Linking of adjacent three-storey buildings for mitigation of structural pounding during earthquakes

The reports after major earthquakes indicate that the earthquake-induced pounding between insufficiently separated buildings may lead to significant damage or even total collapse of structures. An intensive study has recently been carried out on mitigation of pounding hazards so as to minimize the structural damages or prevent collisions at all. The aim of this paper is to investigate the effectiveness of the method when two adjacent three-storey buildings with different (substantially different) dynamic properties are connected at each storey level by link elements (springs, dashpots or viscoelastic elements). The results of the study indicate that connecting the structures by additional link elements can be very beneficial for the lighter and more flexible building. The largest decrease in the response of the structure has been obtained for links with large stiffness or damping values, which stands for the case when two buildings are fully connected and vibrate in-phase. Moreover, by comparing the effectiveness of different types of link elements, it has been confirmed that the use of viscoelastic elements reduces the peak displacement of the structure at lower stiffness and damping values comparing to the case when spring and dashpot elements are applied alone. On the other hand, the results of the study demonstrate that applying the additional link elements does not really change the response of the heavier and stiffer building. The final conclusion of the study indicates that linking two buildings allows us to reduce the in-between gap size substantially while structural pounding can be still prevented.     

地震作用下隔震简支梁桥碰撞反应的振动台试验

由地震引发的碰撞是影响桥梁地震反应以及造成桥梁破坏的重要因素。本文对地震作用下隔震简支梁桥的碰撞反应进行了振动台试验。设计制作1个两跨简支的隔震梁桥模型,试验研究了梁间隙、邻梁质量比、隔震支座类型等参数对桥梁碰撞反应的影响。试验结果表明邻梁间隙、邻梁质量比、隔震支座类型等参数对桥梁的碰撞反应有着显著的影响。邻梁间隙越大,碰撞次数越少;邻梁质量比越大,撞击力越大。铅芯橡胶支座比板式橡胶支座耗能能力更强,可以有效降低邻梁之间的撞击力甚至避免碰撞发生。从而为桥梁防碰撞设计提供了可靠的试验依据。     

Earthquake simulator testing of pounding between adjacent buildings

Two-storey-building frames have been designed and built in an effort to investigate the pounding phenomenon of adjacent buildings during earthquakes. Static tests have been first performed to determine the static characteristics and the support conditions of the test structures. Sinusoidal and random acceleration signal tests have been subsequently performed to determine the dynamic characteristics of the test structures. Two series of tests were carried out using the shaking table simulator. In the first case, the dynamic response has been recorded without pounding, while in the second case, the test structures have been placed with zero-gap separation and pounding was induced. Input energy time histories were correlated and compared with and without pounding. The experimental results were compared with analytical ones based on a formulation of the contact impact problem by the Lagrange multiplier method. Good agreement between the experimental and the analytical results was achieved.     

Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding

Major earthquakes in the past indicated that pounding between bridge decks may result in significant structural damage or even girder unseating. With conventional expansion joints, it is impossible to completely avoid seismic pounding between bridge decks, because the gap size at expansion joints is usually not big enough in order to ensure smooth traffic flow. With a new development of modular expansion joint (MEJ), which allows a large joint movement and at the same time without impeding the smoothness of traffic flow, completely precluding pounding between adjacent bridge decks becomes possible. This paper investigates the minimum total gap that a MEJ must have to avoid pounding at the abutments and between bridge decks. The considered spatial ground excitations are modelled by a filtered Tajimi‐Kanai power spectral density function and an empirical coherency loss function. Site amplification effect is included by a transfer function derived from the one‐dimensional wave propagation theory. Stochastic response equations of the adjacent bridge decks are formulated. The effects of ground motion spatial variations, dynamic characteristics of the bridge and the depth and stiffness of local soil on the required separation distance are analysed. Soil–structure interaction effect is not included in this study. The bridge response behaviour is assumed to be linear elastic. Copyright © 2009 John Wiley & Sons, Ltd.     

Experimental and analytical study on pounding reduction of base‐isolated highway bridges using MR dampers

Pounding between adjacent superstructures has been a major cause of highway bridge damage in the past several earthquakes. This paper presents an experimental and analytical study on pounding reduction of highway bridges subjected to earthquake ground motions by using magnetorheological (MR) dampers. An analytical model, which incorporates structural pounding and MR dampers, is developed. A series of shaking table tests on a 1:20 scaled base‐isolated bridge model are performed to investigate the effects of pounding between adjacent superstructures on the dynamics of the structures. Based on the test results, the parameters of the linear and the nonlinear viscoelastic impact models are identified. Performance of the semiactive system for reducing structural pounding is also investigated experimentally, in which the MR dampers are used in conjunction with the proposed control strategy, to verify the effectiveness of the MR dampers. Structural responses are also simulated by using the established analytical model and compared with the shaking table test results. The results show that pounding between adjacent superstructures of the highway bridge significantly increases the structural acceleration responses. For the base‐isolated bridge model considered here, the semiactive control system with MR dampers effectively precludes pounding. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation of relative displacement of two adjacent asymmetric structures

The most straightforward method to mitigate seismic pounding damage to adjacent structures is to provide adequate separation distance between them to completely preclude pounding during strong shaking. Many studies on the necessary separation distance between adjacent structures have been reported recently. Seismic codes around the world also specify the minimum required separation distances. However, all those required separations were derived by considering only the lateral responses of structures. For asymmetric structures with coupled torsional–lateral responses, the required separations are not well investigated. This paper presents some parametric study results on the relative displacement of adjacent asymmetric structures by considering their coupled torsional–lateral responses. Random vibration method is employed in the analysis. Both elastic and inelastic responses are considered. Effects of vibration frequencies, torsional stiffness and eccentricities of adjacent structures on their relative displacements are investigated. Numerical results are presented in dimensionless form and are discussed with respect to the current code specifications. Copyright © 2001 John Wiley & Sons, Ltd.     

城市桥梁粘滞阻尼器防地震碰撞分析与参数设计

研究了粘滞阻尼器防止城市梁桥地震碰撞反应的效果并提出了其参数设计方法。分析了线性粘滞阻尼器与非线性粘滞阻尼器阻尼系数的等效关系。运用随机振动理论与随机等效线性化理论建立了邻联间安装粘滞阻尼器后最大相对位移及墩顶最大位移的计算方法。以控制邻联最大相对位移小于实际间隙为目标,提出了防碰撞粘滞阻尼器参数设计方法。对1座4跨隔震连续梁桥进行了仿真分析,结果表明:粘滞阻尼器能有效抑制邻联的碰撞反应且不会显著增大桥墩的延性需求。在相同阻尼系数的情况下,粘滞阻尼器的速度指数越小,其防碰撞效果越好。利用人工波进行的时程分析结果验证了参数设计方法的可行性。     

Damage‐based seismic planar pounding analysis of adjacent symmetric buildings considering inelastic structure–soil–structure interaction

In cities and urban areas, building structures located at close proximities inevitably interact under dynamic loading by direct pounding and indirectly through the underlying soil. Majority of the previous adjacent building pounding studies that have taken the structure–soil–structure interaction (SSSI) problem into account have used simple lumped mass–spring–dashpot models under plane strain conditions. In this research, the problem of SSSI‐included pounding problem of two adjacent symmetric in plan buildings resting on a soft soil profile excited by uniaxial earthquake loadings is investigated. To this end, a series of SSSI models considering one‐directional nonlinear impact elements between adjacent co‐planar stories and using a method for direct finite element modeling of 3D inelastic underlying soil volume has been developed to accurately study the problem. An advanced inelastic structural behavior parameter, the seismic damage index, has been considered in this study as the key nonlinear structural response of adjacent buildings. Based on the results of SSSI and fixed base case analyses presented herein, two main problems are investigated, namely, the minimum building separation distance for pounding prevention and seismic pounding effects on structural damage in adjacent buildings. The final results show that at least three times, the International Building Code 2009 minimum distance for building separation recommended value is required as a clear distance for adjacent symmetric buildings to prevent the occurrence of seismic pounding. At the International Building Code‐recommended distance, adjacent buildings experienced severe seismic pounding and therefore significant variations in storey shear forces and damage indices. Copyright © 2016 John Wiley & Sons, Ltd.     

基于随机振动理论确定桥梁地震碰撞的临界间隙

确定梁桥邻跨间避免地震碰撞的最小间隙,对于梁桥地震碰撞危险性预测及防地震碰撞措施的设计有着显著意义。本文基于随机振动理论建立梁桥地震碰撞邻跨临界间隙的计算方法,分析模型采用跨径不等的两跨简支梁桥,且考虑隔震支座非线性恢复力的影响。文中首先建立了系统的非线性运动方程;随后运用随机等效线性化理论将其线性化;最后在复模态空间推导了临界碰撞间隙的均值与方差的计算方法。人工地震动的非线性时程分析结果验证了本文算法的正确性。参数分析表明,临界间隙随邻跨长度比增大而增大,随支座屈服力与上部结构重量比值减小而增大,随隔震支座屈服位移增大而增大,随桥墩振动周期增大而增大。隔震支座屈服前后刚度比值对临界间隙大小影响很小。     

Energy dissipating restrainers for highway bridges

Recent destructive earthquakes have demonstrated the vulnerability of highway bridges to collapse due to excessive movement beyond the available seat widths at expansion joints. This paper investigates the efficacy of using energy dissipating restrainers at expansion joints for preventing collapse of highway bridges in the event of a severe earthquake. The restrainer consists of a nonlinear viscous damper and an elastic spring connected in parallel or in series. Two-dimensional finite element analysis using bilinear hysteretic models for bridge substructure joints and nonlinear gap elements for expansion joints is performed on example bridges with one or two expansion joints. The analytical study demonstrates that the energy dissipating restrainers are effective in reducing the relative opening displacements and impact forces due to pounding at the expansion joints, without significantly increasing ductility demands in the bridge substructures.     

Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Modelling three‐dimensional non‐linear seismic performance of elevated bridges with emphasis on pounding of girders

Unseating of bridge girders/decks during earthquakes is very harmful to the safety and serviceability of bridges. Evidence from recent severe earthquakes indicates that in addition to damage along longitudinal direction, lateral displacement and rotation of bridge girders caused by pounding to adjacent girders can also lead to unseating. To simulate this effect, 3D modelling of the dynamic performance of whole bridge structures, including pounding, is needed strongly. This paper presents a 3D model that is practically suitable to precisely analyse pounding between bridge girders. Experiments have been conducted to verify the proposed pounding model. The 3D non‐linear modelling of steel elevated bridges is also discussed. A general‐purpose dynamic analysis program for bridges, namely dynamic analysis of bridge systems (DABS) has been developed. Seismic analyses on a chosen three‐span steel bridge are conducted for several cases including pounding as a case study. The applicability of the proposed pounding model is illustrated by the computations. The effects of poundings on the response of bridge girders are discussed and the computation results are given. Copyright © 2002 John Wiley & Sons, Ltd.     

A lagrange multiplier solution method for pounding of buildings during earthquakes

An effective solution method for studying the pounding response of two or more adjacent buildings during earthquakes is presented. The method is based on the Lagrange multiplier approach by which the geometric compatibility conditions due to contact are enforced. The energy and momentum balance criteria for the contacting bodies are satisfied according to the laws of impact with proper post-impact conditions, which can also take into account local energy absorption phenomena during impact. A solution scheme is proposed which can be incorporated easily into existing computer programs for static and dynamic analysis of structures. The applicability of the algorithm is illustrated in a number of selected sample problems and the correlation of numerical results to analytical solutions, whenever possible, is very satisfactory.     

Relative displacement response spectra with pounding effect

To avoid unseating of a deck, an adequate seat width must be provided. The seat width is basically determined from maximum relative displacement between two bridge segments. Under a strong ground excitation, pounding between two decks may occur at a joint. The pounding will affect the response of two bridge segments. This research is conducted to investigate the effect of pounding on the relative displacement between two adjacent bridge segments. A simplified analytical model of two linear single‐degree‐of‐freedom systems is employed. To take into account the pounding, the laws of conservation of momentum and energy are applied. The analytical results are represented in the form of relative displacement response spectra with pounding effect. It is found that due to the pounding the relative displacement can be amplified, resulting in the requirement of a longer seat width to support a deck. The formulation of normalized relative displacement response spectra is presented together with an application example. It is found that the seat width determined from the relative displacement response spectra with pounding effect becomes close to the value specified in the Japanese design specifications for structures with large difference of natural periods. Copyright © 2001 John Wiley & Sons, Ltd.     

Shake table tests of structures subject to pounding

Pounding between adjacent structures during earthquakes may significantly modify their response in terms of forces and displacements. In addition, it has a considerable influence on acceleration and thus on floor response spectra. Therefore, pounding may be unfavorable to the response of equipment. Despite extensive research in this field, the effects of pounding on structures are difficult to quantify accurately. This article presents results of shake table tests carried out on two representative scale adjacent structures subject to pounding. Besides investigating the effects of the gap between structures and the excitation signal, this study examines also the effect of tying the two structures together by means of rigid links to suppress pounding. The results of the experimental campaign are then compared with those of numerical simulations. Analyses and experimental results show good agreement regarding both impact forces and interstorey drifts.     

Earthquake induced pounding between adjacent buildings considering soil-structure interaction

Many closely located adjacent buildings have suffered from pounding during past earthquakes because they vibrated out of phase.Furthermore,buildings are usually constructed on soil;hence,there are interactions between the buildings and the underlying soil that should also be considered.This paper examines both the interaction between adjacent buildings due to pounding and the interaction between the buildings through the soil as they affect the buildings’ seismic responses.The developed model consists of adjacent shear buildings resting on a discrete soil model and a linear viscoelastic contact force model that connects the buildings during pounding.The seismic responses of adjacent buildings due to ground accelerations are obtained for two conditions:fixed-based(FB) and structure-soil-structure interaction(SSSI).The results indicate that pounding worsens the buildings’ condition because their seismic responses are amplified after pounding.Moreover,the underlying soil negatively impacts the buildings’ seismic responses during pounding because the ratio of their seismic response under SSSI conditions with pounding to those without pounding is greater than that of the FB condition.     

Implications of seismic pounding on the longitudinal response of multi-span bridges - an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach. Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is cssential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Reduction of pounding effects in elevated bridges during earthquakes

Pounding of adjacent superstructure segments in elevated bridges during severe earthquakes can result in significant structural damage. The aim of this paper is to analyse several methods of reduction of the negative effects of collisions induced by the seismic wave propagation effect. The analysis is conducted on a detailed three‐dimensional structural component model of an isolated highway bridge. The results show that the influence of pounding on the structural response is significant in the longitudinal direction of the bridge and significantly depends on the gap size between superstructure segments. The smallest response can be obtained for very small gap sizes and for gap sizes large enough to prevent pounding. Further analysis indicates that the bridge behaviour can be effectively improved by placing hard rubber bumpers between segments and by stiff linking the segments one with another. The experimental results show that, for the practical application of such connectors, shock transmission units can be used. Copyright © 2000 John Wiley & Sons, Ltd.     

双向地震作用下互通式斜交桥梁地震响应及碰撞效应分析

斜交桥梁由于其不规则的结构形式使其受力规律与规则桥梁相比具有特殊性和复杂性,在地震作用下梁体的平动与转动存在弯扭耦合效应,导致结构动力响应分析复杂。针对斜交桥梁的结构特点,建立包含桩土相互作用的三维有限元模型,在考虑水平双向地震作用下,采用反应谱法及时程分析法对京包高速公路某互通式斜交桥梁进行地震反应分析。结果表明:互通式简支斜交桥梁的地震响应受地震动输入方向的影响较大,在考虑碰撞效应后,碰撞涉及结构部位的地震位移显著增加,地震内力也出现较大差异,即说明在斜交桥梁抗震设计时有必要适当考虑地震动输入方向和梁端与墩台及相邻梁端的碰撞效应。     

Experimental investigation of spatially varying effect of ground motions on bridge pounding

Pounding between adjacent bridge structures with insufficient separation distance has been identified as one of the primary causes of damage in many major earthquakes. It takes place because the closing relative movement is larger than the structural gap provided between the structures. This relative structural response is controlled not only by the dynamic properties of the participating structures but also by the characteristics of the ground excitations. The consequence of the spatial variation of ground motions has been studied by researchers; however, most of these studies were performed numerically. The objective of the present research is to experimentally evaluate the influence of spatial variation of ground motions on the pounding behaviour of three adjacent bridge segments. The investigation is performed using three shake tables. The input spatially varying ground excitations are simulated based on the New Zealand design spectra for soft soil, shallow soil and strong rock using an empirical coherency loss function. Results confirm that the spatially nonniform ground motions increase the relative displacement of adjacent bridge girders and pounding forces. Copyright © 2012 John Wiley & Sons, Ltd.