Lead core heating in lead rubber bearings subjected to bidirectional ground motion excitations in various soil types

This paper investigates the response of lead rubber bearings (LRBs) under bidirectional earthquake excitations when lead core heating effect is of concern. For this purpose, a series of nonlinear response history analyses were conducted with a bilinear force‐deformation relation for LRBs. In the considered bilinear representation, the strength of LRBs deteriorates because of lead core heating under cyclic motions. Response of LRBs was studied in terms of maximum isolator displacements (MIDs) and maximum lead core temperature as a function of isolator characteristics (characteristic strength to weight ratio, Q/W, and post‐yield isolation period, T). Nonlinear response history analyses were performed using two sets of ground motions clustered according to their soil classifications. To quantify the interacted effects of coupled analysis and lead core heating on MID, unidirectional analyses were also performed. Furthermore, the efficacy of equivalent lateral force procedure in estimating the MID of LRBs was also tested for the cases in which temperature‐dependent behavior of LRBs was considered. The results demonstrate that the temperature rises in the lead core of LRBs in bidirectional analyses are approximately 50% higher than that of unidirectional ones. It decreases with increasing Q/W ratio and T. It is also revealed that equivalent lateral force procedure gives close estimations for MID with some overestimation even for temperature‐dependent behavior of LRBs. Copyright © 2013 John Wiley & Sons, Ltd.     

Change in response of bridges isolated with LRBs due to lead core heating

This study focuses on the response of seismic isolated bridges subjected to near-field ground motions with distinct pulse type behavior in terms of maximum isolator displacements (MIDs) and maximum isolator forces (MIFs) transferred to the substructure. The employed isolation systems are composed of lead rubber bearings (LRBs) with bi-linear force-deformation relations that consider cycle-to-cycle deterioration in the yield strength of the LRBs due to heating of the lead core. MIDs and MIFs with due consideration of cycle-to-cycle deterioration are compared with that of non-deteriorating ones. Bounding analyses are also performed for comparison purposes. Nonlinear response history analyses are conducted with two bins of ground motions recorded at different soil conditions to investigate the effect of ground motion characteristics. Results indicate that MIDs are overestimated by lower bound analyses when seismic isolated bridges are subjected to near-field motions with high velocity pulses especially for the bearings with higher Q/W ratios.     

Performance of seismic‐isolated bridges with and without elastic‐gap devices in near‐fault zones

In this paper, the efficiency of providing elastic‐gap devices (EGDs) to improve the performance of seismic‐isolated bridges (SIBs) in near‐fault (NF) zones is investigated. The device is primarily made of an assembly of circular rubber bearings and steel plates to provide additional elastic stiffness to the SIB upon closure of a gap. The EDG is intended to function at two performance levels under service and maximum considered design level (MCDL) NF earthquakes to reduce isolator displacements while keeping the substructure forces at reasonable levels. A parametric study, involving more than 500 nonlinear time history analyses of realistic and simplified structural models of typical SIBs, is conducted using simulated and actual NF ground motions to investigate the applicability of the proposed solution. It is found that providing EGD is beneficial for reducing the isolator displacements to manageable ranges for SIBs subjected to MCDL NF ground motions regardless of the distance from the fault and characteristics of the isolator. It is also found that providing EGD resulted in an improved performance of the isolators in terms of the reduction of heat generated by the isolators. Further analyses conducted using a realistic structural model of an existing bridge and five NF earthquakes confirmed that EGD may be used to reduce the displacement of the isolators while keeping the substructure base shear forces at reasonable ranges for SIBs located in NF zones. Copyright © 2008 John Wiley & Sons, Ltd.     

强震下斜交桥地震反应与减隔震性能分析

针对斜交桥在破坏性地震中发生破坏和损伤的突出问题,采用铅芯橡胶支座(LRB)进行隔震和滞回耗能。基于OpenSees平台建立了不同斜度的传统非隔震和全桥采用LRB隔震的4跨斜交连续梁桥动力分析模型,沿2个水平方向输入远场地震动和具有向前方向性效应、滑冲效应以及无速度脉冲效应的近断层地震动,并进行非线性时程计算,研究桥墩和挡块的损伤状态、主梁旋转度、碰撞力与斜交桥斜度的关系以及LRB对斜交桥抗震性能的影响。结果表明:向前方向性效应和滑冲效应的脉冲型地震动作用下的斜交桥地震反应和损伤明显大于无速度脉冲近断层和远场地震动作用; 采用LRB隔震后,明显降低了固定墩的地震损伤,桥墩位移减震率可达到50%以上; LRB隔震桥主梁与挡块的间隙宜结合桥梁的地震风险和设计位移进行确定。     

基于汶川地震的LRB与RB隔震连续梁桥地震响应对比研究

为了研究铅芯橡胶支座(LRB)和板式橡胶支座(RB)对连续梁桥地震响应及隔震效果的影响,分别采用Bouc - Wen滞回恢复力模型模拟LRB的力-位移非线性特性,采用直线型恢复力模型模拟RB的本构关系,通过结构离散建立了非隔震、LRB隔震和RB隔震3种连续梁桥的有限元计算模型,运用四阶显式Runge - Kutta迭代法和Newmark时间积分法联合求解增量形式的全桥动力微分方程,并结合算例对3种连续梁桥有限元计算模型分别输入汶川地震波进行非线性时程对比分析.结果表明:LRB在控制梁体与支座位移,降低结构加速度和墩、台底内力响应方面均比RB的效果要显著;采用RB隔震后,梁体与支座的位移响应均较大,在桥梁隔震设计时要予以充分重视.     

Study on effects of damping in laminated rubber bearings on seismic responses for a ⅛ scale isolated test structure

The effects of damping in various laminated rubber bearings (LRB) on the seismic response of a ?‐scale isolated test structure are investigated by shaking table tests and seismic response analyses. A series of shaking table tests of the structure were performed for a fixed base design and for a base isolation design. Two different types of LRB were used: natural rubber bearings (NRB) and lead rubber bearings (LLRB). Three different designs for the LLRB were tested; each design had a different diameter of lead plug, and thus, different damping values. Artificial time histories of peak ground acceleration 0.4g were used in both the tests and the analyses. In both shaking table tests and analyses, as expected, the acceleration responses of the seismically isolated test structure were considerably reduced. However, the shear displacement at the isolators was increased. To reduce the shear displacement in the isolators, the diameter of the lead plug in the LLRB had to be enlarged to increase isolator damping by more than 24%. This caused the isolator stiffness to increase, and resulted in amplifying the floor acceleration response spectra of the isolated test structure in the higher frequency ranges with a monotonic reduction of isolator shear displacement. Copyright © 2002 John Wiley & Sons, Ltd.     

Development of a tunable friction pendulum system for semi‐active control of building structures under earthquake ground motions

The Friction Pendulum System (FPS) isolator is commonly used as a base isolation system in buildings. In this paper, a new tunable FPS (TFPS) isolator is proposed and developed to act as a semi‐active control system by combining the traditional FPS and semi‐active control concept. Theoretical analysis and physical tests were carried out to investigate the behavior of the proposed TFPS isolator. The experimental and theoretical results were in good agreement, both suggesting that the friction force of the TFPS isolator can be tuned to achieve seismic isolation of the structure. A series of numerical simulations of a base‐isolated structure equipped with the proposed TFPS isolator and subjected to earthquake ground motions were also conducted. In the analyses, the linear quadratic regulator (LQR) method was adopted to control the friction force of the proposed TFPS, and the applicability and effectiveness of the TFPS in controlling the structure's seismic responses were investigated. The simulation results showed that the TFPS can reduce the displacement of the isolation layer without significantly increasing the floor acceleration and inter‐story displacement of the superstructure, confirming that the TFPS can effectively control a base‐isolated structure under earthquake ground motions.     

Shake table tests on a mass eccentric model with base isolation

A mass eccentric structure is usually more seismically vulnerable than its concentric counterpart because of the coupled torsional–translational response of such structures. In this work, dynamic characteristics and response of a five‐storey benchmark model with moderate mass eccentricity were investigated using a shake table, simulating four different ground motions. The effectiveness of laminated rubber bearings (LRB) and lead‐core rubber bearings (LCRB) in protecting eccentric structures was examined and evaluated in relation to translational and torsional responses of the benchmark model. It was observed that both translational and torsional responses were significantly reduced with the addition of either a LRB or LCRB isolated system regardless of the nature of ground motion input. The LRB were identified to be more effective than LCRB in reducing model relative displacements, the relative torsional angle as well as accelerations, and therefore provided a better protection of the superstructure and its contents. On the other hand, LCRB rendered a smaller torsional angle and absolute displacement of the base isolation system, hence a more stable structural system. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic isolation of cable‐stayed bridges for near‐field ground motions

This study examines the efficacy of using seismic isolation to favorably influence the seismic response of cable‐stayed bridges subjected to near‐field earthquake ground motions. In near‐field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many cable‐stayed bridges have significant structural response modes. This combination of factors can result in large tower accelerations and base shears. In this study, lead–rubber bearing seismic isolators were modeled for three cable‐stayed bridges, and three cases of isolation were examined for each bridge. The nine isolated bridge configurations, plus three non‐isolated configurations as references, were subjected to near‐field earthquake ground motions using three‐dimensional time‐history analyses. Introduction of a small amount of isolation is shown to be very beneficial in reducing seismic accelerations and forces while at the same time producing only a modest increase in the structural displacements. There is a low marginal benefit to continue to increase the amount of isolation by further lengthening the period of the structure because structural forces and accelerations reduce at a diminishing rate whereas structural displacements increase substantially. In virtually all cases the base shears in the isolated bridges were reduced by at least 50several instances by up to 80individual near‐field records showed large variability from one record to the next, with coefficients of variation about the mean as large as 50assessing the characteristics of near‐field ground motion for use in isolation design of cable‐stayed bridges. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimation of inelastic displacement ratio for base‐isolated structures

This study develops a straightforward approximate method to estimate inelastic displacement ratio, C₁ for base‐isolated structures subjected to near‐fault and far‐fault ground motions. Taking into account the inelastic behavior of isolator and superstructure, a 2 degrees of freedom model is employed. A total of 90 earthquake ground motions are selected and classified into different clusters according to the frequency content features of records represented by the peak ground acceleration to peak ground velocity ratio, A_p/V_p. A parametric study is conducted, and effective factors in C₁ (i.e., fundamental vibration period of the superstructure, T_s; postyield stiffness ratio of the superstructure, α_s; strength reduction ratio, R; vibration period of the isolator, T_b; strength of the isolator, Q; ratio of superstructure mass to total mass of the system, γ_m) are recognized. The results indicate that the practical range of C₁ values could be expected for base‐isolated structures. Subsequently, effective parameters are included in simple predictive equations. Finally, the accuracy of the proposed approximate equations is evaluated and verified through error measurement, and comparisons are made in the analyses.     

断层走向对刚构桥地震反应的影响

我国西部部分连续刚构桥临近地震断层建设,在抗震分析时通常会忽略断层走向与桥梁纵桥向夹角对其地震反应的影响。利用Midas Civil软件建立4座墩高不同的大跨度连续刚构桥模型,选取10组近断层强震记录进行时程分析,研究断层走向对刚构桥地震反应(位移和弯矩反应)的影响。结果显示：在水平双向近断层地震动输入下,桥梁主墩及主梁纵桥向地震反应在断层走向与纵桥向夹角为75°～135°范围内最大,而横桥向最大地震反应则发生在夹角为0°～30°或120°～180°范围;在三向近断层地震动输入下,与仅考虑水平双向地震动输入下的桥梁地震反应相比,竖向地震动对主梁竖向弯矩响应的影响较大,特别是主墩和主梁的交界处,增大比例可达2倍及以上。就文章选取的4座桥梁算例,不考虑断层走向和桥梁纵桥向的夹角则存在低估桥梁地震反应的可能,低估误差在15%～40%左右。     

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.     

Non‐structure‐specific intensity measure parameters and characteristic period of near‐fault ground motions

This paper focuses on the effects of long‐period pulse of near‐fault ground motions on the structural damage potential. Two sets of near‐fault ground motion records from Chi‐Chi, Taiwan earthquake and Northridge earthquake with and without distinct pulse are selected as the input, and the correlation analysis between 30 non‐structure‐specific intensity measure parameters and maximum inelastic displacements and energy responses (input energy and hysteretic energy) of bilinear single degree of freedom systems are conducted. Based on the frequency characteristic of near‐fault ground motions with remarkable long‐period components, two intensity indices are proposed, namely, the improved effective peak acceleration (IEPA) and improved effective peak velocity (IEPV). In addition a new characteristic period of these ground motions is defined based on IEPA and IEPV. Numerical results illustrate that the intensity measure parameters related to ground acceleration present the best correlation with the seismic responses for rigid systems; the velocity‐related and displacement‐related parameters are better for medium‐frequency systems and flexible systems, respectively. The correlation curves of near‐fault ground motions with velocity pulse differ from those of ground motions without pulse. Moreover, the improved parameters IEPA and IEPV of near‐fault impulsive ground motions enhance the performance of intensity measure of corresponding conventional parameters, i.e. EPA and EPV. The new characteristic period based on IEPA and IEPV can better reflect the frequency content of near‐fault ground motions. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimating the seismic displacement of friction pendulum isolators based on non‐linear response history analysis

A procedure for developing equations that estimate the isolator displacement due to strong ground motion is applied to buildings isolated with the friction pendulum system. The resulting design equations, based on rigorous non‐linear analysis, offer an alternative to the iterative equivalent‐linear methods used by current U.S. building codes. The governing equations of the system are reduced to a form such that the median normalized displacement of the system due to an ensemble of ground motions is found to depend on only the isolation period—a function of the curvature of the isolator—and the friction force at incipient slip normalized by peak ground velocity. The normalization is effective in minimizing the dispersion of the normalized displacement for an ensemble of ground motions, implying that the median normalized displacement is a reliable estimate of response. The design equations reflect the significant (20 to 38%) increase in displacement when the excitation includes two lateral components of ground motion instead of just one component. Equivalent‐linear methods are shown to underestimate by up to 30% the exact median displacement determined by non‐linear response history analysis for one component of ground motion, and building codes include at most a 4.4% increase for a second component. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of equivalent lateral force procedure in estimating seismic isolator displacements

Simplified methods of analysis described in codes and specifications for seismically isolated structures are always used either directly in special cases or for checking the results of nonlinear response history analysis (RHA). In this study, the maximum isolator displacements and base shears determined by nonlinear RHA are compared with those determined by the equivalent lateral force (ELF) procedure in order to assess the accuracy of the simplified method in the case of earthquakes with near field characteristics. Features of this study are that the ground motions used in analysis are selected and scaled using contemporary concepts and that the ground excitation is considered bi-directional. It is shown that the simplified method provides acceptably accurate predictions of shear isolator displacements and shear forces for a range of isolator properties and ground motions representative of stiff and soft soil conditions.     

Experimental and analytical studies of structures seismically isolated with an uplift‐restraining friction pendulum system

This paper presents findings from a comprehensive analytical and experimental study on the uplift‐restraining XY‐FP sliding isolation system. To investigate the effectiveness of the XY‐FP isolator and provide a rational basis for evaluating the efficacy of the developed mathematical model, an extensive experimental program was conducted on the earthquake simulator at the University at Buffalo. The experimental program involved a slender, five‐storey, scale‐model frame seismically isolated with four XY‐FP isolators subjected to simulations of historical horizontal and vertical ground motions. The experimental response demonstrates the validity of the concept and provides evidence for the effectiveness of the XY‐FP isolator in preventing uplift. A comprehensive analytical model capable of emulating the mechanical behaviour of the XY‐FP isolator is developed and implemented in program 3D‐BASIS‐ME. The newly enhanced program is used to predict the dynamic response of the seismically‐isolated model structure. Comparison of analytical predictions with experimental results attests to the efficacy of the analytical model for simulating the response of the XY‐FP isolator. With its appealing conceptual simplicity and its proven effectiveness, the new uplift‐restraining isolator has the potential to facilitate the application of seismic isolation even under the most extreme of conditions, including but not limited to near‐fault strong ground motions and uplift‐prone structural systems. Copyright © 2005 John Wiley & Sons, Ltd.     

A stochastic model and synthesis for near‐fault impulsive ground motions

The orientations of ground motions are paramount when the pulse‐like motions and their unfavorable seismic responses are considered. This paper addresses the stochastic modeling and synthesizing of near‐fault impulsive ground motions with forward directivity effect taking the orientation of the strongest pulses into account. First, a statistical parametric analysis of velocity time histories in the orientation of the strongest pulse with a specified magnitude and various fault distances is performed. A new stochastic model is established consisting of a velocity pulse model with random parameters and a stochastic approach to synthesize high‐frequency velocity time history. The high‐frequency velocity history is achieved by integrating a stochastic high‐frequency accelerogram, which is generated via the modified K‐T spectrum of residual acceleration histories and then modulated by the specific envelope function. Next, the associated parameters of pulse model, envelope function, and power spectral density are estimated by the least‐square fitting. Some chosen parameters in the stochastic model of near‐fault motions based on correlation analysis are regarded as random variables, which are validated to follow the normal or lognormal distribution. Moreover, the number theoretical method is suggested to select efficiently representative points, for generating artificial near‐fault impulsive ground motions with the feature of the strongest pulse, which can be used to the seismic response and reliability analysis of critical structures conveniently. Finally, the simulated ground motions demonstrate that the synthetic ground motions generated by the proposed stochastic model can represent the impulsive characteristic of near‐fault ground motions. Copyright © 2014 John Wiley & Sons, Ltd.     

近断层地震作用下设备-结构耦合隔震体系动力响应分析

建立设备-结构耦合隔震体系模型,选取近断层脉冲型和非脉冲型地震波各50条,计算耦合隔震体系的动力响应。分析表明,近断层脉冲型地震动对耦合隔震体系的影响大于非脉冲型地震动,且对主体结构的影响大于对设备的影响;近断层脉冲型地震作用下的隔震层位移、层间位移、楼层加速度、设备加速度和设备位移的平均响应分别达到非脉冲型地震作用的2.25倍、2.17倍、2.24倍、1.17倍和1.20倍。进行设备-结构耦合隔震体系设计时,需考虑近断层地震动脉冲作用的影响,同时需注意引起主体结构和设备最大响应的地震动不一定相同。     

Theory and experimental study for sliding isolators with variable curvature

Because a conventional isolation system with constant isolation frequency is usually a long‐period dynamic system, its seismic response is likely to be amplified in earthquakes with strong long‐period wave components, such as near‐fault ground motions. Seismic isolators with variable mechanical properties may provide a promising solution to alleviate this problem. To this end, in this work sliding isolators with variable curvature (SIVC) were studied experimentally. An SIVC isolator is similar to a friction pendulum system (FPS) isolator, except that its sliding surface has variable curvature rather being spherical. As a result, the SIVC's isolation stiffness that is proportional to the curvature becomes a function of the isolator displacement. By appropriately designing the geometry of the sliding surface, the SIVC is able to possess favorable hysteretic behavior. In order to prove the applicability of the SIVC concept, several prototype SIVC isolators, whose sliding surfaces are defined by a sixth‐order polynomial function, were fabricated and tested in this study. A cyclic element test on the prototype SIVC isolators and a shaking table test on an SIVC isolated steel frame were all conducted. The results of both tests have verified that the prototype SIVC isolators do indeed have the hysteretic property of variable stiffness as prescribed by the derived formulas in this study. Moreover, it is also demonstrated that the proposed SIVC is able to effectively reduce the isolator drift in a near‐fault earthquake with strong long‐period components, as compared with that of an FPS system with the same friction coefficient. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of supplemental damping on LRB and FPS seismic isolators under near-fault ground motions

Numerical simulations are performed to assess the effects of near-fault ground motions on base-isolated buildings that consist of either lead-rubber (LRB) or friction-pendulum system (FPS) bearings in addition to supplemented viscous dampers. While LRB and FPS isolation systems have been applied for a number of years, the addition of supplemental damping devices is being currently considered for strong ground motions to reduce the isolator displacements. However, the main problem in this case is that the addition of damping may increase both internal deformation and absolute accelerations of the superstructure and thus may defeat many of the gains for which base isolation is intended. In the present paper, a detailed and systematic investigation on the performance of LRB and FPS isolation systems, provided with supplemental viscous damping under the effect of near-fault ground motions, has been carried out by using commercial finite element software.