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.     

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.     

Seismic response of multi‐span simply supported bridges to a spatially varying earthquake ground motion

This paper carries out a parametrical study of the pounding phenomenon associated with the seismic response of multi‐span simply supported bridges with base isolation devices. In particular, the analyses focus on the causal relationship between pounding and the properties of a spatially varying earthquake ground motion. In order to include the effect of the torsional component of pounding forces on the seismic response of the whole structure, a three‐dimensional (3D) finite element model has been defined and 3D non‐linear time‐history analyses have been performed. A parametrical study on the size of the gaps between adjacent bridge decks has highlighted that the pounding effects are amplified when the spatially varying ground motion time histories at each support are considered. Because of a spatially varying input, the pounding forces can assume values 3–4 times larger than those derived by a conventional seismic analysis with uniform input or with spatial input but considering ground motion wave passage effect only. The numerical results show that in order to achieve an acceptably safe structural performance during seismic events, a correct design of the isolation devices should take into account the relative displacements calculated by means of a non‐linear time‐history analysis with multi‐support excitation. Copyright © 2002 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.     

A Hertz contact model with non‐linear damping for pounding simulation

This paper investigates the cogency of various impact models in capturing the seismic pounding response of adjacent structures. The analytical models considered include the contact force‐based linear spring, Kelvin and Hertz models, and the restitution‐based stereomechanical approach. In addition, a contact model based on the Hertz law and using a non‐linear hysteresis damper (Hertzdamp model) is also introduced for pounding simulation. Simple analytical approaches are presented to determine the impact stiffness parameters of the various contact models. Parameter studies are performed using two degree‐of‐freedom linear oscillators to determine the effects of impact modelling strategy, system period ratio, peak ground acceleration (PGA) and energy loss during impact on the system responses. A suite of 27 ground motion records from 13 different earthquakes is used in the analysis. The results indicate that the system displacements from the stereomechanical, Kelvin and Hertzdamp models are similar for a given coefficient of restitution, despite using different impact methodologies. Pounding increases the responses of the stiffer system, especially for highly out‐of‐phase systems. Energy loss during impact is more significant at higher levels of PGA. Based on the findings, the Hertz model provides adequate results at low PGA levels, and the Hertzdamp model is recommended at moderate and high PGA levels. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental study on earthquake‐induced pounding between structural elements made of different building materials

The phenomenon of earthquake‐induced structural pounding has attracted the researchers' attention for several years now. The aim of this paper is to show the results of two experiments concerning interactions between elements made of different building materials, such as steel, concrete, timber and ceramic. The first experiment was conducted by dropping balls from different height levels onto a rigid surface, whereas the second one was focused on pounding‐involved response of two tower models excited on a shaking table. The results of the impact experiment show that the value of the coefficient of restitution depends substantially on the prior‐impact velocity as well as on the material used. Based on these results, the appropriate formulations have been suggested to be applied in the numerical simulations. The results of the shaking table tests show a considerable influence of the material used for colliding elements on the behaviour of structures during earthquakes. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

Earthquake‐induced interaction between adjacent reinforced concrete structures with non‐equal heights

The influence of the structural pounding on the ductility requirements and the seismic behaviour of reinforced concrete structures designed to EC2 and EC8 with non‐equal heights is investigated. Special purpose elements of distributed plasticity are employed for the study of the columns. Two distinct types of the problem are identified: Type A, where collisions may occur only between storey masses; and Type B, where the slabs of the first structure hit the columns of the other (72 Type A and 36 Type B pounding cases are examined). Type A cases yielded critical ductility requirements for the columns in the pounding area mainly for the cases where the structures were in contact from the beginning of the excitation. In both pounding types the ductility requirements of the columns of the taller building are substantially increased for the floors above the highest contact storey level probably due to a whiplash behaviour. The most important issue in the pounding type B is the local response of the column of the tall structure that suffers the hit of the upper floor slab of the adjacent shorter structure. In all the examined cases this column was in a critical condition due to shear action and in the cases where the structures were in contact from the beginning of the excitation, this column was also critical due to high ductility demands. It can be summarized that in situations of potential pounding, neglecting its possible effects leads to non‐conservative building design or evaluation that may become critical in some cases. Copyright © 2004 John Wiley & Sons, Ltd.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Optimal maintenance strategies for structures in seismic zones

In this paper an approach is developed for establishing optimal maintenance (repair) strategies of structures in seismic zones. The approach is based on expected future costs and the main decision variable is a damage threshold for repair given an acceptable reliability level. It is considered that structural damage accumulates over a number of earthquakes until a threshold is reached or exceeded, after which the structure is repaired so that there is no remaining damage. A Markov model is implemented for such a process of damage accumulation during future earthquakes. An algorithm is proposed for computing non‐linear structural response to earthquakes using a damage function model. This algorithm is used to evaluate transition probabilities between damage states based on simulations of future earthquakes of given intensities. Expressions are derived for evaluating expected life‐cycle damage costs and structural reliability as a function of time and of the damage threshold for repair. As an application, a single‐degree‐of‐freedom structural system is studied. In addition, the paper addresses the case of instrumented structures where information from earthquake response records is available. Such information is incorporated into the formulation for maintenance strategies by means of a Bayesian approach for updating the probability distribution of structural damage and of non‐linear behaviour parameters so that predictions about costs and reliability are improved. Copyright © 2002 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

An isolation system for limited seismic gaps in near‐fault zones

The ability of a recently proposed seismic isolation system, with inherent self‐stopping mechanism, to mitigate or even eliminate seismic pounding of adjacent structures is investigated under severe near‐fault earthquakes. The isolation system is referred to as roll‐in‐cage (RNC) isolator. It is a rolling‐based isolator that provides in one unit the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, hysteretic energy dissipation, and resistance to minor vibration loads. In addition, the RNC isolator is distinguished by a self‐stopping (buffer) mechanism to limit the bearing displacement under excitations stronger than a design earthquake or at limited seismic gaps, and a linear gravity‐based self‐recentering mechanism to prevent permanent bearing displacement without causing vertical fluctuation of the isolated structure. A previously developed multifeature SAP2000 model of the RNC isolator is improved in this paper to account for the inherent buffer mechanism's damping. Then, the effectiveness of the isolator's buffer mechanism in limiting peak bearing displacements is studied together with its possibly arising negative influence on the isolation efficiency. After that, the study investigates how to alleviate or even eliminate those possibly arising drawbacks, due to the developed RNC isolator's inner pounding as a result of its buffer activation, to achieve efficient seismic isolation with no direct structure‐to‐structure pounding, considering limited seismic gaps with adjacent structures and near‐fault earthquakes. The results show that the RNC isolator could be an efficient solution for aseismic design in near‐fault zones considering limited seismic gaps. Earthquake Engineering and Structural Dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

A fuzzy–random analysis model for seismic performance of framed structures incorporating structural and non‐structural damage

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate‐to‐strong earthquakes; however, the financial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is affected by structural as well as non‐structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non‐structural damages is required. This paper presents a fuzzy–random model for the performance reliability analysis of RC framed structures considering both structural and non‐structural damages. The limit state for each performance level is defined as an interval of inter‐storey drift ratios concerning, respectively, the non‐structural and structural damage with a membership function, while the relative importance of the two aspects is reflected through the use of an appropriate cost function. To illustrate the methodology, herein the non‐structural damage is represented by infill masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single‐threshold performance definition. The proposed model provides a good basis for incorporating different aspects into the performance assessment of a building system. Copyright © 2005 John Wiley & Sons, Ltd.     

Time‐domain viscoelastic analysis of earth structures

In this paper two causal models that approximate the nearly frequency‐independent cyclic behaviour of soils are analysed in detail. The study was motivated by the need to conduct time‐domain viscoelastic analysis on soil structures without adopting the ad hoc assumption of Rayleigh damping. First, the causal hysteretic model is introduced in which its imaginary part is frequency independent the same way that is the imaginary part of the popular non‐causal constant hysteretic model. The adoption of an imaginary part that is frequency independent even at the zero‐frequency limit, in conjunction with the condition that the proposed model should be causal, yields a real part that is frequency dependent and singular at zero frequency. The paper shows that the causal hysteretic model, although pathological at the static limit, is the mathematical connection between the non‐causal constant hysteretic model and the physically realizable Biot model. The mathematical structure of the two causal models is examined and it is shown that the causal hysteretic model is precisely the high‐frequency limit of the Biot model. Although both models have a closed‐form time‐domain representation, only the Biot model is suitable for a time‐domain viscoelastic analysis with commercially available computer software. The paper demonstrates that the simplest, causal and physically realizable linear hysteretic model that can approximate the cyclic behaviour of soil is the Biot model. The proposed study elucidates how the dynamic analysis of soil structures can be conducted rigorously in terms of the viscoelastic properties of the soil material and not with the ad hoc Rayleigh damping approach which occasionally has been criticized that tends to overdamp the higher vibration modes. The study concludes that under pulse‐type motions the Rayleigh damping approximation tends to overestimate displacements because of the inappropriate viscous type of dissipation that is imposed. Under longer motions that induce several cycles, the concept of equivalent viscous damping is more appropriate and the Rayleigh damping approximation results to a response that is comparable to the response computed with a rigorous time‐domain viscoelastic finite element analysis. Copyright © 2000 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.