Prediction of spatially distributed seismic demands in specific structures: Ground motion and structural response

The efficacy of various ground motion intensity measures (IMs) in the prediction of spatially distributed seismic demands (engineering demand parameters, (EDPs)) within a structure is investigated. This has direct implications to building‐specific seismic loss estimation, where the seismic demand on different components is dependent on the location of the component in the structure. Several common IMs are investigated in terms of their ability to predict the spatially distributed demands in a 10‐storey office building, which is measured in terms of maximum interstorey drift ratios and maximum floor accelerations. It is found that the ability of an IM to efficiently predict a specific EDP depends on the similarity between the frequency range of the ground motion that controls the IM and that of the EDP. An IMs predictability has a direct effect on the median response demands for ground motions scaled to a specified probability of exceedance from a ground motion hazard curve. All of the IMs investigated were found to be insufficient with respect to at least one of magnitude, source‐to‐site distance, or epsilon when predicting all peak interstorey drifts and peak floor accelerations in a 10‐storey reinforced concrete frame structure. Careful ground motion selection and/or seismic demand modification is therefore required to predict such a spatially distributed demands without significant bias. Copyright © 2009 John Wiley & Sons, Ltd.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.     

Computation of bridge seismic fragility by large‐scale simulation for probabilistic resilience analysis

Seismic resilience of structures and infrastructure systems is a fast developing concept in the field of disaster management, promoting communities that are resistant and quickly recoverable in case of an extreme event. In this contest, probabilistic seismic demand and fragility analyses are two key elements of the seismic resilience assessment in the majority of the proposed methodologies. Several techniques are available to calculate fragility curves for different types of structures. In particular, to assess the seismic performance of the regional transportation infrastructure, methods for the fragility curve estimation for entire classes of bridges are required. These methods usually rely on a set of assumptions, partially because of the limited information. Other assumptions were introduced at the time when computational resources were inadequate for a purely numerical approach and closed‐form solutions were a convenient alternative. For instance, some of these popular assumptions are aimed at simplifying the model of the engineering demand. In this paper, a simulation‐based methodology is proposed, to take advantage of the computational resources widely available today and avoid such assumptions on the demand. The resulting increase in accuracy is estimated on a typical class of bridges (multi‐span simply supported). Most importantly, the quantitative impact of the assumptions is assessed in the context of a life‐cycle loss estimation analysis and resilience analysis. The results show that some assumptions preserve an acceptable level of accuracy, but others introduce a considerable error in the fragility curves and, in turn, in the expected resilience and life‐cycle losses of the structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Deaggregation of seismic loss of spatially distributed buildings

The catastrophic nature of seismic risk resides in the fact that a group of structures and infrastructure is simultaneously excited by spatially correlated seismic loads due to an earthquake. For this, both earthquake-to-earthquake (inter-event) and site-to-site (intra-event) correlations associated with ground motion prediction equations must be taken into account in assessing seismic hazard and risk at multiple sites. The consideration of spatial correlation of seismic demand affects aggregate seismic losses as well as identified scenario seismic events. To investigate such effects quantitatively, a simulation-based seismic risk model for spatially distributed structures is employed. Analysis results indicate that adequate treatment of spatial correlation of seismic demand is essential and the probability distribution of aggregate seismic loss can be significantly different from those based on the assumptions that seismic excitations are not correlated or fully correlated. Furthermore, the results suggest that identified scenario events by deaggregation in terms of magnitude and distance become more extreme if the spatial correlation is ignored.     

Computational and rapid expected annual loss estimation methodologies for structures

Expected annual loss (EAL), which can be expressed in dollars, is an effective way of communicating the seismic vulnerability of constructed facilities to owners and insurers. A simplified method for estimating EAL without conducting time‐consuming non‐linear dynamic analyses is presented. Relationships between intensity measures and engineering demand parameters resulting from a pushover analysis and a modified capacity‐spectrum method are combined with epistemic and aleatory uncertainties to arrive at a probabilistic demand model. Damage measures are established to determine thresholds for damage states from which loss ratios can be defined. Financial implications due to damage can then be quantified in the form of EAL by integrating total losses for all likely earthquake scenarios. This rapid loss estimation method is verified through the computationally intensive incremental dynamic analysis, with the results processed using a distribution‐free methodology. To illustrate the application of the proposed method, the seismic vulnerability of two highway bridge piers is compared; one bridge is traditionally designed for ductility while the other is based on an emerging damage avoidance design (DAD) philosophy. The DAD pier is found to have a clear advantage over the conventional pier; the EAL of the DAD pier is less than 20% of its ductile counterpart. This is shown to be primarily due to its inherent damage‐free behaviour for small to medium earthquake intensities, whose contribution to EAL is significantly more than that of very rare events. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimized earthquake response of multi‐storey buildings with seismic isolation at various elevations

The response of multi‐storey structures can be controlled under earthquake actions by installing seismic isolators at various storey levels. By vertically distributing isolation devices at various elevations, the designer is provided with numerous options to appropriately adjust the seismic performance of a building. However, introducing seismic isolators at various storey levels is not a straightforward task, as it may lead to favourable or unfavourable structural behaviour depending on a large number of factors. As a consequence, a rather chaotic decision space of seismic isolation configurations arises, within which a favourable solution needs to be located. The search for favourable isolators' configurations is formulated in this work as a single‐objective optimization task. The aim of the optimization process is to minimize the maximum floor acceleration of the building under consideration, while constraints are specified to control the maximum interstorey drift, the maximum base displacement and the total seismic isolation cost. A genetic algorithm is implemented to perform this optimization task, which selectively introduces seismic isolators at various elevations, in order to identify the optimal configuration for the isolators satisfying the pre‐specified constraints. This way, optimized earthquake response of multi‐storey buildings can be obtained. The effectiveness of the proposed optimization procedure in the design of a seismically isolated structure is demonstrated in a numerical study using time‐history analyses of a typical six‐storey building. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of seismic response of bridges under asynchronous excitation and comparisons with Eurocode 8-2 provisions

The paper aims to evaluate the way Eurocode 8 treats the consideration of asynchronous earthquake ground motion during the seismic design of bridges, and to discuss alternative solutions for cases wherein existing provisions do not lead to satisfactory results. The evaluation of EC8-2 new provisions and simplified methods is performed through comparison with a more refined approach whereas an effort is made to quantitatively assess the relative importance of various design and analysis assumptions that have to be made when spatial variability of ground motion is taken into consideration, based on the study of the dynamic response of 27 different bridges. It is concluded that, despite the complexity of the problem, there are specific cases where EC8 provisions can be safely and easily applied in practice, while in other cases ignoring the effect of asynchronous excitation or performing simplified calculations can significantly underestimate the actual seismic demand.     

A critical examination of seismic response uncertainty analysis in earthquake engineering

The last decade of performance‐based earthquake engineering (PBEE) research has seen a rapidly increasing emphasis placed on the explicit quantification of uncertainties. This paper examines uncertainty consideration in input ground‐motion and numerical seismic response analyses as part of PBEE, with particular attention given to the physical consistency and completeness of uncertainty consideration. It is argued that the use of the commonly adopted incremental dynamic analysis leads to a biased representation of the seismic intensity and that when considering the number of ground motions to be used in seismic response analyses, attention should be given to both reducing parameter estimation uncertainty and also limiting ground‐motion selection bias. Research into uncertainties in system‐specific numerical seismic response analysis models to date has been largely restricted to the consideration of ‘low‐level’ constitutive model parameter uncertainties. However, ‘high‐level’ constitutive model and model methodology uncertainties are likely significant and therefore represent a key research area in the coming years. It is also argued that the common omission of high‐level seismic response analysis modelling uncertainties leads to a fallacy that ground‐motion uncertainty is more significant than numerical modelling uncertainty. The author's opinion of the role of uncertainty analysis in PBEE is also presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Approximate seismic risk assessment of building structures with explicit consideration of uncertainties

An approximate seismic risk assessment procedure for building structures, which involves pushover analysis that is performed utilizing a deterministic structural model and uncertainty analysis at the level of the equivalent SDOF model, is introduced. Such an approach is computationally significantly less demanding in comparison with procedures based on uncertainty analysis at the level of the entire structure, but still allows for explicit consideration of the effect of record‐to‐record variability and modelling uncertainties. A new feature of the proposed pushover‐based method is the so‐called probabilistic SDOF model. Herein, the proposed methodology is illustrated only for reinforced concrete (RC) frames, although it could be implemented in the case of any building structure, provided that an appropriate probabilistic SDOF model is available. An extensive parametric analysis has been performed within the scope of this study in order to develop a probabilistic SDOF model, which could be used for the seismic risk assessment of both code‐conforming and old, that is, non code‐conforming RC frames. Based on the results of risk analysis for the four selected examples, it is shown that the proposed procedure can provide conservative estimates of seismic risk with reasonable accuracy, in spite of the employed simplifications and the relatively small number of Monte Carlo simulations with Latin hypercube sampling, which are performed at the level of the SDOF model. An indication of the possible default values of dispersion measures for limit‐state intensities in the case of low to medium‐height RC frames is also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic interferometry,intrinsic losses and Q‐estimation*

Seismic interferometry is the process of generating new seismic traces from the cross‐correlation, convolution or deconvolution of existing traces. One of the starting assumptions for deriving the representations for seismic interferometry by cross‐correlation is that there is no intrinsic loss in the medium where the recordings are performed. In practice, this condition is not always met. Here, we investigate the effect of intrinsic losses in the medium on the results retrieved from seismic interferometry by cross‐correlation. First, we show results from a laboratory experiment in a homogeneous sand chamber with strong losses. Then, using numerical modelling results, we show that in the case of a lossy medium ghost reflections will appear in the cross‐correlation result when internal multiple scattering occurs. We also show that if a loss compensation is applied to the traces to be correlated, these ghosts in the retrieved result can be weakened, can disappear, or can reverse their polarity. This compensation process can be used to estimate the quality factor in the medium.     

A practice‐oriented estimation of the failure probability of building structures

In the presented practice‐oriented probabilistic approach for the seismic performance assessment of building structures, the SAC‐FEMA method, which is a part of the broader PEER probabilistic framework and permits probability assessment in closed form, is combined with the pushover‐based N2 method. The most demanding part of the PEER probabilistic framework, that is incremental dynamic analysis, is replaced by the much simpler N2 method, which requires considerably less input data and much less computational time, but which can, nevertheless, often provide: acceptable estimates for the mean values of the structural response. Using some additional simplifying assumptions that are consistent with seismic code procedures, an explicit equation for a quick estimation of the annual probability of “failure” (i.e. the probability of exceeding the near collapse limit state) of a structure can be derived, which is appropriate for practical applications, provided that predetermined default values for the dispersion measures are available. In the paper, this simplified approach is summarized and applied to the estimation of the “failure” probability of reinforced concrete frame buildings representing both old structures, not designed for earthquake resistance, and new structures designed according to Eurocode 8. The results of the analyses indicate a high probability of the “failure” of buildings, which have not been designed for seismic loads. For a building designed according to a modern code, the conservatively determined probability of “failure” is about 30 times less but still significant (about 1% over the lifetime of the structure). Copyright © 2011 John Wiley & Sons, Ltd.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.     

Development and assessment of damage‐to‐loss models for moment‐frame reinforced concrete buildings

The assessment of earthquake loss often requires the definition of a relation between a measure of damage and a quantity of loss, usually achieved through the employment of a damage‐to‐loss model. These models are frequently characterized by a large variability, which inevitably increases the uncertainty in the vulnerability assessment and earthquake loss estimation. This study provides an insight on the development of damage‐to‐loss functions for moment‐frame reinforced concrete buildings through an analytical methodology. Tri‐dimensional finite element models of existing reinforced concrete buildings were subjected to a number of ground motion records compatible with the seismicity in the region of interest, through nonlinear dynamic analysis. These results were used to assess, for a number of damage states, the probability distribution of loss ratio, taking into consideration member damage and different repair techniques, as well as to derive sets of fragility functions. Then, a vulnerability model (in terms of the ratio of cost of repair to cost of replacement, conditional on the level of ground shaking intensity) was derived and compared with the vulnerability functions obtained through the combination of various damage‐to‐loss models with the set of fragility functions developed herein. In order to provide realistic estimates of economic losses due to seismic action, a comprehensive study on repair costs using current Portuguese market values was also carried out. The results of this study highlight important issues in the derivation of vulnerability functions, which are a fundamental component for an adequate seismic risk assessment. © 2015 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

A probabilistic framework for correlated seismic downtime and repair cost estimation of geo‐structures

An important component of probabilistic risk assessment methods is the development of models to quantify the direct consequences of damage to geo‐structural components for a given intensity of the hazard. This paper presents a general probabilistic framework for correlated repair cost and downtime estimation of geo‐structures exposed to seismic hazards. The framework uses as input the results of nonlinear time‐history analysis of geo‐structures for the set of earthquake records that are representative of the seismic hazard models for the region of interest. The repair cost and downtime are estimated for individual earthquakes probabilistically considering the uncertainties associated with damage states. In addition, the formulation of the repair cost and downtime accounts for the reduction in the repair requirements as the number of damaged components in the given damage state increases. An analytical linear and two bilinear regression models are proposed for conditional correlated seismic repair cost and downtime estimation of geo‐structures given the intensity measure. The proposed framework is demonstrated by developing seismic repair models of a typical pile‐supported wharf structure on the west coast of the United States. The presented framework is general and can be applied to other types of geo‐structures and hazards and can include other decision variables such as loss of life as well. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessing uncertainty in estimation of seismic response for PBEE

State‐of‐the‐art approaches to probabilistic assessment of seismic structural reliability are based on simulation of structural behavior via nonlinear dynamic analysis of computer models. Simulations are carried out considering samples of ground motions supposedly drawn from specific populations of signals virtually recorded at the site of interest. This serves to produce samples of structural response to evaluate the failure rate, which in turn allows to compute the failure risk (probability) in a time interval of interest. This procedure alone implies that uncertainty of estimation affects the probabilistic results. The latter is seldom quantified in risk analyses, although it may be relevant. This short paper discusses some basic issues and some simple statistical tools, which can aid the analyst towards the assessment of the impact of sample variability on fragility functions and the resulting seismic structural risk. On the statistical inference side, the addressed strategies are based on consolidated results such as the well‐known delta method and on some resampling plans belonging to the bootstrap family. On the structural side, they rely on assumptions and methods typical in performance‐based earthquake engineering applications. Copyright © 2017 John Wiley & Sons, Ltd.     

Pushover-based seismic risk assessment and loss estimation of masonry buildings

A pushover-based seismic risk assessment and loss estimation methodology for masonry buildings is introduced. It enables estimation of loss by various performance measures such as the probability of exceeding a designated economic loss, the expected annual loss, and the expected loss given a seismic intensity. The methodology enables the estimation of the economic loss directly from the results of structural analysis, which combines pushover analysis and incremental dynamic analysis of an equivalent SDOF model. The use of the methodology is demonstrated by means of two variants of a three-storey masonry building both of which have the same geometry, but they are built, respectively, from hollow clay masonry (model H) and solid brick masonry (model S). The probability of collapse given the selected design earthquake corresponding to a return period of 475 years was found to be negligible for model H, which indicates the proper behaviour of such a structure when designed according to the current building codes. However, the corresponding probability of collapse of model S was very high (46%). The expected total loss given the design earthquake was estimated to amount to 28 000 € and 290 000 €, respectively, for models H and S. The expected annual loss per 100 m² of gross floor area was estimated to amount to 75 € and 191 €, respectively, for models H and S. For the presented examples, it was also observed that nonstructural elements contributed more than 50% of the total loss.     

THREE-DIMENSIONAL OPTIMUM MULTICHANNEL VELOCITY FILTERS*

Design procedures and characteristics of three stacking filters are discussed which may find application in various three-dimensional velocity filtering problems. These filters are derived in the time-domain as optimum multichannel Wiener filters. Random stationary functions are assumed as stochastic models for the seismic traces. All power and crosspower spectra which are the basic elements of the multichannel normal equations are statistically averaged according to specific three-dimensional considerations. Various properties of the input traces may be incorporated in the design of the optimum filters. With fairly general assumptions about the input these filters are deterministic in the sense that they are applicable to a broad class of input traces with similar statistics in amplitudes and arrival times of signals.     

Effects of two alternative representations of ground‐motion uncertainty on probabilistic seismic demand assessment of structures

A probabilistic representation of the entire ground‐motion time history can be constructed based on a stochastic model that depends on seismic source parameters. An advanced stochastic simulation scheme known as Subset Simulation can then be used to efficiently compute the small failure probabilities corresponding to structural limit states. Alternatively, the uncertainty in the ground motion can be represented by adopting a parameter (or a vector of parameters) known as the intensity measure (IM) that captures the dominant features of the ground shaking. Structural performance assessment based on this representation can be broken down into two parts, namely, the structure‐specific part requiring performance assessment for a given value of the IM, and the site‐specific part requiring estimation of the likelihood that ground shaking with a given value of the IM takes place. The effect of these two alternative representations of ground‐motion uncertainty on probabilistic structural response is investigated for two hazard cases. In the first case, these two approaches are compared for a scenario earthquake event with a given magnitude and distance. In the second case, they are compared using a probabilistic seismic hazard analysis to take into account the potential of the surrounding faults to produce events with a range of possible magnitudes and distances. The two approaches are compared on the basis of the probabilistic response of an existing reinforced‐concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake in Los Angeles, California. Copyright © 2007 John Wiley & Sons, Ltd.