Development of fragility functions for geotechnical constructions: Application to cantilever retaining walls

Fragility curves constitute an emerging tool for the seismic risk assessment of all constructions at risk. They describe the probability of a structure being damaged beyond a specific damage state for various levels of ground shaking. They are usually represented as two-parameter (median and log-standard deviation) cumulative lognormal distributions. In this paper a numerical approach is proposed for the construction of fragility curves for geotechnical constructions. The methodology is applied to cantilever bridge abutments on surface foundation often used in road and railway networks. The response of the abutment to increasing levels of seismic intensity is evaluated using a 2D nonlinear FE 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 on the soil strain level. The effect of soil conditions and ground motion characteristics on the global soil and structural response is taken into account considering different typical soil profiles and seismic input motions. The objective is to assess the vulnerability of the road network as regards the performance of the bridge abutments; therefore, the level of damage, is described in terms of the range of settlement that is observed on the backfill. The effect of backfill material to the overall response of the abutment wall is also examined. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the structure geometry, the input motion and the soil properties as well as the associated uncertainties. The proposed fragility curves are verified based on observed damage during the 2007 Niigata-Chuetsu Oki earthquake.     

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 fragility curves of shallow tunnels in alluvial deposits

In this paper a numerical approach is proposed for the construction of fragility curves for shallow metro tunnels in alluvial deposits, when subjected to transversal seismic loading. The response of the tunnel is calculated under quasi static conditions applying the induced seismic ground deformations which are calculated through 1D equivalent linear analysis for an increasing level of seismic intensity. The results of the present numerical analyses are compared with selected closed form solutions, highlighting the limitations of the latter, while indicative full dynamic analysis are performed in order to validate the results of the quasi-static method. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the tunnel geometries and strength characteristics, the input motion and the soil properties as well as the associated uncertainties. The comparison between the new fragility curves and the existing empirical ones highlights the important role of the local soil conditions, which is not adequately taken into account in the empirical curves.     

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.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

Fragility curves for reinforced concrete buildings to seismically triggered slow-moving slides

Probabilistic fragility functions have been developed for low-rise, reinforced concrete buildings subjected to earthquake triggered slow-moving slides, applying a recently published methodology by the same authors [5] (Fotopoulou and Pitilakis, 2012). We performed an extensive numerical parametric study considering different idealized slope configurations, soil and geological settings, as well as distances of the structure to the slope's crest and foundation typologies. Various features of the structural damage are explored, highlighting trends on the building's behavior to the permanent co-seismic slope deformations. The proposed generalized probabilistic fragility curves have been developed as a function of the expected outcrop peak ground acceleration (PGA) as provided by modern seismic codes, i.e. EC8, or the induced permanent slope ground displacements (PGD) for different slope angles, water table level and soil type, foundation typology and seismic design code. Detailed sensitivity analyses of the above parameters, reveal their relative importance for the vulnerability analysis and the quantitative risk assessment of low-rise RC buildings subjected to earthquake triggered slow-moving slides.     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

SV波斜入射下混凝土重力坝易损性分析

易损性分析是评估不同强度地震作用下混凝土重力坝各级破坏概率的有效方法。目前重力坝易损性分析通常假定地震波为垂直入射,然而在近断层区域,地震波往往是倾斜入射的,地震波斜入射对重力坝地震响应有显著影响。从太平洋地震工程研究中心数据库选取16条地震动记录,采用黏弹性人工边界结合等效节点荷载实现SV波斜入射波动输入。采用增量动力分析方法对地震动峰值加速度进行调幅,以印度Koyna混凝土重力坝为研究对象,以坝顶相对位移为抗震性能指标,建立SV波斜入射下重力坝不同震损等级的易损性曲线。结果表明,与垂直入射相比,相同震损等级和相同地震动强度下,斜入射时重力坝破坏概率减小;当PGA接近重力坝实际遭受的地震动强度时,入射角为15°和30°时破坏概率与垂直入射相比最大减小率分别为27.3%和68.2%;各地震强度下,15°和30°斜入射相对于垂直入射的破坏概率差异值最大分别达36.6%、83.9%。因此,混凝土重力坝抗震性能分析应考虑地震波斜入射的影响。研究结果也可为近断层区域混凝土重力坝安全风险评估提供参考。     

Seismic fragility assessment of low-rise stone masonry buildings

Many historic buildings in old urban centers in Eastern Canada are made of stone masonry reputed to be highly vulnerable to seismic loads.Seismic risk assessment of stone masonry buildings is therefore the first step in the risk mitigation process to provide adequate planning for retrofit and preservation of historical urban centers.This paper focuses on development of analytical displacement-based fragility curves reflecting the characteristics of existing stone masonry buildings in Eastern Canada.The old historic center of Quebec City has been selected as a typical study area.The standard fragility analysis combines the inelastic spectral displacement,a structure-dependent earthquake intensity measure,and the building damage state correlated to the induced building displacement.The proposed procedure consists of a three-step development process:(1) mechanics-based capacity model,(2) displacement-based damage model and(3) seismic demand model.The damage estimation for a uniform hazard scenario of 2% in 50 years probability of exceedance indicates that slight to moderate damage is the most probable damage experienced by these stone masonry buildings.Comparison is also made with fragility curves implicit in the seismic risk assessment tools Hazus and ELER.Hazus shows the highest probability of the occurrence of no to slight damage,whereas the highest probability of extensive and complete damage is predicted with ELER.This comparison shows the importance of the development of fragility curves specific to the generic construction characteristics in the study area and emphasizes the need for critical use of regional risk assessment tools and generated results.     

按现行规范设计的Ⅷ度区RC框架结构的倒塌性能评估

选取按照现行规范设计的既有建筑进行有限元建模,考虑地震动的不确定性对其进行大量增量动力分析(IDA),得到模型的IDA曲线簇。在此基础上对其进行地震需求概率分析和概率抗震能力分析,拟合得到结构的易损性曲线,据此对结构的倒塌概率进行定量评估,并比较基于非线性分析与性能评估软件PERFORM-3D的纤维模型和塑性铰模型的分析结果。结果表明:按照我国现行规范设计的钢筋混凝土(RC)框架结构,在预期的罕遇地震作用下倒塌概率较小,可满足"大震不倒"的要求;基于PERFORM-3D的截面纤维模型所得的RC框架结构,经非线性分析所得的倒塌概率相对保守,安全储备更高。     

椭圆空洞对盾构隧道地震易损性曲线影响研究

采用增量动力分析方法,探究水平向地震下地层空洞对盾构隧道地震响应特征的影响规律。针对管片损伤及周边地层应力,选择弯矩比作为性能评价指标,峰值加速度(PGA)及峰值速度(PGV)作为衡量地震强度指标(IM),阐明椭圆形空洞对管片抗震性能的影响,得到隧道结构的地震易损性曲线。研究表明：椭圆空洞加大了浅埋盾构隧道的地震破坏概率;PGA与PGV均可作为IM并获得相应的隧道易损性曲线;使用弯矩比作为破坏指标,PGV作为地震动指标,其对应的易损性曲线对地层变异性更敏感。研究结论可为潜在空洞发育区防震方案的制定提供参考。     

Analytical fragility analysis of southern Illinois wall pier supported highway bridges

An analytical fragility analysis was conducted in order to characterize the seismic vulnerability of existing southern Illinois wall pier supported highway bridges to potential earthquakes. To perform this fragility analysis, a detailed inventory survey was first taken of the wall pier bridges identified in an earlier random sampling of southern Illinois priority emergency route bridges. From the survey three types of wall pier bridges were identified. Of those identified, hammerhead and regular wall pier supported bridges represented nearly 90% of the population. Incorporating structural variations determined from the random sample survey, nearly 100 three‐dimensional nonlinear finite element models were constructed. Each model was subjected to a randomly assigned synthetic earthquake representative of those that could potentially occur within the region. From these analyses, a series of wall pier supported bridge fragility curves were produced. In addition, a liquefaction fragility analysis was conducted in order to characterize the seismic vulnerability of southern Illinois wall pier supported highway bridge sites to liquefaction in potential earthquakes. To perform this second fragility analysis, wall pier bridges within the southern Illinois random sample that may be susceptible to liquefaction were identified. A soil profile from each of these susceptible bridge sites was then subjected to randomly assigned bedrock motions, and an Arias intensity liquefaction analysis was carried out. From these analyses, a fragility curve for the potentially liquefiable wall pier supported bridge sites was produced. Overall results of this study indicate that southern Illinois wall pier supported bridges are moderately vulnerable to structural damage in a 2% probability of exceedance in 50 year earthquake, and in some cases they could also be highly vulnerable to on‐site liquefaction events. Copyright © 2009 John Wiley & Sons, Ltd.     

Fragility estimation and sensitivity analysis of an idealized pile-supported wharf with batter piles

The main objective of the present study is to develop seismic fragility curves of an idealized pile-supported wharf with batter piles through a practical framework. Proposing quantitative limit states, analytical fragility curves are developed considering three engineering demand parameters (EDPs), including displacement ductility factor (µ_d), differential settlement between deck and behind land (DS) and normalized residual horizontal displacement (NRHD). Analytical fragility curves are generated using the results of a numerical model. So, the accuracy and reliability of resulted fragility curves directly depend on how accurate the seismic demand quantities are estimated. In addition, the seismic performance of pile-supported wharves is highly influenced by geotechnical properties of the soil structure system. Hence, a sensitivity analysis using the first-order second-moment (FOSM) method is performed to evaluate the effects of geotechnical parameters uncertainties in the seismic performance of the wharf.Herein, the seismic performance of the wharf structure is simulated using the representative FLAC2D model and performing nonlinear time history analyses under a suit of eight ground motion records. Incremental dynamic analysis (IDA) is used to estimate the seismic demand quantities. As a prevailing tool, adopted fragility curves are useful to seismic risk assessment. They can also be used to optimize wharf-retrofit methods. The results of sensitivity analysis demonstrate that uncertainties associated with the porosity of loose sand contribute most to the variance of both NRHD and µ_d. While in the case of differential settlement, the friction angle of loose sand contributes most to the variance.     

Post-earthquake estimates of different ground motion intensity measures for the 2012 Emilia earthquake

Estimates of the earthquake ground motion intensity over a geographical area have multiple uses, that is, emergency management, civil protection and seismic fragility assessment. In particular, with reference to fragility assessment, it is of interest to have estimates of the values of different ground-motion intensity measures in order to correlate them with the observed damage. To this purpose, the present paper uses a procedure recently proposed in the literature to estimate the ground-motion intensity for the 2012 Emilia mainshocks, considering different ground motion intensity measures and directionality effects. Ground motion prediction equations based on different site effect models, and spatial correlation models are calibrated for the Emilia earthquakes. The paper discusses the accuracy of the shakemaps obtained using the different soil effect models considered and presents the obtained shakemaps as supplementary material. The procedure presented in the paper is aimed at providing ground motion intensity values for seismic fragility assessment and is not intended as a tool to estimate shakemaps for rapid emergency assessment.     

Development of empirical and analytical fragility functions using kernel smoothing methods

Fragility functions that define the probabilistic relationship between structural damage and ground motion intensity are an integral part of performance‐based earthquake engineering or seismic risk analysis. This paper introduces three approaches based on kernel smoothing methods for developing analytical and empirical fragility functions. A kernel assigns a weight to each data that is inversely related to the distance between the data value and the input of the fragility function of interest. The kernel smoothing methods are, therefore, non‐parametric forms of data interpolation. These methods enable the implicit treatment of uncertainty in either or both of ground motion intensity and structural damage without making any assumption about the shape of the resulting fragility functions. They are particularly beneficial for sparse, noisy, or non‐homogeneous data sets. For illustration purposes, two types of data are considered. The first is a set of numerically simulated responses for a four‐story steel moment‐resisting frame, and the second is a set of field observations collected after the 2010 Haiti earthquake. The results demonstrate that these methods can develop continuous representations of fragility functions without specifying their functional forms and treat sparse data sets more efficiently than conventional data binning and parametric curve fitting methods. Moreover, various uncertainty analyses are conducted to address the issues of over‐fitting, bias, and confidence intervals. Copyright © 2014 John Wiley & Sons, Ltd.     

考虑不确定因素的山岭隧道地震易损性研究

基于均匀设计法,考虑围岩和衬砌的不确定性,提出了一种高效计算山岭隧道地震易损性的模型。基于该模型,得到了计算岩石山岭隧道结构的易损性计算曲线。根据计算结果得出:（1）均匀设计法能够考虑多种不确定性并为计算生成好的样本参数;（2）根据计算所得的地震结构易损性曲线与经验易损性曲线相对比,得出所提出的计算模型有较好的适用性。当交通隧道穿越地震带时,所提出的地震易损性曲线分析可为隧道线路规划以及设计参考。     

Ground motion duration effect on responses of hydraulic shallow-buried tunnel under SV-waves excitations

Although intensive research of the influence of ground motion duration on structural cumulative damage has been carried out, the influence of dynamic responses in underground tunnels remains a heated debate. This study attempts to highlight the importance of the ground motion duration effect on hydraulic tunnels subjected to deep-focus earthquakes. In the study, a set of 18 recorded accelerograms with a wide-range of durations were employed. A spectrally equivalent method serves to distinguish the effect of duration from other ground motion features, and then the seismic input model was simulated using SV-wave excitation based on a viscous-spring boundary, which was verified by the time-domain waves analysis method. The nonlinear analysis results demonstrate that the risk of collapse of the hydraulic tunnel is higher under long-duration ground motion than that of short-duration ground motion of the same seismic intensity. In a low intensity earthquake, the ground motion duration has little effect on the damage energy consumption of a hydraulic tunnel lining, but in a high intensity earthquake, dissipation of the damage energy and damage index of concrete shows a nonlinear growth trend accompanied by the increase of ground motion duration, which has a great influence on the deformation and stress of hydraulic tunnels, and correlation analysis shows that the correlation coefficient is greater than 0.8. Therefore, the duration of ground motion should be taken into consideration except for its intensity and frequency content in the design of hydraulic tunnel, and evaluation of seismic risk.

     

Performance-based seismic assessment of a large diameter extended pile shaft in a cohesionless soil

The seismic behavior of a large diameter extended pile shaft founded on a dense sandy site is investigated in this paper. First, a deterministic analysis is conducted including both nonlinear dynamic analysis(NDA) and pushover analysis to gain insights into the behavior of the pile and make sure an appropriate modeling technique is utilized. Then a probabilistic analysis is performed using the results of NDA for various demands. To this end a set of 40 pulse-like ground motions are picked and subsequently 40 nonlinear dynamic and pushover analyses are performed. The data obtained from NDA are used to generate probabilistic seismic demand model(PSDM) plots and consequently the median line and dispersion for each plot are computed. The NDA and pushover data are also plotted against each other to find out to what extent they are correlated. These operations are done for various engineering demand parameters(EDPs). A sensitivity analysis is done to pick the most appropriate intensity measure(IM) which would cause a minimum dispersion in PSDM plots out of 7 different IMs. Peak ground acceleration(PGA) is found to be the most appropriate IM. Pushover coefficient equations as a function of PGA are proposed which can be applied to the pushover analysis data to yield a better outcome with respect to the NDA. At the end, the pacific earthquake engineering research(PEER) center methodology is utilized to generate the fragility curves using the properties obtained from PSDM plots and considering various states of damage ranging from minor to severe. The extended pile shaft shows more vulnerability with a higher probability with respect to minor damage compared to severe damage.     

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.     

Seismic risk assessment of liquid storage tanks via a nonlinear surrogate model

A performance‐based earthquake engineering approach is developed for the seismic risk assessment of fixed‐roof atmospheric steel liquid storage tanks. The proposed method is based on a surrogate single‐mass model that consists of elastic beam‐column elements and nonlinear springs. Appropriate component and system‐level damage states are defined, following the identification of commonly observed modes of failure that may occur during an earthquake. Incremental dynamic analysis and simplified cloud are offered as potential approaches to derive the distribution of response parameters given the seismic intensity. A parametric investigation that engages the aforementioned analysis methods is conducted on 3 tanks of varying geometry, considering both anchored and unanchored support conditions. Special attention is paid to the elephant's foot buckling formation, by offering extensive information on its capacity and demand representation within the seismic risk assessment process. Seismic fragility curves are initially extracted for the component‐level damage states, to compare the effect of each analysis approach on the estimated performance. The subsequent generation of system‐level fragility curves reveals the issue of nonsequential damage states, whereby significant damage may abruptly appear without precursory lighter damage states.