Seismic response analysis of bridges isolated with friction pendulum bearings

A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and efficiency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side effect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. © 1998 John Wiley & Sons, Ltd.     

Effect of isolator and ground motion characteristics on the performance of seismic‐isolated bridges

This paper presents the effect of isolator and substructure properties as well as the frequency characteristics and intensity of the ground motion on the performance of seismic‐isolated bridges (SIBs) and examines some critical design clauses in the AASHTO Guide Specification for Seismic Isolation Design. For this purpose, a parametric study, involving more than 800 non‐linear time history analyses of simplified structural models representative of typical SIBs, is conducted. The results from the parametric study are then used to derive important design recommendations and conclusions that may be used by bridge engineers to arrive to a more sound and economical design of SIBs. It is found that the SIB response is a function of the peak ground acceleration to peak ground velocity ratio of the ground motion. Thus, the choice of the seismic ground motion according to the characteristics of the bridge site is crucial for a correct design of the SIB. It is also found that the characteristic strength of the isolator may be chosen based on the intensity and frequency characteristics of the ground motion. Furthermore, the isolator post‐elastic stiffness is found to have a notable effect on the response of SIBs. Copyright © 2005 John Wiley & Sons, Ltd.     

On the response of yielding seismically isolated structures

This paper investigates the seismic response of yielding isolated structures. To establish a general understanding of the nonlinear response of seismically isolated structures, this study first investigates the nonlinear response of isolated structures subjected to steady‐state harmonic motion and nonlinear transient ground excitation. The response of both viscously damped and hysteretically damped isolation systems is investigated in three phases. Initially, basic insights are gained through simple nonlinear two degrees of freedom (2‐DOF) models subjected to harmonic motion of varying frequencies. Next, the transient response analysis of the nonlinear 2‐DOF model is investigated for a wide range of isolation system and superstructure properties. The results obtained from both approaches indicate that the yielding behavior of a structure on an isolation system is significantly different from that of the comparable fixed‐base structure. Finally, the response of the nonlinear 2‐DOF system model is compared with that of a 15‐story, three‐dimensional model. Based on the results of these analytical investigations, some important considerations for the design of seismically isolated structures are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Direct displacement-based design of seismically isolated bridges

A Displacement-Based Design (DBD) procedure for bridges equipped with different seismic Isolation Systems (IS’s) is proposed. It has been derived from the Direct DBD method recently developed by Priestley and co-workers. The key aspect of the proposed procedure is the definition of a uniform target displacement of the deck, which is assigned by the designer to accomplish a given performance level, expressed through limit values of the maximum IS displacement and of the pier drift, respectively. The proposed design procedure has been developed for four different idealized force-displacement cyclic behaviours of IS’s, which can be used to describe the response of a wide variety of IS’s, including: (i) Lead-Rubber Bearings (LRB), (ii) High-Damping Rubber Bearings (HDRB), (iii) Friction Pendulum Bearings (FPB), (iv) Combinations of either Low-Damping Rubber Bearings (LDRB) or FPB and Viscous Dampers (VD), (v) Combinations of lubricated Flat Sliding Bearings (FSB) and LDRB, (vi) Combinations of FSB and Steel Yielding Devices (SYD), (vii) Combinations of FSB, Shape Memory Alloy (SMA)-based Re-centring Devices and VD. In the paper, the background and implementation of the design procedure is presented first, then some validation studies through nonlinear time-history analyses on different configurations of continuous deck and multi-span simply supported deck bridges are illustrated.     

Stochastic energy analysis of seismic isolated bridges

In this paper, a parametric stochastic analysis of isolated bridge is proposed with the aim to assess isolation performance and to investigate effects of energetic influence on protection efficiency. The analysis has been carried out in terms of two stochastic parameters of pear-deck maximum displacement and hysteretic energy response, of which a qualitative trend has been observed.Isolated bridge is described by a simple two degree of freedom (TDoF) Bouc–Wen hysteretic model, which has been introduced for its intrinsic ability in reproducing a wide range of real devices behavior. With the aim of taking into consideration intrinsic stochastic nature of seismic events, the ground motion and the structural response have been described by random vibration approach. Results obtained show that protection achieved by shifting structural natural period and reducing input energy by devices dissipation have counteracting effects if related to deck lateral displacement.     

Seismic performance of highway bridges with fusing bearing components for quasi‐isolation

Modern highway bridges in Illinois are often installed with economical elastomeric bearings that allow for thermal movement of the superstructure, and steel fixed bearings and transverse retainers that prevent excessive movement from service‐level loadings. In the event of an earthquake, the bearing system has the potential to provide a quasi‐isolated response where failure of sacrificial elements and sliding of the bearings can cause a period elongation and reduce or cap the force demands on the substructure. A computational model that has been calibrated for the expected nonlinear behaviors is used to carry out a parametric study to evaluate quasi‐isolated bridge behavior. The study investigates different superstructure types, substructure types, substructure heights, foundation types, and elastomeric bearing types. Overall, only a few bridge variants were noted to unseat for design‐level seismic input in the New Madrid Seismic Zone, indicating that most structures in Illinois would not experience severe damage during their typical design life. However, Type II bearing systems, which consist of an elastomeric bearing and a flat PTFE slider, would in some cases result in critical damage from unseating at moderate and high seismic input. The sequence of damage for many bridge cases indicates yielding of piers at low‐level seismic input. This is caused by the high strength of the fixed bearing element, which justifies further calibration of the quasi‐isolation design approach. Finally, the type of ground motion, pier height, and bearing type were noted to have significant influence on the global bridge response. 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.     

A pseudo‐force iterative method with separate scale factors for dynamic analysis of structures with non‐proportional damping

Dynamic equilibrium equations of structural systems with non‐proportional damping are coupled through the damping terms. Such coupling invalidates application of the classical modal superposition method. In this paper, a mode‐superposition pseudo‐force method is proposed. The coupled equilibrium equations are solved by an iterative process in which the coupling terms are treated as pseudo‐forces. A scale factor for each mode of the system is obtained by optimizing the iteration convergence. Through these uniquely solved scale factors, the modified modal equations not only converge much faster but also yield results with higher accuracy. A proof of the convergence of the iterative process is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

基于经验统计方法的桥梁震害预测辅助决策系统

选择场地、结构、地震动和抗震设防4大类18个因素作为考虑因素，以国内外桥梁震害预测经验统计方法为主体构成了知识库，开发了与GIS结合的桥梁震害预测辅助决策系统BSVAS。该系统可初步用于大中城市防震减灾桥梁震害预测工作，并为基于GIS的防震减灾管理系统的更新提供可能。     

A simplified method of constructing fragility curves for highway bridges

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

A parametric study of seismic behavior of roller seismic isolation bearings for highway bridges

A roller seismic isolation bearing is proposed for use in highway bridges. The bearing utilizes a rolling mechanism to achieve seismic isolation and has a zero post‐elastic stiffness under horizontal ground motions, a self‐centering capability, and unique friction devices for supplemental energy dissipation. The objectives of this research are to investigate the seismic behavior of the proposed bearing using parametric studies (1) with nonlinear response history analysis and (2) with equivalent linear analysis according to the AASHTO guide specifications, and by comparing the results from both analysis methods (3) to evaluate the accuracy of the AASHTO equivalent linear method for predicting the peak displacement of the proposed bearing during an earthquake. Twenty‐eight ground motions are used in the studies. The parameters examined are the sloping angle of the intermediate plate of the bearing, the amount of friction force for supplemental energy dissipation, and the peak ground acceleration levels of the ground motions. The peak displacement and base shear of the bearing are calculated. Results of the studies show that a larger sloping angle does not reduce the peak displacement for most of the parametric combinations without friction devices. However, for parametric combinations with friction devices, it allows for the use of a higher friction force, which effectively reduces the peak displacement, while keeping a self‐centering capability. The AASHTO equivalent linear method may underestimate the peak displacement by as much as 40%. Vertical ground motions have little effect on the peak displacement, but significantly increase the peak base shear. Copyright © 2009 John Wiley & Sons, Ltd.     

Transverse free vibrations of continuous bridges with abutment restraint

This paper analyzes the dynamic behaviour of continuous bridges with transverse abutment restraint. These are a particular class of multi‐span bridges whose transverse motion is restrained at the abutments. The transverse dynamic behaviour of these partially‐restrained bridges is described by a model consisting of a two‐dimensional simply‐supported beam with intermediate visco‐elastic restraints. A minimal set of characteristic problem parameters that completely describe the dynamic response is initially identified and an analytical solution is developed for particular configurations. The influence of these characteristic parameters on the properties of the dynamic systems are analyzed by considering the undamped and the damped free vibrations separately. Successively, in order to cover more general and complex configurations of realistic bridges, an extension of the definition of the characteristic parameters is proposed. The results obtained considering selected case studies are finally presented. Copyright © 2011 John Wiley & Sons, Ltd.     

规则型隔震房屋的自振特性和地震反应分析方法

文中根据规则型隔震房屋的刚度、质量和阻尼分布的特点，改进了阻尼比的简化计算表达式。此外还归纳给出了自振周期、振型和地震反应计算公式。文中还将我们提出的隔震结构振型阻尼比公式与Kelly的相应公式进行了数值比较，两式的复杂程度虽几无差异，但文中的公式更为精确。文中提出的简化计算公式可以方便地在一般房屋结构隔震方案设计和地震反应的振型叠加分析中应用。     

Dynamics and seismic performance of rocking bridges accounting for the abutment-backfill contribution

The present study explores analytically the concept of rocking isolation in bridges considering for the first time the influence of the abutment-backfill system. The dynamic response of rocking bridges with free-standing piers of same height and same section is examined assuming negligible deformation for the substructure and the superstructure. New relationships for the prediction of the bridge rocking motion are derived, including the equation of motion and the restitution coefficient at each impact at the rocking interfaces. The bridge structure is found to be susceptible to a failure mode related to the failure of the abutment-backfill system, which can occur prior to the well-known overturning of the rocking piers. Thus, a new failure spectrum is proposed called Failure Minimum Acceleration Spectrum (FMAS) which extends the overturning spectrum put forward in previous studies, and it differs in principle from the latter. The comparison with the dynamic response of bridges modelled as rocking frames without abutments reveals not only that seat-type abutments and their backfill have a generally beneficial effect on the seismic performance of rocking pier bridges by suppressing the free rocking motion of the frame system, but also that the simple frame model cannot capture all salient features of the rocking bridge response as it misses potential failure modes, overestimating the rocking bridge's safety when these modes are critical.     

Evaluation of simplified methods of analysis for structures with triple friction pendulum isolators

Triple friction pendulum isolators, that exhibit behavior with amplitude‐dependent strength and instantaneous stiffness, represent a new development in seismic isolation. The application of simplified methods of analysis for this type of seismically isolated structures requires development of tools of simplified analysis and demonstration of their accuracy. This paper describes these tools and presents validation studies based on a large number of nonlinear response history analysis results. It is shown that simplified methods of analysis systematically provide good and often conservative estimates of isolator displacement demands and good estimates of isolator peak velocities. Copyright © 2009 John Wiley & Sons, Ltd.     

既有桥梁承载能力评估方法

既有桥梁结构承载能力的评估涉及桥梁状态评定、养护与管理、维修与加固等，不仅是桥梁工程师的基本职责，也是广大业主所非常关心的。本文指出了桥梁评估与设计的基本区别，介绍了桥梁承载力评估的静力方法，分析了中美两国桥梁评估规范的异同。接着提出了一套既有桥梁结构承载能力评估的动力方法，该方法结合现场环境振动试验和有限元分析，具有显著的优点。文中采用2个典型桥例，分析了不同评估方法的结果与结论。最后依据发展要求，讨论了进一步研究的主要方向。     

Robustness of simplified analysis methods for rocking structures on compliant soil

Recognizing the beneficial effect of nonlinear soil–foundation response has led to a novel design concept, termed ‘rocking isolation’. The analysis and design of such rocking structures require nonlinear dynamic time history analyses. Analyzing the entire soil–foundation–structure system is computationally demanding, impeding the application of rocking isolation in practice. Therefore, there is an urgent need to develop efficient simplified analysis methods. This paper assesses the robustness of two simplified analysis methods, using (i) a nonlinear and (ii) a bilinear rocking stiffness combined with linear viscous damping. The robustness of the simplified methods is assessed by (i) one-to-one comparison with a benchmark finite element (FE) analysis using a selection of ground motions and (ii) statistical comparison of probability distributions of response quantities, which characterize the time history response of rocking systems. A bridge pier (assumed rigid) supported on a square foundation, lying on a stiff clay stratum, is used as an illustrative example. Nonlinear dynamic FE time history analysis serves as a benchmark. Both methods yield reasonably accurate predictions of the maximum rotation θ_max. Their stochastic comparison with respect to the empirical cumulative distribution function of θ_max reveals that the nonlinear and the bilinear methods are not biased. Thus, both can be used to estimate probabilities of exceeding a certain threshold value of θ. Developed in this paper, the bilinear method is much easier to calibrate than the nonlinear, offering similar performance.     

Extraction of hysteretic properties of seismically isolated bridges from quick‐release field tests

A simple procedure for identifying hysteretic properties of seismically isolated bridges from full‐scale quick‐release tests is presented in this paper. An analytical solution for the quick‐release response of a SDOF system with a bilinear spring is derived. Based on the solution, some characteristics of such systems are obtained. A time domain optimization method is employed to identify the hysteretic properties of the lead–rubber bearings installed in seismically isolated bridges. The total damping effects of the isolation system are expressed as a combination of the rate‐independent (hysteretic) damping and the linear viscous damping. The Menegotto–Pinto (MP) model and bilinear model are used to represent the force–displacement relation of the lead–rubber bearings. In both the longitudinal and transverse directions the bridges have been idealized as single degree of freedom (SDOF) systems. Time histories recorded from the field quick‐release tests on two bridges are used for the examples presented herein. The hysteretic loops of the isolators obtained from laboratory tests are compared with those obtained using the optimization method, and they agree well. In conclusion, the procedure shown in this paper can be used to identify the essential in situ hysteretic characteristics of isolation bearings from quick‐release field testing. Copyright © 2001 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of isolation on fragility curves of highway bridges based on simplified approach

The trend of isolating highway bridges is on the rise after the recent large earthquakes in Japan, the United States, and other countries. Recent investigation shows that isolated systems perform well against seismic forces as the substructures of such systems experience less lateral forces due to energy dissipation of the isolation device. Hence, it is anticipated that there might be an effect on fragility curves of highway bridges due to isolation. In this study, 30 isolated bridge models were considered (and they were designed according to the seismic design code of highway bridges in Japan) to have a wider range of the variation of structural parameters, e.g. pier heights, weights, and over-strength ratio of structures. Then, fragility curves were developed by following a simplified procedure using 250 strong motion records, which were selected from 5 earthquake events that occurred in Japan, the USA, and Taiwan. It is observed that the level of damage probability for the isolated system is less than that of the non-isolated one for a lower level of pier height. However, having the same over-strength ratio of the structures, the level of damage probability for the isolated system is found to be higher for a higher level of pier height compared to the one of the non-isolated system. The proposed simple approach may conveniently be used in constructing fragility curves for a class of isolated bridge structures in Japan that have similar characteristics.