相邻偏心高层建筑物间的振动台碰撞试验

地震引起的相邻建筑物间的碰撞过去多次强烈地震中出现,并造成了较为严重的结构破坏。为研究此问题,设计建造了两座缩尺钢质模型来模拟香港两座相邻的21层建筑,对其进行了一系列振动台碰撞试验,试验结果表明复杂结构间的碰撞可能是周期性的、群周期性的或混沌的,这主要取决于间距、结构参数以及地震动参数。碰撞引起的能量传递可能对较柔较轻的邻近建筑造成较严重的地震反应和破坏。     

Dimensional analysis of the earthquake‐induced pounding between adjacent structures

In this paper the dynamic response of two and three pounding oscillators subjected to pulse‐type excitations is revisited with dimensional analysis. Using Buckingham's Π‐theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless Π‐terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self‐similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete self‐similarity or self‐similarity of the second kind with respect to the mass ratio. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance of base‐isolated reinforced concrete buildings under bidirectional seismic excitation considering pounding with retaining walls including friction effects

Seismic pounding of base‐isolated buildings has been mostly studied in the past assuming unidirectional excitation. Therefore, in this study, the effects of seismic pounding on the response of base‐isolated reinforced concrete buildings under bidirectional excitation are investigated. For this purpose, a three‐dimensional finite element model of a code‐compliant four‐story building is considered, where a newly developed contact element that accounts for friction and is capable of simulating pounding with retaining walls at the base, is used. Nonlinear behavior of the superstructure as well as the isolation system is considered. The performance of the building is evaluated separately for far‐fault non‐pulse‐like ground motions and near‐fault pulse‐like ground motions, which are weighted scaled to represent two levels of shaking viz. the design earthquake (DE) level and the risk‐targeted maximum considered earthquake (MCE_R) level. Nonlinear time‐history analyses are carried out considering lower bound as well as upper bound properties of isolators. The influence of separation distance between the building and the retaining walls at the base is also investigated. It is found that if pounding is avoided, the performance of the building is satisfactory in terms of limiting structural and nonstructural damage, under DE‐level motions and MCE_R‐level far‐fault motions, whereas unacceptably large demands are imposed by MCE_R‐level near‐fault motions. In the case of seismic pounding, MCE_R‐level near‐fault motions are found to be detrimental, where the effect of pounding is mostly concentrated at the first story. In addition, it is determined that considering unidirectional excitation instead of bidirectional excitation for MCE_R‐level near‐fault motions provides highly unconservative estimates of superstructure demands. Copyright © 2014 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.     

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.     

On poundings of a seismically isolated building with adjacent structures during strong earthquakes

This paper presents selected indicative results from an extensive parametric investigation that has been performed in order to assess the effects of potential earthquake‐induced poundings on the overall dynamic response of seismically isolated buildings. In particular, a seismically isolated building and its adjacent fixed‐supported buildings are subjected to various earthquake excitations that induce structural impact among the buildings in series. The results indicate that the seismically isolated building may hit against the adjacent buildings at the upper floor levels before the occurrence of any pounding at the isolation level with the surrounding moat wall. The severity of the impact depends on the dynamic properties of the adjacent buildings, in combination with the earthquake characteristics. Copyright © 2009 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.     

Sensitivity analysis of pounding between adjacent structures

This article deals with sensitivity of the response of pounding buildings with respect to structural and earthquake excitation parameters. A comprehensive sensitivity analysis is carried out by means of Monte Carlo simulations of adjacent single degree of freedom impacting oscillators. This sensitivity analysis, based on Sobol's method, computes sensitivity indexes which provide a consistent measure of the relative importance of parameters such as the dimensionless main excitation frequency, the mass and frequency ratios of the structures, and the coefficient of restitution. Moreover, the influence of nonlinear behavior of the impacting structures is also considered. The consequences of pounding on the structures themselves are analyzed in terms of maximum force and nonlinear demand amplification compared with the case without pounding. As for the influence of pounding on the floor response spectra, the quantity of interest is the maximum impact impulse. The overall conclusions of this analysis are that the frequency ratio is the most important parameter as far as the maximum force and nonlinear demand are concerned. Regarding the maximum impact impulse, the mass and frequency ratios are, in general, the most influential parameters, the mass ratio being predominant for low frequencies of the oscillator of interest.     

Effects of balanced impact damper in structures subjected to walking and vertical seismic excitations

This study investigates whether a balanced impact damper (BID) with a vertically suspended impact body colliding with shock absorbing rubber can suppress vibrations of a floor slab subjected to walking and vertical seismic excitations. The impact body is suspended by coil springs to sustain its deadweight and centralize it within the gap, and collides with the stopper when its amplitude exceeds the specified gap width. The stopper is covered by a shock‐absorbing rubber made of polyurethane gel. The installed BID was evaluated in a single degree‐of‐freedom model of a floor slab subjected to vertical excitations. Simulations revealed that the installed BID properly controls the vibrations. Next, the effects of the BID installed on a steel plate were investigated in shaking table tests. The BID effectively suppressed vertical vibrations of the plate subjected to sinusoidal waves, seismic motions, and walking excitations. In addition, the shaking table tests were accurately simulated by the developed mathematical model of the damper. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Tests on low‐ductility RC frames under high‐ and low‐frequency excitations

The response of low‐ductility reinforced concrete (RC) frames, designed typically for a non‐seismic region, subjected to two frequencies of base excitations is studied. Five half‐scaled, two‐bay, two‐storey, RC frames, each approximately 5 m wide by 3.3 m high, were subjected to both horizontal and/or vertical base excitations with a frequency of 40 Hz as well as a lower frequency of about 4 Hz (close to the fundamental frequency) using a shake table. The imposed acceleration amplitude ranged from 0.2 to 1.2g. The test results showed that the response characteristics of the structures differed under high‐ and low‐frequency excitations. The frames were able to sustain high‐frequency excitations without damage but were inadequate for low‐frequency excitations, even though the frames exhibited some ductility. Linear‐elastic time‐history analysis can predict reasonably well the structural response under high‐frequency excitations. As the frames were not designed for seismic loads, the reinforcement detailing may not have been adequate, based on the crack pattern observed. The effect of vertical excitation can cause significant additional forces in the columns and moment reversals in the beams. The ‘strong‐column, weak‐beam’ approach for lateral load RC frame design is supported by experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental study of the semi‐active control of building structures using the shaking table

A magnetorheological (MR) damper has been manufactured and tested and a non‐linear model is discussed. The parameters for the model are identified from an identification set of experimental data; these parameters are then used to reconstruct the force vs. displacement and the force vs. velocity hysteresis cycles of the MR damper for the hysteretic model. Then experiments are conducted on a three‐storey frame model using impact excitation, which identifies dynamic parameters of the model equipped with and without the MR damper. Natural frequencies, damping ratios and mode shapes, as well as structural properties, such as the mass, stiffness and damping matrices, are obtained. A semi‐active control method such as a variable structure controller is studied. Based on the ‘reaching law’ method, a feedback controller is presented. In order to evaluate the efficiency of the control system and the effect of earthquake ground motions, both numerical analysis and shaking table tests of the model, with and without the MR damper, have been carried out under three different ground motions: El Centro 1940, Taft 1952, and Ninghe 1976 (Tangshan Earthquake in Chinese). It is found from both the numerical analysis and the shaking table tests that the maximum accelerations and relative displacements for all floors are significantly reduced with the MR damper. A reasonable agreement between the results obtained from the numerical analysis and those from the shaking table tests is also observed. On the other hand, tests conducted at different earthquake excitations and various excitation levels demonstrate the ability of the MR damper to surpass the performance of a comparable passive system in a variety of situations. Copyright © 2003 John Wiley & Sons, Ltd.     

Damped resonant appendages to increase inherent damping in buildings

It is demonstrated that the addition of a tuned mass-spring-dashpot system with a relatively small mass and a high damping ratio can be an effective way to increase the inherent damping characteristics of buildings and reduce, thus, their response to earthquake excitations. The demonstration is based on a theoretical formulation and on numerical and experimental studies that confirm this formulation. In the theoretical formulation, it is shown first that, if certain conditions are satisfied, the damping ratios in two of the modes of the system that is formed by a building and an appendage in resonance are approximately equal to the average of the corresponding damping ratios of the building and the appendage. Based on this finding, it is then shown that an attached appendage with a high damping ratio and tuned to the fundamental frequency of a building may increase the damping ratio in the fundamental mode of the building to a value close to half the damping ratio of the appendage. In the numerical study, the response of a ten-storey shear building is analysed under two different earthquake ground motions with and without the proposed resonant appendages. Appendages with damping ratios of 20 and 30 per cent are considered. In this study, it is found that under one of the ground motions the maximum displacement of the building's roof is reduced 30 per cent with the appendage with 20 per cent damping and 39 per cent with the one with 30 per cent damping. Similarly, with these two appendages the building's base shear is reduced 31 and 41 per cent, respectively. In the experimental study, a wooden three-storey structural model is tested in a shaking table with and without an appendage designed and constructed to have a damping ratio of 53-5 per cent. The test is conducted under random and sinusoidal base excitations. In the shaking table test under random excitation, the attached appendage reduces the response of the model 38-6 per cent, while in that under sinusoidal vibration 45-2 per cent.     

Dynamics of submerged intake towers including interaction with dam and foundation

The dynamics of a coupled concrete gravity dam-intake tower–reservoir water–foundation rock system is numerically studied considering two hollow slender towers submerged in reservoir of gravity dam. The system is investigated in the frequency-domain using frequency response functions of the dam and the towers, and in the time-domain using time-history seismic analysis under a real earthquake ground motion. The analyzes are separately conducted under horizontal and vertical ground motions. The coupled system is three-dimensionally modeled using finite elements by Eulerian–Lagrangian approach. It is shown that presence of the dam significantly influences the dynamic response of the towers under both horizontal and vertical excitations; however the dam is not affected by the towers. When the dam is present in the model, the water contained inside the towers has different effects if the foundation is rigid, but it alleviates the towers motion if the foundation is flexible. It is concluded that the effects of foundation interaction are of much importance in the response of tall slender towers when they are located near concrete gravity dams.     

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.     

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.     

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.     

Modelling damage potential of high‐frequency ground motions

Damage to building structures due to underground blast‐induced ground motions is a primary concern in the corresponding determination of the safe inhabited building distance (IBD). Because of the high‐frequency nature of this category of ground motions and especially the presence of significant vertical component, the characteristics of structural response and damage differ from those under seismic type low‐frequency ground motions. This paper presents a numerical investigation aimed at evaluating reinforced concrete (RC) structure damage generated by underground blast‐induced ground excitation. In the numerical model, two damage indices are proposed to model reinforced concrete failure. A fracture indicator is defined to track the cracking status of concrete from micro‐ to macrolevel; the development of a plastic hinge due to reinforcement yielding is monitored by a plastic indicator; while the global damage of the entire structure is correlated to structural stiffness degradation represented by its natural frequency reduction. The proposed damage indices are calibrated by a shaking table test on a 1: 5‐scale frame model. They are then applied to analyse the structural damage to typical low‐ to high‐rise RC frames under blast‐induced ground motions. Results demonstrate a distinctive pattern of structural damage and it is shown that the conventional damage assessment methods adopted in seismic analysis are not applicable here. It is also found that the existing code regulation on allowable peak particle velocity of blast‐induced ground motions concerning major structural damage is very conservative for modern RC structures. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

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.