra, 36(4):1976-1994
Abstract | Incremental dynamic analysis (IDA) is widespread to evaluate the seismic response of structures. It employs one records set scaled to multiple intensity levels (IMLs) to estimate the structural response distribution. However, the dominating earthquake scenarios differ with the intensity, and a single set introduces bias that increases with scaling. The response is, however, better estimated using multiple stripe analysis (MSA) by selecting multiple hazard consistent record sets at different IMLs via, for example, conditional spectrum (CS) method. Still, IDA remains a popular tool, and would benefit from a single “good” set that would be more amenable to scaling with minimal bias. We explore alternatives of a “multi-level” CS (CSML) scheme, whereby the seismic properties of multiple IMLs are combined to derive a single set. Combined with advanced IMs, CSML provides a viable trade-off between the more accurate and complex method of CS–MSA versus the conceptually and practically simpler IDA.
Kazantzi A.K., Vamvatsikos D. (2020). Seismic and vibration performance for an industrial steel building. ASCE Practice Periodical on Structural Design and Construction, 25(2): 05020001
Kohrangi M., Papadopoulos A.N., Bazzurro P., Vamvatsikos D. (2020). Correlation of spectral acceleration values of vertical and horizontal ground motion pairs. Earthquake Spectra, 36(4): 2112-2128
Abstract | We present correlation coefficient estimates between a number of ground motion intensity measures (IMs), as measured from the NGA-West2 database, with focus on the correlation of vertical–vertical and vertical–horizontal ground motion components. The IMs considered include spectral accelerations with periods from 0.01 to 10 s, peak ground acceleration, peak ground velocity, and significant duration (for 5%–75% and 5%–95% definitions). To facilitate their use, parametric equations are also fitted to the correlation models. Finally, the dependence of the obtained correlation coefficients to magnitude, distance, and Vs30 is evaluated.
Kazantzi A.K., Vamvatsikos D., Miranda E. (2020). Evaluation of seismic acceleration demands on building nonstructural elements. ASCE Journal of Structural Engineering, 146(7): 04020118
Abstract | As proven by several past earthquakes, seismic losses associated with nonstructural damage in modern buildings are likely to significantly exceed those associated with structural damage. Hence, to satisfactorily assess the overall seismic performance of a building and consequently the associated losses, it is paramount to properly account for the nonstructural damage through the adequate estimation of acceleration demands that are imposed on its acceleration-sensitive nonstructural elements in any one-floor level during an earthquake. Component acceleration amplification factors, ap, which measure how much the acceleration of a component is amplified relative to the peak floor acceleration are evaluated by floor motions recorded during earthquakes on instrumented buildings in the United States. The study shows that component amplification factors currently used in codes significantly underestimate acceleration demands for components whose periods are tuned or nearly tuned to modal periods of the supporting structure. Simplified equations are proposed to estimate component acceleration amplifications. The study also evaluates inelastic floor acceleration spectral ordinates. As a result of the filtering and amplification of the ground motion by the structure, the results show that even small levels of nonlinearity in the nonstructural element or its attachment to the structure lead to significant reductions in acceleration demands.
Kazantzi A.K., Vamvatsikos D., Miranda E. (2020). The effect of damping on floor spectral ordinates as inferred from instrumented buildings. Bulletin of Earthquake Engineering, 18: 2149–2164
Abstract | This study investigates the effect of damping on the seismic demands imposed on lightweight nonstructural components. The investigation was performed utilizing a total of 113 floor acceleration recordings obtained from instrumented buildings located in California. Results are presented as damping modification factors, which provide information on the seismic demands imposed on secondary systems with various levels of damping relative to 5% damped components. Evaluations of the results indicate a strong period dependence, with the effect of damping being much larger for components that are tuned or nearly tuned and much smaller for components with periods far from the modal periods of the supporting building. Therefore, a better characterization of the effect of damping is achieved if the damping modification factors are a function of the ratio of the period of the component to the modal periods of the supporting structure. As expected, record-to-record variability increases as the level of damping in the secondary component deviates from 5% damping, with an overall probability distribution that is approximately lognormal. Thus, a full probabilistic characterization of the influence of damping on component response is offered via a parametric, period- and damping-dependent model of the mean and lognormal standard deviation of the damping modification factor.
Tsarpalis P., Bakalis K., Thanopoulos P., Vayas I., Vamvatsikos D. (2020). Pre-normative assessment of behaviour factor for lateral load resisting system FUSEIS pin-link. Bulletin of Earthquake Engineering, 18(6): 2681–2698
Abstract | A pre-normative assessment is presented for the q-factor of the FUSEIS pin-link steel lateral load resisting system for use in low/mid-rise buildings, within Eurocode 8. It is achieved by using the INNOSEIS methodology, a performance based methodological procedure to define behaviour factors for innovative systems. Applying this methodology, consistent behaviour factors can be obtained based on the definition of a set of structures to represent each class of buildings, with the use of nonlinear static and dynamic analysis methods and the incorporation of the effect of aleatory and epistemic uncertainty on the actual systems’ performance, to reach a uniform level of safety across the entire building population.
Sakka E.G., Bilionis D.V., Vamvatsikos D., Gantes C.J. (2020). Onshore wind farm siting prioritization based on investment profitability for Greece. Renewable Energy, 146: 2827-2839
Abstract | A feasibility study is presented on mid-size onshore wind farms in Greece, taking into consideration two metrics for the evaluation of the profitability of the pertinent investment, namely the net present value, and the internal rate of return. An operationally complete wind park of ten 3.2 MW turbines is considered, incorporating all required power conversion/transmission, and transportation infrastructure that an owner would have to construct. Actual wind speed data are employed from 285 weather stations installed throughout the country and covering a period of 1 to 12 years. The costs of installation, operation, and financing are explicitly accounted for over a standard lifecycle of twenty years. Given the regulated wholesale price for renewable electrical power, the proximity of many sites to ports, and the relatively uniform cost of investing, it is the wind potential that remains the governing factor affecting the financial viability of the wind park. Accordingly, the most profitable areas are the Aegean islands, the south-central mainland coastline, east Peloponnese, and south Attica. Most other regions of mainland Greece are found to be either marginally profitable or to generate a net loss given the current wholesale prices, wind turbine technology and investment costs.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2019). Conditional spectrum bi-directional record selection for risk assessment of 3D structures using scalar and vector IMs. Earthquake Engineering and Structural Dynamics, 48(9): 1066-1082
Summary | Several proposals are explored for the hazard and intensity measure (IM) consistent selection of bidirectional ground motions to assess the performance of 3D structural models. Recent studies have shown the necessity of selecting records that thoroughly represent the seismicity at the site of interest, as well as the usefulness of efficient IMs capable of estimating the response of buildings with low scatter. However, the advances realized are mostly geared towards the structural analysis of 2D models. Few are the combined record, and IM selection approaches suggested expressly for nonlinear dynamic analysis of 3D structural models, especially when plan asymmetry and torsion sensitivity come into play. Conditional spectrum selection is leveraged and expanded here to offer a suite of approaches based on both scalar and vector IMs that convey information from two orthogonal horizontal components of the ground motion. Applications on multiple 3D building models highlight the importance of (a) employing the same IM for both record selection and response assessment and (b) maintaining hazard consistency in both horizontal components, when using either a scalar or a vector IM. All tested approaches that respect these conditions can be viable, yet the one based on the geometric mean of multiple spectral ordinates from both components over a period range seems to hold the most promise for general use.
Vamvatsikos D., Bakalis K., Kohrangi M., Pyrza S., Castiglioni C., Kanyilmaz A., Morelli F., Stratan A., D’ Aniello M., Calado L., Proença J.M., Degee H., Hoffmeister B., Pinkawa M., Thanopoulos P., Vayas I. (2020). A risk-consistent approach to determine EN1998 behaviour factors for lateral load resisting systems. Soil Dynamics and Earthquake Engineering, 131: 106008
Abstract | A risk-consistent approach is proposed for the evaluation of behaviour factors that are compatible with Eurocode 8, using nonlinear static and dynamic analysis. It comprises seven discrete steps, involving hazard assessment and record selection at multiple sites, designing and modelling multiple archetype buildings and assessing their performance vis-à-vis target safety objectives. In all cases, uncertainty is incorporated and propagated to the final results whereby a flexible verification procedure is offered to account for the confidence of the investigator on the data available. An example application is offered on steel concentrically braced frames, highlighting the need for selecting appropriate performance targets for Europe. The overall added value goes beyond the current state of art, offering a consistent risk basis for the seismic design of different systems that is compatible with current uniform hazard design spectra and can benefit from future risk-targeted hazard maps.
Silva V., Akkar S., Baker J.W., Bazzurro P., Castro J.M., Crowley H., Dolsek M., Galasso C., Lagomarsino S., Monteiro R., Perrone D., Pitilakis K., Vamvatsikos D. (2019). Current challenges and future trends in analytical fragility and vulnerability modelling. Earthquake Spectra, 35(4):1927-1952
Abstract | The lack of empirical data regarding earthquake damage or losses has propelled the development of dozens of analytical methodologies for the derivation of fragility and vulnerability functions. Each method will naturally have its strengths and weaknesses, which will consequently affect the associated risk estimates. With the purpose of sharing knowledge on vulnerability modeling, identifying shortcomings in the existing methods, and recommending improvements to the current practice, a group of vulnerability experts met in Pavia (Italy) in April 2017. Critical topics related to the selection of ground motion records, modeling of complex real structures through simplified approaches, propagation of aleatory and epistemic uncertainties, and validation of vulnerability results were discussed, and suggestions were proposed to improve the reliability and accuracy in vulnerability modeling.
Farag M.M.N., Mehanny S.S.F., Kohrangi M., Vamvatsikos D., Bakhoum M.M. (2019). Precast beam bridges with a buffer-gap-elastomeric bearings system: uncertainty in design parameters and randomness in ground records. ASCE Journal of Bridge Engineering, 24(5): 04019034
Abstract | The buffer–gap–elastomeric bearings system used in precast girder bridges with relatively short piers is one of the efficient hybrid seismic isolation schemes. However, there are many uncertain environmental, material, and geometric parameters affecting gap size and, hence, the response of the bridge to earthquakes. To investigate, four different configurations of a three-span continuous bridge were designed for a high-seismicity site in Egypt, considering short or tall bridge piers of high or limited ductility. The performance of each bridge configuration was studied using nonlinear dynamic analysis under ground motions selected to be compatible with the site hazard. Two different treatments of parameter uncertainty were used: a mean parameter model, in which uncertainty was essentially disregarded, versus a random parameter model, represented by 60 realizations of each bridge generated via Latin Hypercube Sampling. Different intensity measures were also studied, showing that the geometric mean of multiple spectral ordinates over a period range that encompassed the vibration characteristics of both a closed-gap and open-gap model best satisfied both efficiency and sufficiency requirements. All in all, parameter uncertainty was shown to be an important issue for such bridges, requiring appropriate consideration for accurate assessment.
Papadopoulos A.N., Vamvatsikos D., Kazantzi A.K. (2019). Development and application of FEMA P-58 compatible story loss functions. Earthquake Spectra, 35(1): 95-112
Abstract | The quantification of seismic performance, using metrics meaningful to both engineers and stakeholders, has been a focal point of research in performance-based earthquake engineering. The prevalent paradigm is currently offered by the FEMA P-58 guidelines in the form of a component-by-component approach that provides detailed assessment capabilities at the cost of requiring a complete inventory of the structural, nonstructural, and content components. In an attempt for simplification, a fully compatible story-by-story approach is offered instead, where story loss functions are employed to directly relate monetary losses to engineering demand parameters given the story area. These functions can be adjusted for application to different situations, assuming the ratio of cost and quantity of each component category inventory remains relatively constant. As an example, they are generated for a standard inventory makeup, characteristic of low/mid-rise steel office buildings. They are shown to offer a favorable compromise of simplicity and accuracy that lies between the component-by-component and building-level approaches that are currently prevalent in building-specific and regional loss assessment, respectively.
Bakalis K., Kazantzi A.K., Vamvatsikos D., Fragiadakis M. (2019). Seismic performance evaluation of liquid storage tanks using nonlinear static procedures. ASME Journal of Pressure Vessel Technology, 141(1), 010902
Abstract | A simplified approach is presented for the seismic performance assessment of liquid storage tanks. The proposed methodology relies on a nonlinear static analysis, in conjunction with suitable “strength ratio-ductility-period” relationships, to derive the associated structural demand for the desired range of seismic intensities. In the absence of available relationships that are deemed fit to represent the nonlinear-elastic response of liquid storage tanks, several incremental dynamic analyses are performed for variable post-yield hardening ratios and periods in order to form a set of data that enables the fitting of the response. Following the identification of common modes of failure such as elephant’s foot buckling (EFB), base plate plastic rotation, and sloshing wave damage, the aforementioned relationships are employed to derive the 16%, 50%, and 84% percentiles for each of the respective response parameters. Fragility curves are extracted for the considered failure modes, taking special care to appropriately quantify both the median and the dispersion of capacity and demand. A comparison with the corresponding results of incremental dynamic analysis (IDA) reveals that the pushover approach offers a reasonable agreement for the majority of failure modes and limit states considered.
Kohrangi M., Vamvatsikos D., Bazzuro P. (2019). Pulse-like versus non-pulse-like ground motion records: Spectral shape comparisons and record selection strategies. Earthquake Engineering and Structural Dynamics, 48(1): 46-64
Summary | Pulse‐like records are well recognized for their potential to impose higher demands on structures when compared with ordinary records. The increased severity of the structural response usually caused by pulse‐like records is commonly attributed to the spectral increment around the pulse period. By comparing the building response to sets of spectrally equivalent pulse‐like and ordinary records, we show that there are characteristics of pulse‐like records beyond the shape of the acceleration response spectrum that affect the results of nonlinear dynamic analysis. Nevertheless, spectral shape together with the ratio of pulse period to the first‐mode structural period, Tp/T1, are confirmed as “sufficient” predictors for deformation and acceleration response metrics in a building, conditioned on the seismic intensity. Furthermore, the average spectral acceleration over a period range, AvgSA, is shown to incorporate to a good proxy for spectral shape, and together with Tp/T1, form an efficient and sufficient intensity measure for response prediction to pulse‐like ground motions. Following this latter route, we propose a record selection scheme that maintains the consistency of Tp with the hazard of the site but uses AvgSA to account for the response sensitivity to spectral shape.
Baltzopoulos G., Baraschino R., Iervolino I., Vamvatsikos D. (2018). Dynamic analysis of single-degree-of-freedom systems (DYANAS): A graphical user interface for OpenSees. Engineering Structures, 177: 395-408
Abstract | Non-linear dynamic response of SDOF systems enjoys widespread application in earthquake engineering, sometimes as a testing ground for cumbersome analytical procedures, but often as a direct proxy of first-mode-dominated structures, within the family of simplified, pushover-based methods for seismic structural assessment and/or design. This article presents DYANAS, a MATHWORKS-MATLAB®-based graphical user interface that uses the OpenSees finite element platform to perform nonlinear dynamic analysis of single-degree-of-freedom (SDOF) oscillators. The scope of this open-source, freely distributed software is to serve as a tool for earthquake engineering research. The main advantages offered by the DYANAS interface are ease in the definition of the required analysis parameters and corresponding seismic input, efficient execution of the analyses themselves and availability of a suite of convenient, in-built post-processing tools for the management and organization of the structural responses. The types of dynamic analysis frameworks supported are incremental, multiple-stripe and cloud. Simultaneous consideration of pairs of uncoupled dynamic systems gives the possibility for intensity measures to refer to bidirectional ground motion. In the paper, an outline of the types of dynamic analysis frameworks typically used in performance-based earthquake engineering is provided, followed by a detailed description of the software and its capabilities, that include an array of post-processing tools. In order to properly place this software tool within its natural performance-based earthquake engineering habitat, some example applications are provided at the end of the paper.
Giannopoulos D., Vamvatsikos D. (2018). Ground motion records for seismic performance assessment: To rotate or not to rotate? Earthquake Engineering and Structural Dynamics, 47(12): 2410-2425
Summary | The response of a non‐circular structure strongly depends on the orientation of the horizontal ground motion components vis‐à‐vis the structure’s principal axes. At the same time, the structural response is also a function of accelerogram characteristics that give rise to considerable record‐to‐record variability even when the incident angle is neglected. Therefore, when the structural orientation relative to the fault geometry is unknown and we have limited resources for estimating the distribution of structural response given the seismic intensity, the question arises as to whether it is preferable to use (1) few records rotated to multiple orientations, (2) many records, each at a random incident angle, or (3) some combination of the two. To this purpose, we subjected several single‐degree‐of‐freedom systems and one plan‐asymmetric multi‐degree‐of‐freedom structure to a pulsive and a non‐pulsive set of ground motions using different combinations of record set size and incident angle rotations. In all cases, the natural record‐to‐record variability of the (unrotated) waveforms clearly outweighed the influence of the record orientation. In addition, the choice of an intensity measure that utilizes the geometric mean of spectral accelerations in both horizontal axes at one or more periods of vibration was found to further enhance this difference, essentially nullifying the already small effect of the incident angle. In all cases, spending any significant proportion of the limited number of dynamic analyses to incorporate the effect of incident angle was detrimental to the fidelity of the estimated performance.
Bakalis K., Kohrangi M., Vamvatsikos D. (2018). Seismic intensity measures for liquid storage tanks. Earthquake Engineering and Structural Dynamics, 47(9): 1844-1863
Summary | A series of scalar and vector intensity measures is examined to determine their suitability within the seismic risk assessment of liquid storage tanks. Using a surrogate modelling approach on a squat tank that is examined under both anchored and unanchored support conditions, incremental dynamic analysis is adopted to generate the distributions of response parameters conditioned on each of the candidate intensity measures. Efficiency and sufficiency metrics are used in order to perform the intensity measure evaluation for individual failure modes, while a comparison in terms of mean annual frequency of exceedance is performed with respect to a damage state that is mutually governed by the impulsive and convective modes of the tank. The results reveal combinations of spectral acceleration ordinates as adequate predictors, among which the average spectral acceleration is singled out as the optimal solution. The sole exception is found for the sloshing‐controlled modes of failure, where mainly the convective period spectral acceleration is deemed adequate to represent the associated response due to their underlying linear relationship. A computationally efficient method in terms of site hazard analysis is finally proposed to serve in place of the vector‐valued intensity measures, providing a good match for the unanchored tank considered and a more conservative one for the corresponding anchored system.
Bakalis K., Vamvatsikos D. (2018). Seismic fragility functions via nonlinear response history analysis. ASCE Journal of Structural Engineering, 144(10): 04018181
Abstract | The estimation of building fragility, i.e., the probability function of seismic demand exceeding a certain limit state capacity given the seismic intensity, is a common process inherent in any seismic assessment study. Despite this prolific nature, the theory and practice underlying the various approaches for fragility evaluation may be opaque to their users, especially regarding the handling of demand and capacity uncertainty, or the generation of a single fragility curve for multiple failure conditions, using either an intensity measure or engineering demand parameter basis. Hence, this paper provides a comprehensive guide that compiles all necessary information for generating fragility curves of single structures based on the results of nonlinear dynamic analysis. Although various analysis methods are discussed, incremental dynamic analysis is invoked to clearly outline different methodologies that rely either on response parameter or intensity measure ordinates. Step-by-step examples are presented for each case, under both a deterministic and an uncertain limit state capacity framework, using limit states that range from simple structural damage to the global collapse of the structure.
Kazantzi A.K., Vamvatsikos D. (2018). The hysteretic energy as a performance measure in analytical studies. Earthquake Spectra, 34(2): 719-739
Abstract | Hysteretic energy dissipation is often employed as a measure of performance for systems subjected to earthquake excitation. This mainly stems from quasi-static cyclic tests where fuller hysteresis loops (i.e., higher energy absorption) are taken to indicate better performance when comparing systems with similar strength under the same cyclic loading protocol. However, seismic loading offers a different proving ground, where energy absorption is strongly correlated with energy input, while the nonstationary loads imply that the beneficial hysteretic effects observed in a cyclic test may never be realized. Given the current state of art in models and methods of performance-based earthquake engineering, we ask whether earthquake records at a given seismic intensity will cause peak/residual displacements or accelerations that favor models having fuller hysteresis. Using incremental dynamic analysis on story-level oscillators with varying hysteretic characteristics, it is demonstrated that hysteretic energy dissipation does not consistently correlate with seismic performance.
Melissianos V., Vamvatsikos D., Gantes C.J. (2017). Performance-based assessment of protection measures for buried pipes at strike-slip fault crossings. Soil Dynamics and Earthquake Engineering, 101: 1-11
Abstract | Onshore buried steel pipelines are vulnerable to fault rupture, where large ground displacements are imposed on the crossing pipe and thus protection measures are often necessary to avoid failure. A three-step methodology based on the framework of performance-based earthquake engineering is presented on assessing the effectiveness of protection measures against the consequences of strike-slip faulting on pipes. Firstly, the randomness of the fault movement is quantified, next the pipeline mechanical behavior is numerically assessed and finally the results are combined to extract the strain hazard curves, which are easy-to-handle engineering decision making tools. The various protection measures used in engineering practice or proposed in the literature are evaluated through the mean annual rate of exceeding strain values, also including a simple safety checking format at the strain level. Conclusions are extracted from the proposed assessment methodology on the efficiency of measures with reference to engineering practice and safety requirements of the pipeline operator.
Bakalis K., Vamvatsikos D., Fragiadakis M. (2017). Seismic risk assessment of liquid storage tanks via a nonlinear surrogate model. Earthquake Engineering and Structural Dynamics, 46(15): 2851-2868
Abstract | A performance‐based earthquake engineering approach is developed for the seismic risk assessment of fixed‐roof atmospheric steel liquid storage tanks. The proposed method is based on a surrogate single‐mass model that consists of elastic beam‐column elements and nonlinear springs. Appropriate component and system‐level damage states are defined, following the identification of commonly observed modes of failure that may occur during an earthquake. Incremental dynamic analysis and simplified cloud are offered as potential approaches to derive the distribution of response parameters given the seismic intensity. A parametric investigation that engages the aforementioned analysis methods is conducted on 3 tanks of varying geometry, considering both anchored and unanchored support conditions. Special attention is paid to the elephant’s foot buckling formation, by offering extensive information on its capacity and demand representation within the seismic risk assessment process. Seismic fragility curves are initially extracted for the component‐level damage states, to compare the effect of each analysis approach on the estimated performance. The subsequent generation of system‐level fragility curves reveals the issue of nonsequential damage states, whereby significant damage may abruptly appear without precursory lighter damage states.
Baltzopoulos G., Baraschino R., Iervolino I., Vamvatsikos D. (2017). SPO2FRAG: Software for seismic fragility assessment based on static pushover. Bulletin of Earthquake Engineering, 15(10): 4399-4425
Abstract | SPO2FRAG (Static PushOver to FRAGility) is introduced, a MATLAB®-coded software tool for estimating structure-specific seismic fragility curves of buildings, using the results of static pushover analysis. The SPO2FRAG tool (available online at http://wpage.unina.it/iuniervo/doc_en/SPO2FRAG.htm) eschews the need for computationally demanding dynamic analyses by simulating the results of incremental dynamic analysis via the SPO2IDA algorithm and an equivalent single-degree-of-freedom approximation of the structure. Subsequently, fragility functions may be calculated for multiple limit states, using the intensity-measure-based analytical approach. The damage thresholds may also be random variables and uncertainty in estimation of the fragility parameters may be explicitly accounted for. The research background underlying the various modules comprising SPO2FRAG is presented together with an operational description of how the various functions are integrated within the software’s graphical user interface. Two illustrative SPO2FRAG applications are also offered, using a steel and a reinforced concrete moment resisting frame. Finally, the software’s output is compared with the results of incremental dynamic analysis as validation of SPO2FRAG’s effectiveness.
Olmati P., Vamvatsikos D., Stewart M. (2017). Safety factor for structural elements subjected to impulsive blast loads. International Journal of Impact Engineering, 106: 249-258
Abstract | Design of blast loaded structures is usually carried out following a deterministic rather than a probabilistic approach. The design load scenario would cover the plausible load conditions (typically some conservative estimate) that a structure would experience if an explosion occurs but the probability that the structure will satisfy the design performances for the considered scenario remains unknown. Applying a performance-based design framework typically requires arduous Monte Carlo simulations, but a probabilistic design could also be achieved by a single structural analysis when consistent safety factors are applied to the load and the structural resistance. Such a factor is proposed herein for the case of components subjected to impulsive blast loads. The dependence of the safety factor on the amount of explosive, stand-off distance and their variability is estimated numerically and provided by means of regression formulas. A design example using the proposed safety factor is carried out and Monte Carlo simulation is used for verification. The results confirm the validity of the proposed safety factor approach and its applicability for the performance-based design of blast loaded structures using the current design practice methods.
Katsanos E.I., Vamvatsikos D. (2017). Yield Frequency Spectra and seismic design of code-compatible RC structures: an illustrative example. Earthquake Engineering and Structural Dynamics, 46(11):1727-1745
Summary | The seismic design of an eight‐story reinforced concrete space frame building is undertaken using a yield frequency spectra (YFS) performance‐based approach. YFS offer a visual representation of the entire range of a system’s performance in terms of the mean annual frequency (MAF) of exceeding arbitrary global ductility or displacement levels versus the base shear strength. As such, the YFS framework can establish the required base shear and corresponding first‐mode period to satisfy arbitrary performance objectives for any structure that may be approximated by a single‐degree‐of‐freedom system with given yield displacement and capacity curve shape. For the eight‐story case study building, deformation checking is the governing limit state. A conventional code‐based design was performed using seismic intensities tied to the desired MAF for safety checking. Then, the YFS‐based approach was employed to redesign the resulting structure working backwards from the desired MAF of response (rather than intensity) to estimate an appropriate value of seismic intensity for use within a typical engineering design process. For this high‐seismicity and high‐importance midrise building, a stiffer system with higher base shear strength was thus derived. Moreover, performance assessment via incremental dynamic analysis showed that while the code‐design did not meet the required performance objective, the YFS‐based redesign needed only pushover analysis results to offer a near‐optimal design outcome. The rapid convergence of the method in a single design/analysis iteration emphasized its efficiency and practicability as a design aid for practical application. Copyright © 2017 John Wiley & Sons, Ltd.
Kohrangi M., Bazzurro P., Vamvatsikos D., Spillatura A. (2017). Conditional spectrum based ground motion record selection using average spectral acceleration. Earthquake Engineering and Structural Dynamics, 46(10):1667-1685
Summary | The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.
Kohrangi M., Vamvatsikos D., Bazzurro P. (2017). Site dependence and record selection schemes for building fragility and regional loss assessment. Earthquake Engineering and Structural Dynamics, 46(10):1625-1643
Summary | When performing loss assessment of a geographically dispersed building portfolio, the response or loss (fragility or vulnerability) function of any given archetype building is typically considered to be a consistent property of the building itself. On the other hand, recent advances in record selection have shown that the seismic response of a structure is, in general, dependent on the nature of the hazard at the site of interest. This apparent contradiction begs the question: Are building fragility and vulnerability functions independent of site, and if not, what can be done to avoid having to reassess them for each site of interest? In the following, we show that there is a non‐negligible influence of the site, the degree of which depends on the intensity measure adopted for assessment. Employing a single‐period (e.g., first‐mode), spectral acceleration would require careful record selection at each site and result to significant site‐to‐site variability of the fragility or vulnerability function. On the other hand, an intensity measure comprising the geometric mean of multiple spectral accelerations considerably reduces such variability. In tandem with a conditional spectrum record selection that accounts for multiple sites, it can offer a viable approach for incorporating the effect of site dependence into fragility and vulnerability estimates. Copyright © 2017 John Wiley & Sons, Ltd.
Bakalis K., Fragiadakis M., Vamvatsikos D. (2017). Surrogate modeling for the seismic performance assessment of liquid storage tanks. ASCE Journal of Structural Engineering, 143(4): 04016199
Abstract | A three-dimensional surrogate model is presented for the seismic performance assessment of cylindrical atmospheric liquid storage tanks. The proposed model consists of a concentrated fluid mass attached to a single vertical beam-column element that rests on rigid beam-spokes with edge springs. The model is suitable for rapid static and dynamic seismic performance assessment. Contrary to other simplified models for tanks, its properties are determined through a simple structural analysis that can be performed in any nonlinear analysis software, without the need for complex finite-element models. The results compare favorably to those of three-dimensional finite-element models on three tanks of varying aspect ratios. A step-by-step example of the modeling procedure is presented for a squat unanchored tank, and a sensitivity analysis is conducted in order to investigate the effect of various modeling parameters on the seismic response of the proposed tank model.
Melissianos V., Vamvatsikos D., Gantes C.J. (2017). Performance assessment of buried pipelines at fault crossings. Earthquake Spectra, 33(1): 201-218
Abstract | A methodology for seismic performance assessment of onshore buried steel pipelines at fault crossings is presented. Probabilistic fault displacement hazard analysis is performed at first to determine the magnitude of the three fault displacement components in space. Next, three-dimensional (3-D) structural analysis of the pipeline via a nonlinear beam-type finite element model allows accounting for the different effect of imposed displacements in each axis. Finally, convolving of seismic hazard and structural response results in joint hazard surfaces of compressive and tensile strains that can be used to estimate the mean annual rate of exceeding any limit-state of interest under the influence of demand and capacity uncertainty.
Baltzopoulos G., Vamvatsikos D., Iervolino I. (2016). Analytical modelling of near-source pulse-like seismic demand for multi-linear backbone oscillators. Earthquake Engineering and Structural Dynamics, 45(11): 1797-1815
Abstract | Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single-degree-offreedom (SDOF) oscillator, are well-established tools in the performance-based earthquake engineering paradigm. Initially, such procedures made recourse to inelastic spectra derived for simple elastic-plastic bilinear oscillators, but the request for demand estimates that delve deeper into the inelastic range, motivated investigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, near-source (NS) pulse-like ground motions have been receiving increased attention, since they can induce a distinctive type of inelastic demand. Pulse-like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double-sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology for incorporating this NS effect in the implementation of nonlinear static procedures. Both of the aforementioned lines of research motivate the present study on the ductility demands imposed by pulse-like NS ground motions on oscillators that feature pinching hysteretic behavior with trilinear backbone curves. Incremental dynamic analysis (IDA) is used considering one hundred and thirty pulse-like-identified ground motions. Median, 16% and 84% fractile IDA curves are calculated and fitted by an analytical model. Leastsquares estimates are obtained for the model parameters, which importantly include pulse period Tp. The resulting equations effectively constitute an R – μ – T – T p relation for pulse-like NS motions. Potential applications of this result towards estimation of NS seismic demand are also briefly discussed.
Dimopoulos A.I., Tzimas A.S., Karavasilis T.L., Vamvatsikos D. (2016). Probabilistic economic seismic loss estimation in steel buildings using post-tensioned moment-resisting frames and viscous dampers. Earthquake Engineering and Structural Dynamics, 45(11): 1725-1741
Summary | The potential of post‐tensioned self‐centering moment‐resisting frames (SC‐MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic‐resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC‐MRFs; or (iv) SC‐MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P‐58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post‐tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post‐tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post‐tensioning and supplemental viscous damping by showing that the SC‐MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2016). Implications of IM selection for seismic loss assessment of 3D buildings. Earthquake Spectra. Earthquake Spectra, 32(4):2167-2189
Abstract | Present building-specific loss assessment state-of-art involves the convolution of seismic hazard and building seismic demands. The latter is conditioned on spectral acceleration, Sa(T1), at the building’s first mode as the ground motion intensity measure (IM) and is typically estimated by carrying out nonlinear dynamic analyses on a two-dimensional (2-D) model. By new proposals on the use of improved IMs that can introduce higher fidelity, the accuracy in loss estimation becomes an open question. In reply, we offer a uniform basis for comparing the loss estimates for a set of eight different scalar and vector IMs whose hazard can be predicted with existing GMPEs. Despite all eight being legitimate IMs, and despite the consistent use of conditional spectrum record selection, we find large differences in the estimated loss hazard. This points to the large uncertainty still lingering when connecting hazard to loss. Among the IMs considered here, the vector IMs and at least a scalar average of spectral accelerations showed a remarkable stability in their predictions for the three-dimensional (3-D) buildings, pointing to a potential for reliable applications.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2016). Vector and scalar IMs in structural response estimation: Part II – Building Demand Assessment. Earthquake Spectra. Earthquake Spectra, 32(3): 1525-1543
Abstract | The advantages and disadvantages of using scalar and vector ground motion intensity measures (IMs) are discussed for the local, story-level seismic response assessment of three-dimensional (3-D) buildings. Candidate IMs are spectral accelerations, at a single period (Sa) or averaged over a period range (Saavg). Consistent scalar and vector probabilistic seismic hazard analysis results were derived for each IM, as described in the companion paper in this issue (Kohrangi et al. 2016). The response hazard curves were computed for three buildings with reinforced concrete infilled frames using the different IMs as predictors. Among the scalar IMs, Saavg tends to be the best predictor of both floor accelerations and inter story drift ratios at practically any floor. However, there is an improvement in response estimation efficiency when employing vector IMs, specifically for 3-D buildings subjected to both horizontal components of ground motion. This improvement is shown to be most significant for a tall plan-asymmetric building.
Kohrangi M., Bazzurro P., Vamvatsikos D. (2016). Vector and scalar IMs in structural response estimation: Part I – Hazard Analysis. Earthquake Spectra, 32(3): 1507-1524
Abstract | A realistic assessment of building economic losses and collapse induced by earthquakes requires the monitoring of several response measures, both story-specific and global. The prediction of such response measures benefits from using multiple ground motion intensity measures (IMs) that are, in general, correlated. To allow the inclusion of multiple IMs in the risk assessment process, it is necessary to have a practical tool that computes the vector-valued hazard of all such IMs at the building site. In this paper, vector-valued probabilistic seismic hazard analysis (VPSHA) is implemented here as a post-processor to scalar PSHA results. A group of candidate scalar and vector IMs based on spectral acceleration values, ratios of spectral acceleration values, and spectral accelerations averaged over a period range are defined and their hazard evaluated. These IMs are used as structural response predictors of three-dimensional (3-D) models of reinforced concrete buildings described in a companion paper (Kohrangi et al. 2016).
Moschen L., Adam C., Vamvatsikos D. (2016). A response spectrum method for peak floor acceleration demands in earthquake excited structures. Probabilistic Engineering Mechanics, 46: 94-106
Abstract | This paper addresses the prediction of the median peak floor acceleration (PFA) demand of elastic structures subjected to seismic excitation by means of an adapted response spectrum method. Modal combination is based on a complete quadratic combination (CQC) rule. In contrast to previous studies, in the present contribution closed form solutions for the correlation coefficients and peak factors entering the CQC rule are derived using concepts of normal stationary random vibration theory. A ground motion set, which matches the design response spectrum for a specific site and a target dispersion, is used to define the stochastic base excitation. The response spectrum method is tested for various planar and spatial generic high-rise structures subjected to this particular ground motion set. A comparison of the outcomes with the results of computationally more expensive response history analyses shows the applicability and accuracy of the proposed simplified method.
Olmati P., Petrini F., Vamvatsikos D., Gantes C. (2016). Simplified fragility-based risk analysis for impulse governed blast loading scenarios. Engineering Structures, 117: 457-469
Abstract | Blast-loaded structures are presently assessed and designed following a deterministic approach, where only a set of structural analyses under worst-case design scenarios are carried out in order to verify each limit state. As a rational alternative, a conditional probabilistic approach is introduced to offer comprehensive risk assessment and to allow the design with user-defined confidence in meeting performance targets in view of uncertainties. To simplify the probabilistic consideration of the uncertain parameters, the determination of the blast hazard and the structural response are decoupled into the evaluation of blast hazard curves and structural fragilities curves, respectively, by introducing a single conditioning intensity measure. This is chosen to be the impulse density, shown to be sufficient for impulse-governed scenarios, achieving a reduction of the computational effort by several orders of magnitude without introducing bias. Furthermore a problem-specific safety factor formulation is introduced to incorporate the influence of uncertainties in a simple manner, akin to current engineering practice. As a proof-of-concept test, a steel built-up blast resistant door is subjected to an accidental detonation of mortar rounds in a military facility. The equivalent single degree of freedom model is adopted in order to conduct the structural analyses, while detailed finite element analyses are carried out for validation. Finally, the conditional approach risk analysis on the steel door is compared against the results obtained through the comprehensive (probabilistic) unconditional approach, showing the validity of both the proposed intensity measure and safety factor formulation.
Vamvatsikos D., Aschheim M.A. (2016). Performance-based seismic design via Yield Frequency Spectra. Earthquake Engineering and Structural Dynamics, 45(11): 1759-1778
Summary | Yield frequency spectra (YFS) are introduced to enable the direct design of a structure subject to a set of seismic performance objectives. YFS offer a unique view of the entire solution space for structural performance. This is portrayed in terms of the mean annual frequency (MAF) of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system having specified yield displacement and capacity curve shape. YFS can be computed nearly instantaneously using publicly available software or closed‐form solutions, for any system whose response can be satisfactorily approximated by an equivalent nonlinear single‐degree‐of‐freedom oscillator. Because the yield displacement typically is a more stable parameter for performance‐based seismic design compared with the period, the YFS format is especially useful for design. Performance objectives stated in terms of the MAF of exceeding specified ductility (or displacement) thresholds are used to determine the lateral strength that governs the design of the structure. Both aleatory and epistemic uncertainties are considered, the latter at user‐selected confidence levels that can inject the desired conservatism in protecting against different failure modes. Near‐optimal values of design parameters can be determined in many cases in a single step. Copyright © 2016 John Wiley & Sons, Ltd.
Vamvatsikos D., Kazantzi A., Aschheim M.A (2016). Performance-based seismic design: Avant-garde and code-compatible approaches. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 2(2): C4015008
Abstract | Current force-based codes for the seismic design of structures use design spectra and system-specific behavior factors to satisfy one or two predefined structural limit states . In contrast, performance-based seismic design aims to design a structure to fulfill any number of target performance objectives, defined as user-prescribed levels of structural response, loss, or casualties to be exceeded at a mean annual frequency less than a given maximum. First, a review of recent advances in probabilistic performance assessment is offered. Second, the salient characteristics of methodologies that have been proposed to solve the inverse problem of design are discussed. Finally, an alternative approach is proposed that relies on a new format for visualizing seismic performance, termed yield frequency spectra (YFS). YFS offer a unique view of the entire solution space for structural performance of a surrogate single-degree-of-freedom oscillator, incorporating uncertainty and propagating it to the output response to enable rapid determination of a good preliminary design that satisfies any number of performance objectives.
Vamvatsikos D., Pantazopoulou S.J. (2016). Simplified mechanical model to estimate the seismic vulnerability of heritage unreinforced masonry buildings. Journal of Earthquake Engineering, 20(2): 298-325
Abstract | Traditional or historic masonry structures occur in large populations throughout the world, particularly in preserved historical city clusters. Being non-engineered and aging these structures are in urgent need of assessment and seismic repair/rehabilitation. However, traditional masonry presents important challenges to computational modeling, owing to complexity of structural system, material inhomogeneity, and contact interactions that collectively can only be addressed through detailed 3D nonlinear representation. In this article, a simple performance assessment model is developed in order to address the need for preliminary assessment tools for this class of structures. The objective is to be able to rapidly identify buildings that are at higher risk in the event of a significant earthquake, potentially justifying a second round of more detailed evaluation. The proposed model defines the characteristics of a Single Degree of Freedom representation of the building, formulating consistent 3D shape functions to approximate its fundamental mode of vibration considering both in-plane and out-plane wall bending as a result of insufficient diaphragm action. Parametric expressions for the dynamic properties are derived in terms of the important geometric, material, and system characteristics, and are used to express local demand from global estimates. Acceptance criteria are established both in terms of deformation and strength indices to guide retrofit. An application example of the proposed assessment methodology is included to demonstrate the ability of the model to reproduce the essential features of traditional masonry buildings under seismic action.
Kazantzi A.K., Vamvatsikos D. (2015). Intensity measure selection for vulnerability studies of building classes. Earthquake Engineering and Structural Dynamics, 44(15): 2677-2694
Summary | The selection of a scalar Intensity Measure (IM) for performing analytical vulnerability (loss) assessment across a building class is addressed. We investigate the ability of several IM choices to downgrade the effect of seismological parameters (sufficiency) as well as reduce the record‐to‐record variability (efficiency) for both highrise and lowrise sets of ‘index’ buildings. These characteristics are explored in unprecedented detail, employing comparisons and statistical significance testing at given levels of local engineering demand parameters (story drift ratios and peak floor accelerations) that relate to losses, instead of global variables such as the maximum interstory drift. Thus, a detailed limit‐state‐specific view is offered for the suitability of different scalar IMs for loss assessment. As expected, typical single‐period spectral values are found to introduce unwanted bias at high levels of scaling, both for a single as well as a class of buildings. On the other hand, the geometric mean of the spectral acceleration values estimated at several periods between the class‐average second‐mode and an elongated class‐average first‐mode period offers a practical choice that significantly reduces the spectral‐shape bias without requiring the development of new ground motion prediction equations. Given that record selection remains a site‐ and building‐specific process, such an improved IM can help achieve reliable estimates for building portfolios, as well as single structures, at no additional cost. Copyright © 2015 John Wiley & Sons, Ltd.
Fragiadakis M., Vamvatsikos D., Lagaros N., Karlaftis M., Papadrakakis M. (2015). Seismic Assessment of Structures and Lifelines. Journal of Sound and Vibration, 334: 29-56
Abstract | We discuss the current state-of-the-art on the assessment of systems (structures and lifelines) subjected to seismic loading. Severe earthquakes are random events that may have a devastating outcome. Therefore, the treatment of seismic loading and its effects has many layers due to the random nature of the problem and also its consequences. We attempt to provide a wide approach to the problem, referencing the major contributions in the field and discussing the most suitable methods for tackling the challenges involved. Our study extends from modeling seismic hazard to the modeling and analysis of structures and lifelines. Emphasis is given to probabilistic performance estimation frameworks and the rational treatment of uncertainty, a major element of contemporary earthquake engineering.
Kazantzi A.K., Vamvatsikos D., Lignos D.G. (2014). Seismic performance of a steel moment-resisting frame subject to strength and ductility uncertainty. Engineering Structures, 78: 69-77
Abstract | The reliable estimation of the seismic performance of structures requires quantifying the aleatory and epistemic uncertainties of the system parameters. This is efficiently achieved for a case study of a four-story steel moment-resisting frame through several important advances. First, a state-of-the-art numerical model is formed with full spatial parameterization of its strength and plastic deformation properties. Empirical relationships derived from experimental data are used to model the cyclic behavior of steel sections using probabilistically distributed parameters that include intra- and inter-component correlation. Finally, incremental dynamic analysis and Monte Carlo simulation are employed to accurately assess the seismic performance of the model under the influence of uncertainties. Of interest is the extent to which model parameter uncertainties may trigger negative demand-capacity correlation in structural fragility evaluation, where, for example, a lower ductility capacity for a component may decrease the threshold for local failure while at the same time raising the local demand estimate from an uncertainty-aware model. With respect to the examined steel moment-resisting frame and considering three construction quality levels (i.e. very good, average, low) as per FEMA P-58, it is shown that, despite the good agreement of the evaluated structural demands obtained with and without consideration of the model parameter uncertainties for well-designed modern buildings, the potential demand-capacity correlation is likely to give rise to unconservative estimates of fragility for local damage-states, especially in cases where substandard quality control is exercised during construction.
Vamvatsikos D. (2014). Seismic Performance Uncertainty Estimation via IDA with Progressive Accelerogram-wise Latin Hypercube Sampling. ASCE Journal of Structural Engineering, 140(8): A4014015
Abstract | An algorithm is proposed for the rapid estimation of the influence of model parameter uncertainties on the seismic performance of structures using incremental dynamic analysis (IDA) and Monte Carlo simulation with Latin hypercube sampling. It builds upon existing methods that quantify the uncertainty for structural models with nondeterministic parameters by performing IDA with multiple ground motion records on each model realization out of a predetermined sample. However, their practical application is restricted due to (1) the inability to determine a priori the required number of samples and (2) the disproportionate increase of the number of analyses in realistic multiparameter models. To address these issues, two fundamental changes are incorporated. First, Latin hypercube sampling is applied progressively by starting with a small sample that is doubled successively until the desired accuracy is achieved. Second, parameter sampling is performed on a record-by-record basis rather than maintaining the same model over an entire record suite, thus expanding the model sample size without increasing the number of nonlinear dynamic analyses. Using strong-column and weak-column models of a steel moment-resisting frame, the algorithm is shown to possess excellent scalability, extending the original methodology to be applicable to large-scale models with hundreds of random variables.
Fragiadakis M., Vamvatsikos D., Aschheim M. (2014). Application of nonlinear static procedures for seismic assessment of regular RC moment frame buildings. Earthquake Spectra, 30(2): 767-794
Abstract | The applicability of nonlinear static procedures for estimating the seismic demands of typical regular RC moment-resisting frames is evaluated. This work, conducted within the framework of the ATC-76-6 project, shows the degree to which nonlinear static methods can characterize global and local response demands vis-à–vis those determined by nonlinear dynamic analysis for three RC moment-frame buildings. The response quantities (engineering demand parameters) considered are peak story displacements, story drifts, story shears, and floor overturning moments. The single-mode pushover methods evaluated include the N2 and the ASCE-41 coefficient methods. Multi-modal pushover methods, such as modal pushover analysis and the consecutive modal pushover method, were also evaluated. The results indicate that the relatively good performance of the single-mode methods observed for low-rise buildings rapidly deteriorates as the number of stories increases. The multi-modal techniques generally extend the range of applicability of pushover methods, but at the cost of additional computation and without ensuring the reliability of the results.
Vamvatsikos D. (2014). Accurate application and second-order improvement of the SAC/FEMA probabilistic formats for seismic performance assessment. ASCE Journal of Structural Engineering, 140(2): 04013058
Abstract | The SEAONC/ATC/CUREE (SAC/FEMA) probabilistic framework is based on a closed-form expression to estimate analytically the value of the risk integral convolving seismic hazard and structural response. Despite its practicality, implementation has been hindered by reduced accuracy due to a number of approximations that are needed to achieve a desirable form, the most significant being the power-law fitting of the seismic hazard curve. To mitigate this problem, two approaches are given: (1) selecting an appropriately biased power-law fit, and (2) offering a novel closed-form expression involving a second-order approximation. Where blind application of the original format could involve errors in excess of 100% for the predicted mean annual frequency of limit-state (LS) exceedance, biased fitting reduces it to less than 50% for many practical cases, whereas the new closed-form expression consistently brings it below 10%. While other sources of error still remain, the robustness achieved opens new avenues of application for this popular format.
Fragiadakis M., Christodoulou S.E., Vamvatsikos D. (2013). Reliability assessment of urban water distribution networks under seismic loads. Water Resources Management, 27(10): 3739-3764
Abstract | Presented herein is a methodology for the seismic assessment of the reliability of urban water distribution networks (UWDN) based on general seismic assessment standards, as per the American Lifelines Alliance (ALA) guidelines, and localized historical records of critical risk-of-failure metrics pertaining to the specific UWDN under assessment. The proposed methodology is applicable to UWDN under both normal or abnormal operating conditions (such as intermittent water supply), and the assessment of reliability incorporates data of past non-seismic damage, the vulnerabilities of the network components against seismic loading, and the topology of a UWDN. Historical data obtained using records of pipe burst incidents are processed to produce clustered ‘survival curves’, depicting the pipes’ estimated survival rate over time. The survival curves are then used to localize the generalized fragility values of the network components (primarily pipes), as assessed using the approach suggested by the ALA guidelines. The network reliability is subsequently assessed using Graph Theory (Djikstra’s shortest path algorithm), while the system reliability is calculated using Monte Carlo simulation. The methodology proposed is demonstrated on a simple small-scale network and on a real-scale district metered area (DMA). The proposed approach allows the estimation of the probability that a network fails to provide the desired level of service and allows for the prioritization of retrofit interventions and of capacity-upgrade actions pertaining to existing water pipe networks.
Vamvatsikos D. (2013). Derivation of new SAC/FEMA performance evaluation solutions with second-order hazard approximation. Earthquake Engineering and Structural Dynamics, 42(8): 1171-1188
Summary | A novel set of SAC/FEMA‐style closed‐form expressions is presented to accurately assess structural safety under seismic action. Such solutions allow the practical evaluation of the risk integral convolving seismic hazard and structural response by using a number of idealizations to achieve a simple analytical form. The most heavily criticized approximation of the SAC/FEMA formats is the first‐order power‐law fit of the hazard curve. It results to unacceptable errors whenever the curvature of the hazard function becomes significant. Adopting a second‐order fit, instead, allows capturing the hazard curvature at the cost of necessitating new analytic forms. The new set of equations is a complete replacement of the original, enabling (a) accurate estimation of the mean annual frequency of limit‐state exceedance and (b) safety checking for specified performance objectives in a code‐compatible format. More importantly, the flexibility of higher‐order fitting guarantees a wider‐range validity of the local hazard approximation. Thus, it enables the inversion of the formulas for practically estimating the allowable demand or the required capacity to fulfill any design objective. Copyright © 2012 John Wiley & Sons, Ltd.
De Luca F., Vamvatsikos D., Iervolino I. (2013). Near-optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis. Earthquake Engineering and Structural Dynamics, 42(4): 523-543
Summary | The piecewise linear (‘multilinear’) approximation of realistic force‐deformation capacity curves is investigated for structural systems incorporating generalized plastic, hardening, and negative stiffness behaviors. This fitting process factually links capacity and demand and lies at the core of nonlinear static assessment procedures. Despite codification, the various fitting rules used can produce highly heterogeneous results for the same capacity curve, especially for the highly‐curved backbones resulting from the gradual plasticization or the progressive failures of structural elements. To achieve an improved fit, the error introduced by the approximation is quantified by studying it at the single‐degree‐of‐freedom level, thus avoiding any issues related to multi‐degree‐of‐freedom versus single‐degree‐of‐freedom realizations. Incremental dynamic analysis is employed to enable a direct comparison of the actual backbones versus their candidate piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limit‐states. In all cases, current code‐based procedures are found to be highly biased wherever widespread significant stiffness changes occur, generally leading to very conservative estimates of performance. The practical rules determined allow, instead, the definition of standardized low‐bias bilinear, trilinear, or quadrilinear approximations, regardless of the details of the capacity curve shape. Copyright © 2012 John Wiley & Sons, Ltd.
Celarec D., Vamvatsikos D, Dolsek M. (2011). Estimation of the seismic risk with consideration of capacity degradation over time for RC buildings. Bulleting of Earthquake Engineering, 9(4): 1137-1155
Abstract | Throughout the world, buildings are reaching the end of their design life and develop new pathologies that decrease their structural capacity. Usually the ageing process is neglected in seismic design or seismic risk assessment but may become important for older structures, especially, if they are intended to be in service even after they exceed their design life. Thus, a simplified methodology for seismic performance evaluation with consideration of performance degradation over time is presented, based on an extension of the SAC/FEMA probabilistic framework for estimating mean annual frequencies of limit state exceedance. This is applied to an example of an older three-storey asymmetric reinforced concrete building, in which corrosion has just started to propagate. The seismic performance of the structure is assessed at several successive times and the instantaneous and overall seismic risk is estimated for the near collapse limit state. The structural capacity in terms of the maximum base shear and the maximum roof displacement is shown to decrease over time. Consequently, the time-averaged mean annual frequency of violating the near-collapse limit state increases for the corroded building by about 10% in comparison to the typical case where corrosion is neglected. However, it can be magnified by almost 40% if the near-collapse limit state is related to a brittle shear failure, since corrosion significantly affects transverse reinforcement, raising important questions on the seismic safety of the existing building stock.
Vamvatsikos D., Dolsek M. (2011). Equivalent Constant Rates for Performance-Based Assessment of Ageing Structures. Structural Safety, 33(1): 8-18
Abstract | Analytical, closed-form solutions are derived for the computation of equivalent constant rates of limit-state exceedance for structures under seismic loads whose capacity is degrading with time. Seismic guidelines currently designate constant, time-independent probabilities or mean annual frequencies of exceedance that are assumed to remain invariable for the entire design life. These are at odds with the time-dependent, ever-increasing exceedance rates of ageing structures. Based on the concept of social equity and discounting of societal investments, the equivalent constant rate provides a basis for judging the safety of structures with time-dependent capacity by allowing comparisons with the code-mandated rates of limit-state exceedance. Starting from the simple SAC/FEMA solution and assuming a power-law degradation of capacity with time and a linear change in the combined epistemic and aleatory variability of capacity, we provide general solutions for the equivalent constant rate and for the limiting case of the average rate over the design life of the structure. The solutions are formulated both in the demand-based and in the intensity-based format, the latter being suitable for all limit-states, even close to global collapse. By using a 7-story reinforced concrete building as an example, we demonstrate the accuracy and the practicality of these approximations for the assessment of an existing structure.
Vamvatsikos D. (2011). Performing Incremental Dynamic Analysis in Parallel. Computers and Structures, 89(1-2): 170-180
Abstract | Incremental dynamic analysis has recently emerged to offer comprehensive evaluation of the seismic performance of structures using multiple nonlinear dynamic analyses under scaled ground-motion records. Being computer-intensive, it can benefit from parallel processing to accelerate its application on realistic structural models. While the task-farming master–slave paradigm seems ideal, severe load imbalances arise due to analysis non-convergence at structural instability, prompting the examination of task partitioning at the level of single records or single dynamic runs. Combined with a multi-tier master–slave processor hierarchy employing dynamic task generation and self-scheduling we achieve a flexible and efficient parallel algorithm with excellent scalability.
Fragiadakis M., Vamvatsikos D. (2010) Fast performance uncertainty estimation via pushover and approximate IDA. Earthquake Engineering and Structural Dynamics, 39(6): 683-703
Abstract | Approximate methods based on the static pushover are introduced to estimate the seismic performance uncertainty of structures having non‐deterministic modeling parameters. At their basis lies the use of static pushover analysis to approximate Incremental Dynamic Analysis (IDA) and estimate the demand and capacity epistemic uncertainty. As a testbed we use a nine‐storey steel frame having beam hinges with uncertain moment–rotation relationships. Their properties are fully described by six, randomly distributed, parameters. Using Monte Carlo simulation with Latin hypercube sampling, a characteristic ensemble of structures is created. The Static Pushover to IDA (SPO2IDA) software is used to approximate the IDA capacity curve from the appropriately post‐processed results of the static pushover. The approximate IDAs allow the evaluation of the seismic demand and capacity for the full range of limit‐states, even close to global dynamic instability. Moment‐estimating techniques such as Rosenblueth’s point estimating method and the first‐order, second‐moment (FOSM) method are adopted as simple alternatives to obtain performance statistics with only a few simulations. The pushover is shown to be a tool that combined with SPO2IDA and moment‐estimating techniques can supply the uncertainty in the seismic performance of first‐mode‐dominated buildings for the full range of limit‐states, thus replacing semi‐empirical or code‐tabulated values (e.g. FEMA‐350), often adopted in performance‐based earthquake engineering.
Vamvatsikos D., Fragiadakis M. (2010). Incremental dynamic analysis for estimating seismic performance uncertainty and sensitivity. Earthquake Engineering and Structural Dynamics, 39(2): 141-163
Abstract | Incremental dynamic analysis (IDA) is presented as a powerful tool to evaluate the variability in the seismic demand and capacity of non‐deterministic structural models, building upon existing methodologies of Monte Carlo simulation and approximate moment‐estimation. A nine‐story steel moment‐resisting frame is used as a testbed, employing parameterized moment‐rotation relationships with non‐deterministic quadrilinear backbones for the beam plastic‐hinges. The uncertain properties of the backbones include the yield moment, the post‐yield hardening ratio, the end‐of‐hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Sensitivity analyses on both the IDA and the static pushover level reveal the yield moment and the two rotational‐ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ (a) Monte Carlo simulation with latin hypercube sampling, (b) point‐estimate and (c) first‐order second‐moment techniques, thus offering competing methods that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a median‐parameter model to estimate the median seismic performance and employing the well‐known square‐root‐sum‐of‐squares rule to combine aleatory randomness and epistemic uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.
Fragiadakis M., Vamvatsikos D., Papadrakakis M. (2006). Evaluation of the influence of vertical irregularities on the seismic performance of a 9-storey steel frame. Earthquake Engineering and Structural Dynamics, 35(12): 1489-1509
Abstract | A methodology based on incremental dynamic analysis (IDA) is presented for the evaluation of structures with vertical irregularities. Four types of storey‐irregularities are considered: stiffness, strength, combined stiffness and strength, and mass irregularities. Using the well‐known nine‐storey LA9 steel frame as a base, the objective is to quantify the effect of irregularities, both for individual and for combinations of stories, on its response. In this context a rational methodology for comparing the seismic performance of different structural configurations is proposed by means of IDA. This entails performing non‐linear time history analyses for a suite of ground motion records scaled to several intensity levels and suitably interpolating the results to calculate capacities for a number of limit‐states, from elasticity to final global instability. By expressing all limit‐state capacities with a common intensity measure, the reference and each modified structure can be naturally compared without needing to have the same period or yield base shear. Using the bootstrap method to construct appropriate confidence intervals, it becomes possible to isolate the effect of irregularities from the record‐to‐record variability. Thus, the proposed methodology enables a full‐range performance evaluation using a highly accurate analysis method that pinpoints the effect of any source of irregularity for each limit‐state. Copyright © 2006 John Wiley & Sons, Ltd.
Vamvatsikos D., Cornell C.A. (2006). Direct estimation of the seismic demand and capacity of oscillators with multi-linear static pushovers through Incremental Dynamic Analysis. Earthquake Engineering and Structural Dynamics, 35(9): 1097-1117
Abstract | SPO2IDA is introduced, a software tool that is capable of recreating the seismic behaviour of oscillators with complex quadrilinear backbones. It provides a direct connection between the static pushover (SPO) curve and the results of incremental dynamic analysis (IDA), a computer‐intensive procedure that offers thorough demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. To achieve this, the seismic behaviour of numerous single‐degree‐of‐freedom (SDOF) systems is investigated through IDA. The oscillators have a wide range of periods and feature pinching hysteresis with backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative‐stiffness segment plus a final residual plateau that terminates with a drop to zero strength. An efficient method is introduced to treat the backbone shape by summarizing the analysis results into the 16, 50 and 84% fractile IDA curves, reducing them to a few shape parameters and finding simpler backbones that reproduce the IDA curves of complex ones. Thus, vast economies are realized while important intuition is gained on the role of the backbone shape to the seismic performance. The final product is SPO2IDA, an accurate, spreadsheet‐level tool for performance‐based earthquake engineering that can rapidly estimate demands and limit‐state capacities, strength reduction R‐factors and inelastic displacement ratios for any SDOF system with such a quadrilinear SPO curve. Copyright © 2006 John Wiley & Sons, Ltd.
Vamvatsikos D., Cornell C.A. (2005). Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthquake Engineering and Structural Dynamics, 34(13): 1573-1600
Abstract | Scalar and vector intensity measures are developed for the efficient estimation of limit‐state capacities through incremental dynamic analysis (IDA) by exploiting the elastic spectral shape of individual records. IDA is a powerful analysis method that involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the intensity measure or IM), thus producing curves of structural response parameterized by the IM on top of which limit‐states can be defined and corresponding capacities can be calculated. When traditional IMs are used, such as the peak ground acceleration or the first‐mode spectral acceleration, the IM‐values of the capacities can display large record‐to‐record variability, forcing the use of many records to achieve reliable results. By using single optimal spectral values as well as vectors and scalar combinations of them on three multistorey buildings significant dispersion reductions are realized. Furthermore, IDA is extended to vector IMs, resulting in intricate fractile IDA surfaces. The results reveal the most influential spectral regions/periods for each limit‐state and building, illustrating the evolution of such periods as the seismic intensity and the structural response increase towards global collapse. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. Copyright © 2005 John Wiley & Sons, Ltd.
Vamvatsikos D., Cornell C.A. (2005). Direct estimation of the seismic demand and capacity of MDOF systems through Incremental Dynamic Analysis of an SDOF Approximation. ASCE Journal of Structural Engineering, 131(4): 589-599
Abstract | Introducing a fast and accurate method to estimate the seismic demand and capacity of first-mode-dominated multidegree-of-freedom systems in regions ranging from near-elastic to global collapse. This is made possible by exploiting the connection between the static pushover (SPO) and the incremental dynamic analysis (IDA). While the computer-intensive IDA would require several nonlinear dynamic analyses under multiple suitably scaled ground motion records, the simpler SPO helps approximate the multidegree-of-freedom system with a single-degree-of-freedom oscillator whose backbone matches the structure’s SPO curve far beyond its peak. Similar methodologies exist but they usually employ oscillators with a bilinear backbone. In contrast, the empirical equations implemented in the static pushover 2 incremental dynamic analysis (SPO2IDA) software allow the use of a complex quadrilinear backbone shape. Thus, the entire summarized IDA curves of the resulting system are effortlessly generated, enabling an engineer-user to obtain accurate estimates of seismic demands and capacities for limit-states such as immediate occupancy or global dynamic instability. Using three multistory buildings as case studies, the methodology is favorably compared to the full IDA.
Vamvatsikos D., Cornell C.A. (2004). Applied Incremental Dynamic Analysis. Earthquake Spectra, 20(2): 523-553
Abstract | We are presenting a practical and detailed example of how to perform incremental dynamic analysis (IDA), interpret the results and apply them to performance-based earthquake engineering. IDA is an emerging analysis method that offers thorough seismic demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a multiply scaled suite of ground motion records. Realization of its opportunities requires several steps and the use of innovative techniques at each one of them. Using a nine-story steel moment-resisting frame with fracturing connections as a test bed, the reader is guided through each step of IDA: (1) choosing suitable ground motion intensity measures and representative damage measures, (2) using appropriate algorithms to select the record scaling, (3) employing proper interpolation and (4) summarization techniques for multiple records to estimate the probability distribution of the structural demand given the seismic intensity, and (5) defining limit-states, such as the dynamic global system instability, to calculate the corresponding capacities. Finally, (6) the results can be used to gain intuition for the structural behavior, highlighting the connection between the static pushover (SPO) and the dynamic response, or (7) they can be integrated with conventional probabilistic seismic hazard analysis (PSHA) to estimate mean annual frequencies of limit-state exceedance. Building upon this detailed example based on the nine-story structure, a complete commentary is provided, discussing the choices that are available to the user, and showing their implications for each step of the IDA.
Vamvatsikos D., Cornell C.A. (2002). Incremental Dynamic Analysis. Earthquake Engineering and Structural Dynamics, 31(3): 491-514
Abstract | Incremental dynamic analysis (IDA) is a parametric analysis method that has recently emerged in several different forms to estimate more thoroughly structural performance under seismic loads. It involves subjecting a structural model to one (or more) ground motion record(s), each scaled to multiple levels of intensity, thus producing one (or more) curve(s) of response parameterized versus intensity level. To establish a common frame of reference, the fundamental concepts are analysed, a unified terminology is proposed, suitable algorithms are presented, and properties of the IDA curve are looked into for both single‐degree‐of‐freedom and multi‐degree‐of‐freedom structures. In addition, summarization techniques for multi‐record IDA studies and the association of the IDA study with the conventional static pushover analysis and the yield reduction R‐factor are discussed. Finally, in the framework of performance‐based earthquake engineering, the assessment of demand and capacity is viewed through the lens of an IDA study. Copyright © 2001 John Wiley & Sons, Ltd.
Georgiadis H.G., Vamvatsikos D., Vardoulakis I. (1999). Numerical implementation of the integral-transform solution to Lamb’s point load problem. Computational Mechanics, 24(2): 90-99
Abstract | The present work describes a procedure for the numerical evaluation of the classical integral-transform solution of the transient elastodynamic point-load (axisymmetric) Lamb’s problem. This solution involves integrals of rapidly oscillatory functions over semi-infinite intervals and inversion of one-sided (time) Laplace transforms. These features introduce difficulties for a numerical treatment and constitute a challenging problem in trying to obtain results for quantities (e.g. displacements) in the interior of the half-space. To deal with the oscillatory integrands, which in addition may take very large values (pseudo-pole behavior) at certain points, we follow the concept of Longman’s method but using as accelerator in the summation procedure a modified Epsilon algorithm instead of the standard Euler’s transformation. Also, an adaptive procedure using the Gauss 32-point rule is introduced to integrate in the vicinity of the pseudo-pole. The numerical Laplace-transform inversion is based on the robust Fourier-series technique of Dubner/Abate-Crump-Durbin. Extensive results are given for sub-surface displacements, whereas the limit-case results for the surface displacements compare very favorably with previous exact results.
BOOKS & CHAPTERS IN EDITED BOOKS
Now - 2011
Kohrangi M., Papadopoulos A.N., Kotha S.R., Vamvatsikos D., Bazzurro P. (2021). Earthquake Catastrophe Risk Modeling, Application to the Insurance Industry: Unknowns and Possible Sources of Bias in Pricing. In: Advances in Assessment and Modeling of Earthquake Loss. Springer: Dordrecht.
Abstract | Mathematical risk assessment models based on empirical data and supported by the principles of physics and engineering have been used in the insurance industry for more than three decades to support informed decisions for a wide variety of purposes, including insurance and reinsurance pricing. To supplement scarce data from historical events, these models provide loss estimates caused to portfolios of structures by simulated but realistic scenarios of future events with estimated annual rates of occurrence. The reliability of these estimates has evolved steadily from those based on the rather simplistic and, in many aspects, semi-deterministic approaches adopted in the very early days to those of the more recent models underpinned by a larger wealth of data and fully probabilistic methodologies. Despite the unquestionable progress, several modeling decisions and techniques still routinely adopted in commercial models warrant more careful scrutiny because of their potential to cause biased results. In this chapter we will address two such cases that pertain to the risk assessment for earthquakes. With the help of some illustrative but simple applications we will first motivate our concerns with the current state of practice in modeling earthquake occurrence and building vulnerability for portfolio risk assessment. We will then provide recommendations for moving towards a more comprehensive, and arguably superior, approach to earthquake risk modeling that capitalizes on the progress recently made in risk assessment of single buildings. In addition to these two upgrades, which in our opinion are ready for implementation in commercial models, we will also describe an enhancement in ground motion prediction that will certainly be considered in the models of tomorrow but is not yet ready for primetime. These changes are implemented in example applications that highlight their importance for portfolio risk assessment. Special consideration will be given to the potential bias in the Average Annual Loss estimates, which constitutes the foundation of insurance and reinsurance policies’ pricing, that may result from the application of the traditional approaches.
Aschheim M., Hernandez-Montes E., Vamvatsikos D., (2019). Design of Reinforced Concrete Buildings for Seismic Performance: Practical Deterministic and Probabilistic Approaches Protection of Built Environment Against Earthquakes. CRC Press.
Book Description | The costs of inadequate earthquake engineering are huge, especially for reinforced concrete buildings. This book presents the principles of earthquake-resistant structural engineering, and uses the latest tools and techniques to give practical design guidance to address single or multiple seismic performance levels.
It presents an elegant, simple and theoretically coherent design framework. Required strength is determined on the basis of an estimated yield displacement and desired limits of system ductility and drift demands. A simple deterministic approach is presented along with its elaboration into a probabilistic treatment that allows for design to limit annual probabilities of failure. The design method allows the seismic force resisting system to be designed on the basis of elastic analysis results, while nonlinear analysis is used for performance verification. Detailing requirements of ACI 318 and Eurocode 8 are presented. Students will benefit from the coverage of seismology, structural dynamics, reinforced concrete, and capacity design approaches, which allows the book to be used as a foundation text in earthquake engineering.
Fragiadakis M., Vamvatsikos D., Aschheim M. (2011). Static versus dynamic methods of analysis for estimating seismic performance. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | Nonlinear static methods are evaluated and compared with nonlinear dynamic methods for estimating the seismic performance of structures. Emphasis is given on assessing the applicability of nonlinear static methods for RC buildings, and on comparing the building’s capacity obtained using nonlinear static and nonlinear response history analysis. The first task refers to the ability of alternative static pushover-based methods to estimate the response at the level of a member or of a story. Plain as well as more elaborate pushover methods such as the Modal Pushover Analysis method and the Consecutive Modal Pushover method are included in our evaluation. The second task refers to the qualitative comparison at the global level between static pushover and nonlinear response history analysis when either the static pushover or the Incremental Dynamic Analysis (IDA) setting is adopted. When the static pushover setting is adopted, we show that nonlinear static methods can be compared with the IDA curve when the base shear instead of spectral acceleration is plotted on the ordinates, while the dispersion among the single-record IDAs is considerably reduced. Alternatively, the comparison can be performed within the IDA setting if appropriate R-C 1-T relationships, simplified or more advanced (e.g. SPO2IDA), are adopted. Each setting shows different qualitative characteristics of the two seismic performance estimation approaches and has different practical applications.
Celarec D., Vamvatsikos D., Dolsek M. (2011). Simplified estimation of seismic risk for buildings with consideration of the structural ageing process. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract |A simplified method for estimating the seismic risk of deteriorating buildings is presented utilizing a probabilistic framework and a simplified nonlinear method for seismic performance assessment of structures. Firstly, the probabilistic methodology with the extension to deteriorating structures is briefly explained. Then the methodology is applied to the example of a four-storey RC frame building with corroded reinforcement in order to estimate the influence of corrosion on seismic risk for the near-collapse limit state. The results reveal that after 50 years from the initiation of corrosion, the peak ground acceleration that causes the structure to violate the defined near collapse limit state decreases by 17% and the seismic risk for the near-collapse limit state increases by 7%, compared to the case where corrosion is neglected. It is also shown that degradation due to corrosion may change the collapse mechanism from ductile to brittle shear failure, raising an important question on the seismic safety of the existing buildings.
Vamvatsikos D. (2011). Some thoughts on methods to compare the seismic performance of alternate structural designs. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | The process of structural design ultimately hinges upon the selection of the top alternative designs from a group of viable choices, ideally choosing the one that best satisfies the requirements, as set by codes or guidelines. Comparing structural configurations to find the best candidate has thus remained a favorite subject of researchers and engineers alike, especially in the case of seismic loads. With the emergence of performance-based earthquake engineering, such comparisons now need to be performed on the basis of the seismic performance, preferably at several limit-states. Such a direct evaluation can become cumbersome, requiring seismic hazard information. Therefore, shortcuts and simpler techniques have been introduced that are generally based on the concept of system fragility, as estimated through the various methods of structural analysis. Still, there is no general consensus on the metrics that can be used for such an evaluation; some researchers adopt force or displacement response quantities derived from static or dynamic methods, while others prefer to compare capacities in terms of intensity or response measures. In order to even out the field, we perform a comparative evaluation of the available choices and point out the pros and cons of each, showing some of the common fallacies that plague the results of such comparisons.
CONFERENCE PAPERS
Now - 1999
Spillatura A., Vamvatsikos D., Kohrangi M., Bazzurro P. (2024). Harmonizing Seismic Performance Via Risk Targeted Spectra: State Of The Art, Dependencies, And Implementation Proposals. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | Structures are typically designed on the basis of ground motion spectral values associated to an “ultimate” limit state of reference, e.g., 10% in 50 years, which gives a measure of the hazard at the site of interest. However, this design approach does not guarantee that the risk will be uniform, even for buildings at sites that share the same design level, as measured, e.g., by the peak ground acceleration, mainly because of differences in hazard curve shape. Aiming to ensure a uniform collapse risk across different sites and buildings, Risk Targeted design maps were first introduced by ASCE7-10 to modify conventional design spectra by employing suitable adjustment factors. As there is more than one approach to define such factors, our objective is to test their effectiveness in matching a specific target risk or, at least, in harmonizing the risk of multiple buildings at different sites with respect to different limit states. To do so, we make use of simplified single-degree-of-freedom structures for several configurations of vibration period and ductility. Although risk matching is shown to be only theoretically possible and unachievable in practice, we claim that harmonization remains a viable and valuable target.
[paper]
Tsarpalis D., Karaferi E., Mohsen K., Vamvatsikos D., Zeppos J. (2024). A Mesoeconomic Resilience Framework For Regional Seismic Assessment Studies. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | On account that modern societies cannot be built on earthquake-proof infrastructure (e.g., buildings, roads, power supplies), increasing resilience through preparedness and adaptation measures is the state-ofart approach to reduce severe consequences to core community functions. From an economic standpoint, the impact of a disaster can be discretized into two parts: (i) the direct losses, which comprise the cost needed to repair/replace the damaged/destroyed assets and (ii) the indirect losses, which are related to the reduction of gross valued added during the post-event period. Currently, most regional risk assessment studies are focusing on the evaluation of the direct losses, either ignoring the indirect part or using qualitative approaches to coarsely assess its impact. In support of risk assessment and crisis mitigation planning, a meso-scale economic resilience framework is proposed that allows a quantitative estimate of indirect loss in tandem with conventional direct loss assessment. The model is based upon a sector-wide approach, in which the individual businesses operating within the community are aggregated into compact sectors. Subsequently, the postevent performance of each sector is assessed using three indices, (a) the infrastructure index to measure the reduced productivity of a sector due to direct infrastructure damages, (b) the input index to propagate disruptions in the supply chain by employing Vendor Dependence Tables, and (c) the output index to reflect the reduction of demand due to disruptions (a) and (b). The model is designed to accommodate the salient characteristics of modern urban societies, addressing complex socioeconomic aspects such as the adaptive behaviour of residents and visitors, and the capability of a sector to redistribute business traffic within or outside the community. The methodology is demonstrated in the historical city of Granada in Spain, using three hypothetical earthquake scenarios of incremental intensity and impact.
[paper]
Denaro S., Valerio C., Bussi G., Faga E., Karaferi E., Tsarpalis D., Vamvatsikos D. (2024). Financial Risk Management For Earthquake Disaster: A Case Study Of Rhodes And Granada. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | A comprehensive disaster risk management strategy is crucial for mitigating the impact of earthquakes and safeguarding valuable cultural heritage. This study, developed within the EU funded project HYPERION, focuses on the cities of Rhodes and Granada, which possess significant cultural assets subject to seismic hazard. Financial risk management plays a pivotal role in this strategy by enabling resource mobilization for efficient disaster response and minimizing long-term financial consequences. Herein we explore the implementation of ex-ante financing options, which are financial arrangements established before disasters occur, to ensure swift and effective response measures. Ex-ante financing options encompass two main approaches: risk retention and risk transfer mechanisms. Risk retention involves setting aside resources, such as contingency funds or individual/shared reserves, for immediate post-disaster use. On the other hand, risk transfer mechanisms shift financial risk to third parties, such as insurance companies or capital markets. To optimize these financing options, we employ a comprehensive approach known as risk layering, which categorizes risks based on their return periods or probabilities. Risk layering facilitates the strategic deployment of various financial tools for each risk layer, resulting in enhanced efficiency and reduced overall costs of risk financing. The aim is to develop a financial risk management strategy based on risk layering for stakeholders in macro-sectors with shared risk characteristics and synergies. We define three risk layers: (i) low-impact, high-frequency risks, where risk retention measures like contingency or mutual funds are most appropriate; (ii) medium-to-severe risks occurring at lower frequencies, for which risk transfer through parametric insurance is identified as the optimal financial risk management tool; and (iii) very high-impact, highly infrequent risks, requiring risk absorption through financial assistance from the public sector and international donors. To determine the most cost-effective thresholds for each layer and stakeholder macrosector, we employ an optimization approach. By tailoring risk management options to the specific needs of different stakeholders and considering their capacity to absorb risk, our research contributes to effective disaster financial risk management for earthquake-prone areas.
[paper]
Chatzidaki A., Vamvatsikos D., Loli M., Tsatsis A. (2024). Multi-Hazard Risk And Resilience Assessment For The Egnatia Odos Highway In Greece. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | Risk and resilience are assessed for the Metsovo-Panagia segment of the Egnatia highway in Greece, focusing on the seismic and the wind hazard. This segment comprises steep slopes, bridges and the operator control building that are vulnerable to the seismic hazard as well as an ensemble of sign-support structures over several kilometers of the highway that are exposed to environmental conditions, thus being susceptive to fatigue damage under wind loading. The aim is to develop a tool for pre-event risk assessment and rapid post-event inspection of critical road infrastructure by combining hazard, vulnerability, and sensor information to predict the resulting consequences. A component-based approach is adopted for the critical highway assets while asset interdependencies are considered to assess the system-level consequences for the entire highway. These are quantified in terms of direct monetary losses and downtime as well as actions that the road operator shall take until repair actions have finished, i.e., number of closed lanes and the allowable speed limit in the remaining open ones. This allows tracing back the consequences after an event to individual components/assets and can help road operators establish inspection prioritization protocols and manage associated incidents, facilitating the rapid assessment of the state of the highway and optimal recovery to full functionality.
[paper]
Karaferis N., Gerontati A., Vamvatsikos D. (2024). From PGA To Anything: Fragility Curve Conversions For Nuclear Power Plant Applications. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | There has been a lot of discussion on intensity measure optimality for conventional structures, touting the advantages of novel metrics of ground motion intensity to improve upon the efficiency and fidelity of seismic assessment. Yet, somehow this revolution of sorts has not transitioned to nuclear power plant assessments, which cling to the time-honored tradition of the peak ground acceleration (PGA). They do so for the simple reasons of stiffness and mass. That would be stiffness in the assets themselves, typically leading to periods of the order of 0.1 to 0.2sec for both the structures and their nested components, but also in the rigidity of regulations in an understandably ultra-cautious industry. Adding the mass (and cost) of engineering effort required to reassess already established fragilities for hundreds of standardized components, it is no wonder that there is too much inertia to allow moving away from PGA. Would it not be great if someone came along and offered a minimal-error approach for converting existing fragility curves from PGA to any intensity measure of choice? Interestingly, the response characteristics of nuclear power plants may actually favor an equivalent one/two-degree-of-freedom-model based procedure that allows disaggregating existing fragilities back into ground-motion-level constituents and reconstructing them anew with the desired intensity measure parameterization. There is little doubt that safeguarding the integrity of nuclear power plants would still require massive computations rather than rely on shortcuts, yet such an approach can give novel intensity measures a fighting chance to prove that they are worth the trouble for nuclear engineering.
[paper]
Karaferis N., Melissianos V.E., Vamvatsikos D. (2024). Seismic Fragility Assessment Of Spherical Pressure Vessels: The Effect Of Fill Ratio Variability. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | Fragility curves are a seismic risk modeler’s bread and butter, relaying the probability of reaching or exceeding each limit state of interest given the ground motion intensity. Yet, as they convey essential information, they also hide assumptions, especially when used to characterize a group of similar or even seemingly identical structures. Chief among them is the concept that the dynamic properties of such structures are invariable and uncorrelated. However, the latter does not necessarily apply to groups of adjacent “identical” spherical pressure vessels, used for storing gaseous products in industrial facilities. The quantity of product contained within a vessel directly affects its dynamic response. Using an ensemble of four “identical” pressure vessels as a case study, a comprehensive set of fragility curves is developed, each corresponding to a different fill ratio of a single vessel. Then, different approaches are explored to combine said fragilities and assess the group of four. These include full-scale Monte Carlo simulation with or without filling level correlation, as well as the computation of a single “law-of-total-variance” fragility curve. The latter approach is decidedly simpler, yet its use cannot be justified without some knowledge of the facility’s operational profile in terms of day-today fluctuation of the filling level, as it can otherwise lead to unconservative and/or biased results.
[paper]
Karaferi E., Kohrangi M., Spillatura A., Tsarpalis D., Vamvatsikos D. (2024). Seismic Risk, Direct, And Indirect Losses For The Historic City Of Rhodes. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | A risk assessment model is developed for the historic city of Rhodes, Greece, with a focus on the buildings, residential and commercial, that are at risk from earthquakes, the main hazard that the city faces. The structural integrity of the buildings of Rhodes is tested under a stochastic event set of spatially correlated ground motion fields. They are generated with the OpenQuake platform via an event-based probabilistic seismic hazard analysis for 10,000 years using the 2020 European Seismic Hazard Model. All commercial or mixed-use buildings are assigned to corresponding lines of business according to census data and expert opinion, while using data from the 2020 European Seismic Risk Model to determine vulnerability functions, and from HAZUS-MH to assess the related downtime. The assessment takes as input the exposure model, the hazard, and the vulnerability of the assets to return the direct and the indirect losses per line of business. This allows the determination of the direct consequences to the city, translated to the economic losses to rebuild or renovate the damaged buildings. Stemming from the direct losses and especially the downtime, a mesoeconomic model is employed to determine the losses caused by business interruption on an event-by-event basis. By thus providing a comprehensive assessment of the risk faced by the city, the model can be used to develop a socioeconomic impact model and support the development of financial mitigation tools.
[paper]
Gerontati A., Karaferis N., Vamvatsikos D., Bazzurro P., Droszcz C. (2024). A Bare-Bones Nuclear Power Plant Case Study To Test Uncertainty Propagation And Correlation Effects. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | The safety of a nuclear power plant is influenced by both aleatory randomness and epistemic uncertainty, as well as the potential inter-component and intra-component correlations. Aleatory randomness arises from inherent variability in the data, while epistemic uncertainty stems from limitations, or incomplete knowledge in models or data. Component correlation refers to the extent to which the properties of various components within a Nuclear Power Plant (NPP) are interdependent and how they may co-vary within a single component (intra-component correlation) or among similar/identical ones (inter-component). Evaluating their effects to completion is a non-trivial operation that requires a full model of the power plant and its components, as well as the overall fault tree. When the goal is the evaluation of alternative approaches to safety assessment, one need not set the bar so high. In this, we offer a pared-down model, comprising simplified models of the reactor building and of one or more non-structural components, together with a simplified fault tree that leads to loss of core cooling capacity. As an example, three alternative cases of perfect, partial, and no correlation are employed to test common causes of failure. Uncertainty is propagated using a Monte Carlo simulation with either classic or progressive Latin hypercube sampling, using the simplified model as an efficient benchmark for NPP-compatible applications.
[paper]
Causse M., Lachanas C.G., Vamvatsikos D., Baillet L. (2024). Constraining Near-Fault Ground Motion Simulations: The Potential Of Observations Of Displaced Grave Slabs. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | The number of seismological observations available in the vicinity of faults is still too limited to fully catch the complexity of strong motion and properly calibrate Ground Motion Models (GMMs). This problem is exacerbated in areas of moderate seismicity, where earthquakes often occur on unknown faults and are only exceptionally recorded in damage areas. Physics-based simulation methods are a very promising approach but they require a very good understanding of the physical processes controlling the strong motion (variability of the rupture process, radiation of high frequency seismic energy, effects of shallow geological structures, etc.), which also requires more observations. Here we propose an approach to constrain near-fault ground motion predictions based on measures of grave slab sliding displacements, e.g., as observed during the Le Teil earthquake in 2019 (Mw 4.9, France) and in Petrinja in 2020 (Mw 6.4, Croatia). In a Bayesian framework, the approach combines a priori information on the ground motion distribution obtained using physics-based simulations and a likelihood function representing the probability of the observed slab displacement for a given ground motion intensity measure, to produce a posterior distribution of ground-motions.
[paper]
Lachanas C.G., Vamvatsikos D., Causse M., Kotha S.R. (2024). The Effect Of Ground-Motion Characteristics And Intensity Measures On The Sliding Of Rigid Bodies. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | The sliding response of rigid bodies is investigated under multiple suites of ground-motion records having different inherent characteristics: Ordinary (no-pulse-like, no-long-duration), near field, pulse-like versus spectrally-matched non-pulse-like twins, and long-duration versus spectrally-matched short-duration twins. A basic Coulomb friction model of a rigid block resting freely on a flat surface is used as a testbed, applying incremental dynamic analysis to assess response statistics under the different suites at multiple levels of intensity. Alternative intensity measures are employed, including the peak ground acceleration, the peak ground velocity, and variants of average spectral acceleration—defined as the geometric mean of spectral accelerations over a range of periods. As engineering demand parameters, both the maximum absolute displacement and the absolute residual displacement are employed. The results indicate a non-trivial sensitivity to duration and pulsiveness, and suggest as well that some intensity measures perform considerably better than others in suppressing sensitivity to such peculiar ground-motion characteristics.
[paper]
Grajales-Ortiz C., Melissianos V.E., Bakalis K., Kohrangi M., Vamvatsikos D., Bazzurro P. (2024). Relationships Between Earthquake-induced Damage And Material Release For Liquid Storage Tanks. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | Liquid storage tanks are critical components in the industrial sector, as large amounts of toxic, volatile, or flammable substances are stored in them. Motivated by their underlying vulnerability to physical damage caused by earthquakes, an empirical relationship is proposed to link the specific type of earthquakeinduced structural damage with the extent of material release that can potentially be triggered. To achieve this goal, an extensive database of recorded seismic-related failures of industrial tanks is examined and suitable damage states are identified. For each tank in the database, material release levels consistent with industry standard procedures for risk assessment are associated with the pertinent damage states. This is done with the consideration of characteristics that affect the seismic behaviour of tanks, such as aspect ratio and filling level. As a result, we propose a series of event trees for industrial liquid storage tanks that associate damage states and combinations thereof with material release levels. These event trees can be exploited for consequence analysis (e.g., to analyse the propagation of damage, or potential domino effects) within the context of seismic risk assessment for industrial facilities.
[paper]
Melissianos V.E., Lachanas C.G., Lignos X.A., Vamvatsikos D., Chatzidaki A., Dasiou M-E., Manetas A. (2024). A Holistic Platform For The Seismic Risk Assessment Of Ancient Monuments. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | The protection of cultural heritage against natural hazards and in particular earthquakes is a critical and challenging task because authorities try to tackle the steady onslaught of extreme seismic events and continuous deterioration of the structure. Countries around the Mediterranean Sea have a portfolio of monuments, some of which are in relatively poor condition and in danger of sustaining non-recoverable damage due to earthquake events. Protecting these monuments becomes more daunting within budget limitations. In this framework, a holistic platform for the seismic risk assessment of ancient monuments has
been developed within the EU-Greece funded research project ARCHYTAS to serve as a decision-support tool to assist the prioritization and restoration actions before a seismic event happens or in a post-event environment, providing a rapid assessment of the monument structural status for the given event. The overall system is presented indicatively for the Aphaia Temple in Aegina island, Greece.
[paper]
Kazantzi A.K., Karaferis N., Melissianos V., Vamvatsikos D. (2024). Seismic Reliability Of Acceleration-Sensitive Ancillary Elements In The New Generation Of Eurocodes. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | The seismic performance of nonstructural/ancillary elements plays a decisive role in the seismic resilience of both ordinary buildings and critical industrial and infrastructure facilities, since damages that are likely to be sustained by such components can undermine the functionality and safety of an otherwise structurally intact structure. Owing to the above, the new generation of Eurocodes invests a great deal of effort towards prescribing appropriate provisions for delivering anchoring systems of acceleration-sensitive nonstructural components that can withstand the (often greatly) amplified floor accelerations with respect to the ground ones. In particular, prEN 1998-1-2:2022 offers a very detailed methodology for estimating the acceleration that is eventually imposed at the component level, accounting for several dynamic attributes of the primary system and the nonstructural component, which are yet not always trivial to determine with an appropriate level of confidence. This paper investigates to what extent the reliability of a code-conforming nonstructural component can be affected by the uncertainties associated with the assumptions made during design. The focus is on the relation of the period of the component to the period of the supporting building using a typical industrial building-type structure as a case-study. On account of the findings that revealed a rather significant sensitivity of the final design product to these uncertainties, the study extended its scope towards reviewing two alternative design methodologies that are offered in prEN 1998-4:2022 for the design of ancillary elements. These two latter approaches are shown to be less sensitive to the designer’s input and can offer more robust designs for the anchorage systems of nonstructural components that are close to tuning with the frequencies of the primary structure.
[paper]
Gerontati A., Karaferis N., Sipcic N., Vamvatsikos D., Bazzurro P., Droszcz C. (2024). A Minimalistic Computational Testbed For Evaluating Fragility Assessment, Record Selection, And Intensity Measure Optimality For Nuclear Powerplants. Proceedings of the 27th International Conference on Structural Mechanics in Reactor Technology (SMiRT27), Yokohama, Japan.
Abstract | Recent advances in Performance-Based Earthquake Engineering (PBEE) have followed their own revolutionary path over the past two decades. Focusing on the assessment of conventional buildings and infrastructure, several innovative proposals on improving fragility assessment have appeared over the years, focusing on record selection, improved intensity measures, as well as novel uncertainty propagation approaches. Whether these are also useful for nuclear powerplant assessment remains a question. Partially owing to the well-established practice and guidelines, introducing novelty in such procedures faces significant hurdles in terms of modeling, computational power, and complexity. In an effort to overcome said difficulties in the context of the METIS Euratom project, we propose a minimalistic computational testbed comprising simplified models of a building, one or more components, and a bare-bones fault tree
to tie them together and propagate uncertainties. The METIS simplified testbed is realized in open source, using Python and OpenSees to offer a fast assessment platform, whereby one can test any number of ideas in a setting that resembles a real case study. Among them are important questions, such as the influence of aftershocks, or clustered seismicity in general, new uncertainty propagation techniques, the use of hazard consistent record selection approaches in place of selection based on the uniform hazard spectrum, as well as the use of new intensity measures that can potentially reduce the aleatory uncertainty in the estimates of risk. Focusing on the latter, we present an example of application of the testbed and its results.
[paper]
Chatzidaki A., Ntaifoti A., Bilionis D.., Gantes C., Vamvatsikos D. (2023). Fatigue damage assessment of the Egnatia Odos sign-support structures under spatially-correlated time-varying wind fields. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | A methodology is proposed for assessing the long-term wind-induced fatigue damage accumulation of steel sign-supporting structures of highways, as it applies to Egnatia Odos. These structures are usually configured as portal, L-shaped or T-shaped frames, consisting of one or two columns and a horizontal beam that supports the sign. During their lifetime, they are exposed to environmental conditions thus being susceptive to corrosion, while the critical load is the wind that subjects them to fatigue due to its dynamic nature. To this scope, the cumulative fatigue damage is computed for the critical connections of the sign-supporting structures on a site-agnostic basis for 10min loading intervals, both for corroded and for non-corroded structures. This data is combined with 10min wind time-series that are compatible with the long-term weather hazard at the location of the structures and are computed based on alternative climate change scenarios. The aim is to assess the damage accumulation due to fatigue for the critical connections of the structures during their lifetime. The proposed methodology allows assessing the long-term risk due to fatigue for an ensemble of spatially distributed sign-support structures and is incorporated into a tool that aims to help road operators rapidly assess the state of the highway assets and help them efficiently manage their inspections.
[paper]
Bilionis D., Vlachakis K., Dasiou M-E., Vamvatsikos D., Vayas I., Lagouvardos K. (2023). Performance-based wind assessment of steel lattice telecommunication towers in coastal regions of Greece. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | Steel lattice towers are widely used for supporting telecommunication antennas. Herein, a performance-based analysis of a 48 m steel lattice telecommunication tower is presented. The tower has been designed according to the Eurocode requirements for coastal areas of Greece considering a basic wind speed value of 33 m/s. First, the fragility assessment (probability of failure) of the particular tower against various combinations of wind speed
and direction is carried out. Then, after elaborating time series of wind data from selected islands or coastal regions throughout Greece and based on the resulting wind speed and direction distributions, the corresponding risk of the tower is calculated for each location and the results are displayed on the geographical map of Greece. In practice, the above procedure introduces a framework for evaluating the performance of steel lattice towers against extreme wind. The present framework can be elaborated as a useful tool by mobile phone companies in the context of planning and/or upgrading their networks. Furthermore, by assessing and comparing the resulting risk levels of the various locations (coastal regions), inferences about the validity of Eurocode National Annex assumption for a single basic wind speed value of 33 m/s for all coastal regions in Greece can be derived.
[paper]
Ntaifoti A., Chatzidaki A., Gantes C., Vamvatsikos D. (2023). Corrosion influence on fatigue resistance of highway sign bridges. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | Road infrastructure (RI) resilience is significant for the prosperity and development of modern societies. Lightweight steel structures, such as sign bridges, constitute an integral part of modern highways and their proper design ensures the safety of the RI users. Sign support structures provide direction instructions and/or traffic information to the drivers and their spans become constantly longer due to lane number increase. A common characteristic of such structures is the large dimensions of signpost plates, compared to the surfaces of the structural members, resulting in a critical role of wind loading in structural design. Moreover, such structures are exposed to harsh environmental conditions, thus being prone to corrosion, attacking the metal surface, creating a rust film, progressively reducing the material thickness, consequently producing a decrease in the structural performance in terms of strength, stiffness, and ductility. Moreover, corrosion accelerates fatigue effects and reduces the remaining lifetime of the connections and hence of the entire structure. In the present work the effect of corrosion on the fatigue resistance of typical sign bridges is quantified. Towards that objective, a methodology to assess the remaining lifetime is developed and applied to typical sign bridge structures of contemporary motorways with different shapes.
[paper]
Vamvatsikos D. (2023). Industrial structure design at the edge of the code: A true story of three little pigs. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract |Three little pigs designed three low-ductility industrial buildings for agricultural usage. Two collapsed under a known extreme hazard. Fortunately, there was no loss of life, but two structures and two livelihoods were destroyed. Was the subpar straw and wood material to blame? Were the designers to be held accountable? History seems to have concluded thus. On the contrary, our recent investigations conclusively show that it was only a case of honest and well-meaning engineers, who were betrayed by an honest and well-meaning design code. They were misled to place their trust on a thought-up q-factor of 1.5 to 2.0 for industrial structure design. This factor was introduced into the code without proper verification, and it could not provide an adequate safety margin for collapse of low-ductility systems under extreme loads. Two, admittedly swine, engineers were framed by the powers that be. Follow us on the journey to uncover one of the greatest misdeeds of history that is still being taught to our children.
[paper]
Lachanas C.G., Vamvatsikos D., Kazantzi A.K. (2023). Intensity measures for assessing the rocking response of server racks in steel buildings. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | Alternative seismic intensity measures (IMs) are examined for the case of non-structural rocking building contents and in particular for the case of server racks standing freely on the higher floors of steel buildings. Observations following recent earthquakes in developed countries have revealed that most of the damages after a seismic event consider non-structural building contents of high value. On the other hand, the selection of a robust
IM is a basic requirement in the context of the performance-based earthquake engineering framework for assessing the seismic risk and the consequential loss/damage of engineering structures or non-structural contents with high fidelity. Hence, a bunch of alternative IMs are tested in terms of efficiency and sufficiency as potential IMs for rocking vulnerability studies. The simple planar rocking block model is employed for running nonlinear dynamic analysis with a set of 34 floor motions that were recorded during past earthquakes on the roof of instrumented steel buildings. Rocking blocks of various shapes and sizes are analyzed that resemble two-dimensional analogues of server racks. After analysis, efficiency and sufficiency of the examined IMs are compared aiming to propose optimal IMs for the case of rocking contents in the different stages of rocking response from rocking uplift to overturning.
[paper]
Melissianos V.E., Kazantzi A.K., Karaferis N., Bakalis K., Vamvatsikos D. (2023). Reduced-order models of steel structures for the seismic risk assessment of oil refineries. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece.
Abstract | Ensuring the structural and operational integrity of oil refineries in case of an earthquake event is of utmost importance for the society, the environment, and the economy. A potential failure in such critical facilities may trigger a number of undesirable situations, such as fire, injuries, environmental pollution, etc. Hence, improving safety plan and increasing seismic resilience is a necessity that requires the development of reliable models and seismic risk assessment tools. Towards this direction, this paper presents a seismic fragility study of two characteristic steel high-rise stacks encountered in oil refineries, namely a relatively low-rise chimney and a process tower. The developed of reduced-order numerical models, the selection of appropriate engineering demand parameters to capture the seismic response of the structures, the calculation of the fragility curves, and finally the evaluation of the overall seismic response are presented. The results could be exploited in the context of a seismic risk assessment study of an oil refinery, as an integrated system.
[paper]
Kazantzi A.K., Elkady A., Vamvatsikos D., Lignos D., Miranda E. (2023). The use of ductile steel fuses for the seismic protection of acceleration sensitive non-structural components: Numerical and Experimental verification. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece.
Abstract | Recent seismic events have showcased the vulnerability of non-structural components to even low- or moderate-intensity earthquakes that occur far more frequently than design-basis ones. Thus, community-critical buildings, such as hospitals, telecommunication facilities, or fire stations, often face lengthy functionality disruptions despite having suffered little structural damage during an earthquake. This paper summarises the numerical, and corroborating experimental, studies that were undertaken as part of the NSFUSE project at the University of Bristol’s shake-table facility. The primary focus was to investigate the concept validity of using ductile steel fuses for protecting acceleration-sensitive non-structural components in the aftermath of earthquakes. The objective was to offer a reliable and inexpensive solution, via replaceable sacrificial elements, for the protection of such components. The experimental program involved a series of planar shake table experiments. These were conducted using narrow-band floor acceleration input signals that were recorded in instrumented buildings through the California Strong Motion Instrumentation Program during three different earthquake events. By changing the mass of the carriage-like test specimen, as well as the fuse height and its cross section, different component-to-building period ratios (tuned and slightly detuned cases) along with yield strength levels were investigated. For each test, the input signals were incrementally scaled, if needed, to induce different ductility demands. The tests provided insight into the seismic performance of non-structural components that are mounted on a structure and the benefits of allowing controlled yielding to occur in the attachments of non-structural components that are tuned or nearly tuned to one of the primary modal periods of the supporting structure.
[paper]
Vamvatsikos D., Lachanas C.G. (2023). Stranger things in seismic response and statistical tools to resolve them. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | Demogorgons, monsters, and mythical creatures do not appear only in Soviet research labs, secretive government facilities or just plain Hawkins, Indiana. They frequently cross-over to earthquake engineering in the form of questions that conform to the paradigm of “Does X matter in seismic response?”. X can be a seismological characteristic, such as duration, vertical component, incident angle, or near-field directivity; it can also be a structural property, such as building period, rocking block size, or plan asymmetry. We, as investigative structural engineers, are vastly more familiar with the latter set of queries and we are clearly better equipped to handle them. We can sometimes even provide definitive answers that most, if not all of us, would agree upon. Instead, questions involving seismological characteristics seem to leave us baffled and stuck in an Upside Down world that resembles structural engineering but is not exactly the same. Wading through its murk, it is good to have some investigative tools and processes that will help us find our way home. In the end, though, we may end up equal parts enlightened and confused, as most questions of whether something of the seismologist world matters for the structural one are nearly-universally answered by uttering “It depends”.
[paper]
Melissianos V.E., Karaferis N.D., Kazantzi A.K., Bakalis K., Vamvatsikos D. (2023). Towards seismic resilience of industrial facilities: the case study of an oil refinery. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | Crude oil refineries are high-importance infrastructure that play a key role in the energy supply chain. Securing the operational and structural integrity of refineries in the aftermath of an earthquake is crucial for avoiding the undesirable consequences of a Natural-Technological (NaTech) incident, such as injuries, environmental pollution, business interruption, and monetary losses. Refineries are designed, constructed, maintained, and operated under a strict framework of standards and regulations. Still, seismic-related NaTech incidents are occurring. Thus, to assess with more confidence and consequently improve, if needed, their seismic resilience, a coherent performance-based framework needs to be utilised, that accounts for the refinery as an integrated system comprising a variety of structural typologies, such as buildings, tanks, and high-rise stacks. These structures have very diverse dynamic properties and hence seismic responses. Towards this objective, a virtual crude oil refinery is examined herein as a case study. The aim is to showcase the steps of a seismic risk assessment framework when applied to such infrastructures, focusing on the evaluation of the seismic hazard, the development of the exposure model, the numerical analysis of the structures, and the preliminary damage assessment of the facility using different earthquake scenarios.
[paper]
Kazantzi A., Karaferis N., Melissianos V.E., Vamvatsikos D. (2023). Design of acceleration-sensitive ancillary elements under uncertainties in the new eurocode. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | The overall seismic safety and operability of industrial building-type structures located in critical infrastructure facilities, largely depend on the seismic performance of their nested and/or supported ancillary elements, namely mechanical and electrical equipment, machinery, vessels, etc. Hence, on account that (a) no or minimal direct structural damages are anticipated in the equipment-supporting structures per se during moderate or even strong earthquake events since such structures are typically overdesigned and (b) the sustained structural damages are mostly due to the inferior seismic performance of the nested ancillary elements that could trigger a series of adverse cascading incidents (e.g., uncontrolled fires, explosions), significant effort has been
invested towards developing a design framework that could deliver safe designs for the latter. Despite the significant advancements in the relevant field, the development of a robust design framework is often undermined by several uncertainties that come into play in the evaluation of the capacity and demand of such nonstructural components. In particular, critical information that is needed for the design of the ancillary elements, such as the dynamic characteristics of the component and the supporting structure, are often abstract and/or require substantial effort for being retrieved with certain confidence. On that basis, the new Eurocode 8, offers three distinct design options that allow for adjustments in the conservatism that is induced in the design of the acceleration-sensitive ancillary elements according to the availability and reliability of information on the overall system. This study investigates, by means of a case study industrial structure, the extent to which the seismic reliability of an otherwise code-compatible component designed to comply with each one of the three alternative Eurocode design routes, is likely to be undermined for small discrepancies of the assumed properties from their actual values.
[paper]
Karaferis N., Vamvatsikos D. (2023). Fragility curve disaggregation examples for localized measures of response. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | In seismic risk assessment, one is often in need of employing fragility curves that are readily available in literature, rather than developing one’s own. Unfortunately, such fragilities are essentially summaries of the detailed intensity measure (IM) versus engineering demand parameter (EDP) information. When, as usual, the original data is not available, finding a way to disaggregate the fragilities back into the individual IM-EDP record responses can be useful. For example, it would allow converting them to arbitrary IMs. The authors have previously presented an idea of using equivalent single-degree-of-freedom (ESDOF) models to achieve this, showing acceptable results for global EDPs, such as roof drift. These global response parameters are typically governed by the fundamental eigenmode of the structure, and are thus easier to capture by the proposed ESDOF models. To further build upon this concept, different multiple-degree of freedom (MDOF) structure examples are examined, validating the results of fragility disaggregation and IM conversion for limit-states based on more localized measures of response, such as interstorey drifts or peak floor accelerations. The accuracy of the method is therefore further challenged, going after local EDPs via a proxy that discards the effect of higher modes. The target is to specify the limits of the proposed methodology and quantify the potential error
introduced by the method’s assumptions, evaluating its usefulness for such cases.
[paper]
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G., (2023). Rocking intensity measures: From interface variables to response proxies. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | In the context of the performance-based earthquake engineering (PBEE) framework an intensity measure (IM) is the interface (or interfacing) variable that links the seismic hazard with the structural fragility/vulnerability for the risk assessment of structures. On the other hand, from the standpoint of structural dynamics, an IM may be used as a proxy for predicting the structural response under a specific ground motion. Hence, depending on the usage per case, different criteria of optimality should be employed. An interface variable needs to be efficient (low conditional dispersion) and sufficient (low dependence on seismological parameters), whereas also its hazard needs to be assessable via available ground motion prediction equations. For the case of a proxy, hazard computability is not necessary, whereas the most important criterion is the capability of the IM to predict the engineering demand parameter (EDP) within a (simple) regression model. Thus, a response proxy needs mainly to offer high correlation and low fitting errors within IM-EDP regression models. Herein, after addressing these two different cases of IM usage, a comparison of alternative IMs for rocking structures is presented, mainly focusing on their use within a PBEE framework for risk assessment. Simple rocking bodies are employed for running incremental dynamic analysis with a set of 105 ordinary (no-pulse-like, no-long-duration) natural ground motions. It is shown that some well-established IMs are both efficient and sufficient for the case of rocking bodies. Still, due to the nature of rocking response, some (e.g., peak ground acceleration) tend to be optimal only in specific regions of response (e.g., rocking initiation). Moreover, dependence on the magnitude of the earthquake is found to be higher than for the distance from the rupture. Finally, IMs that are inefficient and insufficient for risk assessment can be at the same time very effective when used as response proxies.
[paper]
Gerontati A., Vamvatsikos D. (2023). The effect of intensity measure selection and epistemic uncertainties on the estimated seismic performance for non-structural components of nuclear powerplants. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | The seismic performance of a structure/component is influenced by aleatory randomness and epistemic uncertainty, but also by the intensity measure (IM) selected for the assessment. Aleatory randomness results from natural ground motion record variability, while epistemic uncertainty corresponds to modelling assumptions, parameter variability, omissions or simplifications. IM selection, though, depends on the analyst and the data available. Potential
candidate IMs are the peak ground acceleration (a nuclear industry standard), spectral acceleration at a fundamental period of the structure (the relative newcomer), and average spectral acceleration in the range of short periods (the novel option). Their performance in quantifying uncertainty for short-period nuclear powerplants is not given, nor is it necessarily obvious given the sizeable uncertainties involved. To provide a basis for discussion, a singledegree-of-freedom non-structural component in an AP1000 reactor building is used as casestudy. Three alternative uncertainty propagation approaches are employed: (a) Monte Carlo simulation with classic Latin hypercube sampling, (b) Monte Carlo simulation with progressive Latin hypercube sampling and (c) a first-order second-moment method, representing different compromises between speed and accuracy. The resulting fragility curves of the non-structural component are compared in terms of efficiency for assessing its performance, offering evidence in support of optimizing IM selection.
[paper]
Karaferi E., Vamvatsikos D., Kohrangi M., Spillatura A. (2023). Exposure, Vulnerabilities, and scenario seismic risk assessment for the city of Granada. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | A model is developed for the seismic risk assessment of the city of Granada, Spain, focusing on the building stock. For its implementation, in-house software is coded in the objectoriented programming language Python. Firstly, the assets of interest, in this case the different buildings, are identified and classified according to the taxonomy of the 2020 European Seismic Risk Model, appropriately customized for the characteristics of the local stock. The exposure
model is created using the geographical position of each building and aggregating them per city block. Seismic hazard is determined via the 2020 European Seismic Hazard Model. An eventbased probabilistic seismic hazard approach is employed, generating a stochastic event set for a 10,000 year investigation period, together with corresponding spatially-correlated ground motion fields via the OpenQuake platform. For simplicity, a single intensity measure is employed to characterize all buildings. Suitable vulnerability functions are selected to calculate loss. Results are obtained per block for the damage of buildings in terms of assigning them to different damage states as well as defining the cost of replacement. The resulting consequences are grouped across different functions and lines of business. The focus is on offering a preliminary determination of the disruption caused by each event in support of socioeconomic impact
modelling within the HYPERION EU project.
[paper]
Tsarpalis D., Karaferi E., Vamvatsikos D., Kohrangi M., Zeppos J. (2023). A socioeconomic model for estimating indirect consequences of earthquake hazards to cultural heritage communities. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | A socioeconomic model of the residents and visitors (i.e., users) and the local economy (i.e., production and consumption of goods, services, and small businesses) is proposed to simulate the core functions of a cultural heritage community. Given the direct infrastructure damages of an event, as those are derived by vulnerability and hazard assessment, the model is able to quantify the indirect losses per critical business sector as they evolve over time. This is
accomplished by first deriving downtime estimates per sector, propagating the resulting disruptions through the demand-supply chain of the community, and then tracking their eventual recovery. The model is designed to accommodate the salient socioeconomic characteristics of the cultural heritage community, by giving heed to effects such as the adaptive behavior of the site visitors and the occurrence of an adverse event during a high or a low season for tourism. The methodology is finally illustrated and verified on the basis of several earthquake scenarios derived for the historical city of Rhodes, highlighting the potential usage of the tool during risk mitigation planning and post-event decision-making.
[paper]
Elkady A., Vamvatsikos D., Lignos D., Kazantzi A.K., Miranda E. (2022). Experimental study to validate an improved approach to design acceleration-sensitive nonstructural components. Proceedings of the 5th International Workshop on the Seismic Performance of Non-Structural Elements (SPONSE2022), Stanford, CA.
Abstract |
Kazantzi A.K., Miranda E., Vamvatsikos D., Elkady A., Lignos D., (2022). Analytical studies in support of an improved approach to the design of acceleration-sensitive nonstructural elements. Proceedings of the 5th International Workshop on the Seismic Performance of Non-Structural Elements (SPONSE2022), Stanford, CA.
Abstract |
Melissianos V.E., Vamvatsikos D., Danciu L., Basili R. (2022). Code-Based Approach for Estimating the Seismic Fault Displacement for Earthquake-Resistance Design of Buried Pipelines. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract | Buried steel fuel pipelines are vulnerable to ground deformations caused by the activation of the crossing seismic fault. In such case, pipelines develop excessive deformations and strains as they follow the ground movement. Ensuring the structural and operational integrity of pipelines, which are critical energy infrastructure, is of utmost importance. In contrast to a typical deterministic design approach, where the seismicity is not taken into account, the performance-based approach can provide the required balance between safety and economy. Towards this path, an approximate methodology for calculating the fault displacement for a given return period was developed. This displacement is suitable for the design of pipelines crossing active seismic faults. using the database of faults in Europe, a lot of probabilistic fault displacement hazard analyses were executed. The statistical processing of these results led to the development of a set of simplified analytical relations that allow the calculation of the design fault displacement based only on data that are available to the engineer, without the requirement of specialized geological and seismological studies. The proposed methodology gas been adopted as an informative annex in the new version of EN1998-4.
[paper]
Chatzidaki A., Giannelos C., Gerontati A., Vamvatsikos D., Loli M., Tsatsis A. (2022). Seismic risk and resilience assessment for the Metsovo-Panagia segment of Egnatia Odos. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Hassan M., Vasdravellis G., Vamvatsikos D. (2022). Behavior factor for braced frames with high postelastic stiffness. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Lachanas C.G., Vamvatsikos D., Vassileiou M.F. (2022). The influence of the vertical component of the seismic excitation on the probabilistic treatment of the seismic response of rocking rigid bodies. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Vamvatsikos D., Lachanas C.G. (2022). Probabilistic distribution of ground motion via observations of rocking rigid bodies. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Natali A., Morelli F., Salvatore W., Tsarpalis D., Vamvatsikos D. (2022). Experimental validation of plastic ovalization strategy for seismic-resistant automated rack supported warehouses. Proceedings of the ANIDIS2022 Italian National Conference on Earthquake Engineering, Torino, Italy.
Abstract |
Chatzidaki A., Gerontati A., Vamvatsikos D. (2022). Seismic damage and implied traffic delay assessment for a highway bridge of Egnatia Odos Greece. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | The seismic damage and the implied traffic delays are assessed for two structurally independent twin bridges, one per travel direction, which form the G7 bridge of the Egnatia highway in Greece. They are reinforced concrete structures with a monolithic pier-to-deck connection that were built using the cantilever method of construction. To enhance the seismic assessment resolution, a component-based approach is followed that allows evaluating damage scenarios for individual critical bridge components and propagating them to assess the performance of the entire system. This necessitates linking the component damages to the actions that the road operator would take in order effect repairs, i.e., by reducing the speed limit in any of the lanes and/or closing any of them until repairs are finished. These interventions typically lead to traffic delays for the entire highway that are computed on an event basis via event-based probabilistic seismic hazard analysis by considering the component-to-asset and asset-to-system interdependencies. The aim is to develop a decision support tool for pre-event risk assessment and rapid post-event inspection of critical road infrastructure by combining hazard, vulnerability and sensor
information to predict the resulting consequences both on the asset and the system level at every step during an asset’s recovery back to full functionality.
[paper]
Gerontati A., Vamvatsikos D. (2022). A comparison of three scalar intensity measures for non-structural component assessment of nuclear powerplants. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | Three candidate intensity measures are compared in terms of efficiency and sufficiency for assessing the non-structural performance of nuclear powerplant components. These are the peak ground acceleration, the spectral acceleration at the fundamental period of the structure, and the average spectral acceleration in the range of short periods. To do so, single-degree-of-freedom non-structural components of different periods and capacities are considered at different locations within an AP 1000 reactor model. Incremental dynamic analysis is performed for a set of 30 records. The spectral floor accelerations of each SDOF component are monitored and capacity exceedances are recorded to assess the lognormal parameters of component fragility curves. The numerical results demonstrate that average spectral acceleration would be the most useful intensity measure in both efficiency and sufficiency, regardless of location, period or capacity, with the obvious exception of the ground surface. Nevertheless, the conventional choice of the peak ground acceleration remains a very close contender, as it leads to results of low dispersion and little bias for such stiff structures and short-period components.
[paper]
Karaferi E., Melissianos V.,Vamvatsikos D. (2022). A preliminary urban seismic risk model for the City of Rhodes Greece. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | A first-order model is developed for the seismic risk assessment of the water supply network and the structural integrity of the buildings of Rhodes under spatially correlated seismic loading. For its implementation, in-house software is coded in the object-oriented programming language Python. The water supply network is modelled via a graph theory approach and the vulnerability of the buildings takes advantage of the 2020 European Seismic Risk Model. An event-based probabilistic seismic hazard approach is employed, generating ground motion fields for 10,000 years with the OpenQuake platform. The intensity measures used are the peak ground velocity (PGV) for the water pipelines and Sa(1s) for the buildings.
The close correlation of the two allows the creation of spatially cross-correlated PGV and Sa(1s) values that are otherwise not readily available. Results are obtained, per block, for the percentage of people that have no access to water and for the damage of buildings. This is enough to offer a preliminary determination of the disruption caused by each event in terms of available housing and utilities, in support of socioeconomic impact modeling.
[paper]
Karaferis N., Vamvatsikos D. (2022). Intensity measure transformation of fragility curves for 2D buildings using simplified models. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | Seismic fragility curves are an essential tool for any risk assessment endeavour. While there is a wealth of studies that have provided high quality fragilities for many different types of structures, these curves are typically presented in terms of a single intensity measure (IM). To keep using such valuable data, an analyst is either forced to adopt the same (potentially suboptimal) IM, or completely discard them and restart with a new one. Instead, we propose a simple method for transforming a fragility curve to any IM of choice by using an equivalent single-degree-of-freedom model and its incremental dynamic analysis results to disaggregate the fragility to its constituent record-level results. Validation results from two complex 2D building hint that there is promise to this approach, offering nearly-error-free transformations of global-response fragilities at the cost of a few response history analyses of a nonlinear oscillator.
[paper]
Kazantzi A.K., Karaferis N.D., Melissianos V.E., Bakalis K., Vamvatsikos D. (2022). Seismic fragility assessment of two low-rise equipment-supporting RC industrial buildings. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | Open-frame reinforced concrete (RC) buildings for supporting essential mechanical/electrical equipment are encountered in almost all industrial plants. Hence, to ensure the undisrupted operation of an industrial facility, the integrity of such structural assets along with their nested nonstructural components should be verified against a spectrum of natural and man-made hazards. Focusing on the earthquake peril, this study presents an analytical seismic fragility assessment framework for two RC equipment-supporting buildings that are deemed typical to an oil refinery. The proposed fully-probabilistic fragility concept, utilises reduced-order building models for the evaluation of the induced seismic demands and accounts for both drift and acceleration-sensitive failure modes in the definition of the damage states. The findings can be exploited by designers and facility managers for developing efficient pre- and post-event risk-aware mitigation/response strategies and are delivered in a manner that can be readily integrated into the seismic performance assessment framework of an entire industrial facility.
[paper]
Lachanas C.G., Vamvatsikos D. (2022). Preliminary seismic risk assessment of ancient columns across Attica for application in decision support systems. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | An approach for preliminary seismic risk assessment is presented for portfolios of cultural heritage assets of classical antiquity. As an example, three ancient columns are considered, located at different sites throughout Attica: The Temple of Aphaia in Aegina, the Temple of Olympian Zeus in the centre of Athens, and the Temple of Poseidon in Sounio. Event-based probabilistic seismic hazard analysis is used for the definition of the seismic hazard via multiple correlated intensity measure fields. The seismic response of the columns is assessed via simplified equations for the prediction of the central value and the dispersion of the lognormal fragility function for rocking blocks. Afterwards, the seismic risk per asset is assessed both in terms of long-term averages, calculating the mean annual frequency of exceeding pre-defined limit states, as well as on an event-by-event basis, calculating the probability of exceeding limit states of interest per asset in scenario events. Overall, a comprehensive tool is offered for supporting decision-making on prioritizing rehabilitation actions for a portfolio of monumental structures.
[paper]
Melissianos V.E., Vamvatsikos D., Danciu L., Basili R. (2022). An engineering approach to fault displacement hazard for lifelines crossing active tectonic faults. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | Lifelines, such as pipelines, tunnels, and bridges are vulnerable to seismic-induced ground displacements caused by the activation of active tectonic faults. Lifelines are forced to follow the ground movement in fault crossings and develop excessive deformation. Safeguarding the integrity of such critical infrastructure is of paramount importance. Contrary to typical deterministic design approaches that discount fault productivity, a performance-based approach can achieve a balance between safety and economy. Towards this goal, a set of simplified expressions is developed for determining fault displacement at given return periods, developed by analyzing the outcome of probabilistic fault displacement hazard analysis (PFDHA) for European faults. The proposed methodology allows the computation of the design fault displacement with data available to the engineer and has been adopted as an informative Annex in EN1998-4.
[paper]
Vamvatsikos D., Lachanas C.G. (2022). Tomb raiders of the lost accelerogram: A fresh look on a stale problem. In: Vacareanu, R., Ionescu, C. (eds) Progresses in European Earthquake Engineering and Seismology. ECEES 2022. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. DOI: 10.1007/978-3-031-15104-0_4
Abstract | Throughout recorded history, accelerograms have displayed an unfortunate tendency to become unrecorded and lost. Statistically speaking, even after the advent of low-cost accelerometers, the ground motion retains an almost 100% chance of staying unobserved at any given point. One may only place some limits on the peak amplitude of ground motion by observing its effects, or lack thereof. To do so, seismologists run to the mountains, looking for fragile geological features, such as precariously balanced rocks. Structural engineers take a slightly more cinematic and sinister approach. They put on their fedora hats (or tank top and shorts, for video game enthusiasts) and go tomb raiding, searching for rocking rigid bodies that may have survived or toppled in graveyards, tombs, mausoleums, churches, and temples. Yet how is one to best make sense of such low-entropy (and sometimes contradictory) uncertain information? Let’s have some fun by blowing an old problem to smithereens, perhaps needlessly bringing to bear all the tools of contemporary earthquake engineering, ranging from ground motion prediction models and correlation structures to rocking body fragilities and Bayesian analysis.
Goldschmidt K., Sadegh-Azard H., Sevbo O., Richard B., Garcia P., Bazzurro P., Vamvatsikos D. (2022). Innovative approaches for seismic fragility analysis within METIS project. Proceedings of the 26th International Conference on Structural Mechanics in Reactor Technology (SMIRT-26), Berlin, Germany.
Abstract | The building and structure related part of the Euratom funded Project METIS (metis-h2020.eu) is focused on the evaluation of fragility curves, giving failure probabilities for increasing ground motion intensity, intensity measure selection, uncertainty quantification and bayesian updating of fragility curves. While METIS improves the methodologies for the seismic assessment of NPPs, work package 6 (WP) focuses on the structural part of the project delivering the methodologies for specific, detailed fragility curves and applying these to the case study. The work will finalize in guidelines for the application of the developed methodologies. In the following, first work within the fragility analysis part of the project and future topics will be presented.
Bilionis D.V., Vlachakis K., Bezas M-Z., Tibolt M., Vamvatsikos D., Vayas I. (2022). Performance-based assessment of a steel lattice power-transmission tower: A case study in Germany. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | Power transmission towers are tall steel lattice structures used for supporting the conductors of a power transmission line, constituting essential parts of an entire power network. Past experience has shown that even a failure of a single tower can cause cascading effects to its adjacent towers leading to a total collapse of a whole line. Transmission towers are susceptible to severe weather conditions including low temperatures, snow and high winds. Specifically, high winds in combination with ice accumulation increase the lateral and vertical loads to levels causing damages ranging from local failures to global collapse. This effect is even more intense in case of aged towers with members weakened by corrosion effects. Herein, the focus is on a single suspension transmission tower widely used in Central Europe and designed according to the EN 50341-1:2012 and EN 50341-2-4:2016 assuming installation in Germany. The structure’s fragility in both initial and corroded state against wind and icing loads was estimated via nonlinear dynamic analyses. The climatic hazard was estimated by deriving the joint probability of wind speed and ice thickness based on meteorological data obtained for Central-East Germany. Finally, the assessment of the structure’s risk for each of the two states considered was made by combining the tower’s fragility results with the climatic hazard. Assessing the risk of a single tower is a precursor of estimating the reliability of an entire power transmission network, offering a useful decision-support tool on the need to maintain or upgrade a power line network.
[paper]
Melissianos V.E., Karaferis N.D., Kazantzi A.K., Bakalis K., Vamvatsikos D. (2022). An integrated model for the seismic risk assessment of an oil refinery. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | Oil refineries play a key role in the energy supply chain. Safeguarding the integrity of such high-importance facilities against natural hazards is crucial because a potential failure may result in a sequence of unwanted events, spanning from business disruption to uncontrolled leakage and/or major accidents. Despite the strict criteria enforced during the design, construction, maintenance, and operation of an oil refinery, Natural-Technological events caused by earthquakes still occur.
Oil refining is a complex process that involves a variety of structural typologies, such as buildings, tanks, chimneys, pipe-racks, pressure vessels, and process towers. These structures have fundamentally different dynamic properties and seismic responses. A comprehensive seismic risk assessment framework is thus required to account for the refinery as an integrated system and provide information about both the structural and operational integrity of the individual assets and the system. In the present study, a virtual crude oil refinery is examined as a case study to demonstrate the steps of a preliminary seismic risk assessment framework, consisting of the seismic hazard calculation, the development of the exposure model, the analysis of the structures at risk, and the damage assessment of the facility. Scenario-based results are presented for the refinery and the critical assets are identified.
[paper]
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2022). Normalized response distribution expressions for ground-supported rigid rocking bodies. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | Estimating the seismic response of ground-supported rocking rigid blocks, is a topic that has attracted significant research interest in the past few decades, since it concerns, among others: (a) several modern structures or ancient monolithic columns that utilize rocking as a seismic protection mechanism and (b) numerous free-standing contents (e.g. museum artefacts) located on the ground floor or lower floors of stiff buildings. In the present research work, by means of a parametric study, utilizing two-dimensional rectangular blocks of varying sizes and ordinary earthquake records, the rocking response at increasing intensity levels was assessed through Incremental Dynamic Analyses. Following the demand evaluation and in order to allow for an easier utilization of the findings in practical applications, simplified approximate equations have been obtained via nonlinear regression analysis. The proposed equations provide an estimate of the peak rocking response distribution, expressed in terms of the normalized, to the dimensionless slenderness angle , peak rocking angle, at increasing ground motion intensity levels.
[paper]
Karaferi E.D., Melissianos V.E., Vamvatsikos D. (2022). Simplified Seismic Risk Assessment for the Water Supply Network of Rhodes, Greece. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | A methodology is developed for the risk assessment of the water supply network of the city of Rhodes under spatially distributed seismic loading. Graph theory is used to implement this methodology by creating in-house software in the object-oriented programming language Python. Multiple seismic events are employed that have been generated with a probabilistic approach for a 10,000 year period using the OpenQuake platform and the 2013 European Seismic Hazard Model. The intensity measure used is the peak ground velocity (PGV). Since a direct generation capability for ground motion fields with spatial correlation is not readily available for PGV, the spatial distribution of the spectral acceleration at a period of 1s was employed, which is strongly correlated
with the ground velocity. Results are obtained for the length of the pipes that will break for each event. The complex topology of the network is efficiently tackled via the graph theory to track which pipes cannot supply water and which need repair. The outcomes of the analysis indicate the percentage of the customers that are left without water in each building block of the city, to assess the population that has no access to water after a destructive event. Finally, curves of the mean annual frequency of exceeding given values of the damaged pipe length and the number of pipe breaks are produced, and the average annual losses are estimated.
[paper]
Gerontati A., Bilionis D.V., Vamvatsikos D., Tibolt M. (2022). Modular modeling and risk assessment of power transmission lines under extreme weather hazards. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | Power transmission lines are the “highways” of electricity, consisting of conductors supported on steel towers. Transmission towers are categorized as support or angle/dead-end based on their capability to resist along-line loads transmitted by the conductors. They are vulnerable to severe weather and in particular the combination of high winds and ice accretion that could lead to catastrophic failures. It is thus of great interest in the system design to arrest the propagation of a single tower failure that may trigger a series of failures of adjacent ones, considerably lengthening the duration of power outage. A modular multi-span model of a power line is proposed for the assessment of the behavior of the tower-line system and the severity evaluation of such failures. Fault tree analysis is employed to examine the failure propagation to adjacent towers under extreme weather hazard, which allows the assessment of consequences at the level of an entire system of interleaved support and angle/dead-end transmission towers. The aggregated economic losses for an operational lifetime of 60 years are investigated using the proposed model versus a simplified approach, where all towers are exclusively characterized as support ones without considering successive failures.
[paper]
Reggiani Manzo N.R., Vassiliou M., Lachanas C.G., Vamvatsikos D. (2022). Α Risk-Based Design Procedure for Negative Stiffness Bilinear Elastic Systems. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | This paper presents uniform risk spectra for systems with lateral negative stiffness, such as free-standing, restrained or curved-end rocking blocks. The spectra are constructed using a simplified system, the Zero Stiffness Bilinear Elastic system, which can satisfactorily predict the response of different systems with negative lateral stiffness. The paper offers the step-by-step methodology for the construction of the spectra. It presents the construction and discussion of the spectra for a site in Athens, Greece using two distinct intensity measures: Peak Ground Velocity and Peak Ground Acceleration.
[paper]
Chatzidaki A., Vamvatsikos D., Auvinen M., Hellsten A., Barmpas F., Lehtonen I. (2022). A baseline approach to downscaling Euro-CORDEX data for wind hazard assessment of the Egnatia Odos highway. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | The wind hazard is assessed for the Egnatia Odos highway in Greece by considering Climate Change effects via the Euro-CORDEX future climatic projections. The aim is to derive spatially correlated region-wide wind fields for a stochastic event set of thousands of storm realizations that are suitable for risk and resilience assessment of the entire highway network. The coarse spatial and temporal resolutions of the Euro-CORDEX wind projections prohibit their use as a direct input in weather-related risk and resilience assessment of highway structures that may measure down to a few meters in size and require at most 10-min average wind speeds. To improve the temporal scale resolution, we leverage machine learning tools and continuous measurements from National weather stations to generate composite “Frankenstein” days comprising 144 jigsaw pieces of actually measured 10-min wind time-histories that are scaled and matched together to form a continuous daily record. These point-estimates, valid only at the locations of the weather stations, are expanded spatially by employing high-fidelity Computational Fluid Dynamic simulations that take into account the topographic complexity of the site to simulate turbulent wind flows, thus generating spatially correlated wind fields of 10-min average wind speeds. These allow estimating load distribution and risk on (i) an event-by-event basis and (ii) in the long-term for an ensemble of spatially-distributed highway assets that are vulnerable to wind actions, such as signpost bridges and power network pylons.
[paper]
Vamvatsikos D., Chatzidaki A. (2022). The HAPI sensor-aware framework for infrastructure risk and resilience assessment. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | The (new) 20’s have allowed us to dream big on protecting our infrastructure from natural hazards. Powerful computers, machine learning, terrestrial and airborne sensors are at our disposal to help us quantify the consequences of potential hazardous events that may come in the future, are already unfolding, or have already happened. Owing to its origins in four European projects, namely HYPERION, ARCHYTAS, PANOPTIS and INFRASTRESS, the HAPI framework has been formulated to perform pre/trans/post-event risk and resilience assessment of diverse infrastructure, comprising different layers of networked, loosely-connected or autonomous assets within a city, region or country. Building upon the well-worn basis of hazard-exposure-vulnerability that underpins practically all insurance risk estimates, HAPI enables assessment of cascading (e.g., mudflow/landslide after earthquake) and cotemporaneous (e.g., extreme precipitation, temperature, ice and wind scenario) hazards, while it offers sensor integration with near-real-time updating of predictions based on hazard/asset/consequence information input. Both “static” memoryless hazards (e.g., earthquake), as well as “dynamic” time-dependent hazards (e.g., climate projections) are incorporated in tandem with static/dynamic vulnerabilities, allowing the tracking of complex phenomena, such as climate change, and their effect on the aging/corrosion/fatigue of a diverse set of assets, including buildings, bridges, piping, powerlines, highways and cultural heritage monuments. At the very basis lies a vast database of hazard and asset realization scenarios, employing Total Probability Discrete Event Simulation to explicitly track network interdependencies and propagate uncertainty from our source information to the projected integrated-system functionality and eventual recovery.
[paper]
Tsantaki S., Vamvatsikos D., Angiolilli M., Cattari S., Tariq M. (2022). A basis for defining archetypes for non-engineered low-rise unreinforced brick masonry residential buildings of Pakistan. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | The salient characteristics of low-rise unreinforced brick masonry residential buildings of Northern Pakistan are presented, aiming to provide a basis for defining archetypes suitable for seismic vulnerability assessment in this area. Firstly, an overview of the typical geometrical characteristics, the mechanical properties of the commonly used materials, the main structural features, and observed damage patterns of such buildings is given. Available test data on a set of wallets and a single room consistent with the configuration and construction practices in Northern Pakistan are selected. The wall strength reference values and the effect of construction issues that influence the boundary conditions, such as the wall-to-wall and wall-to-slab connections, are studied, too. The consistency between the failure mechanisms activated by the experimental tests and those predicted by analytical strength criteria available in the literature is shown; this is used as a tool to define the most plausible values of mechanical parameters to be adopted as a reference in seismic safety building evaluation. These results constitute the preliminary but necessary step to address structural models for building and class vulnerability assessment of, arguably, one of the most dominant and vulnerable building types in Pakistan, and by extension, of a large part of South Asia.
[paper]
Zafeiropoulos C., Protopapadakis E., Chatzidaki A., Doulamis A., Vamvatsikos D., Zotos N., Bogdos G., Kostaridis A., Schmidt F., Ientile S., Sevilla I., Tilon S., Rallis I. (2022). A holistic monitoring scheme for road infrastructures. Proceedings of the 15th International Conference on Pervasive Technologies Related to Assistive Environments (PETRA ’22), 622–627. DOI: 10.1145/3529190.3534745
Abstract | This monitoring system aims at increasing the resilience of the road infrastructures and ensuring reliable network availability under unfavourable conditions, such as extreme weather, landslides, and earthquakes. The main target is to combine downscaled climate change scenarios (applied to road infrastructures) with simulation tools (structural/geotechnical) and actual data (from existing and novel sensors), so as to provide the operators with an integrated tool able to support more effective management of their infrastructures at planning, maintenance and operation level. Towards this, the proposed framework aims to use high resolution modelling data for the determination and the assessment of the climatic risk of the selected, transport infrastructures and associated expected damages, use existing SHM data (from accelerometers, strain gauges etc.) with new types of sensor-generated data (computer vision) to feed the structural/geotechnical simulator, utilize tailored weather forecasts (combining seamlessly all available data sources) for specific hot-spots, providing early warnings with corresponding impact assessment in real time; develop improved multi-temporal, multi-sensor UAV, computer vision and machine learning-based damage diagnostic for diverse transport infrastructures; design and implement a Holistic Resilience Assessment Platform environment as an innovative planning tool that will permit a quantitative resilience assessment through an end-to-end simulation environment, running “what-if” impact/risk/resilience assessment scenarios. The effects of adaptation measures can be investigated by changing the hazard, exposure and vulnerability input parameters; design and implement a Common Operational Picture, including an enhanced visualisation interface and an Incident Management System. The integrated platform (and its sub-modules) will be validated in two real case studies in Spain and in Greece.
Miano A., Ebrahimian H., Jalayer F., Vamvatsikos D., Prota A. (2022). Cloud to IDA: An efficient procedure for considering structural modelling uncertainties. Proceedings of the 13th International Conference on Structural Safety and Reliability (ICOSSAR), Shanghai, China.
Abstract |
Hassan M., Vasdravellis G., Vamvatsikos D. (2022). Seismic design and assessment of a high post-yield stiffness steel braced frame for residual drift reduction. Proceedings of the 10th International Conference on the Behaviour of Steel Structures in Seismic Areas (STESSA2022), Timisoara, Romania.
Abstract |
Vamvatsikos D., Chatzidaki A. (2021). Fragility and Loss assessment via mixed probabilistic models of seismic demand. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | A mixture model is presented for combining the results of different models or analysis approaches into a single probabilistic seismic demand model that is suitable for fragility assessment. A structure can be represented using different model types or even levels of resolution for the same type, while it may also be analyzed via methods of different complexity, most notably static versus dynamic nonlinear approaches. Combining the results from different sources can be beneficial as it allows updating the results of a simpler approach or combining the strengths of two different models. For example, as the static pushover analysis offers inexpensive yet low-fidelity demand assessment at any level of intensity, its results may be locally or globally updated by adding stripes of (computationally expensive) response history analysis. On the modelling side, different model types may offer accuracy advantages in complementary response regions. This is the case of distributed-plasticity fiber models that offer higher fidelity for reinforced concrete frames at low (pre-capping) deformations, while lumped-plasticity models are more reliable for larger (post-capping) deformations closer to collapse. Through the combination of the results of multiple models of differing fidelity we can potentially better capture the performance of a structure at all levels of seismic intensity. By employing a minimal 5 parameter power-law-based model we offer viable options for forming mixed probabilistic seismic demand models that can combine both different models and different analysis methods into a single output suitable for fragility and loss assessment.
Vamvatsikos, D., Fragiadakis, M., Georgopoulos, I.-O., Koumousis, V. K., Koutsoyiannis, S., Manetas, A. Melissianos, V. E., Papadopoulos, C., Papanikolopoulos, K. E., Toumpakari, E.-E. (2021). The ARCHYTAS intelligent decision-support system for the protection of monumental structures. Proceedings of the 4th International Conference on Protection of Historical Constructions (PROHITECH 2020), Athens, Greece
Abstract | The ARCHYTAS platform is based on using (i) reliable mechanical models and damage thresholds for assessing structural performance (ii) a network of sensors for updating the model parameters, (iii) detailed estimates of earthquake and flood hazard at the sites of interest and (iv) a state-of-art approach for multi-hazard risk assessment that can deliver accurate pre/trans/post-event evaluation of the risk at multiple geographically distributed cultural heritage sites. The core of the proposed system comprises a cloud-deployed computational platform, where data obtained from on-site measuring systems is processed, critical environmental actions are identified and flags are raised to provide alerts on the predicted monument structural condition. The decision-support system is fully uncertainty-aware, employing the concept of the mean annual frequency of limit-state exceedance under specified confidence levels to offer monument-specific courses of action based on the convolution of the current state of the monument (as determined by its best-estimate fragility, and updated by current or past measurements) and the predicted, recorded or evolving hazard. All-in-all, the platform can assist the relevant authorities to prioritize inspection, maintenance and rehabilitation actions be-fore or after events subject to limited available resources.
Lachanas, C. G., Melissianos, V. E., and Vamvatsikos, D. (2021). Spatial variability of ground motion hazard and preliminary regional damage assessment of ancient monuments. Proceedings of the 4th International Conference on Protection of Historical Constructions (PROHITECH 2020), Athens, Greece
Abstract | The seismic hazard is a spatial variable and its distribution depends on the site and soil conditions, the distance from the influencing faults, their geometric characteristics etc. To characterize a future seismic event, multiple correlated Intensity Measure (IM) fields are employed. In Greece and especially in the Attica region, there are numerous monuments of classical antiquity that are spread throughout the territory, e.g., the Temple of Poseidon in Sounio, the Ancient Walls of Piraeus etc., and not only in the center of the city of Athens, where the well-known Parthenon, the Temple of Olympian Zeus, etc. lie. To capture the ensemble risk of such widely distributed antiquities a regional risk assessment approach is adopted, based on the principles of the Performance-Based Earthquake Engineering. Event-Based Probabilistic Seismic Hazard Analysis (PSHA) is used as basis, where the distribution of the ΙΜ fields is evaluated for a stochastic event set, spanning thou-sands of realizations, allowing the estimation of damages over an entire region on an event-by-event basis. A basic application is offered by considering a typical single multi-drum column at each site of interest to assess its performance. Different fragility representation schemes are employed, and their consequences are compared for both the event-based and the classical approach of PSHA as a first decisive step towards the formulation of a comprehensive methodology for the assessment of seismic damages of ancient monuments within a region.
Melissianos, V. E., Lachanas, C. G., and Vamvatsikos, D. (2021). Preliminary seismic risk assessment of monolithic columns of the Aphaia Temple in Aegina. Proceedings of the 4th International Conference on Protection of Historical Constructions (PROHITECH 2020), Athens, Greece
Abstract | Studies on the seismic assessment of monumental structures of antiquity are mostly focused on the estimation of the structural behavior and do not involve the pertinent uncertainties. Towards filling this research gap, a preliminary seismic risk assessment of monolithic columns of the Aphaia Temple in Aegina island, Greece, is presented. A comprehensive application of the framework of Performance-Based Earthquake Engineering is carried out. Site-specific seismic hazard estimation is performed at first by employing Probabilistic Seismic Hazard Analysis. The rocking column is analyzed under seismic excitation by numerically solving the equation of motion in order to extract the fragility curves. Finally, the convolving of seismic hazard and structural response yields the seismic risk of the column that is used to estimate the mean annual rate of exceeding predefined limit states that are associated with damage and collapse of the column.
Loli M., Chatzidaki A., Vamvatsikos D., Gazetas G. (2021). Seismic vulnerability of motorway bridge on active landside. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | The western section of Egnatia Odos motorway in Greece runs through a challenging mountainous terrain where geohazards are exacerbated by moderate seismicity. Located a few kilometers east of the town of Metsovo, the twin girder bridges of the Panagia interchange have their central piers founded on an active landslide. Being part of a research project that aims to develop a tool for rapid inspection and assessment of the motorway, this study presents a thorough seismic vulnerability analysis of the hybrid caisson–pile group foundation system that supports the most critical piers of the interchange. This foundation system has been designated as a slope stabilizing measure, in addition to carrying the loads transmitted by the bridge superstructure. Numerical modelling with nonlinear 3D finite elements has been employed, together with site-specific hazard-consistent selection of ground motion records. A hybrid numerical approach has been developed using segregated models of varying refinement with rational approximation of interactions between the nonlinear response of soil, the movement of the slope, the kinematic distress imposed upon the foundation and the inertial loads from the vibration of the superstructure. The method estimates pile performance under large-scale, dynamic landslide action with sufficient engineering accuracy for cases where slope actions dominate the response. The softening behavior of the sliding surface is calibrated versus monitored slope displacements. The effect of groundwater recharge after heavy rainfall is incorporated in the vulnerability analysis in a simplified manner, using different scenarios for water table elevation. Focusing on the performance of the foundations, damage is described in terms of their permanent displacements and curvatures. Results indicate that a range of excitations with an exceedance
probability of 2% in 50 years are capable of inflicting substantial permanent pile damage, even complete failure, if combined with a fully saturated soil condition. The computed residual foundation displacements can serve as input for a detailed structural model simulating the performance of the superstructure for estimating the bridge vulnerability.
Kazantzi A.K., Vamvatsikos D. (2021). Attribute-driven fragility curves through class disaggregation. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | Fragility curves are an important ingredient in the seismic loss assessment process. For a regional scale loss estimation, to reduce to reasonable levels the computational burden associated with determining the seismic demands for individual buildings, analytical seismic fragilities are instead evaluated on a broad building class basis. The latter process essentially involves representing a population of buildings having similar characteristics with a set of characteristic “index” buildings to avoid analyzing every single building within this population. For the definition and modeling of index buildings, two main options are currently available, these being (a) defining a limited number of index buildings to represent the class and modeling them with relatively complex, yet more accurate, MDOF systems, and (b) defining numerous index buildings to represent the class and modeling them with simplified approximate SDOF systems. Apparently, the dilemma of defining the optimal way to sample the index buildings comes down to the use of few MDOFs or many SDOFs. Despite the fact that the use of many SDOFs is a rather attractive option, given that they are an easy and computationally inexpensive choice in terms of both modeling and analysis, they are often a bad approximation of the actual problem. This is the case, for example, of tall or irregular buildings, where non-negligible higher modes render the SDOF approximation ineffective. Then, the more expensive and accurate MDOF option has to be employed. However, using a limited number of MDOFs to represent the class of interest inherently offers very little flexibility towards capturing individual buildings that might belong to that class yet their salient features do not necessarily match those of the “average” index building. Aggregating the results of all index buildings into a single class fragility means that one cannot provide a more accurate answer than the mean class fragility plus some dispersion, even if the building in question actually closely matches one of the underlying index ones. This may not matter for estimating long-term average losses over a region, but it becomes increasingly important as the size of the portfolio is reduced and individual structures stand out. To resolve the aforementioned issue, we propose here a method for adding substance back to the class fragility and consequently obtaining fine-grained attribute-driven fragility estimates. The term attribute-driven is key in our approach, since it implies that the process explicitly accounts for the specific characteristics of the building in question. It is essentially a meso-scale approach that stands between the building-specific FEMA P-58 style approach (micro-scale) and the building-class approach (macro-scale). Our testbed is a population of modern high-rise reinforced concrete buildings, represented by seven index buildings, for which we have evaluated fragility functions. With this information at hand, our proposed approach employs statistical methodologies for effectively disaggregating the index building fragility functions, to provide attribute-aware response and collapse fragility spot estimates for individual sample buildings, other than the index ones, that belong to the same class.
Melissianos V.E., Dasiou M.E., Vamvatsikos D. (2021). Seismic risk assessment of the ancient temple of Aphaia in Greece. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | The protection of cultural heritage against natural hazards has attracted significant research efforts and funding during the last decades, recognizing its importance in humanity’s history and raising public awareness on this issue. In Greece, there are numerous monuments that have been exposed to environmental actions, and, consequently, many are classified as deteriorating structures. In addition, earthquakes pose a significant threat to their structural integrity and contribute to the accumulation of damage. The evaluation of the seismic performance of such heritage assets is a complex computational problem, especially as their structural elements are either not rigidly connected, or connected by weak mortar, and thus prone to rocking due to the seismic excitation.
Research on the seismic assessment of monuments is quite limited to the estimation of the structural behavior, thus excluding the incorporation of pertinent uncertainties. The aim of the study is to contribute to the seismic risk assessment of monuments. The framework of Performance-Based Earthquake Engineering is applied, comprising of four successive and interconnected steps: (1) the European seismic source model is used to estimate the seismic hazard in terms of a scalar intensity measure, (2) the structure is modeled with a discrete element approach. The rocking and/or sliding of the individual stone blocks are accurately addressed by the software since, during the calculation, it locates each contact and computes the motion of each block from the forces that are developed at the joints. Results in terms of maximum displacements are obtained from the analysis and related to damage states. (3) The limit-state and the aleatory and epistemic uncertainties are defined for the determination of discrete damage states and the associated fragility curves, and (4) the seismic risk is calculated in terms of the mean annual frequency of exceeding each limit state. The aforementioned methodology is applied to a free-standing column and a colonnade of two columns with an architrave at the ancient Temple of Aphaia, located on the Greek island of Aegina and built between 510 and 470 BC, comprising a significant example of the Archaic architecture.
Vamvatsikos D., Melissianos V., Kostaridis A., Kazantzi A.K, Karaferis N., Chatzidaki A., Diagourtas D., Bakalis K. (2021). The PANOPTIS-INFRASTRESS framework for infrastructure risk assessment. Proceedings of the 8th International Conference on Civil Protection & New Technologies (SafeGreece 2021), Athens, Greece.
Reggiani Manzo N., Lachanas C.G., Vassiliou M.F., Vamvatsikos D. (2021). Uniform risk spectra for negative stiffness systems. Proceedings of the COMPDYN2021 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Athens, Greece.
Abstract | This paper presents uniform risk spectra for negative stiffness systems that do not exhibit hysteretic damping, named Negative Stiffness Bilinear Elastic (NSBE) systems. The NSBE oscillator can be used to describe the dynamics of deformable rocking systems with or without restraining systems flexible enough to lead to an overall negative stiffness. It can also be used to describe rocking systems equipped with curved extensions at their base. It has been shown that the response of an NSBE system can be well predicted using the response of a Zero Stiffness Bilinear Elastic (ZSBE) system, which is a bilinear system of constant restoring force. The ZSBE system is a single parameter system; therefore it is simple to construct design spectra for it. For a wide range of ZSBE system strength values, this paper employs Incremental Dynamic Analysis using 105 ordinary (non-pulse-like, non-long-duration) ground motions to obtain the fragility functions for predefined limit-states of the ZSBE seismic response. Fragility functions per limit-state are convolved with the seismic hazard to compute the Mean Annual Frequency of exceedance (MAF). For this study, the seismic hazard curve for a site at Athens Greece is used as it is obtained via probabilistic seismic hazard analysis. Finally, uniform risk spectra per limit-state are obtained by computing the MAF for all the ZSBE oscillators. These spectra can be used for the design of NSBE systems, including rocking oscillators.
Manzo N.R., Lachanas C.G., Vassiliou M., Vamvatsikos D. (2021). Uniform risk spectra for negative stiffness systems. Proceedings of the 8th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN 2021, Athens, Greece.
https://doi.org/10.3929/ethz-b-000492004
[paper]
Abstract | This paper presents uniform risk spectra for negative stiffness systems that do not exhibit hysteretic damping, named Negative Stiffness Bilinear Elastic (NSBE) systems. The NSBE oscillator can be used to describe the dynamics of deformable rocking systems with or without restraining systems flexible enough to lead to an overall negative stiffness. It can also be used to describe rocking systems equipped with curved extensions at their base. It has been shown that the response of an NSBE system can be well predicted using the response of a Zero Stiffness Bilinear Elastic (ZSBE) system, which is a bilinear system of constant restoring force. The ZSBE system is a single parameter system; therefore it is simple to construct design spectra for it. For a wide range of ZSBE system strength values, this paper employs Incremental Dynamic Analysis using 105 ordinary (non-pulse-like, non-long-duration) ground motions to obtain the fragility functions for predefined limit-states of the ZSBE seismic response. Fragility functions per limit-state are convolved with the seismic hazard to compute the Mean Annual Frequency of exceedance (MAF). For this study, the seismic hazard curve for a site at Athens Greece is used as it is obtained via probabilistic seismic hazard analysis. Finally, uniform risk spectra per limit-state are obtained by computing the MAF for all the ZSBE oscillators. These spectra can be used for the design of NSBE systems, including rocking oscillators.
Fasoulakis Z., Vamvatsikos D., Papadopoulos V. (2021). Buckling strength of bolted steel members from plain angle sections with multivariate stochastic imperfections. Proceedings of the 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering UNCECOMP 2021, Athens, Greece.
Abstract | Spatial uncertain quantities such as the geometric imperfections are found of paramount importance when investigating the behaviour of thin-walled structures. The present work addresses the probabilistic estimation of the buckling capacity of single-bolted members from plain angle sections with stochastic geometric imperfections. The simulation is based on detailed experimental data of imperfections measured by an inhouse built set-up. The quatro-variate non-stationary stochastic processes herein combine the spectral representation method along with the method of separation, incorporating correlations between the imperfection components. The spectral separability check is also performed through a minor investigation. A large-scale nonlinear finite-element problem is defined to estimate the stochastic buckling capacities (in the frame of Monte Carlo simulation) for a bolted angle-section column. More uncertain parameters are then included, namely material properties and lateral load (wind pressure), towards an extended range of applicability. To this end, in order to improve the computational performance, the Latin hypercube sampling method is adopted. The resulting density distributions, presented in both tabular and graphical forms, reveal the influence of each parameter (and their combinations) on the buckling load variability and can be used also for probabilistic assessment.
Karaferis N., Vamvatsikos D. (2021). Seismic action combination rules for the design of azimuth-independent structures. Proceedings of the 8th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN2021, Athens, Greece
Abstract | The validity of the typical 100/30 combination rule for horizontal seismic action effects is investigated for the design of structures that are axially symmetric along the vertical direction. The 100/30 rule stipulates that one should combine 100% of the seismic action in one principal direction (as estimated by the design spectrum) with 30% of the action in the other principal direction, and vice-versa. Having been derived for azimuth-dependent structures, having e.g., a rectangular plan, it takes advantage of the fact that the two horizontal components of ground motion are only partially correlated, with peaks that in general do not happen simultaneously, to reduce the overall design loads. On the contrary, vertical liquid storage tanks, silos and chimneys are examples of azimuth-independent structures, which by virtue of their symmetry will always experience the worst-possible incidence angle of a ground motion. To quantify the effect of axisymmetry we employed a database of 150 records with three components of ground motion. The results show that an 106/106 combination rule, or more accurately a 1.12 amplification factor on the design spectrum in a single direction, rather than the 1.04 implied by the 100/30, is adequate to account for the effects of axisymmetry. Still, this value depends on the definition of the underlying design spectrum, and whether, e.g., the maximum, arbitrary or geometric mean component is employed, which should be accounted for in all calculations.
Melissianos V., Karaferis N., Vamvatsikos D., Kazantzi A., Bakalis K. (2021). An integrated model for the seismic risk assessment of an oil refinery. Proceedings of the ICONHIC2022 – Preparatory Workshop 2021, Athens, Greece.
Abstract |
Kohrangi M., Papadopoulos A.N., Kotha S.R., Vamvatsikos D., Bazzurro P. (2021). Earthquake Catastrophe Risk Modeling, Application to the Insurance Industry: Unknowns and Possible Sources of Bias in Pricing. In: Advances in Assessment and Modeling of Earthquake Loss. Springer: Dordrecht.
Abstract | Mathematical risk assessment models based on empirical data and supported by the principles of physics and engineering have been used in the insurance industry for more than three decades to support informed decisions for a wide variety of purposes, including insurance and reinsurance pricing. To supplement scarce data from historical events, these models provide loss estimates caused to portfolios of structures by simulated but realistic scenarios of future events with estimated annual rates of occurrence. The reliability of these estimates has evolved steadily from those based on the rather simplistic and, in many aspects, semi-deterministic approaches adopted in the very early days to those of the more recent models underpinned by a larger wealth of data and fully probabilistic methodologies. Despite the unquestionable progress, several modeling decisions and techniques still routinely adopted in commercial models warrant more careful scrutiny because of their potential to cause biased results. In this chapter we will address two such cases that pertain to the risk assessment for earthquakes. With the help of some illustrative but simple applications we will first motivate our concerns with the current state of practice in modeling earthquake occurrence and building vulnerability for portfolio risk assessment. We will then provide recommendations for moving towards a more comprehensive, and arguably superior, approach to earthquake risk modeling that capitalizes on the progress recently made in risk assessment of single buildings. In addition to these two upgrades, which in our opinion are ready for implementation in commercial models, we will also describe an enhancement in ground motion prediction that will certainly be considered in the models of tomorrow but is not yet ready for primetime. These changes are implemented in example applications that highlight their importance for portfolio risk assessment. Special consideration will be given to the potential bias in the Average Annual Loss estimates, which constitutes the foundation of insurance and reinsurance policies’ pricing, that may result from the application of the traditional approaches.
Vamvatsikos D. (2021). A Dürüm Döner View of Seismic Risk Assessment. Proceedings of the 9th Turkish Conference on Earthquake Engineering (9TCEE2021), Istanbul, Turkey.
Abstract | A dürüm döner (DD) is a magnificent culinary invention, without which any visit to Turkey would never be complete. Its excellent combination of bread and meat, with the occasional mix of tomato, onions and mayonnaise, is readily available to complement any walk around the sokaks and plazas of any
Turkish city and town. The experience is inherently addictive, and Dr. V is no stranger to it. Contemplating a sabbatical in Turkey comes with an increased hazard of ample DD availability, and heightened risk of high calorie intake. When a powerful stakeholder (Mrs. V) steps in to question this sabbatical plan, how is Dr. V to show that he will be able to conduct research while safeguarding his enviable cuddly figure? Three nearby vendors of excellent but highly variable DDs, one exposed yet enterprising researcher, and one tough uncompromising stakeholder come together in a nail-biting risk assessment drama to play out in view of the Bosporus.
Bazzurro P, Kohrangi M, Bakalis K, Vamvatsikos D. (2020). Bi-directional Conditional-Spectra-Based Record Selection for Horizontal and Vertical Ground Motions. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | Conditional Spectra (CS) based record selection is a state-of-the-art approach to select sets of records for performing nonlinear response time history analysis consistent with the seismic hazard at a specific site. So far this method has been developed and applied mainly to select horizontal components of the ground motion. There are many structural or nonstructural building components, however, and entire structures that are also sensitive to the vertical component of ground motion, e.g., due to concurrent vertical and horizontal deformability, uplifting and/or rocking. Thus, we aim here to further extend the CS approach to select a set of hazard consistent 3-component records. The proposed method is applied to the risk assessment of a liquid storage tank located at a site of major oil refineries in Elefsina, Greece. Tanks are prone to uplifting due to horizontal excitations, a behavior that can be exacerbated when the vertical component of the ground motion is considered. Therefore, a realistic seismic assessment of such structures cannot be carried out without simultaneously accounting for all three translational components of the ground motion. To this end in the case study we tested different record selection approaches with and without consideration of the vertical motions, as well as with and without vertical ground motions hazard consistency. Overall, there is a non-negligible dependence of the tank response to the effects of the vertical component, which should be included. Neglecting it typically result to an underestimation of about 20%. In addition, we recommend incorporating the hazard consistency of the vertical component in the record selection because it does have an impact on the tank response.
Miano A., Ebrahimian H., Jalayer F., Vamvatsikos D., Prota A. (2020). Impact of sampling techniques on uncertainty propagation with non-linear dynamic analysis. Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan
Abstract | The Method: Quantifying the impact of modelling uncertainty on the seismic performance assessment is a crucial issue for existing buildings, considering the partial information available related to material properties, construction details and the uncertainty in the capacity models. It has been proved that the effect of structural modelling uncertainties on the seismic performance of existing buildings can be comparable to that of uncertainty in ground motion representation. In this work, the impact of different sampling techniques such as Standard Monte Carlo simulation and Latin Hypercube sampling with Simulated Annealing on the uncertainty propagation with non-linear dynamic analysis has been investigated. Two alternative non-linear dynamic analysis procedures, namely, Incremental Dynamic Analysis and Cloud Analysis are explored. The types of uncertainty encompass record-to-record variability, structural modelling parameters and the fragility model parameters. A one-to-one sampling approach has been adopted in which each of the ground motion records is paired up with a different realization of the structural model. The Application: The case-study structure consists of three stories with a semi-embedded story. The structure lies on soil type B (according to national Italian code NTC 2018 site classification). The building is constructed in the 1960s and is designed for gravity loads only. The structure is composed of bi-dimensional parallel frames, without transversal beams. The main central frame in the structure is used herein as structural model. The finite element model of the frame is constructed, using OpenSees, assuming that the non-linear behaviour in the structure is modelled as distributed plasticity. The Beam-with-hinges element from the library of OpenSees is used to model the distributed plasticity. As the uniaxial material from OpenSees library, Pinching4 Material is used. The points on the backbone curve are defined as cracking, yielding, spalling and the ultimate, respectively. These points are obtained based on moment-curvature analysis of beam-column elements subjected to flexure and axial force. The lateral force-deformation response of the element is obtained by considering as a spring the flexural-compression response of the element (section analysis for normal stresses) which is acting in series with a shear spring and a spring representing the fixed-end rotations. The total lateral force deformation response of the element considers the interaction between the shear, bar-slip and the axial-flexural response. A large ground motion set of 160 records from NGA West2 Database, ITACA (Italian Accelerometric Archive), and recent Iranian recordings (International Institute of Earthquake Engineering, IIEES, personal communication) has been employed. Cloud Analysis and IDA have been implemented with the complete set of 160 un-scaled records. Moreover, Cloud Analysis and IDA have been carried out with subsets of respectively 50 and 30 ground motion records.
Chatzidaki A., Bakalis K., Vamvatsikos D. (2020). Seismic resilience assessment for the G7 highway bridge in Greece. Proceedings of the 11th European Conference on Structural Dynamics (EURODYN 2020), Athens, Greece
Abstract | The seismic risk is assessed for two twin bridges, one per direction, forming the G7 branch of the Egnatia Odos highway in Greece. These are structurally independent horizontally-curved cantilevered-deck three-span reinforced concrete structures with a monolithic pier-to-deck connection that have been designed circa 2004 according to Greek and European standards. The aim is to develop a tool for pre-event risk assessment and rapid post-event inspection of critical road infrastructure by combining hazard, vulnerability and sensor information (where available) to predict the resulting consequences. To enhance the assessment resolution, a component-based approach is followed, allowing us to evaluate damage scenarios for individual critical components (i.e., piers and bearings) and propagate them to the system-level performance. Consequences are quantified in terms of repair losses, downtime, and traffic capacity losses, the latter identified as the number of closed lanes and the allowable speed limit for the open ones. This allows tracing back the consequences after an event to individual bridge components to help road operators establish bridge inspection prioritization protocols and manage associated incidents, facilitating the rapid assessment of the state of the bridge and optimal recovery to full functionality.
Melissianos V.E., Vamvatsikos D. (2020). Simplified estimation of design fault displacement for buried pipelines at fault crossing. Proceedings of the 11th European Conference on Structural Dynamics (EURODYN 2020), Athens, Greece
Vamvatsikos D., Bazzuro P. (2019). Decision Support, Resilience and Sustainable Reconstruction of Historical City Cores under Seismic Threat: The HYPERION Approach, Proceedings of the 8th International Conference on Seismology and Earthquake Engineering SEE8, Tehran, Iran.
Abstract | Historical city cores are a blend of cultural heritage (CH), residential function and economic activity that forms the heart of many urban areas in the world. When built in seismic areas, they become the obvious soft spot that can cripple the local and regional economy even if moderate seismic events occur. Tackling their vulnerability and enhancing their resilience is a complex endeavor with far-reaching social, environmental and economic repercussions, which mirrors the intricate nature of historical areas. The breadth of the investigation invariably requires considering (a) CH assets (historic buildings, monuments, bridges, canals), (b) nearby/supporting non-CH structures and infrastructure (slopes, newer bridges, transmission power lines, telecommunication towers, etc.), as well as (c) the interconnectivity among them that makes a historical core function. To further complicate matters, each structure has been built to different design standards and level of workmanship while typically having witnessed many decades, centuries or even millennia of life, as well as successful or failed rehabilitation interventions. In light of these challenges, the HYPERION project was conceived, bringing together 26 European organizations (municipal/regional/national authorities, universities, private entities, and cultural heritage agencies) to leverage existing tools and services together with novel technologies in order to deliver an integrated resilience assessment platform. Its focus is addressing multi-hazard risk understanding, better preparedness, faster, adapted and efficient response, and sustainable reconstruction of historic areas subject to multiple hazards. Herein, the seismic hazard, risk and resilience modules of HYPERION are discussed, highlighting the core directions of research to be undertaken in this on-going project.
Kohrangi M., Bazzurro P., Vamvatsikos D., (2019). An Urban Seismic Risk and Resilience Model for Isfahan. Proceedings of the 8th International Conference on Seismology and Earthquake Engineering SEE8, Tehran, Iran.
Abstract | Many private and public stakeholders are directly or indirectly affected by the impact of earthquakes in a urban area. Therefore, it is crucial for such organizations to know about the overall level of seismic risk that the assets of their concern face. The portfolio risk assessment studies that estimate such a risk play a fundamental role in the sustainable development of an urban area, providing local and national authorities and other private decision makers with valuable information for devising the most appropriate risk mitigation actions. These actions include post-disaster emergency planning, building retrofitting campaigns, creation of insurance pools, and strategic urban planning, amongst other measures. The greater Isfahan (32°38′N 51°39′E) is a historical and touristic city in the center of Iran. It has a population of about 1.6 million according to the 2016 Census, the third most populous metropolitan area in Iran after Tehran and Mashhad. According to the seismic zonation of the Iranian design code, Isfahan is located in a seismically moderate zone with reference peak ground acceleration, PGA, on rock equal to 0.25g for 475 years return period. Even though the estimated seismicity for Isfahan relative to other seismically active large cities in Iran (such as Tehran, Tabriz and Mashhad) is low, the large number of vulnerable buildings, the large compact population and the importance of the postdisasters functionality of the city (i.e., resilience) for the economy of the country, calls for thorough pre-disaster seismic risk and loss estimation studies. Herein we describe the steps followed to create and interpret a model for assessing the earthquake risk of the city of Isfahan. This includes the procedure and the data used to generate the three ingredients of a risk assessment model, namely the exposure module, the fragility and vulnerability module, the adopted seismic hazard module, and a discussion of the computed seismic risk estimates. The risk assessment is conducted for two likely
earthquake scenarios that contribute the most the seismic hazard of Isfahan. In addition, risk estimates in terms of loss maps for 475 and 2,475 year return periods are generated and critically evaluated.
Kazantzi A.K., Vamvatsikos D. (2019). Performance-based design of friction pendulum bearings for a steel top story spanning two RC towers. Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2019), Crete, Greece
Abstract | The collapse performance of code-designed base-isolated structures has received considerable criticism, having been found to be deficient vis-à-vis conventional buildings in several situations. As a remedy, prescriptive minima have been recommended in the literature for the bearing deformation capacity. These are independent of structure or site characteristics, yet they are already finding use in design. We put this concept to the test by means of a case study of a seismically isolated steel structure that rests on the roof of two adjacent high-rise reinforced concrete towers. To seismically isolate the steel structure Friction Pendulum Bearings (FPBs) are used, and their displacement capacity is determined to comply with a 1% probability of collapse in 50 years performance objective.
The case study possesses two salient features that distinguish it from pertinent past investigations. The first is that the isolated steel structure rests on top of two others and consequently it is subjected to narrow-band roof acceleration time histories, shaped by the filtering of the ground motion excitation through the supporting buildings. The second is that the two supporting towers have different modal characteristics, thus displacement demands imposed to the FPBs are mainly affected by their in-phase or out-of-phase movement. Overall, a case-specific performance-based design approach is shown to achieve the desired safety while requiring 1.5 times lower displacement capacities for the bearings, when compared to prescriptive “performance-based” approaches.
Vamvatsikos D. (2019). Funky structure behavior factors. Proceedings of the 16th D-A-CH Tagung Erdbebeningenieurwesen & Baudynamik, Innsbruck, Austria
Abstract | Behavior (q-)factors are funky. They are fun and they are magic. Just look at how the symbol breaks the boring symmetry of a circle with a random squiggly or straight hanging tail. It perfectly embodies the spirit of the q-factor that on the surface, above the straight line of writing, seems profoundly round and deterministically predictable, while in reality it is all about the tail of unknown shape and magnitude that is hanging underneath. One may choose to ignore this, sweeping all uncertainty under a carpet of expert opinion, or attempt to directly measure it, using the best that the current state-of-art has to offer. The first option may be attractive for typical buildings, where considerable experience has been amassed, but will probably fail in misery for newer systems, interesting structures or unfamiliar situations. To capture this funky nature of the q-factor, let us try to provide a mathematically tractable definition and discuss ways of quantifying it, for a building, an ensemble of similar buildings, or a class of dissimilar buildings of the same structural system, spread over one or more sites.
Chatzidaki A., Vamvatsikos D. (2019). Mixed probabilistic seismic demand models for fragility assessment. Proceedings of the SECED 2019 Conference, Greenwich, UK
Abstract | A mixture model is presented for combining the results of different models or analysis approaches into a single probabilistic seismic demand model that is suitable for fragility assessment. A structure can be represented using different model types or even levels of resolution for the same type, while it may also be analysed via methods of different complexity, most notably static versus dynamic nonlinear approaches. Combining the results from different models or analysis methods can be beneficial as it allows updating the results of a simpler approach or combining the strengths of two different models. For example, different model types may offer accuracy advantages in complementary response regions. This is the case of distributed-plasticity fiber models that offer higher fidelity for reinforced concrete frames at low (pre-capping) deformations, while lumped-plasticity models are more reliable for larger (postcapping) deformations closer to collapse. Through the combination of the results of both models we can potentially better capture the performance of the frame at all levels of seismic intensity. By employing a minimal 5 parameter power-law-based model we offer viable options for forming mixed probabilistic seismic demand models that can combine both different models and different analysis methods into a single output suitable for fragility assessment.
Bakalis K., Vamvatsikos D., Grant D.N., Mistry A. (2019). Downtime assessment of base-isolated liquid storage tanks. Proceedings of the SECED 2019 Conference, Greenwich, UK
Abstract | Seismic base isolation is examined as a design alternative for supporting industrial facility liquid storage tanks against earthquake loading. A 160,000m3 liquid storage tank is adopted as a case study, for which two designs are assessed, one with and one without base isolation. Using a nonlinear surrogate model and a set of ground motion records selected using the conditional spectrum approach for the average spectral acceleration intensity measure, Incremental Dynamic Analysis is employed to derive seismic fragility curves. Consequences of damage are evaluated in terms of downtime, considering the characteristics of petrochemical storage tanks, whereby any repair requires a lengthy list of actions dictated by health and safety requirements. The results reveal considerable benefits when base-isolation is employed, by drastically reducing downtime when sufficient displacement capacity is provided in the isolators.
Vamvatsikos D. (2019). Decision support for road infrastructure resilience: the panoptis perspective. Proceedings of the SECED 2019 Conference, Greenwich, UK
Abstract | The PANOPTIS consortium aims to leverage existing tools and services as well as remote sensing technologies to deliver an integrated platform that can address road infrastructure (RI) multi-hazard resilience. The scope of the project incorporates RI structural components (bridges, overpasses, interchanges, tunnels, slopes, retaining walls, pavements, and surface water drains), non-structural components (tunnel ventilation systems, traffic cameras and signposts), as well as interconnected non-RI components, such as power transmission lines and telecommunication towers. Both detailed and surrogate structural models will be developed for RI and non-RI components, quantifying and incorporating the epistemic uncertainty due to the detailed models’ reduction to surrogacy to allow a rapid high-resolution assessment of vulnerability, whereby loss, functionality and downtime become directly tied to rehabilitation/emergency action planning. The focus is on the development of a rapid-response decision-support tool that will employ measured data immediately after any seismic event to issue inspection prioritization protocols, facilitate the rapid assessment of the state of the RI, and help increase its resilience to catastrophic events.
Melissianos V., Vamvatsikos D., Gantes C. (2019). Empirical expressions for predicting the buckling failure of buried pipelines under reverse faulting. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Περίληψη | Οι υπόγειοι αγωγοί μεταφοράς καυσίμων αποτελούν κρίσιμο τμήμα της ενεργειακής υποδομής μιας χώρας καθώς εξασφαλίζουν τη μεταφορά και διανομή καυσίμων με οικονομικό τρόπο και ασφάλεια. Στην περίπτωση διέλευσης αγωγών από σεισμογενείς περιοχές, η ενεργοποίηση ενός διασταυρούμενου σεισμικού ρήγματος είναι πιθανό να προκαλέσει βλάβη του αγωγού με κοινωνικές, περιβαλλοντικές και οικονομικές επιπτώσεις. Στην περίπτωση ανάστροφης διάρρηξης, ο αγωγός υπόκειται σε σημαντική θλιπτική καταπόνηση, λόγω της κίνησης του ανερχόμενου τεμάχους του ρήγματος. Οι πιθανές μορφές αστοχίας σε αυτήν την περίπτωση είναι ο τοπικός ή καθολικός λυγισμός και η εφελκυστική θραύση σε θέσεις συγκολλήσεων. Καθοριστικές παράμετροι για το ποιά μορφή αστοχίας θα
είναι κυρίαρχη είναι η τοπική λυγηρότητα του αγωγού (λόγος διαμέτρου προς πάχος D/t) και το βάθος ταφής. Σκοπός της μελέτης είναι η διατύπωση μιας εμπειρικής σχέσης πρόβλεψης της μορφής αστοχίας. Συγκεκριμένα, μέσω παραμετρικών αριθμητικών αναλύσεων και στατιστικής επεξεργασίας των αποτελεσμάτων με τη μέθοδο της γραμμικής διακριτικής ανάλυσης, προτείνεται μια εμπειρική σχέση που διαχωρίζει της περιοχές εμφάνισης των διαφορετικών μορφών αστοχίας στο χωρίο «βάθος ταφής – λόγος D/t» συναρτήσει της γεωμετρίας διασταύρωσης αγωγού – ρήγματος.
Lachanas C., Vamvatsikos D. (2019). Model influence on the estimated seismic response of a 20-story steel moment-resisting frame. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Περίληψη | Τα σύγχρονα λογισμικά πεπερασμένων στοιχείων, παρέχουν τη δυνατότητα μελέτης της συμπεριφοράς των κατασκευών μέσω προσομοιωμάτων διαφορετικών βαθμών πολυπλοκότητας. Εστιάζοντας στην εκτίμηση της σεισμικής απόκρισης ενός κτιρίου μέσω μη γραμμικών δυναμικών αναλύσεων, η αύξηση της πολυπλοκότητας του προσομοιώματος συνεπάγεται αύξηση στο υπολογιστικό κόστος, προκρίνοντας τη χρήση απλούστερων ισοδύναμων προσομοιωμάτων με συνεπαγόμενη αύξηση της αβεβαιότητας. Για μια πρώτη ποσοτικοποίηση της αβεβαιότητας που αφορά τον τύπο του προσομοιώματος, μελετάται ένα σύγχρονα σχεδιασμένο 20-όροφο μεταλλικό κτίριο με πλαισιακό φορέα. Ξεκινώντας από το τρισδιάστατο προσομοίωμα του κτιρίου και ακολουθώντας σταδιακή απλοποίηση του προσομοιώματος σε δισδιάστατο προσομοίωμα πλαισίου πολλών ανοιγμάτων και δισδιάστατο προσομοίωμα πλαισίου ενός ανοίγματος, καταλήγουμε στο ισοδύναμο μονοβάθμιο προσομοίωμα. Στα προσομοιώματα εκτελείται Ικανοτική Δυναμική Ανάλυση.
Από τη σύγκριση προκύπτει ότι για το υπό μελέτη κτίριο η αβεβαιότητα λόγω τύπου προσομοιώματος είναι σχετικά περιορισμένη, ενώ η συνολική αβεβαιότητα κυριαρχείται από τη σημαντική διασπορά στην απόκριση μεταξύ των καταγραφών εντός του κάθε προσομοιώματος.
Kazantzi A.K., Vamvatsikos D., Miranda E (2019). Damping influence on the seismic demands of non-structural components and building contents. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Abstract | In most seismic code provisions, the design of nonstructural elements is based on the evaluation of the (absolute) acceleration demands at the floor levels, usually assuming a critical damping of 5% for those elements. However, the actual critical damping for the nonstructural components is well known to be an unknown parameter, that could well deviate from the abovementioned value, whereas its influence remains by large an unexplored field.
To study the effect of damping on the seismic demands of nonstructural elements 113 actual seismic records obtained from instrumented buildings in the USA were selected. The study concluded that: (a) the use of damping modification factors evaluated based on ground level excitations are not suitable for correcting the nonstructural component spectral accelerations demands and (b) the component damping effect on the imposed to the nonstructural elements floor spectral demands is highly dependent on the proximity of their natural period to that of the building. On account of the above and a detailed statistical analysis two equations are proposed for estimating the mean and coefficient of variation of the component damping modification factors.
Chatzidaki A., Lyritsakis C., Vamvatsikos D., Aschheim M., Hernández-Montes E. (2019). Seismic assessment of a 4-story RC building designed on an intensity versus a performance basis. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece
Περίληψη | Τρεις μεθοδολογίες σχεδιασμού συγκρίνονται ως προς τα αποτελέσματά τους για ένα τετραώροφο κτήριο από οπλισμένο σκυρόδεμα με περιμετρικά πλαίσια ανάληψης οριζοντίων δυνάμεων. Οι δύο είναι μεθοδολογίες σχεδιασμού βάσει επιτελεστικότητας και βασίζονται στη χρήση των Φασμάτων Συχνότητας Διαρροής για να επιτύχουν με αξιοπιστία αυξημένους στόχους επιτελεστικότητας, λαμβάνοντας πλήρως υπόψη τις αβεβαιότητες και τη σεισμική επικινδυνότητα. Η τρίτη χρησιμοποιεί το Φάσμα Σημείου Διαρροής για να επιτύχει ταχεία σύγκλιση σε μια ικανοποιητική σχεδίαση που είναι συμβατή με τις σύγχρονες κανονιστικές διατάξεις. Και στις τρεις περιπτώσεις δημιουργήθηκαν τα μη γραμμικά προσομοίωματα των κτηρίων και πραγματοποιήθηκε Ικανοτική Δυναμική Ανάλυση για την εκ των υστέρων αποτίμηση της επιτυγχανόμενης σεισμικής επιτελεστικότητας. Τα αποτελέσματα δείχνουν ότι όλες οι παραπάνω μέθοδοι ικανοποιούν τις απαιτήσεις του κανονισμού, δηλαδή στόχους επιτελεστικότητας που σχετίζονται με την Προστασία Ζωής.
Ωστόσο, μόνο οι δύο μέθοδοι σχεδιασμού βάσει επιτελεστικότητας επιτρέπουν την ακριβή επίτευξη στόχων που σχετίζονται π.χ. με την προστασία έναντι κατάρρευσης ή στόχους άλλους από την Προστασία Ζωής, που ορίζονται εκ των προτέρων από το μελετητή και πηγαίνουν πέρα από τις διατάξεις του κανονισμού.
Tsarpalis D., Vamvatsikos D., Vayas I. (2019). Structural analysis of pallet racking systems using equivalent beam-column elements. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Περίληψη | Τα Αυτοματοποιημένα Συστήματα Αποθήκευσης Παλετών (ΑΣΑΠ) είναι σύγχρονα μεταλλικά κτίρια μεγάλων διαστάσεων από διατομές ψυχρής ελάσεως. Έχουν διπλή στατική λειτουργία, στηρίζοντας ταυτόχρονα παλέτες και την στέγαση/κάλυψη του κτιρίου. Αν και χρησιμοποιούνται σε περιοχές υψηλής σεισμικότητας, η πραγματική τους πλαστιμότητα είναι άγνωστη και συνήθως σχεδιάζονται με χαμηλούς συντελεστές συμπεριφοράς της τάξεως του 2.0. Ακριβέστερη ποσοτικοποίηση μπορεί να επιτευχθεί μόνο με αξιόπιστη ανελαστική προσομοίωση, η οποία είναι πρακτικώς αδύνατη, τόσο λόγω υπολογιστικού φόρτου, όσο και λόγω της αδυναμίας επίτευξης σύγκλισης, δεδομένου των εκατοντάδων χιλιάδων μελών. Η μόνη τεχνική που μπορεί να βοηθήσει είναι η χρήση ενός απλούστερου προσομοιώματος το οποίο θα ισορροπεί μεταξύ της ακρίβειας των αποτελεσμάτων και της υπολογιστικής απλότητας. Η λύση που προτείνεται περιλαμβάνει την αντικατάσταση των σύνθετων δοκών και υποστυλωμάτων των ραφιών από στοιχεία δοκού-στύλου τύπου Timoshenko. Αρχικά συγκρίνονται τα αποτελέσματα ελαστικών στατικών αναλύσεων και αναλύσεων ιδιομορφών ενώ στη συνέχεια η μέθοδος επεκτείνεται και στη μη γραμμική περιοχή, όπου το ισοδύναμο μοντέλο παρουσιάζει σημαντική μείωση του χρόνου ανάλυσης και βελτίωση της ευρωστίας.
Vamvatsikos D. (2019). Options in determining behavior factors of building classes for modern design codes. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Περίληψη | Η χρήση του συντελεστή συμπεριφοράς συνεχίζει να αποτελεί τη βάση των σύγχρονων σεισμικών κανονισμών για το σχεδιασμό κτιρίων με ελαστικές μεθόδους. Για την καθεαυτό εκτίμηση του συντελεστή συμπεριφοράς όμως, η τρέχουσα βιβλιογραφία προτείνει μια ευρεία πλειάδα από μεθοδολογίες. Αυτές μπορεί να βασίζονται σε στατικές ή δυναμικές αναλύσεις, χρησιμοποιώντας είτε προσδιοριστικές είτε πιθανοτικές μεθόδους, προσεγγίσεις βάσει έντασης ή βάσει διακινδύνευσης, ενώ άλλοτε ακολουθούν πορεία απευθείας εκτίμησης και άλλοτε επαλήθευσης μιας προεπιλεγμένης τιμής. Ιδιαίτερης σημασίας επίσης είναι η επιλογή μίας ή περισσότερων στάθμεων επιτελεστικότητας βάσει των οποίων κρίνεται η καταλληλότητα του συντελεστή συμπεριφοράς ώστε να ικανοποιούνται οι (άμεσες και έμμεσες) απαιτήσεις ασφάλειας του κανονισμού. Για τη σύνθεση μιας μεθόδου συμβατής με τον Ευρωκώδικα 8, αναλύονται όλες οι διαθέσιμες δυνατότητες και παρουσιάζονται τα πλεονεκτήματα και τα μειονεκτήματά τους, με έμφαση στην αξιόπιστη επίτευξη του επιθυμητού επιπέδου ασφάλειας.
Tsarpalis D., Vamvatsikos D., Vayas I. (2019). Simplified models for the nonlinear analysis of ARSW structures under seismic loading. Proceedings of the COMPDYN2019 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Automated Rack Supported Warehouses (ARSW) are the state of the art in storage technology, as they provide substantial savings in terms of cost, space and energy with respect to traditional solutions. Despite their lightness, ARSWs carry very high live loads, by far higher than their self-weight, in contrast to what happens in typical civil engineering structures. Thus, standard design approaches are not applicable, especially when one considers lateral loading, i.e. seismic and wind loading.
In the frame of the STEELWAR project, the behavior factor (q) as well as the seismic fragility shall be assessed for a number of archetype warehouses. FEM modelling for such structures is a tedious task; they consist of hundreds or thousands steel members and nodes connected to each other through simple and semirigid joints. Modern computers accompanied with efficient computational algorithms can handle linear systems with ease and thus, linear analysis can be performed by including all structural components in the analysis model. Problems arise when one considers nonlinear phenomena i.e. material and geometric nonlinearity. Simulations that take into account all ARSW members and their nonlinear response may lead to prohibitive computational costs, while introducing convergence and numerical stability problems. As a direct remedy, a reduced-order physical model is proposed that enables accurate assessment of nonlinear behavior without compromising convergence performance.
Bilionis D.V., Vamvatsikos D. (2019). Wind performance assessment of telecommunication towers: A case study in Greece. Proceedings of the COMPDYN2019 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Steel lattice towers are widely used by telecommunication companies to install radiowave dish antennas for the expansion of their network. They are tall highly-optimized structures for which severe weather conditions including low temperatures, snow and high winds are the governing loading conditions. Specifically, high winds in combination with accumulated ice on the members of the structure and the dishes are the leading causes of collapse. The focus is on a standardized model of a telecommunication tower used by major telecommunication companies in Greece. The model is designed according to European Standards for areas located at distances lower than 10km from the coastline. The tower is 48 meters tall, having a square cross-section whose dimensions generally reduce with height and it employs channel and angle steel sections. Non-linear dynamic analyses were performed in order to estimate the fragility of the structure to wind and/or icing conditions. Wind loads were simulated via a 3D wind field fully capturing the spatial and temporal variation of wind speed over the entire profile of the tower for different reference values of wind speed. The impact of ice was assessed by considering a range of different uniformly thick layers of ice that increase the weight as well as the cross-section area of all members and dishes. The ultimate goal of this work is to provide the fragility functions for every potential combination of wind and icing conditions that could be observed during the service life of the structure. Thus, by incorporating the corresponding climactic hazard surfaces, the risk of tower collapse is estimated over its entire projected lifetime, offering a useful decision support tool to telecommunication companies regarding the need to replace or upgrade their existing tower network on a caseby-case basis.
Kazantzi A.K., Vamvatsikos D. (2019). Prescriptive approaches in performance-based design? A case-study on base isolation. Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP13, Seoul, South Korea
Abstract | The collapse performance of code-designed base-isolated structures has recently received considerable criticism, having been found to be deficient vis-à-vis conventional buildings in several situations. As a remedy, prescriptive minima with a tenuous probabilistic justification have been recommended in the literature for the bearing deformation capacity. These are independent of structure or site characteristics, yet they are already finding use in design. We put this concept to the test by means of a case study of a seismically isolated steel structure that rests on the roof of two adjacent high-rise reinforced concrete towers. To seismically isolate the steel structure, Friction Pendulum Bearings (FPBs) are used, and their displacement capacity is determined to comply with a performance objective of 1% probability of collapse in 50 years. The case study possesses two salient features that distinguish it from pertinent past investigations. The first is that the isolated steel structure rests on top of two others and consequently it is subjected to narrow-band roof acceleration time histories, shaped by the filtering of the ground motion excitation through the supporting buildings. The second is that the two supporting towers have different modal characteristics, thus displacement demands imposed to the FPBs are mainly affected by their in-phase or out-of-phase movement. Overall, a case-specific true performance-based design is shown to achieve the desired safety while requiring 1.5 times lower displacement capacities for the bearings, when compared to prescriptive “performance-based” approaches.
Spillatura A., Vamvatsikos D., Bazzurro P., Kohrangi M. (2019). Issues in harmonization of seismic performance via risk targeted spectra. Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP13, Seoul, South Korea
Abstract | Current seismic design code provisions are mainly based on checking structural performance at a single seismic intensity associated with a pre-defined return period. For instance, in EN1998, a ground motion with 10% probability of exceedance in 50 years is used for design. This design procedure, with the inclusion of partial safety factors, is assumed to provide sufficient safety margin against earthquakes for newly designed buildings. Nevertheless, it does not specifically determine the expected seismic risk related to any performance level or limit state. Therefore, it may result in non-uniform risk for buildings located in different sites within a region (or country), even for places with identical design intensities. Instead, ASCE 7-10 incorporates Risk Targeted design maps that suggest the application of suitable spectra adjustment factors, in order to ensure a reasonably low uniform collapse risk. Making use of simplified single degree of freedom structures defined in several configurations of period and ductility, our aim is to test the effectiveness of the adjustment factors computed under different assumptions. It is shown that, although matching is not practically possible, harmonization remains a viable target, offering insights for possible future adoption of Risk Targeted Spectra in forthcoming seismic codes.
Aschheim M., Hernandez-Montes E., Vamvatsikos D., (2019). Design of Reinforced Concrete Buildings for Seismic Performance: Practical Deterministic and Probabilistic Approaches Protection of Built Environment Against Earthquakes. CRC Press.
Book Description | The costs of inadequate earthquake engineering are huge, especially for reinforced concrete buildings. This book presents the principles of earthquake-resistant structural engineering, and uses the latest tools and techniques to give practical design guidance to address single or multiple seismic performance levels.
It presents an elegant, simple and theoretically coherent design framework. Required strength is determined on the basis of an estimated yield displacement and desired limits of system ductility and drift demands. A simple deterministic approach is presented along with its elaboration into a probabilistic treatment that allows for design to limit annual probabilities of failure. The design method allows the seismic force resisting system to be designed on the basis of elastic analysis results, while nonlinear analysis is used for performance verification. Detailing requirements of ACI 318 and Eurocode 8 are presented. Students will benefit from the coverage of seismology, structural dynamics, reinforced concrete, and capacity design approaches, which allows the book to be used as a foundation text in earthquake engineering.
Margnelli A., Kohrangi M., Giaralis A., Vamvatsikos D. (2018). Influence of non-stationary frequency content of recorded ground motions to seismic demand of multistorey structures via the wavelet-based alpha (α) index. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece
Abstract | This paper contributes a pioneering numerical study to assess statistically, within the performance based earthquake engineering framework, the effect of the evolutionary frequency content observed in field recorded earthquake induced ground motions (GMs) to peak seismic structural response of yielding multi-degree-of-freedom structures. To this aim, the average rate of change of the mean GM frequency content, termed alpha, α, is used as a proxy to quantify the time-varying attributes of recorded GMs. The α index is invariable to GM scaling and is herein computed by wavelet-transforming of GMs using Morlet wavelets. Further, the concept of spectrally equivalent GMs is used in conjunction with a large database of 1222 far-field GMs to construct two sets of 50 GMs each having significantly different median α values but closely matching mean response spectral shapes, as well as effective duration and mean period distributions. Numerical results obtained from applying incremental dynamics analysis (IDA) to a lumped-mass plasticity model of a benchmark 7-storey code-compliant reinforced concrete frame demonstrate that median peak inter-storey drift ratio demand posed by the GM set with high a values is significantly larger from the GM set with low α values having negligible time-variation of mean frequency content. It is further found that the evolving mean GM frequency content introduces significant discrepancy to the median IDA curves irrespective of the quality of the intensity measure used for GM scaling. These findings suggest that the evolutionary GM frequency content should be accounted for in GM record selection used for seismic performance evaluation of structures. To this aim, the a index can serve as a potent record selection criterion.
Moschen L., Adam C., Vamvatsikos D. (2018). On the practical estimation of the distribution of peak foor acceleration demands. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece
Abstract | The present contribution addresses the prediction of the record-to-record dispersion of peak floor acceleration (PFA) demands on elastic spatial structures. The distribution of PFA demands is approximated by an extended Complete-Quadratic-Combination (CQC) modal combination rule, based on a dispersion pseudo-acceleration response spectrum rather than the common median pseudo-acceleration response spectrum. Therefore, the selected ground motions must comply not only with target mean and but also with target dispersion spectral accelerations. Application on elastic spatial steel benchmark structures shows that the proposed methodology yields cumulative distribution functions of the PFA demand that approximate well the corresponding cumulative distributions derived in computationally expensive response history analyses.
Bakalis K., Vamvatsikos D. (2018). Seismic vulnerability assessment for liquid storage tank farms. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece
Abstract | A seismic vulnerability estimation procedure is developed for liquid storage tank-farms, specifically ensembles of atmospheric tanks that are interconnected to provide enhanced storage capacity for a given liquid product. All pertinent sources of uncertainty are considered together with associated intra-and inter-structure correlations, while particular attention is paid to the effect of uncertainty on damage state threshold values. Appropriate decision variables are defined in view of enabling decision-making for the mitigation of seismic losses at the level of the system, rather than the individual structure, focusing on (a) the leakage of stored product and (b) the loss of storage capacity. A case study of nine tanks, evenly split in three types, is undertaken. Whenever uncertain damage state thresholds are considered, Monte-Carlo simulations reveal a significant potential for loss of containment for average spectral accelerations (AvgSa) of 0.30g. While storage capacity is proportionately impacted, a remarkable 30% of the total farm storage volume can survive an AvgSa of 0.5g, thus leaving considerable room for the drainage and repair of damaged tanks in typical operation scenarios.
Kazantzi, A.K., Vamvatsikos D., Miranda E. (2018). Effect of yielding on the seismic demands of nonstructural elements. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece
Abstract | As proven by several past earthquakes, the seismic losses associated with nonstructural damage in contemporary buildings are likely to exceed those associated with structural damage by several orders of magnitude. Hence, for assessing satisfactorily the overall seismic performance of a building and consequently the associated losses, it is paramount to properly account for the nonstructural damage via estimating the acceleration and deformation demands that are imposed to its nonstructural elements and contents in any one floor level during an earthquake. Furthermore, being able to better understand the behavior of nonstructural components during a seismic event could have a direct impact on the pertinent design methodologies. To address such issues, we assess the validity of the dominant code/design approaches with reference to the evaluation of the component amplification factor, ap, which is essentially a measure of how much the acceleration of a component is amplified compared to the peak floor acceleration. The state-of-practice in the evaluation of ap is to account only for the component flexibility and period, an approach that essentially caps ap to a maximum value of 2.5. Instead, we investigate the extent to which this factor may be further amplified if we consider the vibration characteristics of the building that contains the component under consideration by employing actual recorded floor motions from instrumented buildings in the United States. At the same time, we evaluate the effect of yielding in the component or its anchorage in offering protection against such amplified acceleration demands.
Miranda E., Kazantzi, A.K., Vamvatsikos D. (2018). New approach to the design of acceleration-sensitive non-structural elements in buildings. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece.
Abstract | Nonstructural elements are typically at the end of a long chain of uncertainties making them particularly challenging to design or to estimate their seismic performance. Seismic design of nonstructural elements is typically based on over simplistic equations to estimate equivalent static forces that not only neglect the dynamic properties of the nonstructural element and of the building in which they are mounted on, but they also use large component force reduction factors that have no rational basis. Floor motions are characterized by being narrowband motions that produce extremely large accelerations on nonstructural elements whose frequencies of vibration coincide with those of the building in which they are mounted. For many years now, seismic design of structures relies on the identification of predetermined locations where non-linearities are expected to occur in the event of moderate or severe earthquake ground motions and other components and connections are designed to remain elastic. At present time, there is no equivalent approach in the design of nonstructural elements. The purpose of this paper is to introduce a new approach in which a new type of bracing elements of nonstructural elements are designed and detailed to work as fuses that limit forces acting not only in the nonstructural elements but also in the attachments to the structure and in the attachment(s) to the nonstructural element. It is shown that the proposed approach, which accounts for the narrow-band characteristics of floor motions, not only results in reductions in design forces but can also result in important reductions in deformation demands, especially for components that are tuned to modal frequencies of the building in which they are mounted on.
Kohrangi, M., Bazzurro P., Vamvatsikos D. (2018). Conditional spectrum based record selection for nonlinear dynamic analysis of 3D structural models. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece
Abstract | Nonlinear dynamic analysis is commonly used in seismic risk assessment. Record selection is the tool to connect the ground motion to the structural response through a ground motion intensity measure (IM). Naturally, appropriate record selection techniques as well as a good choice of IM have been two important research topics in the last decade. Recent studies have shown the necessity of record selection that thoroughly represents the seismicity at the site of interest. Similarly, many studies have focused on the best choice of IMs capable of estimating the response of specific buildings with the least scatter. The advances put forward by this body of research are geared mostly to structural analysis of buildings modeled in 2D. Few are the specific record selection approaches and IMs suggested expressly for nonlinear dynamic analysis of 3D structural models. Herein, we explore several proposals for conditional spectrum-based record selection for 3D structural models using different IMs. Especially, we present a vector-based conditional spectrum record selection that conveys information from two orthogonal horizontal components of the ground motion. We further explore the application of the newly presented approaches for 3D analysis of several building examples and consequently provide suggestions for their use in seismic risk assessment.
Miranda E., Kazantzi A.K., Vamvatsikos D. (2018). Towards a new approach to design acceleration-sensitive non-structural components. Proceedings of the 11th National Conference on Earthquake Engineering, Los Angeles, CA
Abstract | Nonstructural components often represent the largest portion of the investment in new commercial buildings, typically accounting for 70 to 85% of the total construction cost. Furthermore, damage to nonstructural components can lead not only to serious injuries and even casualties, but can lead to partial or total temporary loss of use of the building and to large economic losses. Nonstructural components are often subjected to seismic motions that are completely different both in amplitude and in frequency content than ground motions. Floor motions are characterized by being narrowband motions that produce extremely large accelerations on nonstructural elements whose frequencies of vibration coincide with those of one of the modal frequencies of the building in which they are mounted. The purpose of this paper is to propose a new approach in which bracing elements of nonstructural elements are designed and detailed to work as fuses that limit forces acting not only in the nonstructural elements but also those acting on the attachments to the structure and on the attachment(s) to the nonstructural element. It is shown that the proposed approach not only results in reductions in design forces but can also result in important reductions in deformation demands, especially for components that are tuned to modal periods of the building in which they are mounted on.
Kohrangi M., Vamvatsikos D., Bazzurro P. (2018). The role of spectral shape and pulse period for record selection in the near field. Proceedings of the 11th National Conference on Earthquake Engineering, Los Angeles, CA
Abstract | Pulse-like records are well recognized for their potential to impose higher demands on structures when compared to ordinary non-pulsive records. This increased building response to pulsive records is often associated with their particular spectral shape, and specifically the spectral increment around the pulse period. Still, others have argued in favor of the time-domain effect of the pulse itself, without focusing on the shape of the spectrum per se. Such issues become important when selecting records, where current catalogue limitations deny us the capability of perfectly satisfying many objectives at the same time. Herein, we provide a fresh outlook on this subject via the use of spectrally equivalent pulse-like and ordinary records. These allow us to distinguish the effect of pulse period from spectral shape and research the degree to which each needs to be satisfied to achieve a hazard-compatible record set. The comparison shows that there are characteristics of structural response to pulse-like records that cannot be predicted by the spectral shape of the input ground motions. Furthermore, the average spectra acceleration over a period range, AvgSA, is shown to be an adequate proxy for spectral shape, and together with Tp/T1 form an efficient and sufficient IM for response prediction to pulse-like ground motions.
Kohrangi M., Vamvatsikos D., Bazzurro P. (2018). Multi-level conditional spectrum-based record selection for IDA. Proceedings of the 11th National Conference on Earthquake Engineering, Los Angeles, CA
Abstract | Incremental Dynamic Analysis (IDA) is a widespread approach to evaluate the seismic response of structures by means of nonlinear dynamic analysis. It employs a single set of ground motion records and scales them up until dynamic instability is reached.The objective of IDA is to obtain the statistics for different Engineering Demand Parameters (EDPs) that gauge the response of the structure. It is well known, however,that the earthquake scenarios dominating the site hazard differ with the intensity of the ground motion and, therefore, the spectral shape of the expected records should reflect this change. Hence, the response of the structure, in general, would be better estimated in a multiple stripe analysis (MSA) framework by multiple sets of records selected to be hazard consistent to different intensity levels via, for example, the conditional spectrum (CS)method. Despite this issue, IDAis still a standard tool in seismic design and assessment. This study tries to quantify the level of bias that derives from using a single set of randomly selected records in IDA versus a multiple set of CS-based hazard consistent records in a MSA setting. We further explore different alternatives of CS for record selection to implement in IDA including a ‘multi-level’ approach,which combines the seismic properties of multiple intensity levels in a single record set. This proposed approach provides a trade-off between the more accurate but more complex method of MSA versus the conceptually and practically simpler IDA.
Vayas I., Vamvatsikos D., Thanopoulos P. (2017). Innovative systems for seismic resistance: The INNOSEIS project. Proceedings of the EUROSTEEL 2017 Conference, Copenhagen, Denmark
Abstract | Following the international trends, extensive research on seismic resistant structures has been carried out in Europe during the last decade, with the introduction of several systems with innovative steel-based elements, as the result of European and national research projects. However, these systems have not claimed a fair share of the steel construction market, as provisions for their design have not been included in the Eurocodes and only a few designers are confident enough to employ them. The INNOSEIS project, which has received funding from the Research Fund for Coal and Steel (RFCS) with the participation of 11 partners, aims to deal with this shortcoming. In this paper, the valorisation actions for 12 such innovative anti-seismic devices are presented. Information documents for all dissipative systems have been produced and combined in a single volume, translated in several European languages, for the dissemination to all partners of the construction sector such as architects, structural engineers, construction companies, steel producers and all potential decision makers of the construction sector. Criteria are proposed as to determine which of the systems are characterised as devices and are subject to CE marking in accordance with EN 15129, and which may be considered as innovative systems that require a code approval in EN 1998-1. For the latter, pre-normative design recommendations are drafted that will allow them to receive the status of code-approved systems. A reliability-based methodological procedure to define values of behaviour factors (q-factors) for building structures is proposed, which will be in turn applied to determine q-factors for structural systems with the anticipated systems. A number of case studies with application examples of realistic steel buildings, in which the systems are employed, are presented. Dissemination of the project includes seminars and workshops in several European and Mediterranean countries, as well as the development of online, printed and electronic material, which is free for all people involved in the construction sector, in order to achieve the wide application of innovative seismic resistance systems in practical design.
Vamvatsikos D., Castiglioni C., Bakalis K., Calado L., D’ Aniello M., Degee H., Hoffmeister B., Pinkawa M., Proenca J.M., Kanyilmaz A., Morelli F., Stratan A., Vayas I. (2017). A risk-consistent approach to determine behavior factors for innovative steel lateral load resisting systems. Proceedings of the EUROSTEEL 2017 Conference, Copenhagen, Denmark
Abstract | A risk-consistent approach is proposed for the evaluation of behaviour factors that are compatible with Eurocode 8 using nonlinear static and dynamic analysis. The proposed process comprises seven discrete steps, involving hazard assessment and record selection at multiple sites, designing and modelling multiple archetype buildings and assessing their performance vis-à-vis target safety objectives. In all cases, uncertainty is incorporated and propagated to the final results whereby a flexible verification procedure is offered to account for the confidence of the investigator on the data available. The value added goes beyond the current state of art, offering a consistent risk basis for the seismic design of different systems that is compatible with current uniform hazard design spectra and future risk-targeted hazard maps.
Bakalis K., Vamvatsikos D., Pyrza S. (2017). Q-factor verification of a 3-storey concentrically braced frame via the INNOSEIS risk-based approach. Proceedings of the 9th Hellenic National Conference on Steel Structures, Larisa, Greece
Abstract | A case study example is presented to support a methodology that evaluates the design behaviour-factor on a risk-basis, using the code-compatible performance targets for life safety and global collapse. The case study employs a 3-storey concentrically braced frame with a detailed physics-based representation of braces. Nonlinear static analysis is conducted to provide an estimate of overstrength and an approximation of the behaviourfactor. Incremental Dynamic Analysis is subsequently performed to obtain a refined representation of response throughout the desired range of seismic intensity. Besides the widely-adopted first-mode spectral acceleration, state-of-the-art intensity measures such as the so-called average spectral acceleration, are used to illustrate the severity of the ground motions considered. The dynamic analysis results for the considered modes of failure are conveniently summarised into fragility functions, which are further convoluted with the seismic hazard function in order to derive the associated mean annual frequency of exceedance. A comparison among the derived and the allowable mean annual frequencies determines the applicability of the behaviour factor for the structure examined, showing that EN1998-compatible factors may accurately be evaluated.
Kazantzi A.K., Vamvatsikos D. (2017). Vibration control of an industrial composite slab subjected to impact loads and improvement of the overall building seismic performance using toggle-brace dampers. Proceedings of the 9th Hellenic National Conference on Steel Structures, Larisa, Greece
Abstract | This paper presents the preliminary findings of a case study, undertaken for enhancing the vibration performance of an industrial two-way composite slab subjected to impact loads as well as for the seismic retrofitting of the entire building. Struts as well as toggle-bracedamper configurations have been effectively combined to achieve the aforementioned twofold goal. With respect to the vibration control of the slab, provided that the availability of the field measurements was not enough to undertake a full forensic engineering study, the proposed strengthening scheme in both directions was selected so as the resulting system fundamental frequency (i.e. beam and girder combined mode) would lie well above the minimum recommended values. Furthermore, in the girder direction, these struts were aligned in a toggle-brace-damper configuration in order to: (a) Employ shallow trusses, due to operation-related restrictions, while (b) magnifying the vertical slab displacements associated with the impact load and (c) the horizontal deformations imparted by seismic loads to this stiff building so that the dampers experience increased velocities and maximize their effectiveness at both the serviceability and the ultimate limit-state.
Vamvatsikos D. (2017). Performance-based seismic design in real life: The good, the bad and the ugly. Proceedings of the ANIDIS2017 Italian National Conference on Earthquake Engineering, Pistoia, Italy
Trailer | Designing a structure to deliver the desired performance under the uncertainties of hazard, materials and questionable models, is largely the Holy Grail of earthquake engineering. A number of methods have appeared in the literature claiming to offer this coveted prize, yet, in my very own opinion, they may require heavy computations or strict assumptions, sometimes offering a useful but partial solution, perhaps delivering something other than what the user expected, or even failing to deliver altogether. This does not necessarily detract from the usefulness of each method, but it does certainly mean that some differentiation among approaches should be maintained, despite all of them being bundled underneath the moniker of “performance-based”. Therefore, due to my heavy exposure to spaggeti westerns from a very young and tender age, my eternal fascination with the work of Sergio Leone and Ennio Morricone, and my desire to pay tribute to the shining geniuses that defined my childhood cosplay days, let me introduce to you what I consider to be il buono, il brutto e il cattivo of performance-based seismic design approaches. And like any good film, I am afraid you will have to read this paper to its conclusion to figure out which is which. I hope you enjoy it.
Vamvatsikos D., Bakalis K., Vayas I., Castiglioni C., Kanyilmaz A., Morelli F., Stratan A., D’ Aniello M., Calado L., Proenca J.M., Degee H., Hoffmeister B., Pinkawa M. (2017). The INNOSEIS approach on determining EN1998-compatible behavior factors for introducing new steel lateral load resisting systems. Proceedings of the 9th Hellenic National Conference on Steel Structures, Larisa, Greece
Abstract | A risk-consistent approach is proposed for the evaluation of behaviour factors that are compatible with Eurocode 8 using nonlinear static and dynamic analysis. The proposed process comprises seven discrete steps, involving hazard assessment and record selection at multiple sites, designing and modelling multiple archetype buildings and assessing their performance vis-à-vis target safety objectives. In all cases, uncertainty is incorporated and propagated to the final results whereby a flexible verification procedure is offered to account for the confidence of the investigator on the data available. The value added goes beyond the current state of art, offering a consistent risk basis for the seismic design of different systems that is compatible with current uniform hazard design spectra and future risk-targeted hazard maps.
Vamvatsikos D., Bakalis K., Pyrza S. (2017). Q-factor verification of a 6-storey concentrically braced frame via the INNOSEIS risk-based approach. Proceedings of the COMPDYN2017 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Abstract | A case study example is presented to support a methodology that evaluates the design behaviour-factor on a risk-basis, using the code-compatible performance targets for life safety and global collapse. The case study employs a 6-storey concentrically braced frame with a detailed physics-based representation of braces. Nonlinear static analysis is conducted to provide an estimate of overstrength and an approximation of the behaviour-factor. Incremental Dynamic Analysis is subsequently performed to obtain a refined representation of response throughout the desired range of seismic intensity. Besides the widely-adopted first-mode spectral acceleration, state-of-the-art intensity measures such as the so-called average spectral acceleration, are used to illustrate the severity of the ground motions considered. The dynamic analysis results for the considered modes of failure are conveniently summarised into fragility functions, which are further convoluted with the seismic hazard function in order to derive the associated mean annual frequency of exceedance. A comparison among the derived and the allowable mean annual frequencies determines the applicability of the behaviour factor for the structure examined, showing that EN1998-compatible factors may accurately be evaluated.
Moschen L., Adam C., Vamvatsikos D. (2017). Simplified prediction of peak floor accelerations in inelastic wall structures. Proceedings of the COMPDYN2017 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Abstract | In this paper a robust method for simplified prediction of peak floor acceleration (PFA) demands in inelastic structural walls is established. In structural walls the plastic mechanism is usually confined to the domain straight above the foundation. It is, thus, reasonable to assume that in wall structures only the response contribution related to the fundamental mode is significantly affected by inelastic deformations. Based on this assumption, a readily developed complete-quadratic-combination (CQC) modal superposition rule for elastic median PFA demand prediction is specialized to inelastic structural walls. In this approach, only the first mode contribution on the PFA demand is affected by inelastic deformations, related to the lateral strength reduction factor identified from the outcomes of a first mode pushover analysis. Since the response contribution of the higher modes is assumed to be elastic, for these modes the relations derived for unlimited elastic structural behavior enter the specialized response spectrum method. Application on a 12-story shear wall shows the accuracy of the predicted median PFA demands derived by the proposed procedure.
Papadopoulos A., Vamvatsikos D., Kazantzi A. (2017). Development of FEMA P-58 compatible story loss functions: steel office buildings in high seismicity regions. Proceedings of the COMPDYN2017 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Abstract | Since their release in 2012, the FEMA P-58 guidelines for seismic performance assessment of buildings have been regarded as the state-of-the-art paradigm for buildingspecific risk assessment and loss estimation. The latter is carried out through a rigorous component-by-component procedure that requires a complete component inventory, along with fragility and repair cost information. A fully compatible story-based approach is investigated herein as a simplified alternative that can potentially reduce the required input data with only a minor drop in accuracy. As an example, a set of story loss functions relating story repair cost with story-level engineering demand parameters are derived for standard inventory makeups of low/midrise steel office buildings. Preliminary results for a 4-story steel building show a promising balance between accuracy and simplicity.
Kohrangi M., Vamvatsikos D., Bazzurro P. (2017). A record selection methodology for vulnerability functions consistent with regional seismic hazard for classes of buildings. Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile
Abstract | Earthquake loss estimation studies for portfolios of buildings are performed routinely for a variety of applications, ranging from risk evaluation and mitigation to post-event emergency assessment. Essential ingredients of such analyses are the vulnerability functions appropriate for different building classes representing the regional inventory. When abundant empirical data are absent, which is often the case, these vulnerability functions are obtained numerically via dynamic analyses informed by sets of ground motion records, usually selected without specific criteria. The implicit assumption is that the vulnerability function of two identical buildings located at different sites in the region would be identical. However, the structural response estimates even of identical buildings are sensitive to the characteristics of the earthquakes that control the hazard at each site in the region. Hence, strictly speaking, vulnerability functions should be both structure- and site-specific. This consideration is always neglected in portfolio loss assessment where identical vulnerability functions are used for buildings in the same class regardless of where they are located. Developing a set of different, site-specific vulnerability functions for like buildings in the same class is, however, impractical. To address this complexity, a record selection scheme is proposed that employs the conditional spectrum (CS) method but uses as a conditioning Intensity Measure (IM) the spectral acceleration (geometrically) averaged over a period range. This conditioning IM is more in sync with the response of a class of buildings rather than with the response of any single one. In addition, this method modifies the standard CS approach by incorporating within a single target CS the variation of the target spectra at multiple sites. An example of this method illustrates the development of a vulnerability function that is consistent with the regional hazard for a class of tall buildings.
Silva V., Casotto C., Vamvatsikos D., Rao A., Villar M. (2017). Presentation of the Risk Modeller’s Toolkit, the open-source software for vulnerability assessment of the Global Earthquake Model. Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile
Abstract | In the last decade several software packages for seismic hazard and risk assessment have been released, thus making it easier for hazard and risk modellers to run complex analyses without the need to code their own implementations of the scientific algorithms. However, the development of the input models for such analyses is often an equally challenging task, and the availability of tools to support experts in this stage is still very limited. Three main input models are required for earthquake risk analysis: a seismic hazard model, an exposure dataset, and a set of physical fragility or vulnerability functions. The latter component describes the probability of damage or loss conditional on different levels of ground shaking, and assumes a special role since an improvement in the seismic performance of the building stock can directly reduce the associated seismic risk.
This study presents the Risk Modeller’s Toolkit (RMTK), a suite of tools to support risk experts in the derivation and verification of fragility or vulnerability models. The development of the RMTK followed an open-source and transparent approach. Thus, its code can found in a public repository (https://github.com/GEMScienceTools/rmtk), and all of the implemented methodologies have been fully documented in the RMTK manual. The current version of the RMTK comprises four modules: 1) generation of structural models, represented by pushover curves or single-degree-of-freedom (SDOF) oscillators, to represent the variability in the capacity of the building stock; 2) conversion of results from multidegree-of-freedom models into the equivalent SDOF systems; 3) derivation of fragility functions by combining capacity models with sets of ground motion records or response spectra; 4) conversion of fragility models into vulnerability functions through the employment of damage-to-loss models. These modules contain some of the most well-known methodologies in seismic vulnerability assessment, which allow the propagation of a wide spectrum of aleatory uncertainties, such as the variability in the structural capacity of the building stock; uncertainty in the definition of the damage criterion; or the record-to-record variability. The employment of distinct fragility methodologies will inevitably lead to different results (epistemic variability), which may have a significant impact on the associated seismic risk estimates.
The RMTK is currently being employed in the development of fragility functions for the most common building classes in South America, eastern Sub-Saharan Africa, Canada, Costa Rica and Nepal. The outcomes of the RMTK are fully compatible with the OpenQuake-engine, the open-source software for seismic hazard and risk analysis of the Global Earthquake Model initiative.
Iervolino I., Baltzopoulos G., Vamvatsikos D., Baraschino R. (2016). SPO2FRAG v1.0: Software for pushover-based derivation of seismic fragility curves. Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete, Greece
Abstract | This article presents SPO2FRAG V1.0, the first (beta) version of the Static PushOver to FRAGility software. The SPO2FRAG software is an interactive and user-friendly tool that can be used for approximate, computer-aided calculation of building seismic fragility functions, based on static pushover analysis. It is coded in MATLAB® environment and is currently under development at the Department of Structures for Engineering and Architecture of the University of Naples Federico II. At the core of the SPO2FRAG tool lies the SPO2IDA algorithm, which permits analytical predictions for incremental dynamic analysis summary fractiles at the single-degree-of-freedom system level. By effectively interfacing SPO2IDA with a series of operations, intended to link the results of static pushover analysis with the variability that typically characterizes non-linear dynamic structural response, SPO2FRAG provides an expedient solution to the computationally demanding task of analytically evaluating seismic building fragility, which would otherwise require a large number of non-linear dynamic analyses.
Mouka T., Vamvatsikos D. (2016). Fatigue assessment of knee joints subject to total arthroplasty. Proceedings of the 11th HSTAM International Congress on Mechanics, Athens, Greece
Abstract | Total knee arthroplasty has become quite widespread, especially among patients of 70+ years. Unfortunately, failure of this surgery is not so uncommon. As a result, a revision surgery is sometimes needed, resulting in a great ordeal for patients. One of the major causes of this failure is the aseptic loosening of either the tibial or the femoral component, with that of the tibial component being more common. Our goal is to evaluate the performance of metallic knee implants used in total knee arthroplasty. More specifically, the aim is to identify critical areas of failure and the prevalent failure mechanisms due to fatigue. A probabilistic analysis will follow, in order to calculate the probability of failure as a function of walking cycles and loads on the knee joint.In the end, it will become possible to predict the likelihood of implant failure in the course of a patient’s lifetime. It will also be possible to determine the probability of failure depending on the patient’s habits and, as a result, how much the patient is allowed to stress the joint after the surgery depending on his/her weight. Similarly, the calculations will offer decision support on how much, if any, weight he/she should lose in order to lessen the probability of failure to an acceptable level. Ultimately, rehabilitation becomes more patient-specific and, therefore, likely much easier and less time-consuming.
Pyrza S., Vamvatsikos D. (2016). Collapse margin and behavior factor evaluation for Eurocode-designed concentric braced frames. Proceedings of the 11th HSTAM International Congress on Mechanics, Athens, Greece
Abstract | Modern structures are designed to trade strength for damage through the stable accumulation of plastic deformations in predefined “energy-dissipating” sacrificial elements. Logistically, this is taken into account by the use of the ubiquitous behavior (or strength reduction) factors that incorporate the effects of both ductility and overstrength to allow a simple and essentially elastic process of design. Despite the importance of such factors, their estimation is not subject to any rigorous rules, leaving large margins of uncertainty, especially for newly introduced lateral-loading systems where experience is lacking. In the US, the estimation of behavior factors has been largely standardized by the introduction of the FEMA P695 guidelines. On the other hand, Eurocode 8 has not been paired with a similar compatible document to allow the seamless introduction of new systems. As an attempt to investigate the potential for introducing such a set of guidelines, an investigation of concentrically-braced frames is undertaken. The aim is to evaluate the currently offered margin of safety against collapse and discuss the possible basis one could use to found a reliable estimation for behavior factors, while accounting for issues of spectral shape, record selection and intensity measure sufficiency.
Bakalis K., Vamvatsikos D. (2015). Direct performance-based seismic design for liquid storage tanks. Proceedings of the SECED 2015 Conference, Cambridge, UK
Abstract | A performance-based design methodology has been developed for liquid storage tanks based on a surrogate, yet robust beam-element model. Following the identification of failure modes through Incremental Dynamic Analysis, appropriate performance levels are defined based on an existing seismic assessment methodology. The concept of Response Frequency Spectra (RFS) is proposed in view of offering a unique representation of the entire solution space for structural performance. RFS find an excellent application for the case of liquid storage tanks by adopting design parameters such as the tank wall thickness and the anchorage ratio. Although the wall thickness changes the strength capacity for the well-known Elephant’s Foot Buckling failure mode, the corresponding probabilities of exceedance are not significantly modified. On the contrary, anchorage seems to be very important as the associated probabilities may be reduced even by 50% in some cases.
Bakalis K., Fragiadakis M., Vamvatsikos D. (2015). Seismic fragility assessment of steel liquid storage tanks. Proceedings of the ASME 2015 Pressure Vessels & Piping Conference PVP2015, Boston, MA
Abstract | A seismic fragility assessment procedure is developed for atmospheric steel liquid storage tanks. Appropriate system and component-level damage states are defined by identifying the failure modes that may occur during a strong ground motion. Special attention is paid to the elephant’s foot buckling failure mode, where the estimation of the associated capacity and demand requires thorough consideration within a probabilistic framework. A novel damage state is introduced to existing procedures with respect to the uncontrollable loss of containment scenario. Fragility curves are estimated by introducing both aleatory and epistemic sources of uncertainty, thus providing a comprehensive methodology for the seismic risk assessment of liquid storage tanks. The importance of dynamic buckling is acknowledged and the issue of non-sequential damage states is finally revealed.
Bakalis K., Fragiadakis M., Vamvatsikos D. (2015). Surrogate modelling of liquid storage tanks for seismic performance design and assessment. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | The finite element method (FEM) is often employed to create detailed models for the seismic assessment and design of liquid storage tanks. This comprehensive approach offers accuracy, which is counter-balanced however by its computational inefficiency, especially for the case of large-scale engineering problems. Regardless of the continuous evolution of computer technology, surrogate models are necessary when such problems of engineering practice are encountered. This study, attempts to develop an appropriate surrogate modelling approach, tailored for the design and seismic risk assessment of liquid storage tanks. A formulation that disregards fluid-structure-interaction is employed in view of providing a reasonable compromise between modelling complexity and error. At the same time, a simplified methodology based on nonlinear static procedures is proposed for the assessment of atmospheric tanks. The comparison with Incremental Dynamic Analysis reveals a reasonable, yet conservative in some cases, match for the damage states considered, thus offering an alternative methodology that may easily be incorporated within code-based provisions.
Baltzopoulos G., Vamvatsikos D., Iervolino I. (2015). Near-source pulse-like seismic demand for multi-linear backbone oscillators. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single-degree-of-freedom (SDOF) oscillator, are well- established tools in the performance based earthquake engineering framework and have gradually found their way into modern codes for seismic design and assessment. Initially, such procedures made recourse to inelastic spectra derived for simple elastic-plastic or bilinear oscillators, but the request for demand estimates, which delve deeper into the inelastic range, shifted the trend towards investigating the seismic demand of oscillators with more complex backbone curves.
Meanwhile, the engineering relevance of near-source (NS) pulse-like ground motions has been receiving increased attention, since it has been recognized that such ground motions can induce a distinctive type of inelastic demand. Pulse-like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double-sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology being proposed for incorporating this NS effect in the implementation of nonlinear static procedures.
Both of the aforementioned lines of earthquake engineering research motivate the present study, which investigates the ductility demands imposed by pulse-like NS ground motions on SDOF oscillators who feature pinching hysteretic behavior with trilinear backbone curves. This investigation uses incremental dynamic analysis (IDA) considering a suite of one hundred and thirty pulse-like-identified ground motions. Median, as well as 16% and 84% fractile, IDA curves are calculated, on which an analytical model is fitted. Least-squares estimates are obtained for the model parameters, which importantly include pulse period Tp. The resulting equations effectively constitute an R-μ-T/Tp relation for pulse-like NS motions. A potential application of this result is briefly demonstrated in an illustrative example of NS seismic demand estimation.
Bilionis D.V., Vamvatsikos D. (2015). Probabilistic fatigue analysis of offshore wind turbines. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Wind Turbines constitute a sustainable and effective solution for the production of energy using wind power. Offshore wind turbines especially are becoming of special interest. However, their design poses great challenges, since an offshore structure is subject to combined wind and wave dynamic loading that is characteristic of the site of installation. The purpose of this paper is to provide a case study of fatigue life assessment for the cross-section at mudline (foundation) of a standard offshore wind turbine with a monopile design, under a probabilistic framework and assuming the thickness of the examined cross-section as the design variable. Two potential sites of construction in the Aegean Sea of Greece were examined. A probabilistic approach was employed in order to determine the fatigue life based on anemological data at each of the two sites of interest. At its basis is an extensive Monte Carlo simulation of wind (velocity) and wave (height, period) characteristics. The results show the dependence of fatigue life on the local wind and wave conditions, the cross-section geometry (i.e. the thickness of the foundation’s pile) and the welded connection detail. All in all, the more benign conditions in the Aegean allow simpler connection details and smaller thickness of foundation pile’s cross-section to still have acceptable performance.
Bilionis D.V., Vamvatsikos D. (2015). A probabilistic approach for fatigue damage analysis of an offshore wind turbine. Proceedings of the 8th GRACM International Congress on Computational Mechanics, Volos, Greece
Abstract | Wind Turbines constitute a sustainable and effective solution for the production of energy using wind power. Offshore wind turbines especially are becoming of special interest. However, their design poses great challenges, since an offshore structure is subject to combined wind and wave dynamic loading that is characteristic of the site of installation. The purpose of this paper is to provide a case study of fatigue life assessment for the cross-section at mudline (foundation) of a standard offshore wind turbine with a monopile design. Two potential sites of construction in the Aegean Sea of Greece were examined. A probabilistic approach was employed in order to determine the fatigue life based on anemological data at each of the two sites of interest. At its basis is an extensive Monte Carlo simulation of wind (velocity) and wave (height, period) characteristics. The results show the dependence of fatigue life on the local wind and wave conditions, the crosssection size (e.g. diameter and thickness of the foundation’s pile) and the welded connection detail. All in all, the more benign conditions in the Aegean allow simpler connection details and smaller in size cross-section of foundation pile’s cross-section to still have acceptable performance.
Bilionis D.V., Vamvatsikos D. (2015). Probabilistic fatigue life assessment of an offshore wind turbine in Greece. Proceedings of the 25th ISOPE International Ocean and Polar Engineering Conference, Kona, USA
Abstract | Wind Turbines constitute a sustainable and effective solution for the production of energy using wind power. Offshore wind turbines especially are becoming of special interest. The purpose of this paper is to provide a case study of fatigue life assessment for specific crosssections of a standard offshore wind turbine with a monopile design, under a probabilistic framework. Two potential sites of construction in the Aegean Sea of Greece were examined. The results show the dependence of fatigue life on the local wind and wave conditions, the cross-section geometry and the welded connection detailing. All in all, the more benign conditions in the Aegean allow simpler connection details to still have acceptable performance.
Bilionis D.V., Vamvatsikos D. (2015). Fatigue analysis of an offshore wind turbine in Mediterranean Sea under a probabilistic framework. Proceedings of the 6th MARINE International Conference on Computational Methods in Marine Engineering, Rome, Italy
Abstract | Wind Turbines constitute a sustainable and effective solution for the production of energy using wind power. Offshore wind turbines especially are becoming of special interest. However, their design poses great challenges, since an offshore structure is subject to combined wind and wave dynamic loading that is characteristic of the site of installation. The purpose of this paper is to provide a case study of fatigue life assessment for the cross-section at mudline (foundation) of a standard offshore wind turbine with a monopile design, under a probabilistic framework and assuming the diameter and thickness of the examined crosssection as the design variables. Two potential sites of construction in the Aegean Sea of Greece (part of Mediterranean Sea) were examined. A probabilistic approach was employed in order to determine the fatigue life based on anemological data at each of the two sites of interest. At its basis is an extensive Monte Carlo simulation of wind (velocity) and wave (height, period) characteristics. The results show the dependence of fatigue life on the local wind and wave conditions, the cross-section size (e.g. diameter and thickness of the foundation’s pile) and the welded connection detail. All in all, the more benign conditions in the Aegean allow simpler connection details and smaller in size cross-section of foundation pile’s cross-section to still have acceptable performance.
Giannopoulos D.G., Vamvatsikos D. (2015). Influence of rotated ground motion components on the response distribution of inelastic oscillators. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Recent research has shown that structures may experience quite different response when the components of any given ground motion record are rotated in the horizontal plane. On the other hand, significant differences are also associated with using different ground motion records. This paper examines whether it is preferable to use a small set of records, each rotated to multiple incidence angles, or a larger set with fewer (or no) rotations, in the case we wish to perform a fixed number of nonlinear dynamic analyses and we have little site information. To this purpose we collected a relatively large, non-pulsive set of records and applied it to an elastoplastic single-degree-of-freedom (SDOF) system. Finally, bootstrapping was performed to investigate the effect of the number of rotation angles studied versus the number of records on the statistics of response. The results indicate that, in all cases, and especially when a small number of nonlinear analyses is allocated, the effect of record-torecord variability clearly outweighs the incidence angle influence. Using a small set of records can lead to unreliable results by both inaccurate estimation of the central value and severe underestimation of the dispersion.
Karavasilis T.L., Dimopoulos A.I., Tzimas A.S., Kamaris G.S., Vamvatsikos D. (2015). Estimation of economic losses in seismic-resistant post-tensioned steel frames with viscous dampers. Proceedings of the 8th International Conference on Advances in Steel Structures, Lisbon, Portugal
Abstract | This paper evaluates the potential of self-centering moment-resisting frames (SCMRFs) with viscous dampers to reduce the economic losses in steel buildings due to strong earthquakes. The evaluation is based on the comparison of different designs of a prototype steel building using as lateral-load resisting system: 1) conventional steel moment resisting frames (MRFs); 2) MRFs with viscous dampers; 3) SC-MRFs; and 4) SC-MRFs with viscous dampers. The economic losses of these four design cases are estimated by developing vulnerability functions according to the ATC-58 methodology. The influence of residual storey drifts on economic losses is examined, by accounting for the possibility of having to demolish a building as a result of excessive residual storey drifts. Results highlight the importance of considering residual story drifts as a demand parameter to economic loss estimation; and show that the use of viscous dampers significantly improves the building’s performance for both SC-MRF and MRF, resulting in lower repair cost.
Kazantzi A.K., Vamvatsikos D. (2015). A next generation scalar intensity measure for analytical vulnerability studies. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | To assess the seismic performance of a structural system within an analytical context, we need, among others, to specify a ground motion Intensity Measure (IM). The wary IM selection is undoubtedly an important step towards the successful implementation of a risk assessment, since insufficient and/or inefficient IMs can induce unwanted bias and variance in the vulnerability estimates. Supplementary issues related to practicality, necessitate the use of IMs for which ground motion prediction relationships exist, such as the elastic response spectral values (i.e. acceleration, velocity and displacement). Several past studies suggested as an improvement the use of IMs defined as the geometric mean of spectral acceleration values computed over a period range. The latter range may span between periods that are below, at or above the fundamental one. Some of these choices were proven to significantly improve both efficiency and sufficiency of the IM compared to more commonly used counterparts.
This study investigates the efficiency and sufficiency of a newly developed scalar IM that combines the geometric mean IM concept with the significant duration of the ground motions. Improving the geometric mean IMs via including the significant duration of the ground motions, was driven by recent findings suggesting there is a strong tie between the collapse capacity of a structure and the ground motion duration. Hence, the performance of the proposed next generation IM is addressed in detail by means of comparisons and statistical significance tests. The testing is performed at specific levels of local engineering demand parameters that are closely related to losses, using a testbed capacity-designed steel moment-resisting frame. It was demonstrated that ground motion duration is closely related to the collapse capacity whereas its effect at lower demand levels is insignificant. Hence, the proposed IM may be employed to improve the estimates in collapse assessment studies. Nevertheless, at least for steel moment-resisting frame buildings that exhibit moderate cyclic degradation rates and sustain most losses prior to the global collapse state, the significant duration is anticipated to only minimally affect the evaluated vulnerability and consequently may be disregarded.
Kazantzi A.K., Vamvatsikos D., Porter K. (2015). Analytical seismic vulnerability assessment for a class of modern low-rise steel MRFs. Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, Vancouver, Canada
Abstract | A set of guidelines was developed for the Global Earthquake Model (GEM), aiming to offer a practical, yet sufficiently accurate, analytical method for assessing the relationship between the ground shaking and the repair cost for a building class. The present work illustrates the methodology for a class of modern low-rise steel moment-resisting frames (SMRFs). The structural analysis is performed using Incremental Dynamic Analysis (IDA). The selection of a single Intensity Measure (IM) to parameterize IDA results and, eventually, vulnerability curves is being tackled through an extended IM comparison study across the entire structural response range considering both interstory drifts and peak floor accelerations. It is demonstrated that scalar IMs, defined as the geometric mean of spectral accelerations values Sagm(Ti) estimated at several periods Ti can have an overall satisfactory performance. Once the uncertain structural response is determined, the methodology proceeds to the vulnerability estimation and consequently to loss assessment that is built upon a simplified componentbased FEMA P-58 style methodology. The end product of this study is a high-quality set of vulnerability curves whose weighted moments are taken as the uncertain vulnerability function of the investigated building class.
Melissianos V.E., Vamvatsikos D., Gantes C.J. (2015). Probabilistic assessment of pipeline – fault crossing. Proceedings of the COMPDYN2015 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece
Abstract | Buried steel pipelines transporting oil and oil products play a vital role in the energy supply chain. Pipelines extend to long distances and thus intercepting tectonic faults, when a seismic area is crossed, is often inevitable and may heavily threat the pipeline integrity. Earthquakes and the associated fault displacements are naturally random events and therefore the imposed large ground displacements on the pipeline have to be considered through a probabilistic perspective. In the present study, a comprehensive seismic risk analysis of buried pipeline – fault crossing is presented, consisting of two steps. The first step is the probabilistic assessment of the fault displacement accounting also for the pertinent uncertainties. The second step is the pipeline structural analysis. The transition from the seismological data to the structural analysis is realized through the fault displacement components as the selected vector intensity measure. The outcome of the proposed methodology is the strain hazard curves for both tensile and compressive longitudinal strains. The resulting strain capacities are compared to strain demands from structural codes in order to assess the potential of pipeline failure due to local buckling or tensile fracture. Furthermore, uncertainty and disaggregation results from the fault displacement hazard analysis are presented for the selection of the appropriate deterministic design scenario and the evaluation of the fault displacement hazard parameters. Lastly, the proposed process is a reliable estimation tool for seismic risk assessment of pipeline – fault crossing and a decision making tool for route selection and application of preventive measures against the consequences of faulting on pipelines.
Melissianos V.E., Vamvatsikos D., Gantes C.J. (2015). Probabilistic assessment of innovative mitigating measures for buried steel pipeline – fault crossing. Proceedings of the ASME 2015 Pressure Vessels & Piping Conference PVP2015, Boston, MA
Abstract | A methodology is presented on assessing the effectiveness of flexible joints in mitigating the consequences of faulting on buried steel pipelines through a comprehensive analysis that incorporates the uncertainty of fault displacement magnitude and the response of the pipeline itself. The proposed methodology is a two-step process. In the first step the probabilistic nature of the fault displacement magnitude is evaluated by applying the Probabilistic Fault Displacement Hazard Analysis, considering also all pertinent uncertainties. The second step is the “transition” from seismological data to the pipeline structural response through the fault displacement components as the adopted vector intensity measure. To mitigate the consequences of faulting on pipelines, flexible joints between pipeline parts are proposed as innovative measure for reducing the deformation of pipeline walls. Thus, the mechanical behavior of continuous pipelines and pipelines with flexible joints is numerically assessed and strains are extracted in order to develop the corresponding strain hazard curves. The latter are a useful engineering tool for pipeline – fault crossing risk assessment and for the effectiveness evaluation of flexible joints as innovative mitigating measures against the consequences of faulting on pipelines.
Vamvatsikos D., Katsanos E.I., Aschheim M.A. (2015). A case study in performance-based design using yield frequency spectra. Proceedings of the SECED 2015 Conference, Cambridge, UK
Abstract | An analytical formulation is offered to allow performance-based seismic design to be achieved following a direct code-compatible procedure. The approach builds upon the use of the yield displacement as a robust system characteristic. A new format for displaying seismic demands known as Yield Frequency Spectra is introduced to quantitatively link performance objectives with the base shear seismic coefficient for a fixed value of yield displacement. Analytical expressions allow estimating the design base shear strength to satisfy any number of performance requirements, foregoing the need for a behaviour factor. The effect of uncertainties is naturally introduced to inject the proper conservatism for, e.g., the natural randomness in the ground motion or lack of knowledge in modelling and analysis. Finally, an 8-story reinforced concrete frame is designed, showing that EN1998 may not achieve the stated performance targets, while the proposed approach can match them with a single iteration.
Vamvatsikos D. (2015). A view of seismic robustness based on uncertainty. Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, Vancouver, Canada
Abstract | A simplified view of robustness and redundancy is presented for the seismic assessment and design of structures. It is argued that the topological simplicity of the seismic load, i.e., its highly correlated nature of application for practically every component in all but the ultra-long structures, means that simpler formulations can be devised compared to blast, wave or wind hazards. In that sense, robustness may be considered to express the influence of structural uncertainties on the seismic performance of the structure, in essence showing the available margin of safety subject to material variability. Quantitatively, a pertinent robustness/redundancy index is defined as the ratio of two different estimates of the mean annual frequency (MAF) of exceeding a limit-state of interest, such as global collapse: On the denominator lies the MAF estimate that incorporates all sources of variability while on the nominator is the estimate that neglects structural uncertainties. It is shown that a simple closed form solution is available that directly relates robustness to the dispersion of response due to model parameter uncertainty. As an example, a steel frame where only beams are allowed to yield is shown to be more robust compared to another version where columns become the sacrificial element.
Voyagaki E., Vamvatsikos D. (2015). Probabilistic assessment of rocking response for simply-supported rigid blocks. Proceedings of the SECED 2015 Conference, Cambridge, UK
Abstract | A probabilistic assessment of the rocking and overturning response of a simplysupported rigid block on a horizontal plane is reported. A two-dimensional rectangular block resting on a rough, horizontal, tensionless and cohesionless rigid base at ground surface is considered, subjected to far field horizontal earthquake excitations. The roughness of the interface is assumed to be sufficiently large to prevent sliding, while the flexibility of the block is neglected. Rocking response curves are calculated for increasing ground motion intensity (or, equivalently, decreasing uplift strength) via Incremental Dynamic Analysis (IDA), and results are summarised in the form of 16%, 50% and 84% fractile IDA curves. By employing non-linear regression analysis, simple expressions are developed for each fractile of peak response to offer a complete probabilistic characterisation of rocking behaviour. Generalised overturning criteria are proposed covering a wide set of excitations and block parameters.
Bakalis K., Vamvatsikos D., Fragiadakis M. (2014). Surrogate modelling and sensitivity analysis of steel liquid storage tanks. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Abstract | Large-capacity atmospheric tanks are widely used to store liquids, such as oil or liquefied natural gas. The seismic risk of such industrial facilities is considerably higher compared to ordinary structures, since even some minor damage induced by a ground motion may have uncontrollable consequences, not only on the tank but also on the environment. Recent earthquakes have shown that heavy damage on tanks may lead to temporary loss of function, usually followed by leakage and/or fire. Therefore, a Performance-Based Earthquake Engineering (PBEE) framework should be employed for the seismic design and performance assessment of such critical infrastructure. Current design codes and guidelines have not fully adopted the performance-based concepts, while their application to industrial facilities is still under research. The proposed PBEE framework consists of a series of nonlinear response history analyses based on a simplified modelling of the tank. Our aim is to improve upon the existing body of work by offering a surrogate model that can be implemented with minimum effort for both anchored and unanchored tanks, for application within a PBEE framework using either static or dynamic analysis methods. In that sense, a robust sensitivity analysis is presented to acknowledge the uncertainties involved in the model presented.
Papageorgiou A., Fragiadakis M., Vamvatsikos D. (2014). Life cycle cost estimation for steel structures. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Summary | The growth of the construction industry led to the publication of guidelines and codes that govern the analysis and the design of structures ensuring the safety of users against various types of actions. Nevertheless, issues concerning the actual cost of each structure, including the occasional cost for repairing seismically induced damage have not been fully integrated in the analysis and design procedure. Moreover, given the need to decrease the energy consumption and the carbon footprint of human activities, it is necessary to examine structural cost in life cycle terms. This implies that the cost estimation should include the initial construction cost, the expected repair cost due to earthquake damage, the energy consumption cost and also the decommissioning cost. The present work aims at investigating the life cycle cost for multi-storey steel structures. The results of non-linear time history analyses are utilized in order to calculate the earthquake damage repair cost as per FEMA P-58, and the estimated cost is combined with the annual energy consumption cost calculated according to the ANSI/ASHRAE 140 standard.
Kazantzi A., Vamvatsikos D., Porter K. (2014). Analytical seismic vulnerability assessment of lowrise steel MRFs. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Abstract | The Global Earthquake Model (GEM; http://www.globalquakemodel.org/) is a grand effort to proffer a comprehensive open source tool for large scale loss assessment studies. For this to be accomplished, an analytical seismic vulnerability assessment methodology needs to be developed that links ground shaking with repair cost for a building class. The test bed for the present study is a set of low/mid-rise steel moment-resisting frames (SMRFs) designed for high seismicity US regions and selected appropriately so as to represent all important aspects within their class. The structural analysis was performed using Incremental Dynamic Analysis (IDA). On that premise, the selection of a single Intensity Measure (IM) to parameterize IDA results and, eventually, vulnerability curves needs to be tackled. It was demonstrated that scalar IMs can have an overall satisfactory performance. Once the uncertain structural response is defined in terms of interstory drifts and floor accelerations, across a wide range of intensities, the methodology proceeds to the vulnerability estimation and consequently to loss assessment. The end product of this study is a high-quality set of vulnerability curves whose weighted moments are taken as the uncertain vulnerability function of the investigated building class.
Dimopoulos A.I., Tzimas A.S., Vamvatsikos D., Karavasilis T.L. (2014). Comparison of seismic losses in steel builidngs using conventional or self-centering moment resisting frames. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Abstract | Steel self-centering moment-resisting frames (SC-MRFs) are a class of resilient structural systems that avoid damage in beams and eliminate residual drifts under the design basis earthquake. In this paper, a building is designed using SC-MRFs or conventional steel moment-resisting frames (MRFs) and the monetary losses of both cases are compared with the aid of the FEMA-P58 methodology. The latter is a performance-based earthquake engineering methodology based on explicit determination of performance (e.g. monetary losses) in a probabilistic manner, where uncertainties in earthquake ground motion, structural response and losses are considered. The results show that SC-MRFs have significantly improved performance compared to conventional MRFs and result in lower seismic losses. The results also highlight the importance of considering residual drifts as a demand parameter controlling whether a building is repairable or needs to be demolished in the aftermath of a strong earthquake.
Bilionis D.V., Vamvatsikos D. (2014). Assessing the behaviour of an offshore wind turbine under uncertain wind and wave dynamic loading. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Summary | Offshore wind turbines constitute a modern solution for the production of energy using wind power. However, they are subject to uncertain loads due to the combination of dynamic parameters, such as wind and waves. For this reason, the valid assessment and appropriate design against those parameters are real challenges for the engineers. The purpose of this paper is to present a methodology for the analysis of a standard offshore wind turbine sited at a specific area in the Aegean Sea. In specific, the loads due to the combination of wind and waves are calculated by statistically processing anemological and wave data of the area using appropriate software. Finally, the calculated loads are used in order to specify the annual fatigue damage and the predicted fatigue life of the structure.
Vamvatsikos D., Ashheim M.A. (2014). Direct performance-based seismic design of a steel moment-resisting frame using Yield Frequency Spectra. Proceedings of the 8th Hellenic National Conference on Steel Structures, Tripoli, Greece
Abstract | Yield Frequency Spectra (YFS) are employed to enable the direct seismic design of a 4-story steel moment-resisting frame subject to a set of performance objectives. YFS offer a unique view of the entire solution space for structural performance. This is measured in terms of the mean annual frequency (MAF) of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system with given yield displacement and backbone capacity curve. Using publicly available software tools or closed-form solutions, YFS can be rapidly computed for any system that is satisfactorily approximated by a single-degree-of-freedom oscillator, e.g., as in any nonlinear static procedure application. Thus, stated performance objectives can be directly related to the strength and stiffness of the structure. The combination of ductility (or displacement)demand and mean annual frequency of exceedance that governs the design is readily determined, allowing either a code-compatible or code-exceeding design to be realized.
Vamvatsikos D., Aschheim M.A. (2014). Direct performance-based seismic design of structures using Yield Frequency Spectra. Proceedings of the 10th U.S. National Conference on Earthquake Engineering, Anchorage, AK, USA
Abstract | Yield Frequency Spectra (YFS) are employed to enable the direct design of a structure subject to a set of performance objectives. YFS offer a unique view of the entire solution space for structural performance. This is measured in terms of the mean annual frequency (MAF) of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system with given yield displacement and backbone capacity curve. Using publicly available software tools or closed-form solutions, YFS can be nearly instantaneously computed for any system whose performance is characterized by response quantities that can be satisfactorily approximated by an equivalent nonlinear single-degree-of-freedom oscillator. Thus, stated performance objectives can be directly related to the strength and stiffness of the structure. The combination of ductility (or displacement) demand and its mean annual frequency of exceedance that governs the design is readily determined, allowing a satisfactory design to be realized in a single step.
Papageorgiou A.V., Fragiadakis M., Vamvatsikos D. (2014). Seismic loss and life-cycle cost assessment for reinforced concrete structures. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | Over the recent years, issues pertaining to the sustainable development of structures have come into focus. Sustainability in development takes into consideration not only the present needs, but also the ones of the forthcoming users of a building. A crucial part is the estimation of the costs related to the erection and use of the structure and finally its decomissioning. Thus, a cradle-to-grave cost estimation of a building, i.e. a complete definition of all the costs during its lifespan, is a crucial part of sustainable design and construction. In order to obtain all the pertinent costs, a critical parameter to consider is the repair and maintenance cost. This becomes very important in seismically active regions where rare events may enforce total asset loss, while the occurrence of even low-intensity events, may cause significant non-structural and building content loss. Our objective is to investigate seismic losses for low/midrise reinforced concrete (RC) frame buildings of the southern of Europe and the Mediterranean where significant seismic activity is observed. As an example an actual building built in Greece in 1950’s is presented. Using state-of-art approaches allows to account for structural member losses as well as non-structural components and contents, offering a holistic view of the lifetime hazard represented by older non-ductile RC frame buildings.
Vamvatsikos D., Aschheim M.A., Kazantzi A.K. (2014). Direct performance-based seismic design: Avant-garde and code-compatible approaches. Proceedings of the 9th European Conference on Structural Dynamics (EURODYN 2014), Porto, Portugal
Abstract | Current force-based seismic design codes use design spectra and system-specific behavior factors to satisfy two pre-defined structural limit-states: Serviceability and Life Safety. Instead, performance-based seismic design aims to design a structure to fulfill any number of target performance objectives, defined as user-prescribed levels of structural response, loss or casualties to be exceeded at a maximum rate less than a given mean annual frequency (MAF). Even at its simplest structural response basis, the inverse probabilistic nature of the requirements has not yet allowed a satisfying solution without cumbersome cycles of re-design and re-analysis. An alternative approach is proposed, relying on a new format for visualizing seismic performance, termed Yield Frequency Spectra (YFS). YFS offer a unique view of the entire solution space for structural performance, as indexed by the MAF of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system with given yield displacement and backbone capacity curve. YFS can be instantly computed for any system that is satisfactorily approximated by a single-degree-of-freedom oscillator, as in any nonlinear static procedure. Thus, stated performance objectives are directly related to the strength and stiffness of the structure while fully incorporating aleatory and epistemic sources of uncertainty, as needed to achieve any required level of confidence. The combination of ductility (or displacement) demand and its exceedance MAF is readily determined, allowing a satisfactory initial design to be realized in a single step. Using a simple safety factor approach given the period and the hazard curve slope, the benefits can also apply to contemporary seismic codes, essentially introducing true performance-based capabilities in a traditional format.
Giaralis A., Vamvatsikos D. (2014). Local wavelet-based spectral “epsilon” modification of ground motions in support of incremental dynamic analysis. Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management (ICVRAM2014), Liverpool, UK
Abstract | A novel scaling algorithm for ground motion accelerograms (GMs) is proposed in support of incremental dynamic analysis used to establish dependable statistical relationships between scalable intensity measures (IMs) and engineering demand parameters (EDPs) within a performance based earthquake engineering framework. Specifically, an iterative harmonic wavelet based scheme is employed to accomplish “surgical” changes to the spectral shape of suites of GMs to span various pre-defined levels of the spectral acceleration at the structural fundamental natural period, the most widely adopted IM. Since the target IM values may not be accomplished precisely by the local spectral modifications, a second step involving global uniform GM scaling is further considered. The proposed algorithm requires significantly smaller global (amplitude) scaling factors compared to the currently used scaling approach in which no initial local GM modification is undertaken. A numerical application of the proposed algorithm to elastoplastic structural systems shows the extent to which spectral shape may influence the displacement response of yielding structures and explains the conservative bias introduced by uniform global scaling.
Georgiou C, Vamvatsikos D., Christodoulou S. (2014). Damage assessment, cost estimating, and scheduling for post-earthquake building rehabilitation using BIM. International Conference on Computing in Civil and Building Engineering, Orlando, FL, USA
Abstract | A methodology is developed for integrated and automated seismic damage assessment, cost estimating, scheduling and three-dimensional (3D) visualizations for postearthquake building rehabilitation. The proposed methodology relies on the development of software based on the integration of tools currently available to the Architectural, Engineering and Construction (AEC) industry such as Building Information Modeling (BIM), a fourth-generation programming language, a relational database management system and construction management tools within the framework for seismic damage assessment developed by the Pacific Earthquake Engineering Research (PEER) Center. This process provides automated generation of 3D damage assessment visualizations, cost estimation and schedule-of-work sequences for reinforced concrete moment-frame buildings, per element, element group, story and building, for specified levels of seismic intensity and given ground motion sets. Ultimately, BIM is enhanced with data about elements’ damage state, the expected rehabilitation cost and duration in the aftermath of an earthquake. Hence, engineers and developers have the unique opportunity to create a holistic picture of any RC moment-frame building’s seismic behavior, which is easily comprehensible by non-engineer owners, customers or shareholders.
Georgiou C, Christodoulou S., Vamvatsikos D. (2014). BIM-based damage assessment and scheduling for post-earthquake building rehabilitation. Proceedings of the 10th European Conference on Product & Process Modelling, Vienna, Austria
Abstract | An a-priori assessment of the post-earthquake condition of structures has long been a target of the Architectural, Engineering and Construction (AEC) industry, with recent efforts by the Pacific Earthquake Engineering Research (PEER) Center highlighting such goal. The aforementioned PEER efforts have developed an appropriate basis for seismic damage assessment, including cost estimation and scheduling for postearthquake building rehabilitation, but visualization tools are notably absent from this framework. The methodology proposed herein relies on the integration of tools currently available to the AEC industry, such as Building Information Modeling (BIM), a fourth-generation programming language, a relational database management system and construction management tools, within the PEER Center framework. The proposed process is automated through the development of appropriate software, providing building information models with data about the building elements’ damage state, 3D damage assessment visualizations, the expected rehabilitation cost and duration, for different levels of seismic intensity.
Voyagaki E., Vachaviolos G., Mylonakis G., Psycharis I.N., Vamvatsikos D. (2014). Toppling criteria of rigid bodies to near-fault ground motions. Proceedings of the 7th Hellenic National Conference on Geomechanics, Athens, Greece
Abstract | The rocking response of a simply supported block on a frictional, cohessionless rigid plane under near – fault seismic excitation is revisited, with the aim of developing simple overturning criteria. To this end, 180 near-fault earthquake recordings, 5 block sizes and 5 slenderness angles are considered – leading to over 4500 cases, which cover a wide range of parameters of practical interest. Useful conclusions are drawn as to the overturning of rigid bodies.
Bakalis K., Vamvatsikos D., Fragiadakis M. (2014). Seismic reliability assessment of liquid storage tanks. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | Large-capacity atmospheric tanks are widely used to store liquids, such as oil or liquefied natural gas. The seismic risk of such industrial facilities is considerably higher compared to ordinary structures, since even some minor damage induced by a ground motion may have uncontrollable consequences, not only on the tank but also on the environment. Recent earthquakes have shown that heavy damage on tanks may lead to temporary loss of essential service, usually followed by leakage and/or fire. Therefore, a Performance-Based Earthquake Engineering (PBEE) framework should be employed for the seismic performance assessment of such critical infrastructure. Current design codes and guidelines have not fully adopted the PBEE concept, while its application to industrial facilities is still at the academic level. This study provides an insight on the seismic risk assessment of liquid storage tanks using a simplified performance-based oriented modelling approach. Appropriate system and component-level damage states are defined by identifying the failure modes that may occur during a strong ground motion. Fragility curves are estimated by introducing both aleatory and epistemic sources of uncertainty, thus providing a comprehensive methodology for the seismic risk assessment of liquid storage tanks.
Kazantzi A.K., Vamvatsikos D., Porter K., Cho I. (2014). Analytical vulnerability assessment of modern highrise RC moment-resisting frame buildings in the Western USA for the Global Earthquake Model. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | The Global Earthquake Model (GEM) has commissioned the preparation of analytical seismic vulnerability guidelines for loss assessment of highrise buildings. The guidelines attempt to provide a practical method to assess the relationship between ground shaking and repair cost for a class of buildings, in face of the time, skill and computational challenges posed by a class rather than a single structure. An example is presented that reflects a class of modern (post-1980) highrise reinforcedconcrete moment-frame (RCMRF) office buildings in the western United States. Seven characteristic “index” buildings were selected through moment-matching, so as to represent all important aspects of the class. Each is modeled and analyzed through Incremental Dynamic Analysis (IDA). To remove issues of sufficiency without performing record selection, an extensive comparative study of intensity measures (IMs) was undertaken. Scalar IMs, defined as the geometric mean of spectral acceleration values at adjacent periods, were found to be satisfactory. Then, for each of the seven index buildings, poor, typical, and superior-quality variants were considered to establish the seismic loss and its ratio over replacement cost new in each case. The end product is a high quality set of vulnerability curves, whose weighted moments are taken as the uncertain vulnerability function of the class.
Melissianos V.E., Vamvatsikos D., Gantes C.J. (2014). Seismic risk assessment of buried pipelines at active fault crossings. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | A methodology is presented on assessing the seismic risk of buried steel pipelines crossing active tectonic faults through a comprehensive analysis by incorporating the uncertainty of the loading resulting from fault movement, soil response and the response of the pipeline itself. The proposed methodology is a two-step process. In the first step Probabilistic Fault Displacement Hazard analysis is implemented to quantify the probabilistic nature of the load, namely the imposed differential displacement on the pipeline due to large permanent fault displacements, incorporating all pertinent uncertainties regarding, for example, seismicity rate, maximum moment magnitude, etc. The second step is the “transition” from seismological data to pipeline structural response through a vector intensity measure represented by the fault displacement components in 3D. Advanced pipeline numerical simulations are then carried out in order to form pipeline strain hazard curves as a useful engineering tool for pipeline fault crossing seismic risk assessment.
Moschen L., Vamvatsikos D., Adam C. (2014). A modified response spectrum method for estimating peak floor acceleration demands in elastic regular frame structures. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | In this paper an extended complete quadratic combination rule for quick assessment of peak floor acceleration demands (PFA) of elastic structures subjected to seismic excitation is proposed. The simplification from time history analysis to the response spectrum method is shown in detail. Based on a relative acceleration formulation combined with nonlinear optimization techniques cross correlation coefficients are determined to estimate relative and absolute PFA demands. For estimation of central tendency and dispersion of the seismic response, regression equations are derived to provide a simple implementation of the method in civil engineering design practice. Application of the proposed procedure to a 24-story moment resisting generic frame structure shows the improvement compared to common response spectrum methods.
Porter K., Cho I.N., Vamvatsikos D., Farokhnia K. (2014). Using representative suites of index buildings to model the seismic vulnerability of an asset class. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Voyagaki E., Vamvatsikos D. (2014). Probabilistic characterization of overturning capacity for simply-supported rigid blocks. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | A probabilistic treatment to the problem of rocking and overturning of a simply-supported rigid block is presented in the context of Performance-Based Earthquake Engineering (PBEE). To this end, a twodimensional rectangular block resting at ground surface on a rough, horizontal, tensionless and cohesionless rigid base is considered, subjected to a suite of 44 horizontal earthquake excitations. The roughness of the interface is assumed to be sufficiently large so that sliding is prevented, while the flexibility of the block and aerodynamic effects are neglected. Rocking response curves are calculated for increasing ground motion intensity (or decreasing uplift strength) via Incremental Dynamic Analysis (IDA), and results are summarized in the form of 16%, 50% and 84% fractile IDA curves. The solution based on a geometrically linearized rocking equation is advantageous, as it limits the problem parameters to just three that is, uplift “yield” strength, pseudo natural frequency and coefficient of restitution (damping), as in the classical yielding oscillator. On the other hand, the slenderness angle of the block is not an essential independent variable, as it simply normalizes the response angle. Generalized overturning criteria are proposed covering a wide set of excitations and block parameters. By employing non-linear regression analysis, simple formulae are developed for both the median/mean and the dispersion of response to provide a complete probabilistic characterization of rocking response for use in PBEE.
Vamvatsikos D., Aschheim M.A. (2014). A code-compatible application of yield frequency spectra for direct performance-based design. Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey
Abstract | An analytical formulation is offered for performance-based seismic design following a direct procedure based on code-like requirements. The approach builds upon the use of the yield displacement as a robust system characteristic. A new format for displaying seismic demands known as Yield Frequency Spectra is introduced to quantitatively link performance objectives with the base shear seismic coefficient, for a fixed value of yield displacement. The closed-form solutions developed in the SAC/FEMA project are inverted to provide analytical solutions for estimating the design base shear strength implied by typical code requirements, involving both strength and displacement limitation checks. It is shown that the consideration of aleatory and epistemic sources of uncertainty result in an increase of 30% or more in the strength required to achieve the stated performance objectives, depending on the site and structure characteristics. While the blanket safety factors embodied in the seismic code may cover this difference, they do so inconsistently. Instead, the simple expressions derived can offer uniform safety at no additional complexity.
Moschen L., Vamvatsikos D., Adam C. (2013). Towards a static pushover approximation of peak floor accelerations. Proceedings of the Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics (VEESD 2013), Vienna, Austria
Abstract | The potential basis of a simplified methodology for estimating the inelastic peak floor acceleration demand (PFA) of multi-story buildings subjected to seismic excitation is explored. Inelastic single-degree-offreedom (SDOF) oscillators are used to find a relation between the lateral strength and the inelastic acceleration demand. Effects of positive as well as negative post yielding stiffness and different damping types are assessed. Using regression analysis, a simplified approach is proposed to estimate inelastic acceleration demands for use within a probabilistic framework. Based on a fundamental mode approximation an existing approach for predicting elastic PFA demands is extended to inelastic multi-story structures. Pros and cons of this methodology are discussed, and further developments are recommended.
Vamvatsikos D., Aschheim M.A., Kazantzi A.K. (2013). Direct performance-based seismic design using yield frequency spectra. Proceedings of the Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics (VEESD 2013), Vienna, Austria
Abstract | Yield Frequency Spectra (YFS) are employed to enable the direct design of a structure subject to a set of performance objectives. YFS offer a unique view of the entire solution space for structural performance. This is measured in terms of the mean annual frequency (MAF) of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system with given yield displacement and backbone capacity curve. Using publicly available software tools or closed-form solutions, YFS can be nearly instantaneously computed for any system that can be satisfactorily approximated by a single-degree-of-freedom oscillator, as in any nonlinear static procedure application. Thus, stated performance objectives can be directly related to the strength and stiffness of the structure. The combination of ductility (or displacement) demand and its mean annual frequency of exceedance that governs the design is readily determined, allowing a satisfactory design to be realized in a single step.
Vamvatsikos D., Dolsek M. (2013). Assessment of structures subject to time-dependent degradation via equivalent constant rates. Proceedings of the Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics (VEESD 2013), Vienna, Austria
Abstract | Analytical, closed-form solutions are presented for the computation of equivalent constant rates of limit-state exceedance for structures under seismic loads whose capacity is degrading with time. Seismic guidelines currently designate constant, time-independent probabilities or mean annual frequencies of exceedance that are assumed to remain invariable for the entire design life. These are at odds with the timedependent, ever-increasing exceedance rates of ageing structures. Based on the concept of social equity and discounting of societal investments, the equivalent constant rate provides a basis for judging the safety of structures with time-dependent capacity by allowing comparisons with the code-mandated rates of limit-state exceedance. Starting from the simple SAC/FEMA solution and assuming a power-law degradation of capacity with time and a linear change in the combined epistemic and aleatory variability of capacity, we provide general solutions for the equivalent constant rate and for the limiting case of the average rate over the design life of the structure. The solutions are formulated both in the demand-based and in the intensity-based format, the latter being suitable for all limit-states, even close to global collapse. By using a 7-story reinforced concrete building as an example, we demonstrate the accuracy and the practicality of these approximations for the assessment of an existing structure.
Vamvatsikos D., Porter K. (2013). Tall building analytical seismic vulnerability functions for the Global Earthquake Model. Proceedings of the 10th International Conference on Structural Safety and Reliability (ICOSSAR), New York
Abstract | Guidelines for developing analytical seismic vulnerability functions are proposed for use within the framework of the Global Earthquake Model (GEM). Emphasis is on high-rise buildings and cases where the analyst has the skills and time to perform nonlinear dynamic analysis. The basis for this effort is formed by the key components of the state-of-art PEER/ATC-58 methodology for loss assessment. Simplified modeling options are proposed to reduce model complexity and ease application for building ensembles. Nonlinear dynamic analysis is employed for the estimation of local story drift and absolute acceleration response to evaluate both structural and non-structural losses. Important sources of uncertainty are identified and propagated using simplified methods based on moment-matching to reduce the computational load. The resulting guidelines allow the generation of vulnerability functions for a class of high-rise buildings with a reasonable amount of effort by an informed engineer.
Kazantzi A.K., Vamvatsikos D., Lignos D.G. (2013). Model parameter uncertainty effects on the seismic performance of a 4-story steel moment-resisting frame. Proceedings of the 10th International Conference on Structural Safety and Reliability (ICOSSAR), New York
Abstract | The reliable estimation of the seismic performance of structures requires quantifying the effect of aleatory and epistemic uncertainties of the system parameters. This is efficiently achieved for a case study of a steel moment-resisting frame through several important advances. First, a state-of-the-art numerical model is formed with full parameterization of its strength properties. Empirical relationships derived from experimental data are used to model the cyclic behavior of steel sections using probabilistically distributed parameters that include intra- and inter-member correlation. Incremental dynamic analysis is employed to accurately assess the seismic performance of the model. Finally, an efficient Monte Carlo simulation algorithm is used, based on record-wise incremental Latin Hypercube Sampling to propagate the uncertainties from the numerous parameters to the actual system demand and capacity. Consequently, this modern steel frame is shown to be only mildly sensitive to parameter uncertainties when quality is tightly controlled.
Vamvatsikos D., Kazantzi A.K. (2013). Seismic fragility and vulnerability assessment using simplified methods for the Global Earthquake Model. Proceedings of the COMPDYN2013 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos, Greece
Abstract | The Global Earthquake Model (GEM) has commissioned the preparation of analytical vulnerability guidelines for general use. Within this framework, a distinct modeling and analysis method hierarchy has been proposed, whereby both detailed and reduced-order models can be analyzed using nonlinear static or dynamic methods. Each subsequent reduction in complexity increases the speed of application, yet generates additional error that needs to be considered in the form of epistemic uncertainty. The available choices represent different levels of compromise between the accuracy achieved and the associated effort needed, meant to suit users having different levels of expertise and resource availability. Our particular focus will be on the middle path that is expected to become the most popular choice, combining (a) a simplified stick model of the structure with (b) a static pushover analysis with accurate record-to-record dispersion information. The entire procedure is cast within an appropriate probabilistic framework that can effortlessly incorporate all the epistemic and aleatory uncertainty sources to become a viable path for evaluating structural fragility for a building class.
Olmati P., Petrini F., Vamvatsikos D., Gantes C. (2013). A stochastic simplified SDOF model of a steel blast door. Proceedings of the XXIV Italian Days on Steel Constructions, Torino, Italy
Abstract | Extreme loads can severely affect civil structures, which are generally not designed with an adequate strength to withstand extreme events. In addition, buildings and critical infrastructures are particularly prone to external man-made bomb attacks. In order to achieve a prescribed level of protection of the building, structural components have to be designed against blast loads. This paper focuses on the design of built-up blast doors made of steel, generally common in storage facilities for ammunitions. Finite Element Analyses (FEAs) are carried out for assessing the behaviour of a built-up door under different levels of detonations. Furthermore, a simplified model accounting for both aleatory and epistemic uncertainties is developed in order to carry out reliability analyses in the future by Monte Carlo (MC) simulations.
Vamvatsikos D. (2012). Accurate application and higher-order solutions of the SAC/FEMA probabilistic format for performance assessment. Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal
Summary | The SAC/FEMA probabilistic framework is based on a pioneering closed-form expression to analytically estimate the value of the risk integral convolving seismic hazard and structural response. Despite its immense practicality, implementation has been hindered by reduced accuracy due to a number of approximations needed to achieve a simple form, the most significant being the power-law approximation of the seismic hazard curve. To mitigate this problem, two approaches are hereby offered, namely (a) selecting an appropriately-biased power-law fit and (b) offering a novel closed-form expression involving a higher order approximation. Where blind application of the original format could involve error in excess of 100% for the predicted mean annual frequency of limit-state exceedance, biased fitting reduces it to less than 25% while for the new closed-form it remains consistently below 10%. Although other sources of error still remain, the robustness achieved opens new avenues of application for this popular format.
Fragiadakis M., Vamvatsikos D., Christodoulou S.E. (2012). Reliability assessment of urban water networks. Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal
Summary | We present a framework for the seismic risk assessment of aging water supply networks in order to evaluate the water networks of the island of Cyprus. The proposed methodology aims at assessing the performance of water pipe networks based on the pipe vulnerabilities that are determined considering survival curves obtained from historical data of damage. The magnitude-distance seismic scenario adopted is consistent with the seismicity of sites mainly controlled by distant and moderate magnitude events. The network reliability is assessed using Graph Theory, while two alternative approaches are compared for calculating the system reliability: the path enumeration method and Monte Carlo simulation. Τhe methodology proposed can estimate the probability that the network fails to provide the desired level of service and thus allows the prioritization of retrofit interventions and capacity-upgrade actions for the existing water pipe networks.
Kazantzi A.K., Vamvatsikos D. (2012). A study on the correlation between dissipated hysteretic energy and seismic performance. Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal
Abstract | The hysteretic energy dissipated by systems undergoing quasi-static or dynamic loading is often thought to represent a useful measure of their performance when subjected to earthquake excitation. In general, fuller hysteresis loops mean higher seismic energy removal from the structure, which is logically taken to imply better performance when comparing systems with similar strength. However, such observations are typically based on quasi-static loading tests. Dynamic loading conditions differ as energy input and energy dissipation are intimately related with the details of the system’s hysteresis, in ways that often defy current intuition. Using incremental dynamic analysis on story-level oscillators with varying hysteresis characteristics, we can map this connection in detail. Structural response, as measured in terms of maximum or residual deformation, is shown to have little connection to the energy absorption. Therefore, hysteretic energy dissipation cannot quantitatively measure seismic performance but perhaps only serve as a general indicator.
Vamvatsikos D., Lignos D.G. (2011). Evaluating the epistemic uncertainty of the seismic demand and capacity for a 9-story steel moment-resisting frame. Proceedings of the 7th Hellenic National Conference on Steel Structures, Volos, Greece
Abstract | The accurate estimation of the seismic performance of steel structures requires reliable information on the effect of our incomplete knowledge of the actual system parameters. Aiming to provide such an outlook we undertake a comprehensive effort to quantify the uncertainty for a single steel moment-resisting frame by bringing together several important advances. Model parameters are described by complete probabilistic distributions including intra-member and inter-member correlation information derived from experimental data from a recently developed database for modeling steel components. Incremental dynamic analysis is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Finally, we use an efficient Monte Carlo simulation algorithm based on incremental Latin Hypercube Sampling to efficiently propagate the uncertainties from the numerous parameters to the actual system demand and capacity. The effect of model parameter uncertainties on the seismic behavior of the 9-story steel moment resisting frame is thus quantified, offering a unique method to assess the actual margin of safety inherent in any steel frame structure.
Fragiadakis M., Vamvatsikos D. (2011). Qualitative comparison of static pushover versus incremental dynamic analysis capacity curves. Proceedings of the 7th Hellenic National Conference on Steel Structures, Volos, Greece
Abstract | The Nonlinear Static Procedure (NSP), also known as ‘pushover’ analysis, is widely adopted in earthquake engineering practice. It is used for the estimation of various engineering demand parameters that provide a measure of the demand (and the capacity) of structures (e.g. displacements, storey drifts, forces, curvatures). Apart from element, or storey-level quantities, many NSPs provide the so-called ‘capacity curve’, i.e. the plot of the roof displacement against the total base shear applied on the building. Alternatively, local or global estimates of the building’s capacity can be obtained with Incremental Dynamic Analysis (IDA), which generates percentile ‘capacity curves’ in terms of seismic intensity versus the demand parameter of choice. The latter method is based on Nonlinear
Response History Analysis (NRHA), and is thus more reliable and accurate compared to NSP. In this work, we study qualitatively the properties of the building capacity curves obtained with either NSP or IDA. We show that the comparison can be performed either in the framework of the static pushover or in that of IDA. When the static pushover setting is adopted, we show that pushover methods can be compared with the results of IDA by plotting the latter in the form of ‘dynamic capacity curves’ where the base shear instead of an intensity measure (e.g., spectral acceleration) is plotted on the ordinates. Alternatively, the comparison can be performed within the IDA setting if appropriate R-C1-T relationships are adopted. Each setting shows the different qualitative characteristics of the two approaches and has different practical applications.
Vamvatsikos D. (2011). Estimating seismic performance uncertainty using IDA with progressive accelerogram-wise latin hypercube sampling. Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering, Zurich
Abstract | An efficient algorithm is presented that allows the rapid estimation of the influence of model parameter uncertainties on the seismic performance of structures using incremental dynamic analysis (IDA) and Monte Carlo simulation with latin hypercube sampling. The fundamental blocks of this methodology have already been proposed as a means to quantify the uncertainty for structural models with non-deterministic parameters, whereby each model realization out of a predetermined sample size is subjected to a full IDA under multiple ground motion records. However, any practical application is severely restricted due to (a) our inability to determine a priori the required number of samples and (b) the disproportionate increase in the number of analyses when dealing with many random variables. Thus, two fundamental changes are incorporated. First, latin hypercube sampling is applied incrementally by starting with a small sample that is doubled successively until adequate accuracy has been achieved. At the same time, instead of maintaining the same properties for a given model realization over an entire ground-motion record suite, parameter sampling is performed on a record-by-record basis, efficiently expanding the model sample size without increasing the number of nonlinear dynamic analyses. Using a steel moment-resisting frame building as a test case, it is shown that the improved algorithm allows excellent scalability and extends the original methodology to be easily applicable to realistic large-scale applications with hundreds of random variables.
De Luca F., Vamvatsikos D., Iervolino I. (2011). Improving the static pushover analysis in the Italian Seismic Code by proper piecewise-linear fitting of capacity curves. Proceedings of the ANIDIS2011 Convention on Seismic Engineering, Bari, Italy
Abstract | An improvement of the Italian Code bilinear fit for static pushover (SPO) curves is put forward aimed at significantly decreasing the error introduced in the conventional SPO analysis by the piecewise linear fitting of the capacity curve. While other issues, such as the relationship to pass from the response of multi-degree-of-freedom to single-degree-of-freedom systems (MDOF – SDOF), have been heavily examined in the last decades and improvements and changes to the original method have been proposed and introduced in codes and guidelines, the piecewise linear fit assumed has not yet been systematically investigated. The determination of an optimal multilinear fit has now become a more pressing issue, since new generation modeling approaches lead to highly curved pushover shapes with significant stiffness changes, especially when explicitly incorporating the initial uncracked stiffness of sections. In such cases, even determining the code-standard equivalent elastic stiffness and yield strength of the simple elastic-plastic approximation can be greatly improved upon. In the approach proposed herein, the error introduced by the piecewise multilinear fit of the force-deformation relationship is quantified by studying it at the SDOF level, away from any interference from MDOF effects. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual curved backbones versus their piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limitstates, allowing an accurate interpretation of the results in terms of performance. An optimized elastic-plastic bilinear fit is the first enhanced solution to decrease systematically the error introduced in the SPO analysis if
compared to the hybrid fit approach provided by the Italian seismic provisions. Moreover this fit allows employing the same R-µ-T (strength reduction factor-ductility-period) relationship already prescribed by the Italian Code.
Giannelos C., Vamvatsikos D. (2011). Simplified seismic performance assessment over the lifetime of a highway bridge subject to pier reinforcement corrosion. Proceedings of the COMPDYN2011 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece
Abstract | The lifetime seismic performance of a typical segmental three-span (75+120+75) Egnatia Odos Highway bridge is assessed, considering the corrosive action of chloride ions that leads to pier strength degradation over time. The aim is to show the influence of corrosion on the seismic demand and capacity over the entire design life of the bridge, as well as the usefulness of simplified single-degree-of-freedom (SDOF) models to minimize the computational cost to non-prohibitive levels for contemporary capabilities. Five different time instants are chosen within the 120 year design life of the bridge. For each instant, the piers’ reinforcement steel loss is calculated via a probabilistic model using Monte Carlo simulation to account for the uncertainty in the factors that affect the corrosion. While incremental dynamic analysis (IDA) of the complex model would be the method of choice for a comprehensive evaluation, we employ instead approximate IDA of equivalent SDOF systems with capacity curves derived by static pushover analysis. Such analyses are efficiently executed for different time moments of the design life of the bridge, taking into account the active pier rebar diameter due to corrosion effects. Thus, the usefulness of the equivalent SDOF system concept combined with nonlinear dynamic analysis or a powerful R-μ-Τ relationship such as SPO2IDA is shown. This usefulness turns to a necessity when more factors of epistemic uncertainty beyond the corrosion process are added in this already complex problem, disproportionately magnifying the required computational load.
De Luca F., Vamvatsikos D., Iervolino I. (2011). Near-optimal bilinear fit of capacity curves for equivalent SDOF analysis. Proceedings of the COMPDYN2011 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece
Abstract | The bilinear approximation of force-deformation capacity curves is investigated for structural systems with non-negative-stiffness. This piecewise linear approximation process factually links capacity and demand; it lies at the core of the nonlinear static assessment procedures, and it has become part of seismic guidelines and codes, such as ASCE-41 and Eurocode 8. Despite codification, the various fitting rules, used to derive the bilinear representation, can produce highly heterogeneous results for the same capacity curve. This is especially valid for highly-curved backbones resulting from structural models with accurate representation of the initial, uncracked, stiffness or buildings characterized by a global collapse mechanism that leads to a gradual plasticization of the elements. The error introduced by the bilinearization of the force-deformation relationship is quantified by studying it at the single-degree-of-freedom (SDOF) level, away from any interference from multi-degree-of-freedom (MDOF) effects, thus avoiding the issue related to MDOF – SDOF approximation. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual backbones versus their bilinear approximations in terms of the spectral acceleration capacity for a continuum of limit-states, allowing a direct comparison of the results in terms of seismic performance. Code-based procedures are found to be less than ideal wherever there are significant stiffness changes, while in general remaining relatively conservative. The practical fitting rules determined allow, instead, a near-optimal fit regardless of the details of the capacity curve shape.
Vamvatsikos D., Aschheim M., Comartin C.D. (2011). A targeted nonlinear dynamic procedure to evaluate the seismic performance of structures. Proceedings of the COMPDYN2011 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece
Abstract | The Targeted Nonlinear Dynamic Procedure is introduced to offer a practical evaluation of the seismic performance of structures. Building upon the SAC/FEMA closedform probabilistic framework it can incorporate all important sources of variability and can be calibrated for conservatism. The hazard curve is combined with the nonlinear dynamic analysis performed for each limit-state using one or two levels of the intensity measure. This is either the elastic first-mode spectral acceleration or the more sufficient inelastic spectral displacement. From the suite of ground motion records only “targeted” subsets are used that are optimally selected to estimate the median and dispersion of the structural response. The simple factored demand and capacity checking format employed allows for a seamless integration with current engineering practice, while rational safety factors add the required degree of conservatism to account for epistemic uncertainties both for ductile and brittle modes of failure. Using a four-story reinforced concrete frame as an example, the proposed approach is shown to provide a relatively simple means to account for important sources of variability in nonlinear response history analysis. It offers powerful analysis options to a knowledgeable user in a format that can be upgraded incrementally and can provide an excellent introduction to sophisticated analysis techniques with more precisely controlled levels of conservatism.
Fragiadakis M., Vamvatsikos D., Aschheim M. (2011). Static versus dynamic methods of analysis for estimating seismic performance. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | Nonlinear static methods are evaluated and compared with nonlinear dynamic methods for estimating the seismic performance of structures. Emphasis is given on assessing the applicability of nonlinear static methods for RC buildings, and on comparing the building’s capacity obtained using nonlinear static and nonlinear response history analysis. The first task refers to the ability of alternative static pushover-based methods to estimate the response at the level of a member or of a story. Plain as well as more elaborate pushover methods such as the Modal Pushover Analysis method and the Consecutive Modal Pushover method are included in our evaluation. The second task refers to the qualitative comparison at the global level between static pushover and nonlinear response history analysis when either the static pushover or the Incremental Dynamic Analysis (IDA) setting is adopted. When the static pushover setting is adopted, we show that nonlinear static methods can be compared with the IDA curve when the base shear instead of spectral acceleration is plotted on the ordinates, while the dispersion among the single-record IDAs is considerably reduced. Alternatively, the comparison can be performed within the IDA setting if appropriate R-C 1-T relationships, simplified or more advanced (e.g. SPO2IDA), are adopted. Each setting shows different qualitative characteristics of the two seismic performance estimation approaches and has different practical applications.
Fragiadakis, M., Vamvatsikos, D., and Aschheim, M., (2011). Applicability of Nonlinear Static Procedures to RC Moment Resistant Frames. Proceedings of the 2011 Structures Congress, ASCE/SEI, Las Vegas, NV
Abstract | The applicability of nonlinear static procedures for estimating seismic demands in a variety of building types was evaluated within the recently concluded ATC-76-6 project. Results are reported herein for several pushover methods applied to three RC moment frame buildings, relative to baseline data provided by nonlinear response history analysis. Response quantities include peak interstory drifts, floor accelerations, story shears, and floor overturning moments. The single-mode pushover methods that were evaluated include the N2 and ASCE 41 coefficient methods. Multi-modal pushover methods include the modal pushover with elastic higher modes, and the consecutive modal pushover. Target displacements were estimated using typical R-C1-T relationships. Results indicate that the good performance of the single-mode methods for low-rise buildings rapidly deteriorates as the number of stories increases. Multi-mode techniques generally can extend the range of applicability of static pushover methods, but at the cost of significant additional computation and with uncertainty about the reliability of the results.
Celarec D., Vamvatsikos D., Dolsek M. (2011). Simplified estimation of seismic risk for buildings with consideration of the structural ageing process. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract |A simplified method for estimating the seismic risk of deteriorating buildings is presented utilizing a probabilistic framework and a simplified nonlinear method for seismic performance assessment of structures. Firstly, the probabilistic methodology with the extension to deteriorating structures is briefly explained. Then the methodology is applied to the example of a four-storey RC frame building with corroded reinforcement in order to estimate the influence of corrosion on seismic risk for the near-collapse limit state. The results reveal that after 50 years from the initiation of corrosion, the peak ground acceleration that causes the structure to violate the defined near collapse limit state decreases by 17% and the seismic risk for the near-collapse limit state increases by 7%, compared to the case where corrosion is neglected. It is also shown that degradation due to corrosion may change the collapse mechanism from ductile to brittle shear failure, raising an important question on the seismic safety of the existing buildings.
Vamvatsikos D. (2011). Some thoughts on methods to compare the seismic performance of alternate structural designs. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | The process of structural design ultimately hinges upon the selection of the top alternative designs from a group of viable choices, ideally choosing the one that best satisfies the requirements, as set by codes or guidelines. Comparing structural configurations to find the best candidate has thus remained a favorite subject of researchers and engineers alike, especially in the case of seismic loads. With the emergence of performance-based earthquake engineering, such comparisons now need to be performed on the basis of the seismic performance, preferably at several limit-states. Such a direct evaluation can become cumbersome, requiring seismic hazard information. Therefore, shortcuts and simpler techniques have been introduced that are generally based on the concept of system fragility, as estimated through the various methods of structural analysis. Still, there is no general consensus on the metrics that can be used for such an evaluation; some researchers adopt force or displacement response quantities derived from static or dynamic methods, while others prefer to compare capacities in terms of intensity or response measures. In order to even out the field, we perform a comparative evaluation of the available choices and point out the pros and cons of each, showing some of the common fallacies that plague the results of such comparisons.
Vamvatsikos D., Kouris L.A., Panagopoulos G., Kappos A.J., Nigro E., Rossetto T., Lloyd T.O., Stathopoulos T. (2010). Structural vulnerability assessment under natural hazards: A review. Proceedings of the COST C26 Urban Habitat Constructions under Catastrophic Events Conference, Naples, Italy
Abstract | The state of the art is presented in the field of structural vulnerability assessment under earthquake, landslide, tsunami and wind hazards. We seek common avenues of research and points of contact among the existing philosophies used in these four different fields in the context of multi-hazard assessment frameworks. In essence, this is a step towards the identification of a common underlying structure between different fields that will allow the future unification of vulnerability methodologies under a single framework.
Vamvatsikos D., Pantazopoulou S.J. (2010). Vulnerability assessment of historical city cores – the example of the city of Xanthi. Proceedings of the 9th U.S. National and 10th Canadian Conference on Earthquake Engineering, Toronto, Canada
Abstract | A methodology is developed to address the problem of the collective seismic vulnerability of historical cities. Our focus is the derivation of fragility curves of simple structural models that represent an ensemble of historical masonry buildings. The structural model estimates lateral strength using a Mohr-Coulomb type failure criterion applied on the cross sectional area of load-bearing walls in the building’s plan. Example data are drawn from the building population of the historical city of Xanthi, in Northeastern Greece. The seismic behavior of the simplified systems is efficiently assessed using approximate incremental dynamic analysis via static pushover. Monte Carlo simulation with latin hypercube sampling is applied to include the effect of epistemic uncertainties on the system performance. The result is a simple and efficient evaluation tool that can facilitate a comprehensive performance evaluation of groups of masonry structures in a seamless way that is consistent with current performance-based seismic assessment frameworks.
Vamvatsikos D., Pantazopoulou S.J. (2010). Development of a simplified mechanical model to estimate the seismic vulnerability of cultural heritage masonry buildings. Proceedings of the 9th HSTAM International Congress on Mechanics, Limassol, Cyprus
Abstract | A simplified mechanical model is developed for heritage masonry buildings to address the problem of the collective seismic vulnerability of historical cities. Our focus is the derivation of capacity curves based on parameterized first-mode structural models that are flexible enough to represent an ensemble of similar buildings. The structural model estimates lateral strength using a Mohr-Coulomb type failure criterion of the load-bearing walls deforming in-plane in shear in combination with a yield-line mechanism for the out-of-plane flexural deformation of the orthogonal walls. The resulting equivalent models are simple enough to allow an analytic first-mode representation of their seismic behavior that is suitable for evaluation via static pushover in a manner that is consistent with current performance-based seismic assessment frameworks.
Vamvatsikos D., Zeris C. (2010). Seismic performance sensitivity and uncertainty of an RC building due to random vertical loads and accelerations. Proceedings of the 3rd International fib Congress and Exhibition, Washington, D.C.
Abstract | We investigate the influence of the uncertain value of the gravity loads and the vertical ground motion component on the seismic performance of a nonductile reinforced concrete building. Seismic guidelines typically enforce the use of the Gκ + 0.3Qκ combination, where Gκ, Qκ are the characteristic dead and live loads, respectively. However, their true values and their influence to the seismic response are not known. Using a typical existing five-story reinforced concrete building, we employ incremental dynamic analysis to evaluate the seismic performance under probabilistic load distributions in combination with the use or not of the vertical component of ground motion. Multiple accelerograms are scaled to several levels of intensity, both in the horizontal and in the vertical sense, to evaluate the building capacity in limitstates ranging from serviceability to global dynamic instability and structural collapse. Thus, it is shown that the highly variable live loads tend to increase the response uncertainty especially when they dominate over dead loads. On the other hand, the effect of vertical accelerations depends on the magnitude of the gravity loads, with higher loads causing significant capacity reductions across all limit-states considered.
Fragiadakis M., Vamvatsikos D. (2009). Estimation of uncertain parameters using static pushover methods. Proceedings of the 9th International Conference on Structural Safety and Reliability (ICOSSAR), Osaka, Japan
Abstract | Following recent guidelines (e.g. FEMA-350) seismic performance uncertainty is an essential ingredient for performance-based earthquake engineering. Uncertainty refers to both aleatory uncertainty, raised by the random record-to-record variability, and also to epistemic uncertainty primarily introduced by modeling assumptions or errors. A methodology for the performance-based estimation of the dispersion introduced by parameter uncertainties is developed. The methodology proposed provides an inexpensive alternative to the use of tabulated values, or to performing a series of time-consuming nonlinear response history analyses to obtain parameter uncertainty. As a testbed, the well-known 9-storey LA9 2D steel frame is employed using beam-hinges with uncertain backbone properties. The monotonic backbone is fully described by six parameters, which are considered as random variables with given mean and standard deviation. Using point-estimate methods, first-order-second-moment techniques and latin hypercube sampling with Monte Carlo simulation, the pushover curve is shown to be a powerful tool that can help accurately estimating the uncertainty in the seismic capacity. Coupled with SPO2IDA, a powerful R-μ-T relationship, such estimates can be applied at the level of the results of nonlinear dynamic analysis, allowing the evaluation of seismic capacity uncertainty even close to global dynamic instability.
Vamvatsikos D. (2009). Optimal multi-objective seismic design of a highway bridge by selective use of nonlinear static and dynamic analyses. Proceedings of the 9th International Conference on Structural Safety and Reliability (ICOSSAR), Osaka, Japan
Abstract | A methodology is introduced for the optimal multi-criteria performance-based seismic design of highway bridges based on evolutionary algorithms by selectively employing nonlinear static and dynamic analysis to emulate full Incremental Dynamic Analysis (IDA). IDA is a novel analysis method that can thoroughly estimate the seismic performance of structures using multiple nonlinear timehistory analyses. Simplified methods based on the static pushover (SPO2IDA) are now able to provide a simpler, albeit less accurate alternative. They are thus employed within the optimization framework to rapidly evaluate the potential of candidate designs to enter the Pareto front in each generation. IDA is only applied to a small, elite set that is selected for inclusion. The final result is a sophisticated tool for optimal design that achieves a compromise between the speed of static procedures and the accuracy of dynamic methods to generate Pareto-optimal designs for bridges under seismic loading.
Vamvatsikos D., Akkar S., Miranda E. (2009). Estimating the dynamic instability of oscillators with non-trivial backbones. Proceedings of the COMPDYN2009 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Abstract | Novel empirical relationships are introduced to estimate the median, mean and dispersion of strength ratios to cause dynamic instability in oscillators with non-trivial backbones and arbitrary periods. The backbones investigated range from a simple bilinear elastic-negative shape to a trilinear that includes an elastic, a hardening and a negative stiffness segment that terminates at zero strength. Using 72 ground motion records that were recorded on firm soil we calculate the mean, median, 16% and 84% percentiles of the corresponding lateral strength ratios required for the appearance of dynamic instability. Processing of the results shows the influence of the oscillator parameters to the occurrence of dynamic instability: Lengthening the oscillator period, delaying the onset of negative stiffness and decreasing the negative slope are all shown to delay the appearance of collapse. On the other hand, contrary to current engineering intuition, increasing the hardening stiffness while maintaining the same period and coincident negative branches has only a small effect on the onset of instability. Using nonlinear regression, parametric equations are developed that can accurately capture such effects in a simple, easy-to-use formula.
Celarec D., Dolsek M., Vamvatsikos D. (2009). Estimation of the seismic risk of RC frames with consideration of capacity degradation over time. Proceedings of the COMPDYN2009 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Abstract | The dependence of mankind on the urban built environment is an integral part of culture that is so firmly embedded in our daily life that we are mostly unaware of its existence, as long as functionality is provided. The aging of our structures and the action of natural hazards, such as earthquakes, threaten the functionality of our urban environment and extraordinary expenditures are required to just maintain the status quo. Throughout the world, buildings are reaching the end of their useful life and develop new pathologies that increase their seismic risk, an effect that we aim to capture. In the paper, first, a methodology for structural performance assessment with consideration of capacity degradation over time is presented, utilizing IN2 analysis and an extension of the PEER probabilistic framework to rapidly achieve accurate estimates of limit-state exceedance probabilities of deteriorated structures. In the second part the methodology is applied to an example of a three-storey asymmetric reinforced concrete building. At this stage of the study only an influence of corrosion on longitudinal and transverse reinforcement of the structural elements is considered in the estimation of the seismic risk. The N2 method is used for seismic performance assessment of the structure. It is shown that the capacity in terms of the maximum base shear, as well as in terms of the maximum ground acceleration corresponding to limit states in the nonlinear range, is reduced over time, since the corrosion affects the capacity of both the beams and columns. Consequently, the expected frequency of violating life-safety or near-collapse limit states over the time interval increases in comparison to the typical case where the strength deterioration is neglected.
Fragiadakis D., Vamvatsikos D. (2009). Performance uncertainty estimation using simplified methods of analysis. Proceedings of the COMPDYN2009 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece
Vamvatsikos D., Fragiadakis M. (2008). Seismic performance uncertainty of a 9-story steel frame with non-deterministic beam-hinge properties. Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China
Abstract | The variability in the seismic demand and capacity of a steel frame having beam hinges with uncertain properties is investigated through Incremental Dynamic Analysis (IDA) using both Monte Carlo simulation and approximating techniques. The 9-story steel moment-resisting frame is modeled using parameterized moment-rotation relationships with quadrilinear backbones for the beam plastic-hinges. The uncertain properties of the backbones include the yield moment, the post-yield hardening ratio, the end-of-hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear time history analyses for a suite of ground motion records. IDA sensitivity analysis reveals the yield moment and the two rotational-ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ a) Monte Carlo simulation with latin hypercube sampling, b) point-estimate and c) first-order second-moment techniques, thus offering competing methodologies that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a mean-parameter model to estimate the mean seismic performance and employing the well-known square-root-sum-of-squares rule to combine aleatory randomness and epistemic uncertainty.
Fragiadakis M., Vamvatsikos D. (2008). Approximate seismic performance uncertainty estimation using static pushover methods. Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China
Abstract | An approximate method based on the static pushover is introduced to estimate the seismic performance uncertainty of structures having uncertain parameters. Performance uncertainty is one of the driving forces behind modern seismic guidelines (e.g. FEMA-350) and it is arguably an essential ingredient of Performance-Based Earthquake Engineering (PBEE). We propose a methodology that uses a minimum of static nonlinear analyses and is capable of accurately estimating the demand and capacity epistemic uncertainty. As a testbed, the well-known nine-story LA9 steel frame is employed using beam-hinges with uncertain backbone properties. These range from simple elastic-perfectly plastic backbones with kinematic hardening to full quadrilinear backbones with pinching hysteresis, including an elastic, a hardening, a negative stiffness and a residual plateau branch, terminating with a final drop to zero strength. The properties of the backbone can be fully described by six parameters which are considered uncertain with given mean and standard deviation values. Using latin hypercube sampling with classic Monte Carlo simulation, the pushover curve is shown to be a powerful tool that can accurately estimate the uncertainty in the seismic performance. Coupled with the SPO2IDA tool, such estimates can be applied at the level of the results of nonlinear dynamic analysis, allowing the evaluation of seismic capacity uncertainty even close to global dynamic instability. In summary, the method presented can inexpensively supply the uncertainty in the seismic performance of first-mode dominated buildings, offering for the first time an estimator of the accuracy of typical performance calculations.
Vamvatsikos D., Zeris C. (2008). Influence of uncertain vertical loads and accelerations on the seismic behavior of an RC building. Proceedings of the 3rd Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Abstract | We investigate the influence of the uncertain value of dead loads, live loads and the vertical seismic excitation on the seismic performance of a reinforced concrete structure. Seismic guidelines typically enforce the use of the Gκ + 0.3Qκ combination, where Gκ are the dead loads and Qκ the live loads. However, their true values and their influence to the seismic response are uncertain. Using a typical existing five-story building we employ Incremental Dynamic Analysis to evaluate the seismic performance under probabilistic load distributions in combination with the use or not of the vertical component of ground motion. Multiple accelerograms are scaled to several levels of intensity both in the horizontal and in the vertical sense to evaluate the building capacity in limit-states ranging from serviceability to global dynamic instability and collapse of the structure. In summary, the influence of the loads and the use of the vertical component on the estimated demand and capacity of the structure are quantified, allowing for the extraction of useful conclusions on the assumptions of the code and their impact.
Vamvatsikos D., Christodoulou S., Georgiou C. (2008). Visualizing damage, cost and repair scheduling for post-earthquake building rehabilitation. Proceedings of the 3rd Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Abstract | A methodology is presented for integrated and automated damage assessment, cost estimating, scheduling and 3D visualization for post-earthquake building rehabilitation. The methodology relies on the integration of tools currently-available to the Architectural, Engineering and Construction industry such as relational databases and project management tools with the framework developed by the Pacific Earthquake Engineering Research Center (PEER) for post-earthquake damage assessment, to automate the generation of damage-assessment visualizations, cost estimation and schedule-of-work sequences per element, story or building for a given earthquake scenario. Thus, engineers and constructors can develop a comprehensive view of the structural performance of a building that can be easily communicated to non-engineer clients.
Giannelos C., Vamvatsikos D. (2008). Simplified methods of nonlinear dynamic analysis of a bridge under bi-directional seismic loading. Proceedings of the 3rd Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Abstract | Several possibilities are examined for the simplified nonlinear dynamic analysis of a typical cantilevered-deck three-span bridge (75+120+75m) of Egnatia Odos as a practical tool for estimating seismic behavior. The options presently available to a designer are actually restricted to the static pushover analysis and the full nonlinear dynamic analysis. While the first is often inaccurate for asymmetric structures, the second is usually avoided due to complexity. As an intermediate solution, equivalent oscillators are tested using nonlinear dynamic analysis and having simple or complex, coupled or uncoupled forcedeformation relationships in each direction. Additionally, the roles of the simultaneous excitation in the two horizontal directions and of the horizontal curvature of the deck are examined. Using as reference the full model of the bridge with concurrent excitation in both directions, we estimate the error in omitting any of the above factors. In summary, we calibrate a series of simplifications that can be used by engineers to achieve a simple yet accurate analysis of cantilevered-deck bridges.
Vamvatsikos D. (2007). Performing incremental dynamic analysis in parallel using computer clusters. Proceedings of the COMPDYN2007 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Greece
Abstract | Incremental Dynamic Analysis (IDA) is a novel procedure that has recently emerged to accurately estimate the seismic performance of structures using multiple nonlinear dynamic analyses under scaled ground motion records. Being a computer intensive method, IDA can benefit greatly by parallel execution. Our aim is to accelerate the computation of IDA analyses using realistic structural models and multiple ground motion records on commercial or academic analysis platforms that were designed to be run on a single processor. Taking advantage of an environment of multiple network-connected processors, it becomes possible to complete such difficult tasks “over the weekend”. Several approaches in distributing the computational load between the processors are discussed, examining the feasibility of breaking up tasks at the level of a model (sub-structuring), a single dynamic run, or a single-record IDA study. The latter two methods are the simplest to implement using a task-farming technique where a master processor prescribes tasks for the independent slave processors. It is shown that this approach can be efficiently implemented by modifying the IDA hunt&fill tracing algorithm to balance the computational load among a number of non-identical processors. The result is a flexible, efficient and fault-tolerant parallel platform with excellent scaling that can rapidly perform multiple multi-record IDA studies within the typical computer network found in any engineering office.
Zeris C., Vamvatsikos D., Giannitsas P., Alexandropoulos K. (2007). Impact of FE modeling in the seismic performance prediction of existing RC buildings. Proceedings of the COMPDYN2007 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Greece
Abstract | The choice of available finite element modeling conventions of reinforced concrete (RC) buildings may influence significantly the predicted inelastic seismic performance during the evaluation of existing RC frame redesigns. The problem is investigated by analyzing alternative models of a typical existing five-story RC frame which has been designed for moderate seismicity, using past seismic provisions. Different inelastic finite element models of the structure are established, taking into account a range of practical and more detailed finite element idealizations that range from the widely adopted concentrated plasticity elements to the more complex distributed damage fiber elements, accounting or not for large deformations, joint flexibility, bond or shear deterioration. Following static inelastic analysis, key performance global and local response indices (such as interstory drift and plastic rotations) which are adopted in Performance Based Design, are estimated, to quantify the uncertainty introduced strictly by the modeling conventions alone. It is concluded that key response indicators (collapse mechanism, capacity curve and maximum plastic rotations) can be grossly underestimated strictly due to the model alone, something that should be considered in the normative process by tight modeling guidelines and adequate safety factors.
Vamvatsikos D. (2007). Influence of parameter uncertainties on the seismic performance of oscillators via SPO2IDA. Proceedings of the 10th International Conference on Applications of Statistics and Probability in Civil Engineering, Tokyo
Abstract | The effects of the parameter epistemic uncertainties on the predicted seismic performance are investigated for single-degree-of-freedom systems. The oscillators examined are 5%-damped systems having a complex quadrilinear backbone with pinching hysteresis, including an elastic, a hardening, a negative stiffness and a residual plateau branch, terminating with a final drop to zero strength. The six uncertain properties considered are the post-yield hardening ratio, the end-of-hardening ductility, the slope of the descending branch, the residual strength, the ultimate ductility and the period. Using Monte-Carlo simulation and the SPO2IDA tool for rapid performance estimation, we calculate the increased variability in the predicted limitstate capacities due to the epistemic uncertainty in each parameter. Thus, we are able to evaluate the influence of modeling assumptions to the predicted versus the actual seismic performance of the oscillator and understand the effect of the variability of each parameter to the total system variability at each limit-state.
Vamvatsikos D., Fragiadakis M. (2006). Seismic performance sensitivity of a 9-story steel frame to plastic hinge modeling uncertainties. Proceedings of the 1st European Conference on Earthquake Engineering and Seismology, Geneva
Summary | The effects of different beam-column plastic-hinge modelling assumptions on the seismic behaviour of steel frames are studied through Incremental Dynamic Analysis (IDA). The wellknown 9-story LA9 2D steel frame is used as a testbed by adopting multiple possible momentrotation relationships for the beam plastic-hinges. These are modelled as full quadrilinear backbones with pinching hysteresis, including an elastic, a hardening, a negative stiffness and a residual plateau branch, terminating with a final drop to zero strength. The properties considered include the post-yield hardening ratio, the end-of-hardening rotation, the residual moment capacity and the ultimate rotation reached. The hinge parameters are varied one at a time, globally throughout the building, generating several plausible structural models which differ only in the adopted connection model, some being more brittle and others more ductile. The seismic performance of each resulting frame is then evaluated using IDA, i.e., by performing multiple nonlinear time history analyses for a suite of ground motion records appropriately scaled to several intensity levels. By appropriately post-processing the results the median IDA curves are estimated, forming a solid basis for comparing the different models. Thus, we are able to evaluate the influence of several plastic-hinge modelling assumptions to the seismic performance of the frame and understand the sensitivity of such results that are usually estimated on the basis of a single structural model.
Zeris C., Giannitsas P., Alexandropoulos K., Vamvatsikos D. (2006). Inelastic modeling sensitivity of the predicted seismic performance of an existing RC building. Proceedings of the 1st European Conference on Earthquake Engineering and Seismology, Geneva
Summary | Inelastic modeling of entire reinforced concrete (RC) buildings under seismic excitation is a complex problem that influences directly the predicted seismic performance. Modeling assumptions and conventions adopted become more important in existing RC frame response predictions, due to these structures’ structural characteristics and non conforming detailing. The problem is investigated for a typical existing five-story RC frame which has been designed for moderate seismicity according to the past generation of Greek seismic codes. Different plane frame finite element models are formulated adopting state of the art as well as state of the practice analysis codes and finite element formulations. The seismic performance of each model is estimated, following both a conventional static pushover as well as nonlinear timehistory analyses under different levels of seismic intensity. The models range from the simple yet widely adopted in practice concentrated plasticity elements with axial-flexural strength interaction only, to the more complex distributed damage stiffness or flexibility-based fiber elements accounting or not for joint deformations. The results of the analyses are compared at the global and primarily the local damage prediction levels, to reveal substantial discrepancies and scatter in key performance Response Indices introduced in a Performance Based (re)Design approach by the model limitations, which are often ignored. It is concluded that, in addition to standardization of the criteria and procedures of evaluation, the analytical model for evaluating these Response Indices should also be well defined to avoid error and conflict.
Vamvatsikos D. (2006). Incremental Dynamic Analysis with two components of motion for a 3D steel structure. Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco
Abstract | Incremental dynamic analysis (IDA) is employed to evaluate the seismic performance of a 20-story steel space frame under biaxial seismic loading. Originally developed for planar frames and uniaxial loading, the IDA framework is now extended to 3D. This involves performing a series of nonlinear timehistory analyses under a suite of ground motion records by equally scaling both components of each record to several levels of intensity and recording the structural response. The structure is thus forced to show its complete spectrum of behavior from elasticity to final global instability for combinations of intensities in the two directions. Using proper intensity measures (e.g., spectral acceleration coordinates of the record components) and engineering demand parameters (e.g., maximum interstory drifts), the familiar IDA curves plus novel IDA surfaces are created, representing the structural response and its statistical summary at any intensity level. These enable a rational definition of limit-states and the calculation of the resulting capacities in a manner consistent with current IDA techniques. A powerful analysis procedure is thus created that is capable of thoroughly assessing the seismic performance of 3D structures and may serve as a solid benchmark for evaluating the accuracy of simpler methods.
Vamvatsikos D., Alexandropoulos K, Giannitsas P., Zeris C. (2006). Influence of element modeling on the predicted seismic performance of an existing RC building. Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco
Abstract | The effect of different element modeling formulations for reinforced concrete (RC) elements on the predicted performance of an RC building under seismic excitation is examined. The building selected is a typical existing five-story RC frame designed for moderate seismicity in the late 1960s, according to the older generation of Greek seismic codes with no special provisions for ductile behavior. Fiber elements are used to model the beams and columns using both stiffness and flexibility formulations, which lead to distinctly different behaviors. To evaluate the seismic performance of each alternate model, both static pushover and incremental dynamic analysis are used. The results are compared across all models, both at the local and the global level, to reveal the differences in the predicted seismic performance resulting from such a subtle modeling choice.
Vamvatsikos D., Sigalas I. (2005). Seismic performance evaluation of a horizontally curved highway bridge using incremental dynamic analysis in 3D. Proceedings of the 4th European Workshop on the seismic behaviour of irregular and complex structures, Thessaloniki, Greece
Abstract | The seismic performance of a horizontally curved highway bridge is examined using Incremental Dynamic Analysis (IDA) in 3D. IDA has been successfully applied to two dimensional structures with a single horizontal ground motion component. An extension to three dimensions and two components of motion is needed to capture the performance of this asymmetric structure. It involves performing a series of nonlinear timehistory analyses under a suite of ground motion records, equally scaling both components of each record to several levels of intensity and monitoring the resulting structural response. The complete spectrum of structural behavior is thus recovered, from elasticity to final global instability for combinations of intensities in the two directions. Using a single intensity measure or a vector of two (e.g. spectral coordinates of the record components) and appropriate engineering demand parameters (e.g., maximum peak column drift), the familiar IDA curves plus novel IDA surfaces are created, clearly showing the bridge response and its statistical summary at any intensity level. This is a powerful, albeit resource intensive, analysis procedure that is well suited to evaluate the performance of asymmetric structures under seismic loads and may serve as a solid benchmark for evaluating the accuracy of simpler methods.
Fragiadakis M., Vamvatsikos D., Papadrakakis M. (2005). Evaluation of the influence of vertical stiffness irregularities on the seismic response of a 9-story steel frame. Proceedings of the 4th European Workshop on the seismic behaviour of irregular and complex structures, Thessaloniki, Greece
Abstract | A methodology based on Incremental Dynamic Analysis (IDA) is proposed for evaluating the response of structures with single-storey vertical irregularities. Using the well-known 9-storey LA9 steel frame, the objective is to study the effect of the irregular distribution of stiffness and strength along its height. This is achieved by means of IDA, i.e., by performing nonlinear time history analysis for a suite of twenty ground motion records scaled to several intensity levels. The reference and each modified structure are hence forced to show the complete spectrum of behavior from elasticity to final global instability, allowing the estimation of capacities for the full range of limit-states and enabling a straightforward comparison without needing to “tune” the structures to the same fundamental period and/or the yield base shear. Using the bootstrap method confidence intervals are calculated and hypothesis testing is performed for changes in the median and the dispersion of capacity for each limit-state. Thus, it becomes possible to isolate the effect of irregularities from any possible record-to-record variability. In conclusion, the proposed methodology enables a full-range performance evaluation using a highly accurate analysis method that pinpoints the effect of any source of irregularity for every limit-state.
Vamvatsikos D., Papadimitriou C. (2005). Optimal multi-objective design of a highway bridge under seismic loading through Incremental Dynamic Analysis. Proceedings of the 9th International Conference on Structural Safety and Reliability (ICOSSAR), Rome, Italy
Abstract | A methodology is introduced for the optimal multi-criteria performance-based design of highway bridges under seismic loading based on the concept of Incremental Dynamic Analysis (IDA). IDA is a novel analysis method that can thoroughly estimate the seismic demands and limit-state capacities of a structure under seismic loads by subjecting it to a suite of ground motion records that are suitably scaled to several levels of intensity. The mean annual frequencies (MAFs) of exceeding each limit-state become readily available when combining the results with probabilistic seismic hazard analysis. By thus analyzing each alternate design we are able to directly apply the desirable constraints on the acceptable performance of the bridge and employ evolutionary strategies to perform Pareto optimization and minimize the bridge cost and the MAF of collapse. As an example, the Pareto set is generated for a typical two-span bridge with a single-column pier and a prestressed concrete deck supported on elastomeric bearings. It is shown that improving the bearings provides an inexpensive increase in collapse performance, but further gains necessitate costly strengthening of the pier column. The procedure presented is resource-intensive but highly accurate. It provides important information on the influence of design parameters on the bridge performance and allows their optimal selection.
Vamvatsikos D., Cornell C.A. (2004). Investigating the influence of elastic spectral shape on the limit-state capacities of a 9-story building through IDA. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver
Summary | The influence of the elastic spectral shape on the limit-state capacities of a 9-story steel moment-resisting frame is investigated through the use of Incremental Dynamic Analysis (IDA). IDA is a parametric analysis method that has recently emerged to estimate more thoroughly structural performance under seismic loads. It involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the Intensity Measure, IM), thus producing curves of response parameterized versus intensity level, on top of which limit-states can be defined and corresponding capacities can be calculated. When traditional IMs, such as the peak ground acceleration or the 5%-damped first-mode spectral acceleration, are used, the IM-values of limit-state capacity can display large record-to-record variability. Thus, a large number of ground motion records has to be used to achieve a given level of confidence in the results. By testing a multitude of single spectral values as well as scalar combinations of spectral ordinates on the 9-story frame, several candidate IMs are found that significantly reduce such dispersion and consequently the needed number of records. Furthermore, such results are used to determine the most influential regions (or periods) of the elastic spectrum for each limit-state of the building. Thus, we are able to observe the evolution of such influential periods as the seismic intensity and the response of the building increase, from first yield all the way to global collapse. In conclusion, the ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance of the building and they are shown to provide promising candidates for new, more efficient IMs.
Vamvatsikos D., Jalayer F., Cornell C.A. (2003). Application of Incremental Dynamic Analysis to an RC-structure. Proceedings of the FIB Symposium on Concrete Structures in Seismic Regions, Athens
Vamvatsikos D., Cornell C.A. (2002). The Incremental Dynamic Analysis and its application to Performance-Based Earthquake Engineering. Proceedings of the 12th European Conference on Earthquake Engineering, London
Abstract | Incremental Dynamic Analysis (IDA) is an emerging analysis method that offers thorough seismic demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a multiply scaled suite of ground motion records. Realization of its opportunities requires several innovations, such as choosing suitable ground motion Intensity Measures (IMs) and representative Damage Measures (DMs). In addition, proper interpolation and summarization techniques for multiple records need to be employed, providing the means for estimating the probability distribution of the structural demand given the seismic intensity. Limit-states, such as the dynamic global system instability, can be naturally defined in the context of IDA, thus allowing annual rates of exceedance to be calculated. Finally, the data gathered through IDA can provide intuition for the behavior of structures and shed new light on the connection between the Static Pushover (SPO) and the dynamic response. To illustrate all the above concepts, a complete walkthrough of the methodology is presented by using a 9-storey steel moment-resisting frame with fracturing connections as an example to explain and clarify the application of the IDA to Performance-Based Earthquake Engineering (PBEE).
Vamvatsikos D., Cornell C.A. (2002). Direct estimation of the seismic demand and capacity of MDOF systems through incremental dynamic analysis of an SDOF approximation. Proceedings of the 5th European Conference on Structural Dynamics EURODYN 2002, Munich
Abstract | Introducing a fast and accurate method to estimate the seismic demand and capacity of first-mode dominated multi-degree-of-freedom (MDOF) systems by approximating the Incremental Dynamic Analysis (IDA) through the Static Pushover (SPO) analysis. While the computer-intensive IDA would require several nonlinear dynamic analyses under multiple suitably-scaled ground motion records, the simpler SPO helps approximate the MDOF system with a single-degree-of-freedom (SDOF) oscillator whose backbone matches the structure’s SPO curve far beyond its peak. Thanks to the empirical equations implemented in the SPO2IDA software, the summarized IDA curves of the resulting system are effortlessly generated, enabling an engineeruser to obtain accurate estimates of seismic demands and capacities for limit-states such as global dynamic instability. Using a nine-storey building as a case study, the methodology is favorably compared to the full IDA.
Vamvatsikos D., Cornell C.A. (2002). Practical estimation of the seismic demand and capacity of oscillators with multi-linear static pushovers through Incremental Dynamic Analysis. Proceedings of the 7th U.S. National Conference on Earthquake Engineering, Boston
Abstract | The seismic behavior of numerous single-degree-of-freedom (SDOF) systems is investigated through Incremental Dynamic Analysis (IDA), a computer-intensive procedure that offers thorough (demand and capacity) prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. The oscillators are of moderate period with pinching hysteresis and feature backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative-stiffness segment plus a final residual plateau that terminates with a drop to zero strength. The results of the analysis are summarized into their 16%, 50% and 84% fractile IDA curves which are in turn fitted by flexible parametric equations. The final product is SPO2IDA, an accurate, spreadsheetlevel tool for Performance-Based Earthquake Engineering that is available on the web. It offers effectively instantaneous estimation of demands and global-instability collapse capacities, in addition to conventional strength reduction R-factors and inelastic displacement ratios, for any SDOF system whose Static Pushover curve can be approximated by such a quadrilinear backbone.
Cornell C.A., Vamvatsikos D., Jalayer F., Luco N. (2000). Seismic reliability of steel frames. Proceedings of the 9th IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, Ann Arbor, Michigan
Abstract | This paper presents an introduction to the probabilistic basis for a new set of seismic design and assessment procedures that consider explicitly nonlinear dynamic displacements. Two new seismic design and assessment guidelines make use of these developments. The new 2000 SAC steel moment-resisting seismic design and assessment guidelines prepared for FEMA and a new draft of the ISO offshore seismic guidelines use two different formats derived from this same probabilistic model.
Georgiadis H.G., Vamvatsikos D., Vardoulakis I. (1999). Numerical implementation of the integral-transform solution to Lamb’s point load problem. Proceedings of the 3rd Greek Geomechanics Conference, Volos
TECHNICAL REPORTS, GUIDELINES & STANDARDS
Now - 1999
Kohrangi M., Papadopoulos A.N., Kotha S.R., Vamvatsikos D., Bazzurro P. (2021). Earthquake Catastrophe Risk Modeling, Application to the Insurance Industry: Unknowns and Possible Sources of Bias in Pricing. In: Advances in Assessment and Modeling of Earthquake Loss. Springer: Dordrecht.
Abstract | Mathematical risk assessment models based on empirical data and supported by the principles of physics and engineering have been used in the insurance industry for more than three decades to support informed decisions for a wide variety of purposes, including insurance and reinsurance pricing. To supplement scarce data from historical events, these models provide loss estimates caused to portfolios of structures by simulated but realistic scenarios of future events with estimated annual rates of occurrence. The reliability of these estimates has evolved steadily from those based on the rather simplistic and, in many aspects, semi-deterministic approaches adopted in the very early days to those of the more recent models underpinned by a larger wealth of data and fully probabilistic methodologies. Despite the unquestionable progress, several modeling decisions and techniques still routinely adopted in commercial models warrant more careful scrutiny because of their potential to cause biased results. In this chapter we will address two such cases that pertain to the risk assessment for earthquakes. With the help of some illustrative but simple applications we will first motivate our concerns with the current state of practice in modeling earthquake occurrence and building vulnerability for portfolio risk assessment. We will then provide recommendations for moving towards a more comprehensive, and arguably superior, approach to earthquake risk modeling that capitalizes on the progress recently made in risk assessment of single buildings. In addition to these two upgrades, which in our opinion are ready for implementation in commercial models, we will also describe an enhancement in ground motion prediction that will certainly be considered in the models of tomorrow but is not yet ready for primetime. These changes are implemented in example applications that highlight their importance for portfolio risk assessment. Special consideration will be given to the potential bias in the Average Annual Loss estimates, which constitutes the foundation of insurance and reinsurance policies’ pricing, that may result from the application of the traditional approaches.
Aschheim M., Hernandez-Montes E., Vamvatsikos D., (2019). Design of Reinforced Concrete Buildings for Seismic Performance: Practical Deterministic and Probabilistic Approaches Protection of Built Environment Against Earthquakes. CRC Press.
Book Description | The costs of inadequate earthquake engineering are huge, especially for reinforced concrete buildings. This book presents the principles of earthquake-resistant structural engineering, and uses the latest tools and techniques to give practical design guidance to address single or multiple seismic performance levels.
It presents an elegant, simple and theoretically coherent design framework. Required strength is determined on the basis of an estimated yield displacement and desired limits of system ductility and drift demands. A simple deterministic approach is presented along with its elaboration into a probabilistic treatment that allows for design to limit annual probabilities of failure. The design method allows the seismic force resisting system to be designed on the basis of elastic analysis results, while nonlinear analysis is used for performance verification. Detailing requirements of ACI 318 and Eurocode 8 are presented. Students will benefit from the coverage of seismology, structural dynamics, reinforced concrete, and capacity design approaches, which allows the book to be used as a foundation text in earthquake engineering.
Silva V., Casotto C., Rao A., Villar M., Crowley H., Vamvatsikos D. (2015). OpenQuake Risk Modeller’s Toolkit – User Guide. GEM Technical Report 2015-09. Global Earthquake Model Foundation, Pavia, Italy. DOI: 10.13117/GEM.OPENQUAKE.MAN.RMTK.1.0/02
Summary
The goal of this book is to provide a comprehensive and transparent description of the methodologies adopted during the implementation of the OpenQuake Risk Modeller’s Toolkit (RMTK). The Risk Modeller’s Toolkit (RMTK) is primarily a software suite for creating the
input models required for running seismic risk calculations using the OpenQuake-engine. The RMTK implements several state-of-the-art methods for deriving robust analytical seismic fragility and vulnerability functions for single structures or building classes. The RMTK
also provides interactive tools for post-processing and visualising different results from the OpenQuake-engine seismic risk calculations, such as loss exceedance curves, collapse maps, damage distributions, and loss maps.
The OpenQuake Risk Modeller’s Toolkit is the result of an effort carried out jointly by the IT and Scientific teams working at the Global Earthquake Model (GEM) Secretariat. It is freely distributed under an Affero GPL license (more information available at this link http://www.gnu.org/licenses/agpl- 3.0.html).
D’Ayala D., Meslem A., Vamvatsikos D., Porter K., Rossetto T. (2015). Guidelines for Analytical Vulnerability Assessment of Low/Mid-Rise Buildings. GEM Technical Report 2014-12. Global Earthquake Model Foundation, Pavia, Italy. DOI 10.13117/GEM.VULN-MOD.TR2014.12
Summary
Guidelines (GEM-ASV) for developing analytical seismic vulnerability functions are offered for use within the framework of the Global Earthquake Model (GEM). Emphasis is on low/mid-rise buildings and cases where the analyst has the skills and time to perform non-linear analyses. The target is for a structural engineer with a Master’s level training and the ability to create simplified non-linear structural models to be able to determine the vulnerability functions pertaining to structural response, damage, or loss for any single structure, or for a class of buildings defined by the GEM Taxonomy level 1 attributes. At the same time, sufficient flexibility is incorporated to allow full exploitation of cutting-edge methods by knowledgeable users. The basis for this effort consists of the key components of the state-of-art PEER/ATC-58 methodology for loss assessment, incorporating simplifications for reduced effort and extensions to accommodate a class of buildings rather than a single structure, and multiple damage states rather than collapse only considerations.
To inject sufficient flexibility into the guidelines and accommodate a range of different user needs and capabilities, a distinct hierarchy of complexity (and accuracy) levels has been introduced for (a) defining index buildings, (b) modelling, and (c) analysing. Sampling-wise, asset classes may be represented by random or Latin hypercube sampling in a Monte Carlo setting. For reduced-effort representations of inhomogeneous populations, simple stratified sampling is advised, where the population is partitioned into a number of appropriate subclasses, each represented by one “index” building. Homogeneous populations may be approximated using a central index building plus 2k additional high/low observations in each of k dimensions (properties) of interest. Structural representation of index buildings may be achieved via typical 2D/3D element-by-element models, simpler 2D storey-by-storey (stick) models or an equivalent SDOF system with a
user-defined capacity curve. Finally, structural analysis can be based on variants of Incremental Dynamic Analysis (IDA) or Non-linear Static Procedure (NSP) methods.
A similar structure of different level of complexity and associated accuracy is carried forward from the analysis stage into the construction of fragility curves, damage to loss function definition and vulnerability function derivation.
In all cases, the goal is obtaining useful approximations of the local storey drift and absolute acceleration response to estimate structural, non-structural, and content losses. Important sources of uncertainty are identified and propagated incorporating the epistemic uncertainty associated with simplifications adopted by the user. The end result is a set of guidelines that seamlessly fits within the GEM framework to allow the generation of vulnerability functions for any class of low/mid-rise buildings with a reasonable amount of effort by an informed engineer. Two illustrative examples are presented for the assessment of reinforced-concrete moment-resisting frames with masonry infills and unreinforced masonry structures, while a third example treating ductile steel moment-resisting frames appears in a companion document.
Porter K., Farokhnia K., Vamvatsikos D. and Cho I.H. (2014). Guidelines for component-based analytical vulnerability assessment of buildings and nonstructural elements. GEM Technical Report 2014-13. Global Earthquake Model Foundation, Pavia, Italy. DOI: 10.13117/GEM.VULN-MOD.TR2014.13.
https://storage.globalquakemodel.org/media/publication/GEM-GC-BAVAB-NEGuidelines-201413v01.pdf
Summary
A procedure is offered for the analytical derivation of the seismic vulnerability of building classes, that is, probabilistic relationships between shaking and repair cost as a fraction of replacement cost new for a category of buildings. It simulates structural response, damage, and repair cost for the structural and non-structural components that contribute most to construction cost, and then scales up results to account for the components that were not simulated. It does so for a carefully selected sample of building specimens called index buildings whose designs span the domain of up to three features that are believed to most strongly influence seismic vulnerability within the building class. One uses moment matching to combine results for the index buildings to estimate behaviour and variability of the building class. One can simulate non-structural vulnerability alone by ignoring damage and repair cost for structural components. The work is written for a structural engineer with a master’s degree, skilled in structural analysis, but not necessarily experienced in loss modelling.
The procedure has five steps. In Step 1, the analyst defines the asset class with one, three, or seven specimens of the asset class; the specimens are called index buildings. The choice depends on available resources and the rigor with which the analyst wants to address variabilities within the building class and within the performance of an individual index building. Each index building is assigned a particular structural and non-structural design, including number of stories, structural material, lateral load resisting system (LLRS), geometry, and quantities of each of the top 1 or 2 structural component categories and top 5 or 6 non-structural component categories.
Step 2 is to derive story-level vulnerability functions, without considering collapse. (Collapse is addressed in a later step.) The vulnerability functions express the repair cost of components on the story as a function of story-level excitation (drift, acceleration, or other measures of story-level structural response). Step 3 is to perform a structural analysis at each of many levels of ground motion with the objective of estimating story-level excitation and collapse probability as a function of ground motion. We offer three options for structural analysis, from a very simple approach to multiple nonlinear dynamic structural analyses; the analyst is free to choose among these, again considering available resources and desired rigor.
Step 4 is to derive a building-level vulnerability function by summing story-level losses over stories, factoring up to account for the fact that only the top 6 to 8 structural and non-structural component categories are inventoried, applying the theorem of total probability to consider the probability of collapse. By omitting the top 2 or so structural components, one can create vulnerability functions for only the non-structural components. The vulnerability function is normalized by replacement cost new to depict damage factor as a function of ground motion.
In Step 5, the mean vulnerability function and coefficient of variation of damage factor for the asset class are calculated. The mean damage factor for the asset class is calculated as a weighted average of those of the index buildings. The coefficient of variation is calculated by one of three means: using a proxy from HAZUS in the case of a single index building, as a multiple of the variability of vulnerability between index buildings in the case of three index buildings, or in the case of seven index buildings, by calculating the variance of vulnerability of the weighted sample of index-building-level vulnerability functions, including both between- and within-building variability.
Fragiadakis M., Vamvatsikos D., Aschheim M. (2011). Static versus dynamic methods of analysis for estimating seismic performance. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | Nonlinear static methods are evaluated and compared with nonlinear dynamic methods for estimating the seismic performance of structures. Emphasis is given on assessing the applicability of nonlinear static methods for RC buildings, and on comparing the building’s capacity obtained using nonlinear static and nonlinear response history analysis. The first task refers to the ability of alternative static pushover-based methods to estimate the response at the level of a member or of a story. Plain as well as more elaborate pushover methods such as the Modal Pushover Analysis method and the Consecutive Modal Pushover method are included in our evaluation. The second task refers to the qualitative comparison at the global level between static pushover and nonlinear response history analysis when either the static pushover or the Incremental Dynamic Analysis (IDA) setting is adopted. When the static pushover setting is adopted, we show that nonlinear static methods can be compared with the IDA curve when the base shear instead of spectral acceleration is plotted on the ordinates, while the dispersion among the single-record IDAs is considerably reduced. Alternatively, the comparison can be performed within the IDA setting if appropriate R-C 1-T relationships, simplified or more advanced (e.g. SPO2IDA), are adopted. Each setting shows different qualitative characteristics of the two seismic performance estimation approaches and has different practical applications.
Celarec D., Vamvatsikos D., Dolsek M. (2011). Simplified estimation of seismic risk for buildings with consideration of the structural ageing process. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract |A simplified method for estimating the seismic risk of deteriorating buildings is presented utilizing a probabilistic framework and a simplified nonlinear method for seismic performance assessment of structures. Firstly, the probabilistic methodology with the extension to deteriorating structures is briefly explained. Then the methodology is applied to the example of a four-storey RC frame building with corroded reinforcement in order to estimate the influence of corrosion on seismic risk for the near-collapse limit state. The results reveal that after 50 years from the initiation of corrosion, the peak ground acceleration that causes the structure to violate the defined near collapse limit state decreases by 17% and the seismic risk for the near-collapse limit state increases by 7%, compared to the case where corrosion is neglected. It is also shown that degradation due to corrosion may change the collapse mechanism from ductile to brittle shear failure, raising an important question on the seismic safety of the existing buildings.
Vamvatsikos D. (2011). Some thoughts on methods to compare the seismic performance of alternate structural designs. In: Dolsek M. (ed), Protection of Built Environment Against Earthquakes. Springer: Dordrecht.
Abstract | The process of structural design ultimately hinges upon the selection of the top alternative designs from a group of viable choices, ideally choosing the one that best satisfies the requirements, as set by codes or guidelines. Comparing structural configurations to find the best candidate has thus remained a favorite subject of researchers and engineers alike, especially in the case of seismic loads. With the emergence of performance-based earthquake engineering, such comparisons now need to be performed on the basis of the seismic performance, preferably at several limit-states. Such a direct evaluation can become cumbersome, requiring seismic hazard information. Therefore, shortcuts and simpler techniques have been introduced that are generally based on the concept of system fragility, as estimated through the various methods of structural analysis. Still, there is no general consensus on the metrics that can be used for such an evaluation; some researchers adopt force or displacement response quantities derived from static or dynamic methods, while others prefer to compare capacities in terms of intensity or response measures. In order to even out the field, we perform a comparative evaluation of the available choices and point out the pros and cons of each, showing some of the common fallacies that plague the results of such comparisons.