Observational fragility functions for residential stone masonry buildings in Nepal

This paper outlines the seismic vulnerability of rural stone masonry buildings affected by the 2015 Gorkha earthquake sequence. Summary of field observation is presented first and empirical fragility curves are developed from the detailed damage assessment data from 603 villages in central, eastern and western Nepal. Fragility curves are developed on the basis of 665,515 building damage cases collected during the post-earthquake detailed damage assessment campaign conducted by Government of Nepal. Two sets of fragility functions are derived using peak ground acceleration and spectral acceleration at 0.3 s as the intensity measures. The sum of the results highlights that stone masonry buildings in Nepal are highly vulnerable even in the case of low to moderate ground shaking. The results further indicate that in the case of strong to major earthquakes, most of the stone masonry buildings in Nepal would sustain severe damage or collapse.     

Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method

This study presents a seismic fragility analysis and ultimate spectral displacement assessment of regular low-rise masonry infilled (MI) reinforced concrete (RC) buildings using a coefficient-based method. The coefficient-based method does not require a complicated finite element analysis; instead, it is a simplified procedure for assessing the spectral acceleration and displacement of buildings subjected to earthquakes. A regression analysis was first performed to obtain the best-fitting equations for the inter-story drift ratio (IDR) and period shift factor of low-rise MI RC buildings in response to the peak ground acceleration of earthquakes using published results obtained from shaking table tests. Both spectral acceleration-and spectral displacement-based fragility curves under various damage states (in terms of IDR) were then constructed using the coefficient-based method. Finally, the spectral displacements of low-rise MI RC buildings at the ultimate (or near-collapse) state obtained from this paper and the literature were compared. The simulation results indicate that the fragility curves obtained from this study and other previous work correspond well. Furthermore, most of the spectral displacements of low-rise MI RC buildings at the ultimate state from the literature fall within the bounded spectral displacements predicted by the coefficient-based method.     

Effect of out-of-plane behavior on seismic fragility of masonry buildings in Turkey

This study focuses on the evaluation of seismic safety of unreinforced masonry buildings in Turkey by using fragility curves generated for two behavior modes of load bearing walls: in-plane and out-of-plane. During generation of fragility curves, a force-based approach has been used. There exist two limit states in terms of base shear strength for in-plane behavior mode and flexural strength for out-of-plane behavior mode. To assess the seismic vulnerability of unreinforced masonry buildings in Turkey, fragility curves generated for in-plane behavior were verified by the observed damage during the 1995 Dinar (Turkey) earthquake and fragility curves generated for out-of-plane behavior were verified by the observed damage during the 2010 Elaz?? (Turkey) earthquake. The verification results reveal that the proposed fragility-based procedure can provide an alternative for the seismic safety evaluation of unreinforced masonry buildings in Turkey. Using this procedure, it becomes possible to investigate a large population of masonry buildings located in regions of high seismic risk in a short period of time. The obtained results are valuable in the sense that they can be used as a database during the development of strategies for pre-earthquake planning and risk mitigation for earthquake prone regions of Turkey.     

Seismic vulnerability assessment to slight damage based on experimental modal parameters

The aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f₀ of the structure and ground‐motion displacement response spectra S_D(f₀). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an M_L = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Generation of fragility curves for Turkish masonry buildings considering in‐plane failure modes

This study focuses on the seismic safety evaluation of masonry buildings in Turkey for in‐plane failure modes using fragility curves. Masonry buildings are classified and a set of fragility curves are generated for each class. The major structural parameters in the classification of masonry buildings are considered as the number of stories, load‐bearing wall material, regularity in plan and the arrangement of walls (required length, openings in walls, etc.), in accordance with the observations from previous earthquakes and field databases. The fragility curves are generated by using time history (for demand) and pushover (for capacity) analyses. From the generated sets of fragility curves, it is observed that the damage state probabilities are significantly influenced from the number of stories and wall material strength. In the second stage of the study, the generated fragility curves are employed to estimate the damage of masonry buildings in Dinar after the 1995 earthquake. The estimated damage by fragility information is compared with the inspected visual damage as assessed from the Damage Evaluation Form. For the quantification of fragility‐based damage, a single‐valued index, named as ‘vulnerability score’ (VS), is proposed. There seems to be a fair agreement between the two damage measures. In addition to this, decisions regarding the repair or demolition of masonry buildings in Dinar due to visual damage inspection are on comparable grounds with the relative measure obtained from VS of the same buildings. Hence, the fragility‐based procedure can provide an alternative for the seismic safety evaluation of masonry buildings in Turkey. Copyright © 2007 John Wiley & Sons, Ltd.     

Using experimental data to reduce the single-building sigma of fragility curves: case study of the BRD tower in Bucharest, Romania

The lack of knowledge concerning modelling existing buildings leads to significant variability in fragility curves for single or grouped existing buildings. This study aims to investigate the uncertainties of fragility curves, with special consideration of the single-building sigma. Experimental data and simplified models are applied to the BRD tower in Bucharest, Romania, a RC building with permanent instrumentation. A three-step methodology is applied： （1） adjustment of a linear MDOF model for experimental modal analysis using a Timoshenko beam model and based on Anderson＇s criteria, （2） computation of the structure＇s response to a large set of accelerograms simulated by SIMQKE software, considering twelve ground motion parameters as intensity measurements （IM）, and （3） construction of the fragility curves by comparing numerical interstory drift with the threshold criteria provided by the Hazus methodology for the slight damage state. By introducing experimental data into the model, uncertainty is reduced to 0.02 considering Sd ） as seismic intensity IM and uncertainty related to the model is assessed at 0.03. These values must be compared with the total uncertainty value of around 0.7 provided by the Hazus methodology.     

Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona

Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for seismic evaluation of structures. The capacity spectrum method and the way of obtaining seismic damage scenarios for urban areas starting from capacity and fragility curves are then discussed. The determination of capacity curves for buildings using non-linear structural analysis tools is then explained, together with a simplified expeditious procedure allowing the development of fragility curves. The seismic risk of the buildings of Barcelona, Spain, is analyzed in the paper, based on the application of the capacity spectrum method. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. The information on the buildings was obtained by collecting, arranging, improving and completing a broad database of the dwellings and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled-slab floors. The ArcView software was used to create a GIS tool for managing the collected information in order to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant in Barcelona and, therefore, in spite of the low-to-moderate seismic hazard in the region, the expected seismic risk is considerable.     

考虑震害因子耦合作用的砌体建筑群破坏概率模型研究

砌体建筑群在地震中往往破坏严重损失巨大,合理评估地震作用对不同种类砌体结构造成破坏的风险变得至关重要。传统基于后验概率的地震危险性分析方法忽略了砌体建筑个体差异性的影响,未深入考虑多种震害因子的耦合作用。本文以华南地区砌体建筑群为例,开发了一种集成概率方法来对城市砌体结构的破坏风险进行建模,考虑建筑年代、层数、使用用途和墙厚四类震害因子的耦合影响,采用(Kolmogorov-Smirnov)K-S检验,在设定地震动参数下选取Gaussian分布、Log-Normal分布、Gumbel分布和Beta分布四种概率分布对该地区砌体建筑物的破坏状态概率分布参数进行拟合。通过均方根误差(Root Mean Square Error)RMSE进行拟合优度评价,最终建立基于Gaussian分布和Log-Normal分布的砌体建筑物破坏联合概率模型。最后,以华南地区三个城市典型砌体建筑物为例进行实例对比验证,将基于本文建立的建筑破坏概率模型推算出的砌体建筑群震害矩阵与基于单体结构分析得到的震害矩阵进行对比,与理论值最大偏差为0.033 3。研究表明：本文构建的集成概率方法能够获得更加合理的城市砌体建筑...     

Force and Displacement Based Vulnerability Assessment for Traditional Buildings

Vulnerability assessment for historic buildings is usually carried out using capacity based approaches and prediction of losses is obtained by using normal or lognormal distributions for expected levels of macro seismic intensity or peak ground accelerations. Several authors have outlined the limitations of such approach. The paper presents a method to correlate analysis of seismic vulnerability using a failure mechanisms approach to observed in situ damage. The various aspects of the procedure are highlighted with application to a real case. It is shown how once the typologies within a sample have been identified, fragility curves for each of them can be derived and predictive cumulative damage curve obtained for samples for which direct survey of damage data is lacking. Finally the paper shows how the failure mechanism approach can be used to derive damage scenarios both in terms of spectral acceleration and spectral displacement     

Seismic safety of low ductility structures used in Spain

The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behavior. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.     

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood‐frame houses in Victoria,British Columbia,Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.     

基于试验数据的砌体填充墙易损性研究

本文对砌体填充墙的损伤状态进行了划分,并将损伤状态与常用修复方案相关联,明确了不同损伤状态所需要的修复方案。为了建立适用于中国砌体填充墙的易损性函数,对砌体填充墙面内抗震性能的试验数据进行了统计分析以建立损伤状态与工程需求参数的拟合经验关系。以层间位移角作为填充墙的工程需求参数,通过对数正态分布拟合试验数据。结果表明采用对数正态分布拟合的易损性曲线能够满足Lilliefors检验要求,可将其用于砌体填充墙的易损性评估中。     

Vector-valued fragility functions for seismic risk evaluation

This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e.g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.     

A hybrid method for the vulnerability assessment of R/C and URM buildings

The methodology followed by the Aristotle University (AUTh) team for the vulnerability assessment of reinforced concrete (R/C) and unreinforced masonry (URM) structures is presented. The paper focuses on the derivation of vulnerability (fragility) curves in terms of peak ground acceleration (PGA), as well as spectral displacement (s _d), and also includes the estimation of capacity curves, for several R/C and URM building types. The vulnerability assessment methodology is based on the hybrid approach developed at AUTh, which combines statistical data with appropriately processed (utilising repair cost models) results from nonlinear dynamic or static analyses, that permit extrapolation of statistical data to PGA’s and/or spectral displacements for which no data are available. The statistical data used herein are from earthquake-damaged greek buildings. An extensive numerical study is carried out, wherein a large number of building types (representing most of the common typologies in S. Europe) are modelled and analysed. Vulnerability curves for several damage states are then derived using the aforementioned hybrid approach. These curves are subsequently used in combination with the mean spectrum of the Microzonation study of Thessaloniki as the basis for the derivation of new vulnerability curves involving spectral quantities. Pushover curves are derived for all building types, then reduced to standard capacity curves, and can easily be used together with the S _d fragility curves as an alternative for developing seismic risk scenarios.     

Analytical seismic fragility functions for highway and railway embankments and cuts

A fundamental tool in seismic risk assessment of transportation systems is the fragility curve, which describes the probability that a structure will reach or exceed a certain damage state for a given ground motion intensity. Fragility curves are usually represented by two‐parameter (median and log‐standard deviation) cumulative lognormal distributions. In this paper, a numerical approach, in the spirit of the IDA, is applied for the development of fragility curves for highways and railways on embankments and in cuts due to seismic shaking. The response of the geo‐construction to increasing levels of seismic intensity is evaluated using a 2D nonlinear finite element model, with an elasto‐plastic criterion to simulate the soil behavior. A calibration procedure is followed in order to account for the dependency of both the stiffness and the damping to the soil strain level. The effect of soil conditions and ground motion characteristics on the response of the embankment and cut is taken into account considering different typical soil profiles and seismic input motions. This study will provide input for the assessment of the vulnerability of the road/railway network regarding the performance of the embankments and cuts; therefore, the level of damage is described in terms of the permanent ground displacement in these structures. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity, which is described by PGA. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the element's geometry, the input motion, and the soil properties as well as the associated uncertainties. A relationship between the computed permanent ground displacement on the surface of the embankment and the PGA in the free field is also suggested based on the results of the numerical analyses. Finally, the proposed fragility curves are compared with existing empirical data and the limitations of their applicability are outlined. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic vulnerability and risk assessment: case study of the historic city centre of Coimbra, Portugal

Seismic risk evaluation of built-up areas involves analysis of the level of earthquake hazard of the region, building vulnerability and exposure. Within this approach that defines seismic risk, building vulnerability assessment assumes great importance, not only because of the obvious physical consequences in the eventual occurrence of a seismic event, but also because it is the one of the few potential aspects in which engineering research can intervene. In fact, rigorous vulnerability assessment of existing buildings and the implementation of appropriate retrofitting solutions can help to reduce the levels of physical damage, loss of life and the economic impact of future seismic events. Vulnerability studies of urban centres should be developed with the aim of identifying building fragilities and reducing seismic risk. As part of the rehabilitation of the historic city centre of Coimbra, a complete identification and inspection survey of old masonry buildings has been carried out. The main purpose of this research is to discuss vulnerability assessment methodologies, particularly those of the first level, through the proposal and development of a method previously used to determine the level of vulnerability, in the assessment of physical damage and its relationship with seismic intensity. Also presented and discussed are the strategy and proposed methodology adopted for the vulnerability assessment, damage and loss scenarios for the city centre of Coimbra, Portugal, using a GIS mapping application.     

Seismic fragility curves of as-built single-span masonry arch bridges

Masonry arch bridges are crucial elements in the railway transportation network throughout Europe. Although significant advances in seismic risk assessment of various bridge types have been made by developing fragility curves of generalized classes of structures, there are no comparable tools for masonry arch structures. In this context, this paper presents the construction of seismic fragility curves of single-span masonry bridges according to the limit analysis method. An iterative procedure is implemented to define the capacity curve of the equivalent single degree of freedom system through non-linear kinematic analysis. The process involves determination of the collapse mechanism, calculation of the limit load multiplier, and definition of the thrust line. The intrinsic variability of the seismic action is incorporated with the use of different sets of elastic spectra compatible with EC 8 Type-1 spectrum for various types of soil, with peak ground acceleration varying over the range 0.05–1.5 g. The fragility curves of the generalized classes of single-span masonry bridges are finally obtained from the effective ranges of the main geometric and material parameters affecting arch bridge capacity.     

新疆塔什库尔干5.5级地震建筑结构震害

2017年5月11日新疆塔什库尔干5.5级地震给震区建筑结构造成了不同程度破坏。选择震区钢筋混凝土（RC）框架结构、砖混结构以及土石木结构等3类典型建筑结构,介绍了各类建筑结构地震破坏特点,分析了震害特征与破坏机理。结果表明:RC框架结构在地震中表现出了优异的抗震性能,即使在震中区,破坏也仅仅表现为非结构性破坏,如填充墙开裂和吊顶脱落等;砖混结构绝大多数抗震性能优良,仅震中区的少数建筑物发生了承重墙墙体开裂情况;土石木结构房屋抗震性能最差,地震破坏最为严重,是导致该次地震人员伤亡主要原因。建议地震高烈度设防区房屋建筑应采用抗震性能较好的RC框架结构和砖混结构,而抗震性能差的土石木建筑房屋应尽量避免继续建设和使用。结果可供类似地区房屋建设和建筑结构抗震设计等工作参考。     

Centrifuge modelling for evaluation of seismic behaviour of stone masonry structure

Many surviving ancient monuments are freestanding stone masonry structures, which appear to be vulnerable to horizontal dynamic loads such as earthquakes. However, such structures have stood for thousands of years despite numerous historic earthquakes. This study proposes a scaled-down dynamic centrifuge modelling test to study how these masonry structures resist seismic loading. The test is proposed for seismic risk assessments to evaluate risk of damage from a future seismic event. The seismic behaviour of a 3-storey, freestanding stone block structure has been modelled and tested within a centrifuge. Models were made at 3 different scales and dynamic tests were conducted using different centrifugal acceleration fields so that the behaviours could be transformed to an equivalent full-scale prototype and compared. Data from 2 earthquakes and a sweeping signal were used to simulate the effects of earthquake ground motion within the centrifuge. The acceleration and frequency responses at each storey height of the model were recorded in different centrifugal acceleration fields. Similar behaviours appeared when the results of the small-scale models were transformed to a full-size prototype scale. This confirms that the seismic behaviour of stone masonry structures can be predicted using scaled-down models.     

Description and analysis of building damage due to Pyrgos, Greece earthquake

On March 1993 an earthquake of magnitude M_s = 5·5 shook Pyrgos, a town in Western Peloponnissos, one of the most seismic prone areas in Greece. The damage induced to modern reinforced concrete buildings was rather light in contrast to the damage induced to historic and traditional buildings of adobe, stone or brick masonry which was severe. In order to study the causes of structural damage, detailed data are collected from a rather large statistical sample of 1023 masonry buildings and 22 reinforced concrete framed buildings with visible damage. For each building the number of storeys, the material of construction, as well as the type and the degree of damage are recorded. In addition, consideration is given to the site of the building within the town and the corresponding soil conditions. For reinforced concrete buildings, damage occured mostly in areas with relatively high estimated spectral accelerations and fundamental soil periods of vibration close to those of the buildings. Nevertheless, further analysis is required to explain the selective damage of a very small number of buildings. For masonry houses, the effect of soil conditions is more systematic. Moreover, the effects of the number of storeys as well as the age and material of construction appear to be dominant.