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.     

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.     

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.     

Forces acting on bridge abutments over liquefied ground

Large earthquake-induced displacements of a bridge abutment can occur, when the bridge is built on a floodplain or reclaimed area, i.e., liquefiable ground, and crosses a water channel. Seismic responses of a bridge abutment on liquefiable ground are the consequence of complex interactions between the abutment and surrounding soils. Therefore identification of the factors dominating the abutment response is important for the development of simplified seismic design methods. This paper presents the results of dynamic three-dimensional finite element analyses of bridge abutments adjacent to a river dike, including the effect of liquefaction of the underlying ground using earthquake motions widely used in Japan. The analysis shows that conventional design methods may underestimate the permanent abutment displacements unless the following two items are considered: (1) softening of the soil beneath the liquefiable layer, due to cyclic shearing of the soil surrounding the piles, and (2) the forces acting on the side faces of the abutment.     

梁的约束对液化场地桥台震害模式的影响分析

为深入研究液化场地梁的约束对桥台震害模式的影响,首先在对唐山地震中胜利桥震害调查的基础上,采用有限元软件UWLC对该桥震害进行数值模拟分析,并将数值模拟结果与实际震害结果进行对比验证。研究结果表明:数值模拟结果与实际震害结果基本一致,说明采用UWLC软件进行震害数值模拟分析是可行的。然后对有、无桩基条件下梁的约束力和液化层厚度对桥台震害模式的影响分别进行数值模拟分析。研究结果表明:在地震作用下,桥梁发生落梁破坏后会导致桥台的滑移破坏更为严重。与无桩基的重力式桥台不同,桩基桥台的震害模式均表现为前倾式破坏,这主要是因为桩基础限制了桥台底部的水平移动。梁的约束力对桩基桥台震后残余位移的影响程度要明显小于无桩基桥台。对于重力式桥台,液化砂层对地震波的中高频段有一定滤波作用,反映出液化层的减震作用;而对于桩基桥台,由于桩-土-台身的相互作用,液化砂层的减震效果不明显。     

Use of rubberised backfills for improving the seismic response of integral abutment bridges

Reuse of the 1.5 billion waste tyres that are produced annually is a one of the major worldwide challenges, as waste tyres are toxic and cause pollution to the environment. In recognition of this problem, this paper introduces the reuse of tyres, in the form of derived aggregates in mixtures with granulated soil materials, as previous studies indicated the potential benefits of these materials in the seismic performance of structures. The objective of the present research study is to investigate whether use of rubberised backfills benefits the seismic response of Integral Abutment Bridges (IABs) by enhancing soil-structure interaction (SSI) effects. Numerical models including typical integral abutments on surface foundation with nonlinear conventional backfill material and its alternative form as soil-rubber mixtures are analysed and their response parameters are compared. The research is conducted on the basis of parametric analysis, which aims to evaluate the influence of different rubber-soil mixtures on the dynamic response of the abutment-backfill system under various seismic excitations, accounting for dynamic soil-abutment interaction. The results provide evidence that the use of rubberised backfill leads to reductions in the backfill settlements, the horizontal displacements of the bridge deck, the residual horizontal displacements of the top of the abutment and the pressures acting on the abutment, up to 55, 18, 43 and 47 % respectively, with respect to a conventional backfill comprising of clean sand. Small change in bending moments and shear forces on the abutment wall is also observed. Therefore, rubberised backfills offer promising solution to mitigate the earthquake risk, towards economic design with minimal damage objectives for the resilience of transportation networks.     

Multi‐angle,multi‐damage fragility curves for seismic assessment of bridges

The scope of this study is to investigate the effect of the direction of seismic excitation on the fragility of an already constructed, 99‐m‐long, three‐span highway overpass. First, the investigation is performed at a component level, quantifying the sensitivity of local damage modes of individual bridge components (namely, piers, bearings, abutments, and footings) to the direction of earthquake excitation. The global vulnerability at the system level is then assessed for a given angle of incidence of the earthquake ground motion to provide a single‐angle, multi‐damage probabilistic estimate of the bridge overall performance. A multi‐angle, multi‐damage, vulnerability assessment methodology is then followed, assuming uniform distribution for the angle of incidence of seismic waves with respect to the bridge axis. The above three levels of investigation highlight that the directivity of ground motion excitation may have a significant impact on the fragility of the individual bridge components, which shall not be a priori neglected. Most importantly, depending on the assumptions made for the component to the system level transition, this local sensitivity is often suppressed. It may be therefore necessary, based on the ultimate purpose of the vulnerability or the life cycle analysis, to obtain a comprehensive insight on the multiple damage potential of all individual structural and foundation components under multi‐angle excitation, to quantify the statistical correlation among the distinct damage modes and to identify the components that are both most critical and sensitive to the direction of ground motion and carefully define their limit states which control the predicted bridge fragility. Copyright © 2015 John Wiley & Sons, Ltd.     

Extending the application of integral frame abutment bridges in earthquake‐prone areas by using novel isolators of recycled materials

Integral abutment bridges (IABs) are jointless structures without bearings or expansion joints which require minimum or zero maintenance. The barrier to the application of long‐span integral abutment bridges is the interaction of the abutment with the backfill soil during the thermal expansion and contraction of the bridge deck, that is, serviceability, or when the bridge is subjected to dynamic loads, such as earthquakes. The interaction of the bridge with the backfill leads to settlements and ratcheting of the soil behind the abutment and, as a result, the soil pressures acting on the abutment build up in the long term. This paper provides a solution for the aforementioned challenges by introducing a novel isolator that is a compressible inclusion of reused tyre‐derived aggregates placed between the bridge abutment and the backfill. The compressibility of typical tyre‐derived aggregates was measured by laboratory tests, and the compressible inclusion was designed accordingly. The compressible inclusion was then applied to a typical integral frame abutment model, which was subjected to static and dynamic loads representing in‐service and seismic loads correspondingly. The response of both the conventional and the isolated abutment was assessed based on the settlements of the backfill, the soil pressures and the actions of the abutment. The study of the isolated abutment showed that the achieved decoupling of the abutment from the backfill soil results in significant reductions of the settlements of the backfill and of the pressures acting on the abutment. Hence, the proposed research enables extending the length limits of integral frame bridges subjected to earthquake excitations. Copyright © 2016 John Wiley & Sons, Ltd.     

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P _f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.     

A performance-based adaptive methodology for the seismic evaluation of multi-span simply supported deck bridges

A performance-based adaptive methodology for the seismic assessment of highway bridges is proposed. The proposed methodology is based on an Inverse (I), Adaptive (A) application of the Capacity Spectrum Method (CSM), with the capacity curve of the bridge derived through a Displacement-based Adaptive Pushover (DAP) analysis. For this reason, the acronym IACSM is used to identify the proposed methodology. A number of Performance Levels (PLs), for which the seismic vulnerability and seismic risk of the bridge shall be evaluated, are identified. Each PL is associated to a number of Damage States (DSs) of the critical members of the bridge (piers, abutments, joints and bearing devices). The IACSM provides the earthquake intensity level (PGA) corresponding to the attainment of the selected DSs, using over-damped elastic response spectra as demand curves. The seismic vulnerability of the bridge is described by means of fragility curves, derived based on the PGA values associated to each DS. The seismic risk of the bridge is evaluated as convolution integral of the product between the fragility curves and the seismic hazard curve of the bridge site. In this paper, the key aspects and basic assumptions of the proposed methodology are presented first. The IACSM is then applied to nine existing simply supported deck bridges, characterized by different types of piers and bearing devices. Finally, the IACSM predictions are compared with the results of nonlinear response time-history analysis, carried out using a set of seven ground motions scaled to the expected PGA values.     

玛多地震中大野马岭大桥震害机理分析

2021年5月22日青海玛多发生了M_s7.4级地震,从地震中桥梁震害情况看:此次地震的特点是断层北侧震害轻,南侧震害重。位于断层南侧的野马滩大桥是简支梁桥,发生大量落梁,是此次地震中受损最为严重的大桥之一;而位于北侧的大野马岭大桥是连续梁桥,仅发生了部分挡块开裂。其中原因值得深入研究。本文通过有限元分析软件Midas/Civil建立大野马岭大桥（上行线）模型,进行地震反应分析,讨论分析了大野马岭大桥在此次地震中的震害机理。发现南北向的地震动是造成该桥横向挡块破坏的主要原因,东西向地震动因受到桥台和纵向挡块的约束并没有出现严重损伤。若将该桥由连续梁桥变成简支梁桥,地震反应会有所变化,但总体趋势特点变化并不大。另外,本文通过现有资料选定5组地震动作为输入,进行地震反应分析,比较分析不同地震动对该桥的影响,并验证地震动模拟效果。     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

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.     

基于IDA的高墩大跨桥梁地震易损性分析

针对目前我国桥梁抗震设计规范仅适用于墩高40m以下规则桥梁的现状,以一常见山区高墩大跨连续刚构桥为研究对象,采用IDA方法分析了桥梁结构在15条地震动下的动态响应,得到桥墩各截面在所有地震动作用下的曲率包络图。以高墩最不利截面的材料损伤应变所对应的截面曲率为损伤指标,结合能力需求比对数回归分析,计算了高墩在不同损伤状态下的破坏概率,建立了墩柱易损性曲线,同时还建立了梁端支座的易损性曲线。基于联合失效概率分析方法,形成了桥梁系统易损性曲线。分析结果表明:薄壁空心墩连续刚构桥在强地震作用下高墩发生破坏的部位主要集中在墩顶和墩底区域;墩柱发生完全破坏的概率极小,但桥台处梁端活动支座的地震损伤概率较高;桥梁系统损伤概率能够更加准确地反映高墩大跨桥梁的真实抗震性能。     

Seismic fragility curves for greek bridges: methodology and case studies

This study focusses on the estimation of seismic fragility curves for all common bridge types found in modern greek motorways. At first a classification scheme is developed in order to classify the existing bridges into a sufficient number of classes. A total of 11 representative bridge classes resulted, based on the type of piers, deck, and pier-to-deck connection. Then an analytical methodology for deriving fragility curves is proposed and applied to the representative bridge models. This procedure is based on pushover analysis of the entire bridge and definition of damage states in terms of parameters of the bridge pushover curves. The procedure differentiates the way of defining damage according to the seismic energy dissipation mechanism in each bridge, i.e. bridges with yielding piers of the column type and bridges with bearings (with or without seismic links) and non-yielding piers of the wall type. The activation of the abutment-backfill system due to closure of the gap between the deck and the abutments is also taken into account. The derived fragility curves are subjected to a first calibration against empirical curves based on damage data from the US and Japan.     

Towards probabilistic seismic performance of vehicle-bridge interaction systems: From stochastic dynamic model to fragility analysis

This paper aims to assess the seismic fragility of vehicle-bridge-interaction (VBI) systems considering the effects of vehicle types, traffic conditions, and road surface qualities. A stochastic nonlinear mechanical model for the earthquake-VBI system is developed, and the fragility functions for the proposed VBI model are derived by considering the relevant probabilistic seismic demand parameters. On the basis of a typical four-span continuous prestressed concrete highway bridge in China, a complete numerical model for the VBI system is built considering multiple uncertainties from bridge and vehicle parameters, as well as the road surface qualities. A total of 120 real ground motion records with different combinations of magnitude-source-to-site distance (M-R) and earthquake intensity characteristics are selected. Meanwhile, 80 scenarios in terms of different combinations of vehicle types, vehicle speeds, and road surface irregularities are defined. In this context, 96,000 nonlinear time-history analyses are performed, and the developed fragility models are applied to the VBI system at both component and system levels. Results indicate that the fragilities of pier drift, bearing shear strain, and the overall VBI system increase with the increase of the vehicle weight or the decrease of the vehicle speed, while the vertical deck displacement is dominated by the vehicle weight. It is also found that the road surface quality has a negligible effect on both component and system fragilities.     

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.     

横桥向地面运动作用下独塔部分斜拉桥易损性分析

桥梁作为交通生命线系统中的重要工程,屡次在中等强度地震的作用下,遭受严重破坏甚至整体损毁,因此桥梁结构地震易损性研究在世界各国得到重视和发展。部分斜拉桥作为一种新桥型,由于兼有经济性和美学特性,近十年来在国内外发展迅速,但这种新桥型尚未经受地震的考验,在可能的地震灾害下,部分斜拉桥的地震破坏损伤概率还不明确,有必要开展有关的易损性研究。本文在桥梁地震易损性研究的基础上,分析在横桥向地面运动作用下独塔部分斜拉桥的易损性,定义五级损伤极限状态,建立桥墩、桥塔、限位器和全桥的易损性曲线,研究结果表明在横桥向地面运动作用下,独塔部分斜拉桥全桥易损性主要受到限位器和中墩的控制。     

基于地震动参数的RC框架结构易损性分析

以某典型的12层钢筋混凝土框架结构作为研究对象,研究基于非线性动力时程分析和地震动参数的RC框架结构易损性分析方法。首先采用静力pushover分析判定结构薄弱层,并确定结构性能(capacity)参数;然后应用非线性动力时程分析估计结构地震反应,研究以峰值加速度和基本周期加速度反应谱作为地震动参数结构反应的不确定性,并进一步分析结构地震需求(demand)参数与地震动参数的关系;在此基础上,分别建立该结构基于峰值加速度和加速度反应谱的易损性曲线,通过考虑场地条件对地震动特性的影响,研究场地条件对结构易损性的影响,结果表明不同场地条件下的结构易损性曲线有一定差异。应用本文方法,根据新一代地震区划图或地震安全性评价确定的地震动参数,可以直接估计结构在未来地震中出现不同破坏的概率,这在结构的抗震性能评估和地震损失预测中有一定意义。     

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.