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.     

Dynamic soil–structure interaction effects on the seismic response of suspension bridges

A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 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.     

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.     

Uplift of deck or footings in bridges with distributed mass subjected to transverse earthquake

The eigenvalue problem is analytically formulated in symmetric bridges with distributed mass and moment of inertia under transverse earthquake. The piers are elastically supported on the ground. The deck is monolithically connected to one or two piers for all degrees of freedom and restrained or transversely free at the abutments. The characteristic equation, symmetric normal modes, modal participation factors, and participating mass ratios are given analytically. The problem is expressed in terms of few dimensionless parameters: (i) the radius of gyration of the deck mass divided by the pier height; (ii) the ratio of the rotational stiffness of a footing to that of the pier at the base; (iii) the ratio of flexural stiffness of the outer spans to those of the pier; (iv) the ratio of torsional stiffness of side spans to the rotational stiffness of the pier top; (v) for two piers, the side‐to‐central‐span ratio. Modal response spectrum analysis gives the moment at the base of the footings and the torque in the deck at its supports on the abutments as ratios to the values at incipient uplifting from the ground or the bearings. The peak ground acceleration of the motion at the onset of either one of these two types of nonlinearity is depicted as a function of the dimensionless parameters and the fundamental period of an elastic deck supported only at the abutments, or of a rigid deck on piers fixed against rotation at top and bottom. Copyright © 2015 John Wiley & Sons, Ltd.     

Example of application of response spectrum analysis for seismically isolated curved bridges including soil-foundation effects

This paper presents seismic behaviour of isolated curved bridges in the earthquake prone regions.     

索-桥动态相互作用及行波效应对斜拉桥地震反应的影响

主要研究斜拉桥地震响应中拉索与梁、塔动态相互作用和行波效应的影响,索一桥相互作用的影响是根据结构动力学中广义自由度的概念,把索的振型作为自由度来考虑,通过把索边界节点的位移和索局部振型位移叠加得到索的整体位移,行波效应是通过在不同支承点输人具有一定相位差的同一条地震动模拟.以一座斜拉桥为例进行了数值模拟和参数分析,结果...     

Performance-based seismic assessment of skewed bridges with and without considering soil-foundation interaction effects for various site classes

The seismic behavior of skewed bridges has not been well studied compared to straight bridges. Skewed bridges have shown extensive damage, especially due to deck rotation, shear keys failure, abutment unseating and columnbent drift. This research, therefore, aims to study the behavior of skewed and straight highway overpass bridges both with and without taking into account the effects of Soil-Structure Interaction(SSI) due to near-fault ground motions. Due to several sources of uncertainty associated with the ground motions, soil and structure, a probabilistic approach is needed. Thus, a probabilistic methodology similar to the one developed by the Pacific Earthquake Engineering Research Center(PEER) has been utilized to assess the probability of damage due to various levels of shaking using appropriate intensity measures with minimum dispersions. The probabilistic analyses were performed for various bridge confi gurations and site conditions, including sand ranging from loose to dense and clay ranging from soft to stiff, in order to evaluate the effects. The results proved a considerable susceptibility of skewed bridges to deck rotation and shear keys displacement. It was also found that SSI had a decreasing effect on the damage probability for various demands compared to the fixed-base model without including SSI. However, deck rotation for all types of the soil and also abutment unseating for very loose sand and soft clay showed an increase in damage probability compared to the fixed-base model. The damage probability for various demands has also been found to decrease with an increase of soil strength for both sandy and clayey sites. With respect to the variations in the skew angle, an increase in skew angle has had an increasing effect on the amplitude of the seismic response for various demands. Deck rotation has been very sensitive to the increase in the skew angle; therefore, as the skew angle increased, the deck rotation responded accordingly. Furthermore, abutment unseating showed an increasing trend due to an increase in skew angle for both fixed-base and SSI models.     

Spatial variability effects of ground motions on cable-stayed bridges

In this paper, stochastic analysis of a cable-stayed bridge subjected to spatially varying ground motions is performed. While the ground motion is described by power spectral density (PSD) function, the spatial variability of ground motions is taken into account with the incoherence and the wave-passage effects. The incoherence effect is examined by taking into account two extensively used models. As the effect of the wave-passage effect is investigated by using various wave velocities, the effect of local soil conditions where the bridge supports are constructed is outlined by using homogeneous firm, medium and soft soil conditions. Solutions obtained for the spatially varying ground motions are compared with those of the specialised cases of the ground motion model. Stationary as well as the transient response analyses are performed for the considered bridge model. It is concluded that spatial variability and propagation effects of ground motions have important effects on the dynamic behaviour of the bridge and the variability of the ground motions should be included in the stochastic analysis of cable-stayed bridges.     

温度对铅芯橡胶支座隔震桥梁抗震性能的影响分析

为了研究温度对铅芯橡胶支座（LRB）隔震桥梁抗震性能的影响,以一座七跨连续梁桥为对象,考虑LRB在夏季和冬季不同温度下的力学特性,利用OpenSees对桥梁抗震性能进行研究。通过对不同温度下墩柱、支座及桥梁系统的地震易损性分析,获得了温度对铅芯橡胶支座隔震桥梁抗震性能的影响。结果表明:（1）与夏季相比,冬季低温降低了桥墩的延性及LRB的剪切变形和耗能能力,使地震作用时墩顶位移和支座变形均小于夏季,降低了LRB的减震效果;（2）冬季低温增大了地震作用时桥墩、LRB及桥梁系统在各个破坏状态的损伤概率,在中等及严重破坏状态时损伤概率相比夏季分别增加了8%和15%。在寒冷地区进行LRB隔震桥梁设计时,应考虑低温导致的LRB隔震效果降低对桥梁抗震性能的影响。     

隔震桥梁承受近断层地震之反应分析

台湾集集大地震造成台湾中部地区许多桥梁之倒塌及损坏.本文之主要目的为探讨对一隔震桥梁当其承受由集集大地震记录到的近断层记录时桥梁所具有的动态反应,及比较桥梁在有隔震及无隔震下行为之差异.本文于此选用一三跨连续主梁,混凝土桥柱之高速公路桥梁为分析之范例.桥梁之支承分别采用铰接型式及采用铅心橡胶支承之隔震支承垫两种形式进行分析模拟,并藉此比较隔震桥梁与无隔震桥梁之动态反应的差异性.输入地震记录采用集集地震记录到的近断层地震记录,分析案例包含采用三维动力分析方法去分析桥梁承受实测地震时之动态反应及针对影响隔震桥梁结构隔震效果之参数进行探讨.     

Probabilistic seismic response and reliability assessment of isolated bridges

Bridge seismic isolation strategy is based on the reduction of shear forces transmitted from the superstructure to the piers by two means: shifting natural period and earthquake input energy reduction by dissipation concentrated in protection devices. In this paper, a stochastic analysis of a simple isolated bridge model for different bridge and device parameters is conducted to assess the efficiency of this seismic protection strategy. To achieve this aim, a simple nonlinear softening constitutive law is adopted to model a wide range of isolation devices, characterized by only three essential mechanical parameters. As a consequence of the random nature of seismic motion, a probabilistic analysis is carried out and the time modulated Kanai-Tajimi stochastic process is adopted to represent the seismic action. The response covariance in the state space is obtained by solving the Lyapunov equation for a stochastic linearized system. After a sensitivity analysis, the failure probability referred to extreme displacement and the mean value of dissipated energy are assessed by using the introduced stochastic indices of seismic bridge protection efficiency. A parametric analysis for protective devices with different mechanical parameters is developed for a proper selection of parameters of isolation devices under different situations.     

地震作用下简支梁桥支座-挡块-桥墩相互作用研究

为了提高中小跨径简支梁桥的抗震能力,促进多级抗震设计思想的完善,以汶川地震中的寿江大桥为背景,构建了支座-挡块-桥墩相互作用分析模型,采用增量动力分析（IDA）方法,以挡块强度和墩高作为变化参数,研究了支座滑移、挡块限位和桥墩塑性三者之间抗震性能状态的耦合关系。研究表明:提高挡块强度可有效地控制支座的滑移,但会增大桥墩的曲率延性系数,且桥墩越矮,曲率延性系数增长越快;随着挡块强度的变化,支座滑移比的变化幅度明显大于桥墩曲率延性系数;随着墩高的增大,挡块的相对限位能力会提高;对于中小跨径简支梁桥而言,理想的抗震状态为:允许挡块破坏,使得支座出现小幅滑移,桥墩出现可修复的塑性损伤。因此,在挡块设计中,可优先考虑支座的限位效果,再综合考虑桥墩的地震响应,当桥墩为矮墩时,挡块的设计强度不可过大。     

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.     

Inertial effects in an oceanic circulation model

Abstract

The flow in a mechanically driven thin barotropic rotating fluid system is analysed. The linear theory of Baker and Robinson (1969) is modified and extended into the non-linear regime.

An internal parameter, the “local Rossby number”, is indicative of the onset of nonlinear effects. If this parameter is 0(1) then inertial effects are as important as Coriolis accelerations in the interior of the transport-turning western boundary layer and both of its Ekman layers. The inertial effects in the Ekman layers, ignored in previous explorations of non-linear wind driven oceanic circulation, are retained here and calculated using an approximation of the Oseen type. The circulation problem is reduced to a system of scalar equations in only two independent variables; the system is valid for non-small local Rossby number provided only that the approximate total vorticity is positive.

To complete the solution for small Rossby number a boundary condition for the inertially induced transport is needed. It is found by examining the dynamics controlling this additional transport from the western boundary layer as the transport recirculates through the rest of the ocean basin. The strong constraint of total recirculation within the western boundary layer (zero net inertial transport) is derived.

The calculated primary inertial effects are in agreement with the observations of the laboratory model of Baker and Robinson (1969).

The analysis indicates the extent to which three-dimensional non-linear circulation can be reduced to a two dimensional problem.     

Kinematic soil–structure interaction for long-span cable-supported bridges

A general procedure is presented to study the dynamic soil–structure interaction effects on the response of long-span suspension and cable-stayed bridges subjected to spatially varying ground motion at the supporting foundations. The foundation system is represented by multiple embedded cassion foundations and the frequency-dependent impedance matrix for the multiple foundations system takes into account also the cross-interaction among adjacent foundations through the soil. To illustrate the potential implementation of the analysis, a numerical example is presented in which the dynamic response of the Vincent–Thomas suspension bridge (Los Angeles, CA) subjected to the 1987 Whittier earthquake is investigated. Although both kinematic and inertial effects are included in the general procedure, only the kinematic effects of the soil–structure interaction are considered in the analysis of the test case. The results show the importance of the kinematic soil–foundation interaction on the structural response. These effects are related to the type, i.e. SH-, SV-, P- or Rayleigh waves and to the inclination of the seismic wave excitation. Moreover, rocking components of the foundation motion are emphasized by the embedment of the foundation system and greatly alter the structural response.     

场地条件对桥梁减震设计效果的影响

采用大型有限元程序ANSYS对实桥进行建模,利用时程分析方法,考虑不同场地土、地震动输入、剪切波速等因素的影响,计算分析了桥梁结构使用铅销橡胶支座时,其地震反应值减震率的变化规律,提出了采用铅销橡胶支座进行桥梁减震设计的应用范围.研究结果表明,对于Ⅰ、Ⅱ类场地土,安装有铅销橡胶支座的减震设计桥梁具有良好的减震效果;对于Ⅲ、Ⅳ类场地土,采用相同设计方法的桥梁其减震效果不断降低,尤其当剪切波速小于140m/s后,使用铅销橡胶支座的减震桥梁已达不到减震的设计要求,应采取其他方法来降低桥梁结构的地震反应.     

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.