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.     

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.     

Component correlations in structure‐specific seismic loss estimation

This paper addresses correlations between multiple components in structure‐specific seismic loss estimation. To date, the consideration of such correlations has been limited by methodological tractability, increased computational demand, and a paucity of data for their computation. The effect of component correlations, which arises in various forms, is however a significant factor affecting the results of structure‐specific seismic loss estimation and therefore it is prudent that adequate consideration be given to their effect. This paper provides the details of a tractable and computationally efficient seismic loss estimation methodology in which correlations can be considered. Methods to determine the necessary correlations are discussed, particularly those that can be used in the absence of sufficient empirical data, for which values are suggested based on the judgement. The effects of various assumptions regarding correlations are illustrated via application to a case‐study office structure. It is observed that certain correlation assumptions can lead to errors in excess of 50% in the lognormal standard deviation in the loss given intensity and loss hazard relationships, while full consideration of partial correlations is 50 times more computationally expensive than other assumptions. Copyright © 2009 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.     

基于改进云图法的结构概率地震需求分析

概率地震需求分析是美国太平洋地震工程研究中心(Pacific Earthquake Engineering ResearchCenter,PEER)提出的新一代"性能化地震工程(Performance-Based Earthquake Engineering,PBEE)"理论框架的重要一环。传统的概率地震需求分析方法称为"云图法",这种方法针对确定性结构进行一系列地震动作用下的非线性动力分析,从而得到地震动强度参数与结构地震需求的"云图"。然而,传统的云图法只能考虑地震动的不确定性,而无法考虑结构的不确定性。为此,结合拉丁超立方体抽样技术,提出一种能综合考虑地震动不确定性和结构不确定性的改进云图法,并将传统的概率地震需求分析内容拓展为概率地震需求模型、概率地震需求易损性分析、概率地震需求危险性分析三个层次。以一榀五层三跨钢筋混凝土框架结构为例,分别采用传统云图法和改进云图法对其进行概率地震需求分析,得到了该结构的概率地震需求模型、地震需求易损性曲线和地震需求危险性曲线。分析结果表明:提出的方法可以有效地考虑地震动与结构的不确定性,避免不考虑结构的不确定性而低估结构的地震风险性。     

An improved modal pushover analysis procedure for estimating seismic demands of structures

The pushover analysis （POA） procedure is difficult to apply to high-rise buildings, as it cannot account for the contributions of higher modes. To overcome this limitation, a modal pushover analysis （MPA） procedure was proposed by Chopra et al. （2001）. However, invariable lateral force distributions are still adopted in the MPA. In this paper, an improved MPA procedure is presented to estimate the seismic demands of structures, considering the redistribution of inertia forces after the structure yields. This improved procedure is verified with numerical examples of 5-, 9- and 22-story buildings. It is concluded that the improved MPA procedure is more accurate than either the POA procedure or MPA procedure. In addition, the proposed procedure avoids a large computational effort by adopting a two-phase lateral force distribution..     

Fully probabilistic seismic displacement analysis of spatially distributed slopes using spatially correlated vector intensity measures

Earthquake‐induced slope displacement is an important parameter for safety evaluation and earthquake design of slope systems. Traditional probabilistic seismic hazard analysis usually focuses on evaluating slope displacement at a particular location, and it is not suitable for spatially distributed slopes over a large region. This study proposes a computationally efficient framework for fully probabilistic seismic displacement analysis of spatially distributed slope systems using spatially correlated vector intensity measures (IMs). First, a spatial cross‐correlation model for three key ground motion IMs, that is, peak ground acceleration (PGA), Arias intensity, and peak ground velocity, is developed using 2686 ground motion recordings from 11 recent earthquakes. To reduce the computational cost, Monte Carlo simulation and data reduction techniques are utilized to generate spatially correlated random fields for the vector IMs. The slope displacement hazards over the region are further quantified using empirical predictive equations. Finally, an illustrative example is presented to highlight the importance of the spatial correlation and the advantage of using spatially correlated vector IMs in seismic hazard analysis of spatially distributed slopes. Copyright © 2013 John Wiley & Sons, Ltd.     

基于性态的液化场地多跨桥梁桩基地震响应分析

针对液化场地多跨简支桩基桥梁体系,考虑地震随机性的不确定性和认知的不确定性,结合地震危险性曲线自身的不确定性,推导性态指标危险性曲线的解析表达式.利用地震动强度指标PGV/PGA,输入不同幅值的地震动,进行液化场地多跨桩基桥梁体系地震反应有限元分析.基于有限元数值分析结果,选取地震过程中关键位置位移和弯矩的最大值作为性...     

直接基于位移的结构抗震设计理论研究进展

直接基于位移的抗震设计是实现基于性能抗震设计思想的一条有效途径,其理论主要包括三方面的内容,即直接基于位移的抗震设计方法、位移需求估计方法和目标位移的确定。本文在阅读了大量文献的基础上,对国内外在这三方面的研究进行了介绍,并对今后的研究方向进行了展望。     

Practice‐oriented estimation of the seismic demand hazard using ground motions at few intensity levels

This paper examines the calculation of the seismic demand hazard in a practice‐oriented manner via the use of seismic response analyses at few intensity levels. The seismic demand hazard is a more robust measure for quantifying seismic performance, when seismic hazard is represented in a probabilistic format, than intensity‐based assessments, which remain prevalent in seismic design codes. It is illustrated that, for a relatively complex bridge–foundation–soil system case study, the seismic demand hazard can be estimated with sufficient accuracy using as little as three intensity measure levels that have exceedance probabilities of 50%, 10% and 2% in 50 years which are already of interest in multi‐objective performance‐based design. Compared with the conventional use of the mean demand from an intensity‐based assessment(s), it is illustrated that, for the same number of seismic response analyses, a practice‐oriented ‘approximate’ seismic demand hazard is a more accurate and precise estimate of the ‘exact’ seismic demand hazard. Direct estimation of the seismic demand hazard also provides information of seismic performance at multiple exceedance rates. Thus, it is advocated that if seismic hazard is considered in a probabilistic format, then seismic performance assessment, and acceptance criteria, should be in terms of the seismic demand hazard and not intensity‐based assessments. Copyright © 2013 John Wiley & Sons, Ltd.     

Rapid estimation of earthquake loss based on instrumental seismic intensity: design and realization

As a result of our ability to acquire large volumes of real-time earthquake observation data, coupled with increased computer performance, near real-time seismic instrument intensity can be obtained by using ground motion data observed by instruments and by using the appropriate spatial interpolation methods. By combining vulnerability study results from earthquake disaster research with earthquake disaster assessment models, we can estimate the losses caused by devastating earthquakes, in an attempt to provide more reliable information for earthquake emergency response and decision support. This paper analyzes the latest progress on the methods of rapid earthquake loss estimation at home and abroad. A new method involving seismic instrument intensity rapid reporting to estimate earthquake loss is proposed and the relevant software is developed. Finally, a case study using the M _L4.9 earthquake that occurred in Shun-chang county, Fujian Province on March 13, 2007 is given as an example of the proposed method.     

基于华北区域地震活动性分布的地震危险性评价模型

采用了分布式地震活动性模型. 该模型无需潜在震源区划分,同时简化了地震危险性概率分析方法. 根据破坏性地震目录建立了3个地震活动性模型,利用高斯光滑函数获得了华北区域内的a值分布特征,使用3种典型的衰减模型,分别计算了50年内超越概率10%, 5%和2%的地震动峰值加速度分布. 其分析结果显示了峰值加速度分布特征与我国第四代区划图大体一致,特定地震活动区（太原、 石家庄等地区）的峰值加速度略高于第四代区划图的结果,而这种峰值加速度分布特征与该地区较高的地震活动性特征是一致的. 概率危险性曲线结果表明,唐山、太原和北京等地区的潜在地震危险性比华北区域内其它城市高.      

A site‐consistent method to quantify sufficiency of alternative IMs in relation to PSDA

In probabilistic seismic demand analysis, evaluation of the sufficiency of an intensity measure (IM) is an important criterion to avoid biased assessment of the demand hazard. However, there exists no metric to quantify the degree of sufficiency as per the criterion of Luco and Cornell (2007). This paper proposes a site‐specific unified measure for degree of sufficiency from all seismological parameters under consideration using a total information gain metric. This unified metric for sufficiency supports not only comparison of the performance of different IMs given a response quantity but also assessment of the performance of a particular IM across different response quantities. The proposed sufficiency metric was evaluated for a 4‐story steel moment frame building, and the influence of ground motion selection on the degree of sufficiency was investigated. It was observed that ground motion selection can have a significant impact on IM sufficiency. Because computing the total information gain requires continuous deaggregation across the IM space, an approximate deaggregation technique that allows for a more practical estimation of marginal deaggregation probabilities is proposed. It is expected that the total information gain metric proposed in this paper will aid in understanding the efficiency‐sufficiency relation, thus enabling the selection of a proper scalar IM for a given site and application in probabilistic seismic demand analysis.     

Simplified estimation of the expected annual loss of reinforced concrete buildings

Performance‐based earthquake engineering procedures have now developed to the point that it is possible to evaluate a range of possible decision variables, including the expected annual monetary loss (EAL). Quantification of the EAL is considered to be particularly useful because it could assist with the identification of effective design and retrofit measures that consider seismic performance over a range of intensity levels. Recognizing, however, that existing procedures for the evaluation of EAL tends to be quite time consuming, this paper builds on a recent proposal to use simplified limit state loss versus intensity relationships to compute EAL via a closed‐form equation, without the need to compile an inventory of damageable components and with freedom in the choice of structural analysis method. Various developments to the simplified approach are made in this paper to allow consideration of loss thresholds, non‐uniform damage distributions and the impact of differences in seismic performance in orthogonal directions. In addition, means of accounting for uncertainties in the simplified EAL assessment are described. The work has focused on the assessment of EAL for reinforced concrete frame buildings with details representative of construction practice adopted in Italy in the 1950s through to the early 1970s. By comparing loss assessment results obtained using a refined methodology with those obtained using the new guidelines developed here for two case study buildings, it is concluded that the simplified approach works well. Future research should therefore aim to further validate the approach and extend it to other building typologies and construction eras. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic hazard estimation based on the distributed seismicity in northern China

In this paper, we have proposed an alternative seismic hazard modeling by using distributed seismicites. The distributed seismicity model does not need delineation of seismic source zones, and simplify the methodology of probabilistic seismic hazard analysis. Based on the devastating earthquake catalogue, we established three seismi- city model, derived the distribution of a-value in northern China by using Gaussian smoothing function, and cal-culated peak ground acceleration distributions for this area with 2%, 5% and 10% probability of exceedance in a 50-year period by using three attenuation models, respectively. In general, the peak ground motion distribution patterns are consistent with current seismic hazard map of China, but in some specific seismic zones which in-clude Shanxi Province and Shijiazhuang areas, our results indicated a little bit higher peak ground motions and zonation characters which are in agreement with seismicity distribution patterns in these areas. The hazard curves have been developed for Beijing, Tianjin, Taiyuan, Tangshan, and Ji’nan, the metropolitan cities in the northern China. The results showed that Tangshan, Taiyuan, Beijing has a higher seismic hazard than that of other cities mentioned above.     

Probabilistic economic seismic loss estimation in steel buildings using post‐tensioned moment‐resisting frames and viscous dampers

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. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient method for estimating the collapse risk of structures in seismic regions

Assessing the probability of collapse is a computationally demanding component of performance‐based earthquake engineering. This paper examines various aspects involved in the computation of the mean annual frequency of collapse (λ_c) and proposes an efficient method for estimating the sidesway collapse risk of structures in seismic regions. By deaggregating the mean annual frequency of collapse, it is shown that the mean annual frequency of collapse is typically dominated by earthquake ground motion intensities corresponding to the lower half of the collapse fragility curve. Uncertainty in the collapse fragility curve and mean annual frequency of collapse as a function of the number of ground motions used in calculations is also quantified, and it is shown that using a small number of ground motions can lead to unreliable estimates of a structure's collapse risk. The proposed method is shown to significantly reduce the computational effort and uncertainty in the estimate. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

AP/VP specific inelastic displacement ratio for seismic response estimation of structures

In this study, two new site specific statistical equations are proposed to estimate the inelastic displacement ratio, C₁ of structures subjected to far fault (FF) and near fault (NF) ground motions. The proposed equations consider the effects of fundamental vibration period of the structure, T, lateral strength ratio, R and frequency content of the design earthquake record represented by the A_p/V_p ratio (or T₀ = 2π/A_p/V_p), which is a function of the earthquake magnitude, distance to fault, faulting mechanism and site class. It was observed that the C₁ values obtained from the proposed equations are in good agreement with the calculated results. The flare of the plotted C₁ vs. T/T₀ curves enables the proposed equations to cover nearly all the calculated C₁ data range and give satisfactory results. However, the curves obtained using the C₁ equations of several codes and those available in the literature do not cover the whole calculated C₁ data range and generally give unconservative results (smaller C₁ values) especially in the shorter period range. For the longer period range, the predictions of C₁ obtained from the proposed equation and the ones available in the literature are in good agreement with the calculated C₁ data. Copyright © 2014 John Wiley & Sons, Ltd.     

Error estimation of closed‐form solution for annual rate of structural collapse

With the increasing emphasis of performance‐based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance‐based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed‐form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed‐form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed‐form solution are fit. This study presents a critical review of the closed‐form solution for the annual rate of structural collapse. The closed‐form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed‐form solution. Via a parametric study, the key variables contributing to the error between the closed‐form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed‐form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 John Wiley & Sons, Ltd.