Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

Nonlinear FE model updating and reconstruction of the response of an instrumented seismic isolated bridge to the 2010 Maule Chile earthquake

Nonlinear finite element (FE) modeling has been widely used to investigate the effects of seismic isolation on the response of bridges to earthquakes. However, most FE models of seismic isolated bridges (SIB) have used seismic isolator models calibrated from component test data, while the prediction accuracy of nonlinear FE models of SIB is rarely addressed by using data recorded from instrumented bridges. In this paper, the accuracy of a state‐of‐the‐art FE model is studied through nonlinear FE model updating (FEMU) of an existing instrumented SIB, the Marga‐Marga Bridge located in Viña del Mar, Chile. The seismic isolator models are updated in 2 phases: component‐wise and system‐wise FEMU. The isolator model parameters obtained from 23 isolator component tests show large scatter, and poor goodness of fit of the FE‐predicted bridge response to the 2010 Mw 8.8 Maule, Chile Earthquake is obtained when most of those parameter sets are used for the isolator elements of the bridge model. In contrast, good agreement is obtained between the FE‐predicted and measured bridge response when the isolator model parameters are calibrated using the bridge response data recorded during the mega‐earthquake. Nonlinear FEMU is conducted by solving single‐ and multiobjective optimization problems using high‐throughput cloud computing. The updated FE model is then used to reconstruct response quantities not recorded during the earthquake, gaining more insight into the effects of seismic isolation on the response of the bridge during the strong earthquake.     

Simplified method for real‐time seismic damage assessment of motorway bridges: Transverse direction—Accounting for abutment stoppers

In the context of developing a real‐time seismic damage assessment technique, this paper proposes a simplified model that accounts for abutment stoppers, focusing on the transverse direction. Detailed 3D finite element models of 4 bridges of the Attiki Odos motorway are developed and used as benchmarks to assess its efficiency. The selected bridges vary in length, pier typologies, clearances, and pier‐deck connections. The simplified model entails a SDOF system of a pier, with assemblies of gap elements, lateral and rotational springs, and dashpots (top and bottom), representing the deck, the bearings, the abutment stoppers, and the foundation. The effect of stoppers is initially studied, focusing on the response of the abutment‐embankment system. To shed more light on the role of abutment stoppers, a parametric study is conducted, considering a wide range of clearances. Subsequently, the effect of variabilities in span length and pier height is examined. The simplified method is extended to nonideally symmetric systems and verified against the 3D benchmarks. Finally, the model is modified to account for multicolumn piers. The extended simplified model offers a reasonable prediction of the seismic damage state, reducing significantly the computational cost, and allowing detailed parametric studies. The latter are used to develop nonlinear regression model equations correlating a selected damage index with statistically significant intensity measures. Such equations offer a viable alternative for network‐wide seismic damage assessment as part of a real‐time emergency response framework. A pilot implementation is presented, illustrating the applicability of the proposed methodology.     

A frequency‐dependent and intensity‐dependent macroelement for reduced order seismic analysis of soil‐structure interacting systems

The computational demand of the soil‐structure interaction analysis for the design and assessment of structures, as well as for the evaluation of their life‐cycle cost and risk exposure, has led the civil engineering community to the development of a variety of methods toward the model order reduction of the coupled soil‐structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional finite element model simulation of the complete soil‐structure domain, such as the nonlinear lumped spring, the macroelement method, and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency‐dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil‐structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency‐dependent and intensity‐dependent expansion of the lumped parameter modeling method is proposed in the current paper, materialized through a multiobjective algorithm, capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil‐foundation systems in the framework of nonlinear seismic analysis of soil‐structure interaction systems.     

Vehicle effects on seismic response of a simple‐span bridge during shake tests

Presence of vehicles on a bridge has been observed many times during past earthquakes. Although in practice, the engineers may or may not include the live load contribution to seismic weight in design, current bridge design codes do not specify a certain guideline. A very limited research has been conducted to address this issue from design point of view. The focus of this research is to experimentally assess the effect of a vehicle on the seismic response of a bridge through a large‐scale model. In this scope, a 12‐meter long bridge, having a one lane deck with concrete slab on steel girders, has been shaken under five different ground motions obtained from recent earthquakes that occurred in Turkey, in its transverse direction, both with and without a vehicle on top of the deck. The measured results have indicated that top slab transverse acceleration and bearing displacements can reduce up to 18.7% in presence of a vehicle during seismic tests, which is an indication of reduction in substructure forces. The main reason for the reduction in seismic response of the bridge in the presence of live load can be ascribed to the increase in damping of the system due to mass damper‐like action induced by the vehicle. This beneficial effect cannot be observed in vertical seismic response. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of hysteretic dampers with optimal ductility for the transverse seismic control of cable‐stayed bridges

Cable‐stayed bridges require a careful consideration of the lateral force exerted by the deck on the towers under strong earthquakes. This work explores the seismic response of cable‐stayed bridges with yielding metallic dampers composed of triangular plates that connect the deck with the supports in the transverse direction. A design method based on an equivalent single‐degree of freedom approximation is proposed. This is proved valid for conventional cable‐stayed bridges with 200‐ and 400‐m main spans, but not 600 m. The height of the plates is chosen to (1) achieve a yielding capacity that limits the maximum force transmitted from the deck to the towers, and to (2) control the hysteretic energy that the dampers dissipate by defining their design ductility. In order to select the optimal ductility and the damper configuration, a multi‐objective response factor that accounts for the energy dissipation, peak damper displacement and low‐cycle fatigue is introduced. The design method is applied to cable‐stayed bridges with different spans and deck–support connections. The results show that the dissipation by plastic deformation in the dampers prevents significant damage in the towers of the short‐to‐medium‐span bridges under the extreme seismic actions. However, the transverse response of the towers in the bridge with a 600‐m main span is less sensitive to the dampers. Copyright © 2017 John Wiley & Sons, Ltd.     

大跨度斜拉桥地震响应非线性时程分析

以有限元分析理论为基础,结合某大跨度斜拉桥工程实例,利用ANSYS软件建立有限元模型,通过修正后的El Centro波分别考虑横向、竖向及纵向输入,采用时程分析方法对其进行地震反应分析.计算分析表明:考虑几何非线性后,结构的内力和位移响应明显增大,且对主梁和索塔内力与位移的影响程度及规律也不尽相同,须区别对待分析.同时表明该桥抗震性能良好,地震荷载不控制设计.由此得出结论,对于斜拉桥这类柔性体系, 不可忽视结构几何非线性的影响.     

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.     

Simulation of the seismic performance of the Bolu Viaduct subjected to near‐fault ground motions

The seismic performance of the Bolu Viaduct in the Duzce, Turkey, earthquake of November 1999 was studied via a non‐linear, time‐history analysis of a multi‐degree of freedom model. The viaduct had a seismic isolation system consisting of yielding‐steel energy dissipation units and sliding pot bearings. The Duzce earthquake caused a surface rupture across the viaduct, which resulted in excessive superstructure movement and widespread failure of the seismic isolation system. The effect of the rupture was modeled by a static, differential ground displacement in the fault‐parallel direction across the rupture. The ground motions used in the analysis contain common near‐fault features including a directivity pulse in the fault‐normal direction and a fling step in the fault‐parallel direction. The analysis used a finite element package capable of modeling the mechanical behavior of the seismic isolation system and focused on the structural response of a 10‐span module of the viaduct. This analysis showed that the displacement of the superstructure relative to the piers exceeded the capacity of the bearings at an early stage of the earthquake, causing damage to the bearings as well as to the energy dissipation units. The analysis also indicated that shear keys, both longitudinal and transverse, played a critical role in preventing collapse of the deck spans. Published in 2004 by John Wiley & Sons, Ltd.     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

无缝桥抗震性能的对比研究

本文以一座三跨总长60 m的整体桥为案例桥,分别试设计了同跨径的半整体桥、延伸桥面板桥和常规连续梁桥。通过Midas/Civil软件建立四种桥型的有限元模型,并对其进行了E1和E2反应谱分析和时程分析,对比了四种桥型的结构反应峰值（墩顶位移、桥墩及桩基剪力与弯矩、台底位移、桥台桩基剪力与弯矩）。计算结果表明:当桥梁存在15°的斜交角,整体桥、半整体桥在地震动沿平行于桥台长边方向及其垂直方向输入时更不利,而延伸桥面板桥和常规连续梁桥在地震动沿顺桥向和横桥向输入时更不利。四种桥型在地震作用下:整体桥抗震性能最优异,但其台底位移、桥台桩基的剪力和弯矩最大;半整体桥台底位移、桥台桩基的剪力和弯矩最小,其墩顶位移、桥墩及桩基的剪力和弯矩仅比整体桥大;延伸桥面板桥和常规连续梁桥的墩-梁相对位移远大于整体桥和半整体桥,不适用于地震基本烈度高的区域。     

减隔震桥梁设计方法及抗震性能研究综述

桥梁作为交通系统中的生命线工程,其抗震性能问题尤为重要。桥梁减隔震技术主要通过减隔震装置来降低结构的地震损伤,目前已发展成为提高强震区桥梁抗震能力的重要措施。为促进减隔震技术在中国桥梁工程领域的进一步发展,首先总结减隔震桥梁的设计方法,归纳其地震反应和震害情况,对采用不同减隔震装置桥梁的非线性动力性能、减隔震效果、地震随机响应、易损性及性能优化方法等研究情况进行梳理;其次,概述减隔震技术在斜交桥、曲线桥及铁路桥梁中的应用情况与研究进展,并介绍新型韧性抗震设计理念在桥梁工程领域中的应用情况和发展前景;最后,总结减隔震桥梁的试验研究情况,指出目前减隔震桥梁研究中的不足和发展趋势。     

Seismic isolation of cable‐stayed bridges for near‐field ground motions

This study examines the efficacy of using seismic isolation to favorably influence the seismic response of cable‐stayed bridges subjected to near‐field earthquake ground motions. In near‐field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many cable‐stayed bridges have significant structural response modes. This combination of factors can result in large tower accelerations and base shears. In this study, lead–rubber bearing seismic isolators were modeled for three cable‐stayed bridges, and three cases of isolation were examined for each bridge. The nine isolated bridge configurations, plus three non‐isolated configurations as references, were subjected to near‐field earthquake ground motions using three‐dimensional time‐history analyses. Introduction of a small amount of isolation is shown to be very beneficial in reducing seismic accelerations and forces while at the same time producing only a modest increase in the structural displacements. There is a low marginal benefit to continue to increase the amount of isolation by further lengthening the period of the structure because structural forces and accelerations reduce at a diminishing rate whereas structural displacements increase substantially. In virtually all cases the base shears in the isolated bridges were reduced by at least 50several instances by up to 80individual near‐field records showed large variability from one record to the next, with coefficients of variation about the mean as large as 50assessing the characteristics of near‐field ground motion for use in isolation design of cable‐stayed bridges. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybrid simulation of a multi‐span RC viaduct with plain bars and sliding bearings

This paper deals with the seismic response assessment of an old reinforced concrete viaduct and the effectiveness of friction‐based retrofitting systems. Emphasis was laid on an old bridge, not properly designed to resist seismic action, consisting of 12 portal piers that support a 13‐span bay deck for each independent roadway. On the basis of an OpenSEES finite element frame pier model, calibrated in a previous experimental campaign with cyclic displacement on three 1:4 scale frame piers, a more complex experimental activity using hybrid simulation has been devised. The aim of the simulation was twofold: (i) to increase knowledge of non‐linear behavior of reinforced concrete frame piers with plain steel rebars and detailing dating from the late 1950s; and (ii) to study the effectiveness of sliding bearings for seismic response mitigation. Hence, to explore the performance of the as built bridge layout and also of the viaduct retrofitted with friction‐based devices, at both serviceability and ultimate limit state conditions, hybrid simulation tests were carried out. In particular, two frame piers were experimentally controlled with eight‐actuator channels in the as built case while two frame piers and eight sliding bearings were controlled with 18‐actuator channels in the isolated case. The remaining frame piers were part of numerical substructures and were updated offline to accurately track damage evolution. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of variation of normal force on seismic performance of resilient sliding isolation systems in highway bridges

In this study, a series of shaking table tests are carried out on scaled models of two seismically isolated highway bridges to investigate the effect of rocking motion and vertical acceleration on seismic performance of resilient sliding isolators. In addition, performance of RSI is compared with system having solely natural rubber bearings. Test results show that variation of normal force on sliders due to rocking effect and vertical acceleration makes no significant difference in response of RSI systems. In addition, analytical response of prototype isolated bridge and the model used in experiments is obtained analytically by using non‐linear model for isolation systems. It is observed that for seismically isolated bridges, dynamic response of full‐scale complex structures can be predicted with acceptable accuracy by experiments using a simple model of the structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of vehicle bridge interaction on seismic response and fragility of bridges

This study focuses on understanding and evaluating the effect of vehicle bridge interaction (VBI) on the response and fragility of bridges subjected to earthquakes. A comprehensive study on the effect of VBI on bridge seismic performance is conducted, providing metamodels for seismic response and fragility estimates for bridges in the presence of various types of vehicles. For this purpose, the performance of multispan simply supported concrete girder bridges with varying design and geometric parameters is assessed with 3 different types of stationary trucks placed atop them. To delineate the effects of VBI and additional truck mass, the trucks are modeled in 2 different ways—with additional masses and suspension springs (ie, with VBI) and using additional masses only (without VBI). The results provide insight on VBI effects, such as the fact that when bridge and vehicle mode shapes are in‐phase, the component responses increase and vice versa; additionally, the presence of a heavy axle near a bent increases component responses. Sensitivity analyses are also performed to determine the bridge parameters that significantly alter the component responses in the presence of vehicles. Furthermore, differences in component responses and fragilities highlight that modeling vehicles with additional masses alone is not sufficient to model the effect of truck presence on the seismic response of bridges. Finally, this study concludes that depending on the characteristics of the bridge and the vehicle, presence of a vehicle atop the bridge during an earthquake may be either beneficial or detrimental to bridge performance.     

Enhancing resilience of highway bridges through seismic retrofit

The present study evaluates seismic resilience of highway bridges that are important components of highway transportation systems. To mitigate losses incurred from bridge damage during seismic events, bridge retrofit strategies are selected such that the retrofit not only enhances bridge seismic performance but also improves resilience of the system consisting of these bridges. To obtain results specific to a bridge, a reinforced concrete bridge in the Los Angeles region is analyzed. This bridge was severely damaged during the Northridge earthquake because of shear failure of one bridge pier. Seismic vulnerability model of the bridge is developed through finite element analysis under a suite of time histories that represent regional seismic hazard. Obtained bridge vulnerability model is combined with appropriate loss and recovery models to calculate seismic resilience of the bridge. Impact of retrofit on seismic resilience is observed by applying suitable retrofit strategy to the bridge assuming its undamaged condition prior to the Northridge event. Difference in resilience observed before and after bridge retrofit signified the effectiveness of seismic retrofit. The applied retrofit technique is also found to be cost‐effective through a cost‐benefit analysis. First order second moment reliability analysis is performed, and a tornado diagram is developed to identify major uncertain input parameters to which seismic resilience is most sensitive. Statistical analysis of resilience obtained through random sampling of major uncertain input parameters revealed that the uncertain nature of seismic resilience can be characterized with a normal distribution, the standard deviation of which represents the uncertainty in seismic resilience. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance‐based grouping methods of bridge classes for regional seismic risk assessment: Application of ANOVA,ANCOVA, and non‐parametric approaches

One of the key tasks to enable a regional risk assessment is to group structures with similar seismic performances and generate fragility curves representative of the grouped structures. The grouping has been traditionally performed based primarily on engineering judgment and prior experience. This paper (i) presents an overview of various statistical techniques such as analysis of variance, analysis of covariance, and Kruskal–Wallis test for grouping the bridges of similar performance; (ii) compares the groupings that emerge from the various grouping techniques; and (iii) identifies the method that has more statistical power in creating bridge sub‐classes of distinct structural performance. The grouping is achieved by comparing the structural responses of bridge classes obtained from the non‐linear time history analysis of bridges. The relative merits of these grouping techniques are discussed with the case study of box‐girder bridges in California. Copyright © 2017 John Wiley & Sons, Ltd.