Statistics so far
JOURNAL PAPERS

2024-3
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.
2022
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.
Melissianos V.E. (2022). Onshore Buried Steel Fuel Pipelines at Fault Crossings: A Review of Critical Analysis and Design Aspects. Journal of Pipeline Systems Engineering and Practice, 13(4): 03122002.
Abstract | Onshore buried steel pipeline infrastructure is a critical component of the fuel supply system. Pipeline failure due to seismic actions is socially, environmentally, and economically unacceptable and thus the design of pipelines in geohazard areas, such as fault crossings, remains a hot topic for the pipeline community. There is an intense research effort on the evaluation of the pipeline mechanical behavior and the strength verification at fault crossings. Still, some aspects need in-depth consideration concerning practical applications. A state-of-the-art review is presented on three critical analysis and design aspects, namely, the calculation of the design fault displacement via deterministic and probabilistic methods, the effect of numerical modeling parameters such as soil spring properties, and the alternative pipe protection measures in terms of availability, efficiency, and selection process. The critical review offers a thorough insight into what is available and how to employ it in design, assisting engineers and pipe operators in improving pipe safety.
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.
2021
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.
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.
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.
Bakalis K, Karamanos SA. (2021). Uplift mechanics of unanchored liquid storage tanks subjected to lateral earthquake loading. Thin-Walled Structures, 158: 107145
Abstract | Motivated by the seismic response of unanchored liquid storage tanks, their uplift mechanism under strong lateral loading is examined. Using three-dimensional finite element models, nonlinear static analysis is conducted to define the moment-rotation relationship of uplifting tanks resting on rigid foundation and describe the evolution of critical response parameters with increasing level of lateral loading. Meridional and hoop stress, as well as their distribution and evolution with increased uplift are computed. Comparing the numerical results with the corresponding results from anchored tanks, striking differences are observed on the values of compressive meridional stresses and their distribution around the tank circumference. Cyclic analysis, associated with repeated uplift at both sides of the tank, is also performed, to obtain the corresponding hysteretic response and verify the assumption of nonlinear-elastic tank behaviour, used in several previous works. Finally, an analytical solution is developed, capable of describing tank uplift in an efficient manner. The analytical solution accounts for the special features of uplift, obtained from the finite element solution, and can be used for simple and reliable assessment of seismic performance in unanchored liquid storage tanks.
2020
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.
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.
2019
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.
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.
Z. Fasoulakis, X. Lignos, T. Avraam, S. Katsatsidis. (2019). Investigation on single-bolted cold-formed steel angles with geometric imperfections under compression. Journal of Constructional Steel Research, 162: 1-13
Abstract | The behaviour of cold-formed steel angle members with bolted connections under compression is usually complicated, whereas not significant number of experimental tests is found in the literature. This study offers a better insight on the issue, by comparing experimental tests with a thorough numerical study, both carried out at the Institute of Steel Structures of NTUA. Significant attention is paid for the elaborate measurement of initial geometric imperfections along the member’s length. An in-house built deformation plotter was designed and upgraded for this reason. The compression failure loads of the experimental tests are illustrated both in graphical and tabular form and compared with similar tests of the literature. The results denote a prediction of the EN 1993-3-1 towards the safe side, for the case of the examined bolted cold-formed angles. A simple formula is proposed for the accurate prediction of angle columns’ buckling deformation, wherein the rigidity of the connection is also included. Finally, interesting conclusions are derived for the numerical simulation of cold-forming effects, as well as the shape and amplitude of the initial imperfect geometry, on the basis of the critical buckling load. Further research is in progress, aiming to capture the stochastic buckling response for the case of bolted cold-formed steel angles.
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.
Avgerinou S., Lignos X., Tsarpalis D., Vayas I. (2019) Full-scale tests on used steel storage racks. Steel Construction, 12: 231-242.
Abstract | Industrial storage operators use not only new pallet racking systems, but also old ones for which certification documents possibly do not exist. In order to check the carrying capacity of such racks, in addition to component tests, full‐scale experimental tests were carried out on complete structures to help the development of reliable numerical models. The racks were subjected to vertical and pushover loads in the laboratory using an improved version of the base plates to achieve fixed support conditions. Vertical loading was imposed by filling tanks with water, an operation that was activated and controlled through an innovative hydraulic network specifically designed for this purpose. During the vertical loading tests, a moderate earthquake took place near the experimental facility and this influenced the rack behaviour positively. The spine brace was too flexible in the out‐of‐plane direction and did not participate in the resistance to lateral forces. Distortional buckling of the columns was observed at high lateral loads. The experimental tests allowed the calculation of conservative values for the behaviour factor q.
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.
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.
2018
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.
C. Maraveas, Z. Fasoulakis. (2018), Wind-induced failure analysis and retrofit of an existing steel structure. Open Journal of Civil Engineering, 8: 271-291
Abstract | The “Dimitrios Vikelas” athletic center in Ermoupolis of Syros, Greece, consists of two buildings. Building B has a steel superstructure that was constructed approximately 35 years ago. It was initially used as a boat shelter and no design calculations were made. It contains steel columns with varying cross section heights. The spans are bridged via trusses and I-beams. Significant geometrical inconsistencies are noted among the existing steel connections and failures have been recorded as a result of buckling in several beams and bracings during the service life of the athletic center. The current study presents an investigation performed in order to diagnose building structural problems and propose strengthening and intervention measures. The goal of this study was to improve the load-carrying capacity of the structure in order to comply with the current design codes. Moreover, enhancement of the dynamic properties of the strengthened structure was demonstrated using modal analyses. The structural behavior was determined in a more precise manner via non-linear wind time-history and incremental static analyses. The analytical results explain the development of failures in the existing structure.
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.
2017 - 1999
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.
Fasoulakis Z., Raftoyiannis I., Avraam T. (2017). Experimental and numerical study on single-bolted cold-formed angles under tension and compression. Earthquake Engineering, Frontiers in Built Environment, 3:75
Abstract | Angle sections are commonly designed to bear only axial force, usually neglecting the additional bending moments resulting from the eccentric connection and the shift of the effective centroid. The current work deals with the capacity of single-bolted equal angle sections made from cold-formed steel. The experimental investigation presented herein includes tension and compression tests that subsequently are compared with the corresponding code provisions. Numerical analyses are also presented based on a detailed finite element simulation. Finally, a reliability analysis is implemented in order to demonstrate the reliability of the design rules for cold-formed steel angle columns. Results indicate a small discrepancy on the strength prediction in general by EN 1993-1-3, as well as by the AISI for slender columns and a more conservative one by EN 1993-1-1. A comparison of the above results is clearly illustrated herein in graphical forms.
Maraveas C., Fasoulakis Z., Tsavdaridis K.D. (2017). Mechanical properties of high strength and very high strength at elevated temperatures and after cooling down. Fire Science Reviews, 6:3
Abstract | High-strength steels (HSS) are produced using special chemical composition or/and manufacturing processes. Both aspects affect their mechanical properties at elevated temperatures and after cooling down, and particularly the residual strength and the ductility of the structural members. As HSS equates the design of lighter structural elements, higher temperatures are developed internally compared to the elements designed with conventional carbon steel. Therefore, the low thickness members, along with the severe effect of high temperature on the mechanical properties of the HSS, constitute to the increased vulnerability of such structures in fire. Moreover, the re-use and reinstatement of these structures are more challenging due to the lower residual mechanical properties of HSS after the cooling down period. This paper presents a review of the available experimental studies of the mechanical properties of HSS at elevated temperatures and after cooling down. The experimental results are collected and compared with the proposed material model (reduction factors) of EN1993–1-2. Based on these comparisons, modified equations describing the effect of elevated temperatures on the mechanical properties of HSS are proposed. Also, the post-fire mechanical properties of HSS are examined. A comprehensive discussion on the effect of influencing parameters, such as manufacturing process, microstructure, loading conditions, maximum temperature, and others is further explored.
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.
Maraveas C., Fasoulakis Z., Tsavdaridis K.D. (2017). Post-fire assessment and reinstatement of steel structures. Journal of Structural Fire Engineering, 8(2):181-201
Abstract | Purpose | This paper aims to present technical aspects of the assessment method and evaluation of fire damaged steel structures. The current work focuses on the behavior of structural normal steel (hot-rolled and cold-formed) and high-strength bolts after exposure to elevated temperatures. Information on stainless steel, cast iron and wrought iron is also presented.
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.
Melissianos, V. E., Lignos, X. A., Mpachas, K., and Gantes, C. J. (2017). Experimental Investigation of Pipes with Flexible Joints under Fault Rupture. Journal of Constructional Steel Research, 128: 633-68
Abstract | Objective of the present study is the experimental investigation and comparison of the response of continuous pipes and pipes with internal flexible joints under imposed transverse displacement, modeling seismic fault rupture. Three-point bending tests were performed modeling the deformation of buried pipes subjected to fault offset. The introduction of flexible joints between adjacent pipeline parts is proposed as an alternative protection measure to reduce developing strains due to such offsets. Indeed, experimental results confirmed very significant contribution of flexible joints in strain reduction, thus providing strong promise of effective protection of buried pipes from the principal failure modes occurring in such cases, i.e. local buckling of pipe wall and tensile fracture of girth welds between adjacent pipeline segments. Experimental results have been sufficiently reproduced by numerical simulation accounting for geometric and material nonlinearities and incorporating longitudinal residual stresses due to seam weld. The numerical analyses and corresponding results are also presented in detail.
Gantes, C. J., and Melissianos, V. E. (2016). Evaluation of Seismic Protection Methods for Buried Fuel Pipelines Subjected to Fault Rupture. Frontiers in Built Environment, 2:34
Abstract | Buried steel fuel pipelines are critical lifelines for the society and the economy but are very vulnerable to earthquake-induced ground failure. Traversing seismic areas inevitably results in several pipe-fault crossings. Fault rupture forces a buried pipeline to undergo deformations that could be substantial and heavily endanger its integrity. Due to the grave consequences of a potential pipe failure, mitigating measures are commonly applied at pipe-fault crossings to reduce the effects of a potential fault activation. In this paper, a comparative review of several measures that are used in practice or have been proposed in the technical literature is presented. Numerical analyses are then carried out to compare the effectiveness of commonly used measures and to extract conclusions regarding their applicability. Results indicate that the most efficient among the evaluated measures are pipe placement within culverts and use of flexible joints. Trench backfilling with pumice is a moderately effective measure in terms of pipe protection, while steel grade upgrade, wall thickness increase, and pipe wrapping with geotextile are found to be insufficient protection methods.
Melissianos, V.E., Gantes, C.J. (2017). Numerical Modeling Aspects of Buried Pipeline—Fault Crossing. In: Papadrakakis, M., Plevris, V., Lagaros, N. (eds) Computational Methods in Earthquake Engineering. Computational Methods in Applied Sciences, vol 44. Springer, Cham.
Abstract | Onshore buried steel pipelines transporting oil and gas play a major role in the energy supply chain. Hence, when seismic areas are transversed, fault crossing might be inevitable, which may heavily endanger the pipeline integrity. Thus, the design of buried pipelines at fault crossing remains a research topic of great interest both for the industry and the academia. Experimental, analytical and numerical approaches are used for that purpose. In this chapter, the numerical modeling of pipelines subjected to faulting is addressed and the advantages and disadvantages of the available numerical approaches are highlighted. The impact of fault type on the pipeline mechanical behavior is investigated and numerical considerations, such as the geometrical nonlinearity, the ovalization and the internal pressure are evaluated using a simple, well-established and reliable numerical approach. The outcome of this study provides useful information and guidelines to practicing engineers for the analysis and design of buried pipelines at fault crossings.
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.
Melissianos, V. E., Korakitis, G. P., Gantes, C. J., and Bouckovalas, G. D. (2016). Numerical Evaluation of the Effectiveness of Flexible Joints in Buried Pipelines Subjected to Strike-Slip Fault Rupture. Soil Dynamics and Earthquake Engineering, 90: 395-410
Abstract | Buried steel pipelines transport large amounts of fuel over long distances and inevitably cross active tectonic seismic faults when seismic areas are traversed. Eventual fault activation leads to large imposed displacements on the pipeline, which may then fail due to local wall buckling or tensile weld fracture, having grave financial, social and environmental consequences. In this paper, flexible joints are evaluated as an innovative mitigating measure against the consequences of faulting on pipelines. Joints are introduced in the pipeline in the fault vicinity, aiming at absorbing the developing deformation through relative rotation between adjacent pipeline parts, which then remain relatively unstressed. The effectiveness of flexible joints is numerically evaluated through advanced 3D nonlinear finite element modeling. Extensive parametric analysis is carried out to determine the effect of pipeline – fault crossing angle, fault offset magnitude, joint angular capacity, burial depth and diameter over thickness ratio on the joint efficiency. The uncertainty regarding the fault trace is also addressed.
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.
Melissianos, V. E., and Gantes, C. J. (2016). Buckling and Post-Buckling Behavior of Beams with Internal Flexible Joints Resting on Elastic Foundation Modeling Buried Pipelines. Structures, 7: 138-152
Abstract | The buckling and post-buckling behavior of axially loaded Winkler beams with flexible internal hinges is addressed, aiming to provide a background for the investigation of upheaval buckling of buried pipelines equipped with flexible joints for their protection against activation of reverse seismic faults. In order to acquire qualitative understanding of the interaction between the hinge stiffness and the soil stiffness for different cases, the beams under investigation are considered as either simply-supported or clamped. At first, elastic critical buckling loads and corresponding eigenmodes are numerically obtained using linearized buckling analysis, and eigenmode cross-over is investigated considering soil and hinge rotational stiffness. Geometrically nonlinear analyses with imperfections (GNIA) are then performed, indicating for most cases descending post-buckling paths, thus unstable post-buckling behavior, with the exception of cases of very soft soil. The sensitivity of the response to initial imperfection shape and magnitude is also addressed, to identify their impact on the post-buckling behavior. Beam buckling behavior is moreover examined by considering the beam being surrounded by soil exhibiting different stiffness in the upward and the downward direction. The results are compared to the case of a continuous beam, in order to highlight the impact of internal hinges on the beam overall buckling behavior.
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.
Maraveas C., Fasoulakis Z., Tsavdaridis K.D. (2015). Human induced vibrations on footbridges: a review. American Journal of Applied Sciences, 8(4): 422-433
Abstract | An extensive literature review of human induced vibrations that flexible footbridges experience is addressed in this study. Qualitative information is comprehensively included herein to provide common methods and code recommendations for the practicing engineers. The parameters affecting the dynamic response of footbridges excited by pedestrians are highlighted. In particular, the synchronous lateral excitation is addressed. This investigation can be valuable for the design criteria selection. In addition, this work contributes to the review of numerous case studies correlating important dynamic characteristics for various footbridge structural types, the variability of which confirms the complexity of the issue. Furthermore, vibration upgrading methods are described, focusing on applications of tuned mass dampers and remarkable conclusions are drawn.
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.
Maraveas C., Tasiouli K., Fasoulakis Z. (2015). Assessment of the New Faliron steam-electric station in Greece. WIT Transactions on The Built Environment, 153: 247-259
Abstract | The New Faliron steam-electric station, the first one in Greece, is a listed historical building. The initial structure was constructed at the start of the 20th century but a number of interventions followed until the 1960s. The structure was built with natural stone masonry, steel trusses and floors (with jack arches and joist fillers) and concrete floors reinforced with twisted cold formed rebars. The 12.5m high masonries practically lack any lateral restraints while large openings (doors, windows) exist. This paper presents brief information on the history of the structure, phases of construction, description of structure (dimensions, types of structural systems, etc), material properties and pathology. In addition, detailed information is presented regarding the assessment performed in accordance with the current code specifications (Eurocodes), including seismic actions. Especially for the masonry, a detailed finite element model was developed, whereas the seismic forces were evaluated through alternative methodologies (modal response spectrum analysis per EC8 and time history analyses). For the assessment of the RC part a displacement based methodology was applied as it is restrained by the surrounding masonry walls. From the assessment analysis, useful conclusions are drawn regarding the seismic performance of high masonry structures without lateral restraints and the behaviour of similar industrial structures under seismic effects.
Fasoulakis Z., Avraam T., Raftoyiannis I. (2015). Dynamic buckling of partially-sway frames with varying stiffness using Catastrophe Theory. International Journal of Non-Linear Mechanics, 71: 116-126
Abstract | This work deals with the static and dynamic stability analysis of imperfect partially-sway frames with non-uniform columns. The examined two-bar frames are elastically supported and subjected to an eccentrically vertical load at their joint. Through a linear stability analysis, the effect of the taper ratio of the column cross-section on the buckling capacity of the partially-sway frame is thoroughly discussed. Using a non-linear method an accurate formula has been established for determining the exact asymmetric bifurcation point associated with the maximum load carrying capacity. These findings have been re-derived more readily using Catastrophe Theory (CT) and considering the frame as a one degree-of-freedom (1-DOF) system through an efficient technique. A local analysis allows us to classify, after reduction, the total potential energy (TPE) function of the system to one of the seven elementary Thom׳s catastrophes (with known properties) and to obtain static and dynamic singularity as well as bifurcational sets. It has been found that geometrical and loading imperfections, which are always present in structural engineering problems, have a significant effect on the dynamic buckling loads. The efficiency of the present approach is illustrated via several examples, while results from finite element analyses are in good agreement with the analytical solution presented herein.
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.
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.
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.
T. Avraam, Z. Fasoulakis. (2013). Non-Linear Post-Buckling Analysis of Frames with Varying Cross-Section Columns. Journal of Engineering Structures, 56: 1-7
Abstract | A nonlinear static analysis is performed on an imperfect elastically supported two bar frame, which is subjected to a concentrated vertical load eccentrically at its joint. The column has a variable cross-section whereas the girder has a uniform cross-section. The variation ratio of the column cross- section is extensively investigated in combination with other geometric parameters (ratios of lengths and moments of inertia between column and girder) as well as loading parameters (loading eccentricity). Following a simplified procedure where the horizontal stiffness of the frame is modeled by a spring at the joint of the frame, it has been found that the developed axial force in the girder can be neglected (insignificant deviation of the exact results). Nonlinear finite element analysis is performed to verify the analytical results.
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., 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.
A.K. Kazantzi, T.D. Righiniotis, M.K. Chryssanthopoulos. (2011) A simplified fragility methodology for regular steel MRFs, Journal of Earthquake Engineering; 15(3), 390-403
Abstract | During the last decade, significant progress has been made toward the development of probabilistic methods for the seismic assessment of structures. However, the use of existing analytical fragility methodologies for practical applications related to structures of moderate to low importance remains prohibitive, in part due to substantial computational demands. This paper explores, through a case study, the robustness of a simplified methodology for fragility assessment of regular steel Moment Resisting Frames (MRFs). Through comparisons with a more accurate but computationally demanding methodology, it was confirmed that the “2000 SAC/FEMA” procedure gives robust fragility estimates. Moreover, it was found that a closed-form fragility assessment, where the structural response is evaluated by means of an Equivalent Single Degree Of Freedom (ESDOF) oscillator, can yield sufficiently accurate results for regular steel MRF structures, providing acceptable construction quality has been achieved in the connections.
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.
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.
Kazantzi A.K., Righiniotis T.D., Chryssanthopoulos M.K. (2008). The effect of joint ductility on the seismic fragility of a regular moment resisting steel frame designed to EC8 provisions. Journal of Constructional Steel Research, 64: 987-996
Abstract | In order to evaluate the seismic reliability of moment resisting frames at performance levels associated with highly nonlinear structural responses, structural modelling of the rotational capacity of the joints needs to address potential failure modes. This paper begins by reviewing European experimental studies on the cyclic behaviour of steel joints. A linear regression equation, which relates the joint plastic rotation capacity to the beam depth, is proposed based on an analysis of the test data. Thus, the effect of joint ductility and failure on structural response is quantified, within a probabilistic context, through seismic fragility analysis of a mid-rise steel frame designed to Eurocode 8. The variability in structural demand is estimated at increasing ground shaking intensity levels, and fragility curves, conditional on a given ground motion record, are derived for two different performance levels. The inherent randomness in ground motion is taken into account by using an ensemble of recorded accelerograms. The effect of joint rotation capacity is noticeable in mean fragility curves corresponding to high seismic demand and response levels.
Kazantzi A.K., Righiniotis T.D., Chryssanthopoulos M.K. (2008). Fragility and hazard analysis of a welded steel moment resisting frame. Journal of Earthquake Engineering, 12(4): 596-615
Abstract | With the move towards performance and consequence-based design and assessment of structures under seismic loading, the engineering community is becoming increasingly convinced that design practices need to be developed and checked using probabilistic methods. In this article, a methodology for the probabilistic assessment of low-rise steel buildings is presented and applied to a welded Moment Resisting Frame (MRF). In light of recent field experience for this form of construction, emphasis is given to the modeling of connections, particularly with respect to fracture characteristics. The seismic behavior of the building is assessed by means of nonlinear dynamic time history analyses, using a set of ground motions scaled according to spectral acceleration. Randomness related both to structural properties and earthquake excitation is explicitly taken into account. Fragility curves are generated using the Monte Carlo (MC) simulation method coupled with the Latin Hypercube Sampling (LHS) technique, and the failure probabilities are presented in terms of drift angles at different performance levels. Furthermore, evaluation of the seismic risk through a hazard analysis is presented in order to compare present results with previous pertinent studies. The study reveals that structures experiencing brittle connection fractures undergo large deformations, resulting in a low reliability in terms of achieving code-related performance requirements.
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.
TECHNICAL REPORTS, GUIDELINES & STANDARDS

Now-2014
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.
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.
Melissianos, V.E., Gantes, C.J. (2017). Numerical Modeling Aspects of Buried Pipeline—Fault Crossing. In: Papadrakakis, M., Plevris, V., Lagaros, N. (eds) Computational Methods in Earthquake Engineering. Computational Methods in Applied Sciences, vol 44. Springer, Cham.
Abstract | Onshore buried steel pipelines transporting oil and gas play a major role in the energy supply chain. Hence, when seismic areas are transversed, fault crossing might be inevitable, which may heavily endanger the pipeline integrity. Thus, the design of buried pipelines at fault crossing remains a research topic of great interest both for the industry and the academia. Experimental, analytical and numerical approaches are used for that purpose. In this chapter, the numerical modeling of pipelines subjected to faulting is addressed and the advantages and disadvantages of the available numerical approaches are highlighted. The impact of fault type on the pipeline mechanical behavior is investigated and numerical considerations, such as the geometrical nonlinearity, the ovalization and the internal pressure are evaluated using a simple, well-established and reliable numerical approach. The outcome of this study provides useful information and guidelines to practicing engineers for the analysis and design of buried pipelines at fault crossings.
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

2024
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]
Skoulidou D., Kazantzi A.K. (2024). An Indicator-based Multi-Hazard Risk Assessment Framework For Urban-Scale Applications. Proceedings of the 18th World Conference on Earthquake Engineering, Milan, Italy.
Abstract | Owing to the intensified urbanisation and the multiple stressors that are faced by contemporary cities, there is currently an ever-increasing interest for the development of urban-scale risk assessment methodologies targeting a wide spectrum of natural and man-made perils. Representative examples of such perils are the urban flash floods, the urban heat island effect as well as the air quality degradation, whose intensity and frequency have been increasing during the past years due to the adverse consequences of climate change. In this context, the present research offers a practical indicator-based methodology for providing spatially variable risk estimates across a city network that is likely to be affected by a variety of perils.
The proposed risk assessment methodology accounts for both the physical and the social risk dimensions, while particular emphasis is given in the definition of the vulnerability component, that involves indicators which account for the susceptibility (i.e., propensity to damage/losses) as well as the lack of capacity to cope. The explicit inclusion of indicators that depict the coping capacities of a city against a certain peril, enables the comparative evaluation of several alternative counter measures within the context of the proposed methodology, on the basis of their ability to reduce vulnerability and ultimately to mitigate risk. The method could be exploited, among others, within the framework of a first-order decision support system to eventually contribute in enhancing urban resilience to future hazardous events. The developed risk assessment framework is demonstrated herein by means of a case study urban-scale application, considering the flash flood peril in the city of Milan.
[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]
2023
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]
Bakalis K., Kazantzi A.K. (2023). Composite floors under human-induced vibrations. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | Composite steel-concrete floor systems are widely used in modern construction for achieving long-spans with a low number of intermediate columns. The design of such slender and lightweight floor systems is typically governed by the serviceability limit state requirements, associated with deformations, human comfort perception, and vibration tolerances. To guide designers through the process of delivering floors that are not prone to human-induced vibrations, and hence imposing a feeling of discomfort to their users, a number of design guidelines of variable complexity have been developed in the past few decades [1,2]. In their simplest form, such guidelines adopt several deterministic assumptions regarding the floor damping, the imposed loads, the connection rigidity under service loads, the step frequency, the footpath and the human weight. In this study, sources of uncertainty are discussed. A numerical grillage-based floor model is also presented, that could be utilised for extracting the needed engineering demand parameters for undertaking an assessment of such floor systems when subjected to walking-induced vibrations.
[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]
2022
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 |
2021
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.
Bakalis K, Lignos DG. (2021). Effect of Modelling Uncertainty on Nonlinear Simulations of a 4-Storey Steel Frame Building Tested Through Collapse. Proceedings of the 13th International Conference on Structural Safety and Reliability (ICOSSAR 2021), Shanghai, P.R. China.
2020
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