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.     

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.     

Probabilistic seismic loss assessment of aging bridges using a component‐level cost estimation approach

Deteriorating highway bridges in the United States and worldwide have demonstrated susceptibility to damage in earthquake events, with considerable economic consequences due to repair or replacement. Current seismic loss assessment approaches for these critical elements of the transportation network neglect the effects of aging and degradation on the loss estimate. However, the continued aging and deterioration of bridge infrastructure could not only increase susceptibility to seismic damage, but also have a significant impact on these economic losses. Furthermore, the contribution of individual aging components to system‐level losses, correlations between these components, and uncertainty modeling in the risk assessment and repair modeling are all crucial considerations to enhance the accuracy and confidence in bridge loss estimates. In this paper, a new methodology for seismic loss assessment of aging bridges is introduced based on the non‐homogeneous Poisson process. Statistical moments of seismic losses can be efficiently estimated, such as the expected value and variance. The approach is unique in its account for time‐varying seismic vulnerability, uncertainty in component repair, and the contribution of multiple correlated aging components. A representative case study is presented with two fundamentally distinct highway bridges to demonstrate the effects of corrosion deterioration of different bridge components on the seismic losses. Using the proposed model, a sensitivity study is also conducted to assess the effect of parameter variations on the expected seismic losses. The results reveal that the seismic losses estimated by explicitly considering the effects of deterioration of bridge components is significantly higher than that found by assuming time‐invariant structural reliability. Copyright © 2011 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.     

Influence of spatial correlation of strong ground motion on uncertainty in earthquake loss estimation

In addition to the mean values of possible loss during an earthquake, parameters of the probability distribution function for the loss to a portfolio (e.g. fractiles and standard deviation) are very important. Recent studies have shown that the proper treatment of ground‐motion variability and, particularly, the correlation of ground motion are essential for the estimation of the seismic hazard, damage and loss for distributed portfolios. In this study, we compared the effects of variations in the between‐earthquake correlation and in the site‐to‐site correlation on seismic loss and damage estimations for the extended objects (hypothetical portfolio) and critical elements (e.g. bridges) of a network. A scenario earthquake approach and a portfolio containing a set of hypothetical building and bridges were used for the purpose. We showed that the relative influences of the types of correlation on characteristics of loss distribution and the probability of damage are not equal. In some cases, when the median values of loss distribution or the probability that at least one critical element of a lifeline will be damaged are considered and when the spatial correlation of ground motion is used, the possible variations in the between‐earthquake correlation may be neglected. The shape of the site‐to‐site correlation function (i.e. the rate of decrease of the coefficient of spatial correlation with separation distance) seems also to be important when modelling spatially correlated ground‐motion fields. Copyright © 2010 John Wiley & Sons, Ltd.     

历史地震损失重建研究

历史地震损失重建是地震损失预测的一种方法,也是用于区域地震风险分析模型验证的一种手段。在介绍了历史地震损失重建一般方法的基础上,对方法中等效全损住宅比例估计方法以及住宅结构地震易损性指数的估计方法进行了重点分析,给出了这两个关键参数的可选择的多种估计方法。     

Post‐earthquake bridge repair cost and repair time estimation methodology

While structural engineers have traditionally focused on individual components (bridges, for example) of transportation networks for design, retrofit, and analysis, it has become increasingly apparent that the economic costs to society after extreme earthquake events are caused at least as much from indirect costs as direct costs due to individual structures. This paper describes an improved methodology for developing probabilistic estimates of repair costs and repair times that can be used for evaluating the performance of new bridge design options and existing bridges in preparation for the next major earthquake. The proposed approach in this paper is an improvement on previous bridge loss modeling studies—it is based on the local linearization of the dependence between repair quantities and damage states so that the resulting model follows a linear relationship between damage states and repair points. The methodology uses the concept of performance groups (PGs) that account for damage and repair of individual bridge components and subassemblies. The method is validated using two simple examples that compare the proposed method to simulation and previous methods based on loss models using a power–law relationship between repair quantities and damage. In addition, an illustration of the method is provided for a complete study on the performance of a common five‐span overpass bridge structure in California. Intensity‐dependent repair cost ratios (RCRs) and repair times are calculated using the proposed approach, as well as plots that show the disaggregation of repair cost by repair quantity and by PG. This provides the decision maker with a higher fidelity of data when evaluating the contribution of different bridge components to the performance of the bridge system, where performance is evaluated in terms of repair costs and repair times rather than traditional engineering quantities such as displacements and stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads

Many bridges located in seismic hazard regions suffer from serious foundation exposure caused by riverbed scour. Loss of surrounding soil significantly reduces the lateral strength of pile foundations. When the scour depth exceeds a critical level, the strength of the foundation is insufficient to withstand the imposed seismic demand, which induces the potential for unacceptable damage to the piles during an earthquake. This paper presents an analytical approach to assess the earthquake damage potential of bridges with foundation exposure and identify the critical scour depth that causes the seismic performance of a bridge to differ from the original design. The approach employs the well-accepted response spectrum analysis method to determine the maximum seismic response of a bridge. The damage potential of a bridge is assessed by comparing the imposed seismic demand with the strengths of the column and the foundation. The versatility of the analytical approach is illustrated with a numerical example and verified by the nonlinear finite element analysis. The analytical approach is also demonstrated to successfully determine the critical scour depth. Results highlight that relatively shallow scour depths can cause foundation damage during an earthquake, even for bridges designed to provide satisfactory seismic performance.     

地震经济损失评估之装修破坏损失比厘定研究

随着经济的发展,建筑装修损失占地震总损失的比重越来越大,对于大中城市装修损失的评估越来越引起人们的重视,而损失比是地震经济损失评估中非常关键的参数。本文在对损失比的概念及其国内外研究现状综合分析的基础上,采用现场抽样与专家咨询(Delphi法)相结合的方法,通过加权统计给出了不同结构类型、不同使用功能的建筑装修震害损失比取值范围。最后,将本文给出的取值范围与其它文献取值进行了对比分析,结果表明:在相同破坏等级下,装修破坏损失比要高于主体结构损失比,且在中等破坏及以上破坏等级下,前者要远大于后者。     

Methodology for the development of bridge‐specific fragility curves

A new methodology for the development of bridge‐specific fragility curves is proposed with a view to improving the reliability of loss assessment in road networks and prioritising retrofit of the bridge stock. The key features of the proposed methodology are the explicit definition of critical limit state thresholds for individual bridge components, with consideration of the effect of varying geometry, material properties, reinforcement and loading patterns on the component capacity; the methodology also includes the quantification of uncertainty in capacity, demand and damage state definition. Advanced analysis methods and tools (nonlinear static analysis and incremental dynamic response history analysis) are used for bridge component capacity and demand estimation, while reduced sampling techniques are used for uncertainty treatment. Whereas uncertainty in both capacity and demand is estimated from nonlinear analysis of detailed inelastic models, in practical application to bridge stocks, the demand is estimated through a standard response spectrum analysis of a simplified elastic model of the bridge. The simplified methodology can be efficiently applied to a large number of bridges (with different characteristics) within a road network, by means of an ad hoc developed software involving the use of a generic (elastic) bridge model, which derives bridge‐specific fragility curves. Copyright © 2016 John Wiley & Sons, Ltd.     

The impact of epistemic uncertainty on an earthquake loss model

Models capable of estimating losses in future earthquakes are of fundamental importance for emergency planners, for the insurance and reinsurance industries, and for code drafters. Constructing a loss model for a city, region or country involves compiling databases of earthquake activity, ground conditions, attenuation equations, building stock and infrastructure exposure, and vulnerability characteristics of the exposed inventory, all of which have large associated uncertainties. Many of these uncertainties can be classified as epistemic, implying—at least in theory—that they can be reduced by acquiring additional data or improved understanding of the physical processes. The effort and cost involved in refining the definition of each component of a loss model can be very large, for which reason it is useful to identify the relative impact on the calculated losses due to variations in these components. A mechanically sound displacement‐based approach to loss estimation is applied to a test case of buildings along the northern side of the Sea of Marmara in Turkey. Systematic variations of the parameters defining the demand (ground motion) and the capacity (vulnerability) are used to identify the relative impacts on the resulting losses, from which it is found that the influence of the epistemic uncertainty in the capacity is larger than that of the demand for a single earthquake scenario. Thus, the importance of earthquake loss models which allow the capacity parameters to be customized to the study area under consideration is highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

Comparing Loss Estimation with Observed Damage: A Study of the 1999 Kocaeli Earthquake in Turkey

Loss estimation from future earthquakes is of growing importance in planning earthquake protection strategies in high-risk areas. Loss models based on the spectral displacement approach are now widely used because of generally acknowledged deficiencies in earlier approaches using macroseismic intensity or peak ground-motion parameters. However, there has been to date rather little earthquake damage data by which the new generation of models can be assessed and which can be used to calibrate the parameters involved. The availability of several detailed damage surveys carried out following the 1999 Kocaeli earthquake in Turkey, provides a rare opportunity for such an assessment. In this paper the losses which would be predicted from two different approaches to loss assessment – one using predicted macroseismic intensity, the other using the spectral displacement method – are compared with actual observed losses in the Kocaeli event at two different locations where surveys were carried out. One of these sites was very close to the surface fault rupture (< 3 km distance), the other at a distance of about 4.5 km. It is shown that the predictive methods available generally overestimated the losses at these distances, and a number of possible reasons for these discrepancies are considered. The sensitivity of loss estimates to variations in the key parameters governing the estimation in each case are explored, in particular with respect to modifications in the parameters of the attenuation relationships and the vulnerability parameters. The implications of these results for estimating future losses are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling Seismic Hazard in Earthquake Loss Models with Spatially Distributed Exposure

The prediction of possible future losses from earthquakes, which in many cases affect structures that are spatially distributed over a wide area, is of importance to national authorities, local governments, and the insurance and reinsurance industries. Generally, it is necessary to estimate the effects of many, or even all, potential earthquake scenarios that could impact upon these urban areas. In such cases, the purpose of the loss calculations is to estimate the annual frequency of exceedance (or the return period) of different levels of loss due to earthquakes: so-called loss exceedance curves. An attractive option for generating loss exceedance curves is to perform independent probabilistic seismic hazard assessment calculations at several locations simultaneously and to combine the losses at each site for each annual frequency of exceedance. An alternative method involves the use of multiple earthquake scenarios to generate ground motions at all sites of interest, defined through Monte–Carlo simulations based on the seismicity model. The latter procedure is conceptually sounder but considerably more time-consuming. Both procedures are applied to a case study loss model and the loss exceedance curves and average annual losses are compared to ascertain the influence of using a more theoretically robust, though computationally intensive, procedure to represent the seismic hazard in loss modelling.An erratum to this article can be found at     

传统农村房屋地震灾害平均损失率的统计分析

在多年来地震宏观震害资料整理、研究的基础上，对传统农村房屋的类型进行了划分，统计出农村房屋地震灾害的平均损失率与地震烈度之间的关系，以便在地震发生后能较快地初评估地震在农村地区所造成的经济损失，为快速判断震灾规模提供依据。     

Expected loss‐based alarm threshold set for earthquake early warning systems

Earthquake early warning systems (EEWS) seem to have potential as tools for real‐time seismic risk management and mitigation. In fact, although the evacuation of buildings requires warning time not available in many urbanized areas threatened by seismic hazard, they may still be used for the real‐time protection of critical facilities using automatic systems in order to reduce the losses subsequent to a catastrophic event. This is possible due to the real‐time seismology, which consists of methods and procedures for the rapid estimation of earthquake features, as magnitude and location, based on measurements made on the first seconds of the P‐waves. An earthquake engineering application of earthquake early warning (EEW) may be intended as a system able to issue the alarm, if some recorded parameter exceeds a given threshold, to activate risk mitigation actions before the quake strikes at a site of interest. Feasibility analysis and design of such EEWS require the assessment of the expected loss reduction due to the security action and set of the alarm threshold. In this paper a procedure to carry out these tasks in the performance‐based earthquake engineering probabilistic framework is proposed. A merely illustrative example refers to a simple structure assumed to be a classroom. Structural damage and non‐structural collapses are considered; the security action is to shelter occupants below the desks. The cost due to a false alarm is assumed to be related to the interruption of didactic activities. Results show how the comparison of the expected losses, for the alarm‐issuance and non‐issuance cases, allows setting the alarm threshold on a quantitative and consistent basis, and how it may be a tool for the design of engineering applications of EEW. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.     

ASSESSMENT ON INDIRECT ECONOMIC LOSS OF WENCHUAN EARTHQUAKE DISASTER BASED ON INPUT-OUTPUT ANALYSIS

The scientific and reasonable assessment of disaster loss is the basic work for disaster relief and post-disaster reconstruction.Indirect economic loss is also an important part of scientific assessment for disaster influence.Taking the stricken area of 2008 Wenchuan earthquake in Sichuan as an example,this paper preliminarily analyzed the sections-related indirect economic loss resulting from Wenchuan earthquake by the methods of input-output analysis.The results show that,1) the sections-related indirect economic loss of Wenchuan earthquake reached up to 2 545.32 billion Yuan,which is as much as 3 times the direct economic loss in Sichuan Province.The direct economic loss does not evaluate the effects of Wenchuan earthquake disaster completely,and the indirect economic loss is an inseparable part for the systematic assessment of disaster influence.2) The characteristics of economic losses are not the same among different sectors in Sichuan.The indirect economic losses of industry and other services are the biggest in all sectors of Sichuan.However,the ratios of indirect and direct economic loss in industry,agriculture,construction are the highest,which is over 14.60,8.70 and 7.11,respectively.3) Although the uncertainty exists in the assessment result due to the limitation of input-output model,input-output analysis is still the most wildly used method to assess the indirect economic loss of natural hazard.Furthermore,the data accuracy is also an important factor influencing the economic loss assessment of natural hazard.     

Effect of cumulative seismic damage and corrosion on the life‐cycle cost of reinforced concrete bridges

Bridge design should take into account not only safety and functionality, but also the cost effectiveness of investments throughout a bridge life‐cycle. This paper presents a probabilistic approach to compute the life‐cycle cost (LCC) of corroding reinforced concrete (RC) bridges in earthquake‐prone regions. The approach is developed by combining cumulative seismic damage and damage associated with corrosion due to environmental conditions. Cumulative seismic damage is obtained from a low‐cycle fatigue analysis. Chloride‐induced corrosion of steel reinforcement is computed based on Fick's second law of diffusion. The proposed methodology accounts for the uncertainties in the ground motion parameters, the distance from the source, the seismic demand on the bridge, and the corrosion initiation time. The statistics of the accumulated damage and the cost of repairs throughout the bridge life‐cycle are obtained by Monte‐Carlo simulation. As an illustration of the proposed approach, the effects of design parameters on the LCC of an example RC bridge are studied. The results are valuable in better estimating the condition of existing bridges and, therefore, can help to schedule inspection and maintenance programs. In addition, by taking into consideration the two deterioration processes over a bridge life‐cycle, it is possible to estimate the optimal design parameters by minimizing, for example, the expected cost throughout the life of the structure. A comparison between the effects of the two deterioration processes shows that, in seismic regions, the cumulative seismic damage affects the reliability of bridges over time more than the corrosion even for corrosive environments. Copyright © 2008 John Wiley & Sons, Ltd.     

Developing and testing the Automated Post-Event Earthquake Loss Estimation and Visualisation (APE-ELEV) technique

An automated, real-time, multiple sensor data source relying and globally applicable earthquake loss model and visualiser is desirable for post-event earthquake analysis. To achieve this there is a need to support rapid data ingestion, loss estimation and integration of data from multiple data sources and rapid visualisation at multiple geographic levels. In this paper, the design and development of the Automated Post-Event Earthquake Loss Estimation and Visualisation (APE-ELEV) system for real-time estimation and visualisation of insured losses incurred due to earthquakes is presented. A model for estimating ground up and net of facultative losses due to earthquakes in near real-time is implemented. Since post-event data is often available immediately from multiple disparate sources, a geo-browser is employed to facilitate the visualisation and integration of earthquake hazard, exposure and loss data. The feasibility of APE-ELEV is demonstrated using a test case earthquake that occurred in Tohoku, Japan (2011). The APE-ELEV model is further validated for ten global earthquakes using industry loss data.     

Building service life economic loss assessment under sequential seismic events

Aftershocks have been shown to exacerbate earthquake‐induced financial losses by causing further damage to structural and nonstructural components in buildings that have already been affected by a mainshock event and increasing the duration of disrupted functionality. Whereas seismic loss assessment under isolated events has been addressed thoroughly in previous studies, comparatively less has been accomplished in the area of loss assessment under sequences of mainshock‐aftershock ground motions. The main objective of the current study is to formulate a comprehensive framework for quantifying financial losses under sequential seismic events. The proposed framework is capable of accounting for the uncertainties in the state of structure due to accumulation of earthquake‐induced damage, the time‐dependent nature of seismic hazard in the post‐mainshock environment, and the uncertainties in the occurrence of mainshock and aftershock events. Application of the proposed framework to a 4‐story reinforced concrete moment frame shows that consideration of aftershocks could increase lifecycle earthquake‐induced losses by up to 30% compared with mainshock‐only assessments.