A phenomenological contact‐element model considering slight non‐uniform contact for pounding analysis of highway bridges under seismic excitations

Impact stiffness is an important parameter of the contact‐element models for the analysis and prediction of the pounding responses of highway bridges subjected to seismic excitations. This paper presents a pounding experiment to investigate the inconsistencies between the theoretical and experimental values of the impact stiffness both for the linear impact model and Kelvin impact model presented in literature. The analysis of the impact acceleration and acoustic emission signals indicates that accelerometer performance and the non‐uniform pounding are two important factors that affect the pounding responses. Based on this observation, a phenomenological contact‐element model is proposed based on the actual contact state of highway bridges during the impact. To evaluate the effectiveness of the proposed impact model, a numerical simulation is subsequently conducted. A comparison of the results indicates that the proposed impact model can effectively predict the pounding responses of highway bridges. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

A note on the Hertz contact model with nonlinear damping for pounding simulation

Structural pounding during earthquakes has been recently investigated extensively by using different models of impact force. In this paper, reexamination of the Hertz contact model with nonlinear damping is made. Based on this reexamination, the formula used to determine the damping constant in terms of the spring stiffness, the coefficient of restitution and relative approaching velocity of two colliding bodies is found to be incorrect for pounding simulation in structural engineering. In order to correct this problem, a more accurate approximating formula for the damping constant is theoretically derived. The correctness of the derived analytical formula has been confirmed through numerical simulations. Copyright © 2008 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.     

Analytical expression between the impact damping ratio and the coefficient of restitution in the non‐linear viscoelastic model of structural pounding

Earthquake‐induced structural pounding has been recently intensively studied with the help of different models of impact force. It has been verified through comparisons, that the non‐linear viscoelastic model may be considered somewhat the most accurate one among them. The aim of this short paper is to derive an approximating formula relating the impact damping ratio, as a parameter of the model mentioned, with a more widely used coefficient of restitution. The accuracy of the derived analytical formulation has been confirmed through the comparison with the results of numerical simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

Pounding of structures modelled as non‐linear impacts of two oscillators

A new formulation is proposed to model pounding between two adjacent structures, with natural periods T₁ and T₂ and damping ratios ζ₁ and ζ₂ under harmonic earthquake excitation, as non‐linear Hertzian impact between two single‐degree‐of‐freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis (‘Pounding of buildings modelled by an impact oscillator’ Earthquake Engineering and Structural Dynamics, 1992; 21 :253–274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non‐rigid impacts. When the difference in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the standoff distance. The maximum relative impact velocity of the coupled system can occur at an excitation period T_n^* which is either between those of the two oscillators or less than both of them, depending on the ratios T₁/T₂ and ζ₁/ζ₂. Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters. Copyright © 2001 John Wiley & Sons, Ltd.     

A modified Kelvin impact model for pounding simulation of base-isolated building with adjacent structures

Base isolation can effectively reduce the seismic forces on a superstructure,particularly in low-to medium-rise buildings.However,under strong near-fault ground motions,pounding may occur at the isolation level between the baseisolated building(BIB)and its surrounding retaining walls.To effectively investigate the behavior of the BIB pounding with adjacent structures,after assessing some commonly used impact models,a modified Kelvin impact model is proposed in this paper.Relevant parameters in the modifi...     

Analytical modelling of multi‐mass flexible rocking structures

This paper presents a new analytical model for describing the large rocking response of an elastic multi‐mass structure resting on ideally rigid ground. Using the experimental results from a rocking steel column, the ability of the proposed analytical model to estimate the rocking and translational acceleration response under free vibration, pulse and earthquake excitations is evaluated. It is observed that the classical treatment of impact may result in an unrealistically large transfer of energy to vibrations. Therefore a new Dirac‐delta type impact model that spreads the effects of impact over time and space is proposed. The use of a Dirac‐delta model and accurate restitution factors play a pivotal role in prediction of rocking and acceleration responses. In order to characterize the nonlinear response better, a modal analysis of the linearized system is proposed. With this approach, the vibration mode frequencies and shapes during rocking action were determined. A comparison of analytical and experimental modal estimations suggests good agreement. The results emphasize that the vibration characteristics of several vibration modes are affected by rocking action, and these modes may be excited at impact. Copyright © 2016 John Wiley & Sons, Ltd.     

ON ECCENTRIC SEISMIC POUNDING OF SYMMETRIC BUILDINGS

Results of a parameter study on eccentric pounding of two symmetric single storey systems under seismic excitation are presented. Linear behaviour is assumed, and pounding effect is considered using the restitution coefficient approach. The effect of impact eccentricity is studied on two sets of symmetric models symmetrically and asymmetrically aligned with respect to each other for several gap widths, period dependent gaps and three values of the torsional-to-lateral frequency ratio. Two time histories are used for input. On the whole it was found that impact eccentricity amplifies the response relative to symmetric impact but the effect is not proportional to first impact eccentricity. Also, increasing gap width is likely to be effective when the separation is sufficiently wide practically to eliminate contact. Larger torsional rigidity tends to lower response amplification. SRSS code-type gaps appear to be adequate, or even excessive, when the design spectrum is compatible with the expected earthquake record at the site.     

Non‐linear viscoelastic modelling of earthquake‐induced structural pounding

Past severe earthquakes indicate that structural pounding may cause considerable damage or even lead to collapse of colliding structures if the separation distance between them is not sufficient. Because of its complexity, modelling of impact is an extremely difficult task, however, the precise numerical model of pounding is essential if an accurate structural response is to be simulated. The aim of this paper is to analyse a non‐linear viscoelastic model of collisions which allows more precise simulation of the structural pounding during earthquakes. The effectiveness of the model is verified by comparing the results of numerical analyses with the results of experiments conducted on pounding between different types of structures. The results of the study indicate that, compared to other models, the proposed non‐linear viscoelastic model is the most precise one in simulating the pounding‐involved structural response. Copyright © 2005 John Wiley & Sons, Ltd.     

Mitigation measures for earthquake induced pounding effects on seismic performance of adjacent buildings

Post-earthquake damages investigation in past and recent earthquakes has illustrated that the building structures are vulnerable to severe damage and/or collapse during moderate to strong ground motion. Among the possible structural damages, seismic induced pounding has been commonly observed in several earthquakes. A parametric study on buildings pounding response as well as proper seismic hazard mitigation practice for adjacent buildings is carried out. Three categories of recorded earthquake excitation are used for input excitations. The effect of impact is studied using linear and nonlinear contact force model for different separation distances and compared with nominal model without pounding consideration. The severity of the impact depends on the dynamic characteristics of the adjacent buildings in combination with the earthquake characteristics. Pounding produces acceleration and shear forces/stresses at various story levels that are greater than those obtained from the no pounding case, while the peak drift depends on the input excitation characteristics. Also, increasing gap width is likely to be effective when the separation is sufficiently wide to eliminate contact. Furthermore, it is effective to provide a shock absorber device system for the mitigation of impact effects between adjacent buildings with relatively narrow seismic gaps, where the sudden changes of stiffness during poundings can be smoothed. This prevents, to some extent, the acceleration peaks due to impact. The pounding forces exerted on the adjacent buildings can be satisfactorily reduced.     

Evaluation of uniaxial contact models for moat wall pounding simulations

Moat wall pounding occurs when a base-isolated building displaces beyond the provided clearance and collides with the surrounding retaining wall, inducing very high floor accelerations and interstory drifts. Previous studies on moat wall pounding typically employ simplified models of the superstructure, with a uniaxial contact spring used to model the entire moat wall. Consequently, researchers have developed sophisticated contact models to estimate the normal-direction contact force that is generated during seismic pounding. This study examines how the choice in contact model affects the seismic response of a base-isolated building subjected to impact-inducing ground excitation. Five widely used state-of-the-art contact models are summarized and implemented into an experimentally-calibrated numerical model of a base-isolated moment frame. Results of nonlinear dynamic time history analyses are shown in detail for one ground motion, followed by a larger parametric study across 28 near-fault ground motions. This work shows that peak impact force and base acceleration are moderately sensitive to the choice in contact model, while upper floor accelerations and interstory drifts are practically not affected.     

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。     

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd.     

Transient responses of girder bridges with vertical poundings under near‐fault vertical earthquake

Previous studies on pounding responses of bridge structures mainly focus on the horizontal pounding between adjacent structures. However, the vertical pounding responses of bridge are rarely studied. The aim of this paper is develop a theoretical approach to investigate the transient behavior of continuous bridge under near‐fault vertical ground motions. The transient behavior of bridge manifests as the earthquake‐induced response wave and pounding‐induced response wave travel throughout bridge. Based on a new continuous model of beam–spring–rod, the theoretical solution of bridge responses involving multiple vertical poundings is derived by the expansion of transient wave functions in a series of eigenfunctions. A new theoretical solving approach of the multiple vertical pounding forces is presented based on the transient internal force on the contact surface of the girder and bearing. The numerical results show that the present method can reasonably capture the propagations of the earthquake‐induced response wave and pounding‐induced response wave. The calculations of pounding force by the present method are convergence of the time‐step size and truncation number of wave modes. As the effect of transient wave is taken into account, the numerical results show several transient phenomena involving the vertical pounding, the high pounding force, the multiple‐pounding phenomenon, the vertical separation of girder from the bearing, the dependence of poundings on earthquake period and the narrow period window of poundings. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

地震作用下双薄壁高墩刚构桥桥台处的碰撞效应及减碰措施

针对双薄臂高墩连续刚构桥两侧桥台处主梁与背墙的碰撞现象,基于桥台-背土作用简化模型和Kelvin碰撞模型,采用非线性时程法研究碰撞对双薄臂墩地震剪力、弯矩、曲率和位移,以及支座纵向变形的影响。提出可牺牲背墙、阻尼器、加强型横系梁等三种减碰措施,并对比分析其减碰效果。研究表明:碰撞会显著增大高墩的地震内力和曲率响应,降低墩顶位移和支座的纵向变形;碰撞刚度的变化对碰撞效应的影响在20%以内;可牺牲背墙和阻尼器两种减碰措施均可大幅降低桥墩的地震内力和曲率,使其接近不考虑碰撞时的状态,阻尼器同时还可以保护支座不超过容许变形,而可牺牲背墙则会导致支座的地震破坏;加强型横系梁不能发挥减碰作用,反而会增大桥墩的地震响应。     

A nonlinear impact model for simulating the use of rubber shock absorbers for mitigating the effects of structural pounding during earthquakes

During strong earthquakes, structural poundings may occur between adjacent buildings because of the limited separation distance and the deformations of their stories. A potential mitigation measure for this problem is the incorporation of layers of soft material, such as rubber, which can act as collision bumpers, in order to prevent the sudden impact pulses. In an effort to investigate the effectiveness of such an impact mitigation measure, relevant numerical simulations and parametric studies can be performed. However, none of the known impact models, which are available in the literature, is able to represent the usage of rubber bumpers with sufficient accuracy. The current study presents a simple but efficient methodology that can be used to simulate the incorporation of rubber layers between neighboring structures with relatively narrow seismic gaps. Such methodology will enable us to numerically investigate the effectiveness of using rubber bumpers to mitigate potential earthquake‐induced pounding. In particular, a new nonlinear inelastic force‐based impact model, able to appropriately describe the behavior of rubber under impact loading, taking also into account the limited thickness of the bumper, is introduced. Finally, a numerical example of simulating earthquake‐induced pounding between two multistory buildings with the consideration of rubber bumpers at impact locations is presented. Copyright © 2012 John Wiley & Sons, Ltd.