Analysis of bridge structures crossing strike-slip fault rupture zones: A simple method for generating across-fault seismic ground motions

This article presents a simple and effective method for generating across-fault seismic ground motions for the analysis of ordinary and seismically isolated bridges crossing strike-slip faults. Based on pulse models available in the literature, two simple loading functions are first proposed to represent the coherent (long-period) components of ground motion across strike-slip faults. The loading functions are then calibrated using actual near-fault ground-motion records with a forward-directivity velocity pulse in the fault-normal direction and a fling-step displacement in the fault-parallel direction. The effectiveness of the proposed method is demonstrated by comparing time history responses and seismic demands of ordinary and seismically isolated bridges obtained from nonlinear response history analyses using the actual ground-motion records and the calibrated loading functions. A comprehensive methodology is also presented for selecting the input parameters of the loading functions based on empirical equations and practical guidelines. Finally, an analysis procedure for bridge structures crossing strike-slip faults is introduced based on the proposed method for generating across-fault ground motions and the parameter selection methodology for the loading functions.     

Seismic response of isolated bridges with soil–structure interaction

The modern transportation facilities demand that the bridges are to be constructed across the gorges that are located in seismically active areas and at the same time the site conditions compel the engineers to rest the pier foundation on soil. The purpose of this study is to assess the effects of soil–structure interaction (SSI) on the peak responses of three-span continuous deck bridge seismically isolated by the elastomeric bearings. The emphasis has been placed on gauging the significance of physical parameters that affect the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. The soil surrounding the foundation of pier is modelled by frequency independent coefficients and the complete dynamic analysis is carried out in time domain using complex modal analysis method. In order to quantify the effects of SSI, the peak responses of isolated and non-isolated bridge (i.e. bridge without isolation device) are compared with the corresponding bridge ignoring these effects. A parametric study is also conducted to investigate the effects of soil flexibility and bearing parameters (such as stiffness and damping) on the response of isolated bridge system. It is observed that the soil surrounding the pier has significant effects on the response of the isolated bridges and under certain circumstances the bearing displacements at abutment locations may be underestimated if the SSI effects are not considered in the response analysis of the system.     

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.     

The eigenvalues of isolated bridges with transverse restraints at the end abutments

This paper examines the eigenvalues of multi‐span seismically isolated bridges in which the transverse displacement of the deck at the end abutments is restricted. With this constraint the deck is fully isolated along the longitudinal direction, whereas along the transverse direction the deck is a simple‐supported beam at the end abutments which enjoys concentrated restoring forces from the isolation bearings at the center piers. For moderate long bridges, the first natural period of the bridge is the first longitudinal period, while the first transverse period is the second period, given that the flexural rigidity of the deck along the transverse direction shortens the isolation period offered by the bearings in that direction. This paper shows that for isolated bridges longer than a certain critical length, the first transverse period becomes longer than the first longitudinal period despite the presence of the flexural rigidity of the deck. This critical length depends on whether the bridge is isolated on elastomeric bearings or on spherical sliding bearings. This result is also predicted with established commercially available numerical codes only when several additional nodes are added along the beam elements which are modeling the deck in‐between the bridge piers. On the other hand, this result cannot be captured with the limiting idealization of a beam on continuous distributed springs (beam on Wrinkler foundation)—a finding that has practical significance in design and system identification studies. Finally, the paper shows that the normalized transverse eigenperiods of any finite‐span deck are self‐similar solutions that can be represented by a single master curve and are independent of the longitudinal isolation period or on whether the deck is supported on elastomeric or spherical sliding bearings. Copyright © 2009 John Wiley & Sons, Ltd.     

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 response of multi-frame bridges

Long cast-in-place concrete bridges are often constructed in multiple frames separated by in-span hinges. The multi-frame system offers lower construction and maintenance costs, fewer adverse effects due to creep, post-tensioning, and thermal deformations as a few of its advantages. However, the seismic response of multi-frame bridges has been uncertain owing to the complexities of their discrete system. This study intends to improve the understanding of the seismic response of multi-frame bridge systems and evaluate the applicability of current design assumptions. Responses of multi-frame bridges and comparable single-frame bridges of the same length are compared. Seismic demands on multi-frame bridge columns, abutments, and in-span hinges were investigated through high-fidelity analytical simulations. Approximately 3400 nonlinear time history analyses of prototype bridges with realistic designs were performed using the OpenSees platform. Analysis of variance was implemented along with a factorial design to study the effect of several independent factors, including the number of frames, substructure system, unequal column heights, soil type, ground motion intensity, and capacity-to-demand ratio. It was observed for elastic dynamic analysis that a 90 % modal mass participation ratio is not adequate to accurately estimate dynamic responses. Seismic demands on columns in multi-frame bridges are typically smaller than those in comparable single-frame bridges. The multi-frame system is seismically more robust than the single-frame system, specifically for bridges spanning non-uniform valleys that include unequal column heights. To prevent longitudinal unseating at in-span hinges, it is critical to consider the interaction of transverse and longitudinal responses. The seismic damage to abutment backwalls and backfills in multi-frame bridges is expected to be extensive owing to small expansion joints.     

Dynamic performance analysis of a seismically isolated bridge under braking force

In order to study the dynamic performance of seismically isolated bridges under the most unfavorable loads in the longitudinal direction,a dynamic equation for vehicle braking in the longitudinal direction is established.A four or fiveorder Runge-Kutta method is adopted to obtain the time-history response of a wheel set under braking force.The quadratic discretization method is then used to transform this time-history into a braking and bending force time-history of a structural fixed node,and a dynamic response analysis of the seismically isolated bridge under the vehicle’s braking force is carried out using ANSYS,a universal finite element analysis software.According to the results,seismic isolation design results in a more rational distribution of braking force among piers;the influence of the initial braking velocity on the vehicle braking force is negligible;the location where the first wheel set leaves the bridge is the most unfavorable parking location;a seismic isolation bridge bearing constructed according to typical design methods enters into a yield stage under the braking force, while the shearing force at the bottom of the pier declines as the isolation period is extended;the design requirements can be met when the yield displacement of the seismic isolation bearing is less than 5 mm and the yield strength is greater than the braking force.     

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 viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Shake-table tests and numerical simulation of an innovative isolation system for highway bridges

Damage investigation of small to medium-span highway bridges in Wenchuan earthquake revealed that typical damage of these bridges included: sliding between laminated-rubber bearings and bridge girders, concrete shear keys failure, excessive girder displacements and even span collapse. However, the bearing sliding could actually act as a seismic isolation for piers, and hence, damage to piers for these bridges was minor during the earthquake. Based on this concept, an innovative solation system for highway bridges with laminated-rubber bearings is developed. The system is comprised of typical laminated-rubber bearings and steel dampers. Bearing sliding is allowed during an earthquake to limit the seismic forces transmitting to piers, and steel dampers are applied to restrict the bearing displacements through hysteretic energy dissipation. As a major part of this research, a quarter-scale, two-span bridge model was constructed and tested on the shake tables to evaluate the performance of this isolation system. The bridge model was subjected to a Northridge and an artificial ground motion in transverse direction. Moreover, numerical analyses were conducted to investigate the seismic performance of the bridge model. Besides the test bridge model, a benchmark model with the superstructure fixed to the substructure in transverse direction was also included in the numerical analyses. Both the experimental and the numerical results showed high effectiveness of this proposed isolation system in the bridge model. The system was found to effectively control the pier-girder relative displacements, and simultaneously, protect the piers from severe damage. Numerical analyses also validated that the existing finite element methods are adequate to estimate the seismic response of bridges with this isolation system.     

Restrain of a seismically isolated bridge by external stoppers

The current design of seismically isolated bridges usually combines the use of bearings and stoppers, as a second line of defence. The stoppers allow the development of the in-service movements of the bridge deck, without transmitting significant loads to the piers and their foundations, while during earthquake they transmit the entire seismic action. Despite the fact that stoppers, which restrain the transverse seismic movements of the deck, are used frequently in seismically isolated bridges, the use of longitudinal stoppers is relatively rare, mainly due to the large in-service constraint movements of bridges. The present paper proposes a new type of external longitudinal stoppers, which are installed in stiff sub-structures-boundaries, aiming at limiting the bridge seismic movements. The parametric investigation, which was conducted in order to identify the seismic efficiency of the external stoppers, showed that the interaction of the bridge with the stiff boundaries can lead to significant reductions in the seismic movements of the bridge. Serviceability is appropriately arranged in the paper by expansion joints and approach slabs.     

RC jacketing parameters to retrofit highway bridges

Highway bridges are essential structures in the transportation system of any country in the world. Many highway bridges are reinforced concrete (RC) bridges that were constructed before the 1980s, prior to current seismic regulation codes. The continuous modification of regulation codes makes it necessary to evaluate structures, and in many cases, existing bridges require interventions to increase their seismic capacity. Among the different techniques used to improve bridge capacity, encasing the columns with RC jackets increases the strength and stiffness of the substructure. RC jacketing increases the column cross sections, improves the seismic capacity and reduces the seismic vulnerability of the bridge substructures. This work presents a parametric study to assess the expected demands of seismically deficient medium length highway bridges retrofitted with RC jacketing aimed at determining the best jacket parameters. A suite of twenty strong ground motions, recorded from a subduction seismic source close to the Pacific Coast in Mexico, was selected to characterize the seismic demand. The bridge superstructures are simply supported with five 30 m long spans for a total length of 150 m. The bridge models have five possible pier heights of 5, 10, 15 20 and 25 m and three different jacket thicknesses and steel ratios. Pushover analyses and capacity spectra of the family of accelerograms allow for the determination of the pier demands by obtaining the performance point as the intersection of the capacity and demand curves. The results allow for the determination of the influence of each parameter on the expected seismic behavior of the bridge models, with the aim of selecting the most suitable jacket characteristics to improve the seismic bridge performance.     

Considering dynamic soil structure interaction (SSI) effects on seismic isolation retrofit efficiency and the importance of natural frequency ratio

This paper utilizes and expands on existing coupled BEM–FEM (finite element method) methods for the investigation of the effects of soil structure interaction (SSI) on both an un-retrofitted and seismically isolated typical bridge structure. A simple numerical model of the bridge and surrounding soil is formulated and excited by an earthquake excitation. Utilizing Newmark's β FEM solution method along with the closed form B-spline BIRF method, the structural damped period, composite damping ratio, pier relative displacement, and base shear demand are monitored. From these results, the effects of SSI on this structure are identified. Additionally, the importance of the relative rigidity between the soil-foundation system and the bridge structure is also investigated. The results of the studies indicate that the response of the complete structure system considered is affected by the inclusion of SSI effects. Furthermore, the efficiency of the isolation measures designed using fixed base conditions is decreased by considering SSI over a certain relative rigidity range that is quantified using the structure to soil-foundation natural frequency ratio.     

基于第四代地震区划的跨越发震断层永久位移概率分析方法

本文主要借鉴了Lee(2007)和Youngs(2003)提出的地表永久位移估计方法,联合中国第四代地震区划图的潜在震源区参数,给出了适合中国跨越发震断层永久位移概率分析方法。震害调查表明,近场的结构破坏不仅是地震动引起的,地震地表的破裂或永久位移引起的破坏也占很大比重。应用与概率估计地震动相似的方法,给出不同概率水准的地震地表永久位移,使之服务于穿越地震发震断层管线、桥梁工程的抗震设防,采取有效的抗御永久地表位移措施,减小地震灾害带来的损失。     

Design of bridges against large tectonic deformation

The engineering community has devoted much effort to understanding the response of soil-structure systems to seismic ground motions, but little attention to the effects of an outcropping fault offset. The 1999 earthquakes of Turkey and Taiwan, offering a variety of case histories of structural damage due to faulting, have （re）fueled the interest on the subject. This paper presents a methodology for design of bridges against tectonic deformation. The problem is decoupled in two analysis steps： the first （at the local level） deals with the response of a single pier and its foundation to fault rupture propagating through the soil, and the superstructure is modeled in a simplified manner; and the second （at the global level） investigates detailed models of the superstructure subjected to the support （differential） displacements of Step 1. A parametric study investigates typical models of viaduct and overpass bridges, founded on piles or caissons. Fixed-head piled foundations are shown to be rather vulnerable to faulting-dnduced deformation. End-bearing piles in particular are unable to survive bedrock offsets exceeding 10 cm. Floating piles perform better, and if combined with hinged pile-to-cap connections, they could survive much larger offsets. Soil resilience is beneficial in reducing pile distress. Caisson foundations are almost invariably successful. Statically-indeterminate superstructures are quite vulnerable, while statically-determinate are insensitive （allowing differential displacements and rotations without suffering any distress）. For large-span cantilever-construction bridges, where a statically determinate system is hardly an option, inserting resilient seismic isolation bearings is advantageous as long as ample seating can prevent the deck from falling off the supports. An actual application of the developed method is presented for a major bridge, demonstrating the feasibility of design against tectonic deformation.     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

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.     

Dynamics of inelastic base‐isolated structures subjected to analytical pulse ground motions

Structural design code provisions worldwide prescribe relatively small seismic force reduction factors for seismically base‐isolated structures, making their response to design‐level earthquake excitation essentially elastic. This paper uses the method of dimensional analysis to prove that; in most cases, this is not a conservative design approach but a necessity that emerges from the dynamics of base‐isolated structures. It is shown that allowing typical base‐isolated structures to yield results in large displacement ductility demands for the structure. This phenomenon is caused by the change in the nature of the ground motion excitation as it is transmitted to the structure through the seismic base isolation system as well as by the change in the distribution of displacements between the structure and the isolation bearings caused by yielding of the isolated structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Semi‐active control of sliding isolated bridges using MR dampers: an experimental and numerical study

Sliding base‐isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near‐source pulse‐type earthquakes. It is common practice to incorporate supplemental passive non‐linear dampers into the isolation system to counter increased bearing displacements. Non‐linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi‐active controllable non‐linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a ‘smart’ sliding isolation system, used in a 1:20 scaled bridge model, employing semi‐active controllable magneto‐rheological (MR) dampers is investigated, analytically and experimentally, under several near‐fault earthquakes. A non‐linear analytical model, which incorporates the non‐linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low‐ and high‐damping cases, while maintaining isolation level forces less than the passive high‐damping case. Copyright © 2005 John Wiley & Sons, Ltd.     

Direct estimation of seismic response in reduced-degree-of-freedom isolation and energy dissipation systems

A methodology for the development of design tools for direct estimation of peak inelastic response in reduced-degree-of-freedom (RDOF) isolation and energy dissipation systems is presented. The suggested procedure is an extension of an earlier method addressing purely hysteretic isolation systems. Herein, the dynamic equation of motion is first normalised to reduce the number of design parameters that significantly affect the response. The sensitivity of normalised response quantities to the amplitude of the ground motion is then investigated through extensive parametric nonlinear dynamic analyses of isolated single-degree-of-freedom (SDOF) systems with linear viscous damping using code-based target spectra. Regression analysis is subsequently employed to develop generalised design equations (GDEs) suitable for design. Further investigations are made to address nonlinear viscous damping and the effect of the transverse component of seismic action in two-degree-of freedom (2DOF) systems under bidirectional excitation, making the procedure applicable to common bridge isolation schemes. GDEs constitute an alternative to equivalent linearisation approaches commonly adopted by codes, informing the selection among alternative isolation and energy dissipations schemes without requiring iterative analysis. The approach is incorporated in the Deformation-Based Design methodology for seismically isolated bridges in a forthcoming paper.