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.     

轨道约束系统对高速铁路多跨简支梁桥地震反应的影响

文中结合高速铁路多跨简支梁桥及轨道系统的特点,建立了考虑钢轨、轨道板以及桥梁结构的线桥一体化模型,采用反应谱法研究了轨道约束系统以及相邻后继结构对所选桥跨地震反应的影响。研究结果表明:轨道约束系统对相邻墩高相差较大的多跨简支梁桥的地震反应影响较大,因此对其地震反应分析时应采用线桥一体化模型;由于受端刺等路桥过渡段结构纵向刚度的影响,后继结构的桥梁跨数越少,对边墩地震反应的卸载作用越显著。     

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.     

基础隔震单层偏心结构扭转地震反应分析

采用微分型滞回恢复力模型模拟隔震支座的恢复力特性，对基础隔震单层偏心结构的扭转地震反应进行分析，研究隔震系统偏心距和上部结构偏心距对结构扭转反应的影响。结果表明，采用隔震技术可以显著降低隔震结构的扭转地震反应。     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

基础非线性对桥墩地震反应的影响

在桩基础桥墩滞回特性的模型试验基础上,提出了用Clough模型模拟基础(地基)的恢复力特性。桥墩采用Takeda恢复力模型。用强震记录与人工合成地震动作为输入对铁路简支梁桥进行了非线性地震反应分析,讨论了不同地震动输入及不同地震强度时基础非线性对桥梁地震反应的影响。研究结果表明,考虑基础的非线性一般会使墩顶位移增大,而墩底的曲率明显减小,且随着地震动强度的增加,基础的非线性影响更加明显。     

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.     

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.     

Experimental investigation on seismic behavior of scoured bridge pier with pile foundation

This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.     

Vertical earthquake response of megawatt‐sized wind turbine with soil‐structure interaction effects

The dynamic response of a wind turbine on monopile is studied under horizontal and vertical earthquake excitations. The analyses are carried out using the finite element program SAP2000. The finite element model of the structure is verified against the results of shake table tests, and the earthquake response of the soil model is verified against analytical solutions of the steady‐state response of homogeneous strata. The focus of the analyses in this paper is the vertical earthquake response of wind turbines including the soil‐structure interaction effects. The analyses are carried out for both a non‐homogeneous stratum and a deep soil using the three‐step method. In addition, a procedure is implemented which allows one to perform coupled soil‐structure interaction analyses by properly tuning the damping in the tower structure. The analyses show amplification of the ground surface acceleration to the top of the tower by a factor of two. These accelerations are capable of causing damage in the turbine and the tower structure, or malfunctioning of the turbine after the earthquake; therefore, vertical earthquake excitation is considered a potential critical loading in design of wind turbines even in low‐to‐moderate seismic areas. Copyright © 2015 John Wiley & Sons, Ltd.     

Investigation of the seismic response of high‐rise buildings supported on tension‐resistant elastomeric isolation bearings

In many applications of seismic isolation, such as in high‐rise construction, lightweight construction, and structures with large height‐to‐width aspect ratios, significant tension forces can develop in bearings, raising concerns about the possible rupture of elastomeric bearings and the uplift of sliding bearings. In this paper, a novel tension‐resistant lead plug rubber bearing (TLRB) with improved tension‐resisting capabilities is developed and experimentally and numerically assessed. This TLRB consists of a common lead plug rubber bearing (LRB) and several helical springs. After describing the theory underlying the behavior of the TLRB, the mechanical properties of reduced‐scale prototype bearings are investigated through extensive horizontal and vertical loading tests. The test results indicate that TLRBs can improve the shear stiffness and tension resistance capacity even under significant tensile loads. A series of shaking table tests on scaled models of high‐rise buildings with different aspect ratios were conducted to investigate the dynamic performance of the TLRB and the seismic responses of base‐isolated high‐rise buildings. Three different cases were considered in the shaking table tests: a fixed base condition and the use of TLRB and LRB isolation systems. The results of the shaking table test show that (a) base‐isolated systems are effective in reducing the structural responses of high‐rise buildings; (b) an isolated structure's aspect ratio is an important factor influencing its dynamic response; (c) TLRBs can endure large tensile stresses and avoid rupture on rubber bearings under strong earthquakes; and (d) the experimental and numerical results of the responses of the models show good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of non-linear soil–structure interaction on seismic response of tall slender structures

Some structures may be very massive and may have to be located on relatively soft soil. In such cases, the soil adjacent to the structure behaves in a non-linear fashion and affects the response of the structure to the dynamic loading. An approximate hybrid approach to analyse soil–structure systems accounting for soil non-linearities has been developed in this paper. The approach combines the consistent infinitesimal finite-element cell method (CIFECM) and the finite-element method (FEM). The CIFECM is employed to model the non-linear (near-field) zone of the soil supporting the structure as a series of bounded media. The material properties of the bounded media are selected so that they are compatible with the average effective strains over the whole bounded medium during the excitation. The linear zone of soil away from the foundation, the far-field, is modelled as an unbounded medium using the CIFECM for unbounded media. The structure itself is represented by the FEM. The proposed method is used to model the dynamic response of a one-mass structure and a TV-tower supported on a homogenous stratum and excited by an earthquake. It was found that the secondary soil non-linearity might increase or decrease the base forces of tall slender structures depending on the type of structure, frequency content of the input motion and the dynamic properties of the near-field soil.     

Seismic response of a cable‐stayed bridge deck under multi‐component non‐stationary random ground motion

A Markov method of analysis is presented for obtaining the seismic response of cable‐stayed bridges to non‐stationary random ground motion. A uniformly modulated non‐stationary model of the random ground motion is assumed which is specified by the evolutionary r.m.s. ground acceleration. Both vertical and horizontal components of the motion are considered to act simultaneously at the bridge supports. The analysis duly takes into account the angle of incidence of the earthquake, the spatial correlation of ground motion and the quasi‐static excitation. A cable‐stayed bridge is analysed under a set of parametric variations in order to study the non‐stationary response of the bridge. The results of the numerical study indicate that (i) frequency domain spectral analysis with peak r.m.s. acceleration as input could provide more r.m.s. response than the peak r.m.s. response obtained by the non‐stationary analysis; (ii) the longitudinal component of the ground motion significantly influences the vertical vibration of the bridge; and (iii) the angle of incidence of the earthquake has considerable influence on the deck response. Copyright © 2003 John Wiley & Sons, Ltd.     

A macro‐element model for non‐linear soil–shallow foundation–structure interaction under seismic loads: theoretical development and experimental validation on large scale tests

In this paper, different formulations of a macro‐element model for non‐linear dynamic soil‐structure interaction analyses of structures lying on shallow foundations are first reviewed, and secondly, a novel formulation is introduced, which combines some of the characteristics of previous approaches with several additional features. This macro‐element allows one to model soil‐footing geometric (uplift) and material (soil plasticity) non‐linearities that are coupled through a stiffness degradation model. Footing uplift is introduced by a simple non‐linear elastic model based on the concept of effective foundation width, whereas soil plasticity is treated by means of a bounding surface approach in which a vertical load mapping rule is implemented. This mapping is particularly suited for the seismic loading case for which the proposed model has been conceived. The new macro‐element is subsequently validated using cyclic and dynamic large‐scale laboratory tests of shallow foundations on dense sand, namely: the TRISEE cyclic tests, the Public Works Research Institute and CAMUS IV shaking table tests. Based on this comprehensive validation process against a set of independent experimental results, a unique set of macro‐element parameters for shallow foundations on dense sand is proposed, which can be used to perform predictive analyses by means of the present model. Copyright © 2011 John Wiley & Sons, Ltd.     

多点激励下LRB隔震桥梁地震反应分析

研究了地震地面运动多点激励,即空间变化效应对装有铅芯橡胶支座（Lead Rubber Bearing）的连续梁桥地震反应的影响。首先,利用三角级数法生成了拟合规范反应谱的多点人工地震动时程;然后利用非线性时程分析法数值仿真并比较了某五跨LRB隔震连续梁桥在一致激励、仅考虑地震动行波效应、仅考虑地震动部分相干效应、同时考虑行波和部分相干效应以及同时考虑行波、部分相干和局部场地土效应等七种工况下结构的减震效果。行波效应和部分相干效应对铅芯橡胶支座隔震桥梁影响不大,而局部场地土效应对该类桥梁的地震反应分析影响很大,应该引起重视。     

Seismic response analysis of adjacent liquid‐storage tanks

A refined substructure technique in the frequency domain is developed, which permits consideration of the interaction effects among adjacent containers through the supporting deformable soil medium. The tank‐liquid systems are represented by means of mechanical models, whereas discrete springs and dashpots stand for the soil beneath the foundations. The proposed model is employed to assess the responses of adjacent circular, cylindrical tanks for harmonic and seismic excitations over wide range of tank proportions and soil conditions. The influence of the number, spatial arrangement of the containers and their distance on the overall system's behavior is addressed. The results indicate that the cross‐interaction effects can substantially alter the impulsive components of response of each individual element in a tank farm. The degree of this impact is primarily controlled by the tank proportions and the proximity of the predominant natural frequencies of the shell‐liquid‐soil systems and the input seismic motion. The group effects should be not a priori disregarded, unless the tanks are founded on shallow soil deposit overlying very stiff material or bedrock. Copyright © 2016 John Wiley & Sons, Ltd.     

多维地震输入下曲线匝道桥梁伸缩缝碰撞响应

针对曲线匝道桥梁伸缩缝地震碰撞破坏现象,依托某市多层互通式立交体系中一座独立、单支、多联、曲线、箱梁匝道桥,用Kelvin接触单元模拟了伸缩缝处地震和碰撞效应,建立了全桥空间动力分析模型。利用非线性时程分析法,分别输入单维(X方向、Y方向)和多维共8种地震动工况,分析了曲线匝道桥梁伸缩缝的地震碰撞响应差异。结果表明:曲线匝道桥梁由于曲率的影响,不同方向地震动响应存在耦合效应,其伸缩缝碰撞响应的最不利值应考虑多维地震输入工况,并用碰撞力和碰撞位移双指标控制伸缩缝的地震碰撞响应。