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.     

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。     

Vulnerability of floating tunnel shafts for increasing earthquake loading

Fragility curves constitute the cornerstone in seismic risk evaluations and performance-based earthquake engineering. They describe the probability of a structure to experience a certain damage level for a given earthquake intensity measure, providing a relationship between seismic hazard and vulnerability. In this paper a numerical approach is applied to derive fragility curves for tunnel shafts built in clays, a component that is found in several critical infrastructure such as urban metro networks, airport facilities or water and waste water projects. The seismic response of a representative tunnel shaft is assessed using tridimensional finite difference non-linear analyses carried out with the program FLAC^3D, under increasing levels of seismic intensity. A hysteretic model is used to simulate the soil non-linear behavior during the seismic event. The effect of soil conditions and ground motion characteristics on the soil-structure system response is accounted for in the analyses. The damage is defined based on the exceedance of the concrete wall shaft capacity due to the developed seismic forces. The fragility curves are estimated in terms of peak ground acceleration at a rock or stiff soil outcrop, based on the evolution of damage with increasing earthquake intensity. The proposed fragility models allows the characterization of the seismic risk of a representative tunnel shaft typology and soil conditions considering the associated uncertainties, and partially fill the gap of data required in performing a risk analysis assessment of tunnels shafts.     

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.     

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.     

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.     

Response simulation and seismic assessment of highway overcrossings

Interaction of bridge structures with the adjacent embankment fills and pile foundations is generally responsible for response modification of the system to strong ground excitations, to a degree that depends on soil compliance, support conditions, and soil mass mobilized in dynamic response. This paper presents a general modeling and assessment procedure specifically targeted for simulation of the dynamic response of short bridges such as highway overcrossings, where the embankment soil–structure interaction is the most prevalent. From previous studies it has been shown that in this type of interaction, seismic displacement demands are magnified in the critical bridge components such as the central piers. This issue is of particular relevance not only in new design but also in the assessment of the existing infrastructure. Among a wide range of issues relevant to soil–structure interaction, typical highway overcrossings that have flexible abutments supported on earth embankments were investigated extensively in the paper. Simulation procedures are proposed for consideration of bridge‐embankment interaction effects in practical analysis of these structures for estimation of their seismic performance. Results are extrapolated after extensive parametric studies and are used to extract ready‐to‐use, general, and parameterized capacity curves for a wide range of possible material properties and geometric characteristics of the bridge‐embankment assembly. Using two instrumented highway overpasses as benchmark examples, the capacity curves estimated using the proposed practical procedures are correlated successfully with the results of explicit incremental dynamic analysis, verifying the applicability of the simple tools developed herein, in seismic assessment of existing short bridges. Copyright © 2009 John Wiley & Sons, Ltd.     

Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios

Probabilistic seismic demand models are a common and often essential step in generating analytical fragility curves for highway bridges. With these probabilistic models being traditionally conditioned on a single seismic intensity measure (IM), the degree of uncertainty in the models is dependent on the IM used. Selection of an optimal IM for conditioning these demand models is not a trivial matter and has been the focus of numerous studies. Unlike previous studies that consider a single structure for IM selection, this study evaluates optimal IMs for use when generating probabilistic seismic demand models for bridge portfolios such as would be found in HAZUS‐MH. Selection criteria such as efficiency, practicality, sufficiency, and hazard computability are considered in the selection process. A case study is performed considering the multi‐span simply supported steel girder bridge class. Probabilistic seismic demand models are generated considering variability in the geometric configurations and material properties, using two suites of ground motions—one synthetic and one recorded motion suite. Results show that of the 10 IMs considered, peak ground acceleration (PGA) and spectral acceleration at the fundamental period are the most optimal for the synthetic motions, and that cumulative absolute velocity is also a close contender when using recorded motions. However, when hazard computability is considered, PGA is selected as the IM of choice. Previous studies have shown that spectrally based quantities perform better than PGA for a given structure, but the findings of this study indicate that when a portfolio of bridges is considered, PGA should be used. Copyright © 2007 John Wiley & Sons, Ltd.     

Enrichment of seismic ground motion databases using Karhunen–Loève expansion

Best estimate seismic analysis are generally based on time‐domain simulations of structural responses. The seismic load is then modeled by a stochastic process representing ground motion. For this purpose, the analyst can use recorded accelerograms or work with synthetically generated ones. The number of ground motion time‐histories available for a given scenario and site condition is limited and generally not sufficient for carrying out more advanced probabilistic structural response analysis. It is then necessary to have at our disposal methods that allow for generating synthetic accelerograms that realistically characterize earthquake ground motions. However, most of the methods proposed in literature for generating synthetic accelerograms do not accurately reproduce the natural variability of ground motion parameters (such as PGA, cumulative absolute velocity, and Arias intensity) observed for recorded time histories. In this paper, we introduce a new method for generating synthetic ground motion, based on Karhunen‐Loève decomposition and a non‐Gaussian stochastic model. The proposed method enables the structural analyst to simulate ground motion time histories featuring the properties mentioned above. To demonstrate its capability, we study the influence of the simulation method on different ground motion parameters and on soil response spectra. We finally compute fragility curves to illustrate the practical application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

2016年2月6日美浓6.4级地震P-alert台网强震动记录初步分析

P-alert台网实时数据对地震预警及烈度速报和工程地震研究都是重要的补充,处理分析这些数据对客观衡量P-alert台网数据质量和数据用途有重要意义。对2016年2月6日台湾美浓ML6.4地震P-alert台网获取的记录进行了处理和初步分析,统计分析显示100gal以上加速度记录有112条,200gal以上加速度记录有33条,400gal以上加速度记录有7条,东西向最大峰值加速度为466.4gal,南北向最大峰值加速度为498.4gal,竖直向最大峰值加速度为258.6gal,最大仪器地震烈度为9.5度。竖直向峰值加速度和峰值速度比水平向峰值加速度和峰值速度衰减快。峰值加速度比峰值速度衰减快,观测峰值加速度和峰值速度与台湾西南地区峰值加速度和峰值速度衰减公式比较一致。计算得到了近场台站的永久位移,显示P-alert台网绝大多数永久位移在1cm到5cm之间,最大永久位移达8cm。     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

Bridge–embankment interaction under transverse ground excitation

Seismic performance and dynamic response of bridge–embankments during strong or moderate ground excitations are investigated through finite element (FE) modelling and detailed dynamic analysis. Previous research studies have established that bridge–embankments exhibit increasingly flexible performance under high‐shear deformation levels and that soil displacements at bridge abutment supports may be significant particularly in the transverse direction. The 2D equation of motion is solved for the embankment, in order to evaluate the dynamic characteristics and to describe explicitly the seismic performance and dynamic response under transverse excitations accounting for soil nonlinearities, soil–structure interaction and imposed boundary conditions (BCs). Using the proposed model, equivalent elastic analysis was performed so as to evaluate the dynamic response of approach embankments while accounting for soil–structure interaction. The analytical procedures were applied in the case of a well‐documented bridge with monolithic supports (Painter Street Overcrossing, PSO) which had been instrumented and embankment participation was identified from its response records after the 1971 San Fernando earthquake. The dynamic characteristics and dynamic response of the PSO embankments were evaluated for alternative BCs accounting for soil–structure interaction. Explicit expressions for the evaluation of the critical embankment length L_c are provided in order to quantify soil contribution to the overall bridge system under strong intensity ground excitations. The dynamic response of the entire bridge system (deck–abutments–embankments) was also evaluated through simplified models that considered soil–structure interaction. Results obtained from this analysis are correlated with those of detailed 3D FE models and field data with good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

软土隧道基于地震响应的输入地震动排序

为探讨“最不利地震动”概念在地下结构抗震设计中的适用性,以软土地铁区间隧道为对象建立相应的地层-结构动力分析模型。以直径变形率为分析指标,基于动力时程方法研究18条不同输入地震动作用下隧道结构动力响应的分布及差异性,得出基于隧道地震响应的输入地震动排序,并通过调幅手段对比分析了地面峰值加速度（PGA）和隧道埋深变化对隧道结构地震动响应排序的影响规律。最后,评价了不同输入地震动参数,包括峰值加速度、峰值速度、峰值位移、绝对累积速度（CAV）和阿里亚斯（Arias）强度（I_A）与隧道地震响应之间的相关性。分析结果表明:① 随着PGA从0.5 m/s2增加到2 m/s2,地震动排序发生明显变化,并且不同输入地震动引起的隧道地震响应差异显著提高,最不利地震动引起的直径变形率与平均值的比值从1.1增加到1.9;② 隧道从浅埋到深埋的过程中,地震动排序结果基本保持不变;③ PGA为2 m/s2时,隧道地震响应与基岩面峰值速度（PBV）的相关性最好,相关系数达到0.94,其次是与基岩面峰值位移（PBD）和I_A,相关系数分别为0.62和0.48,相关性最差的是基岩面峰值加速度（PBA）和CAV,相关系数仅为0.37和0.22。研究结论可为今后软土隧道的输入地震动选择提供科学依据。      

Seasonal differences in seismic responses of embankment on a sloping ground in permafrost regions

Because of its direct influence on the amount of unfrozen water and on the strength of intergranular ice in a frozen soil, temperature has a significant effect on all aspects of the mechanical behavior of the active layer in which temperature fluctuates above and below 0 °C. Hence seismic responses of engineering structures such as embankment on a sloping ground in permafrost regions exhibit obvious differences with seasonal alternation. To explore the distinctive seismic characteristics of a railway embankment on the sloping ground in permafrost regions, a coupled water-heat-dynamics model is built based on theories of heat transfer, soil moisture dynamics, frozen soil mechanics, soil dynamics, and so on. A well-monitored railway embankment on a sloping ground in Qinghai–Tibet Plateau is taken as an example to simulate seismic responses in four typical seasons in the 25th service year. The numerical results show that seismic acceleration, velocity and displacement responses are significantly different in four typical seasons, and the responses on October 15 are much higher among the four seasons. When the earthquake is over, there are still permanent differential deformations in the embankment and even severe damages on the left slope on October 15. Therefore, this position should be monitored closely and repaired timely to ensure safe operation. In addition, the numerical model and results may be a reference for maintenance, design and study on other embankments in permafrost regions.     

强震作用下桩-土-断层非线性动力相互作用特性

为研究强震区跨断层桥梁桩基非线性动力相互作用特性,依托海文大桥实体工程,利用MIDAS/GTS有限元软件,建立了桩-土-断层相互作用模型,分析0.20~0.60g地震动强度下断层上下盘桩基加速度响应、桩顶水平位移、桩身弯矩以及桩身剪力响应情况。结果表明:覆盖层土体对桩身加速度放大作用明显,且随着输入地震动强度的增大,放大作用逐渐减弱;覆盖层对地震波的滤波作用显著,随着输入地震动强度的增大,滤波作用逐渐减弱;上盘桩基达到桩顶峰值加速度的时刻滞后于下盘;随着输入地震动强度的增大,上、下盘桩的桩顶产生的永久位移和水平位移峰值逐渐变大,上盘桩顶产生的永久位移和桩顶峰值位移均大于下盘,产生显著的"上盘效应";不同强度地震动作用下,断层上、下盘桩基弯矩均在上部土层界面处达到峰值,剪力均在基岩面处达到峰值,下盘桩基弯矩和剪力峰值大于上盘桩基,呈现出显著的"下盘效应"。在桥梁桩基抗震设计时,应着重考虑断层上、下盘桩基的差异和不同强度地震作用对桩基承载特性的影响。     

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.     

Liquefaction-induced deformation of earthen embankments on non-homogeneous soil deposits under sequential ground motions

Damage of embankments during earthquakes is widely attributed to the liquefaction of foundation soil. Previous studies have investigated the dynamic response of embankments by mainly considering uniform sand foundation and a single earthquake event. However, the foundation of an embankment consists of many sublayers of soil from liquefiable sand to relatively impermeable layer, and during earthquakes a mainshock may trigger numerous aftershocks within a short time which may have the potential to cause additional damage to soil structures. Accordingly, the investigation of liquefaction-induced deformation of earthen embankments on various liquefiable foundation conditions under mainshock–aftershock sequential ground motions is carried out by a series of dynamic centrifuge tests in this study. The liquefiable foundation includes uniform sand profile, continuous layered soil profile, and non-homogeneous soil profiles. Effects of various foundation conditions on embankment deformations are compared and analyzed. From the test results, it is found that the embankment resting on non-homogeneous soil deposits suffer more damage compared to the uniform sand foundation of same relative density. The test results also suggest that the sequential ground motions have a significant effect on the accumulated deformation of embankment.     

考虑填充墙影响的钢筋混凝土厂房结构地震易损性分析

采用对角斜撑模拟纵向填充墙的作用,建立考虑填充墙和不考虑填充墙厂房结构模型,采用拉丁超立方抽样技术建立考虑材料不确定性的结构分析样本,基于随机Pushover分析确定结构不同破坏状态下的统计参数。综合考虑结构材料强度及输入地震动不确定性的影响,通过非线性时程分析开展单层钢筋混凝土厂房结构易损性研究,在此基础上比较结构横、纵向易损性的差异,研究填充墙对结构易损性的影响。研究结果表明:钢筋混凝土厂房结构体系横向地震易损性显著大于纵向地震易损性;对纵向结构体系而言,加入填充墙会明显降低结构易损性,但在相同强度的地震动作用下,填充墙破坏程度比主体结构严重,这与厂房结构的实际震害特征相符。     

Empirical seismic fragility for the precast RC industrial buildings damaged by the 2012 Emilia (Italy) earthquakes

The paper analyses the seismic fragility of precast reinforced concrete buildings using observational damage data gathered after the 2012 Emilia earthquakes that struck Northern Italy. The damage level in 1890 buildings was collected, classified and examined. Damage matrices were then evaluated, and finally, empirical fragility curves were fitted using Bayesian regression. Building damage was classified using a six‐level scale derived from EMS‐98. The completeness of the database and the spatial distribution of the buildings investigated were analysed using cadastral data as a reference. The intensity of the ground motion was quantified by the maximum horizontal peak ground acceleration, which was obtained from ShakeMaps. Copyright © 2017 John Wiley & Sons, Ltd.