Coupling behavior of shear deformation and end rotation of elastomeric seismic isolation bearings

This paper presents a mechanical model for predicting the behavior of elastomeric seismic isolation bearings subject to combined end rotations and shear deformation. The mechanical model consists of a series of axial springs at the top, mid‐height and bottom of the bearing to vertically reproduce asymmetric bending moment distribution in the bearings. The model can take into account end rotations of the bearing, and the overall rotational stiffness includes the effect of the variation of vertical load on the bearing and the imposed shear deformation. Static bending tests under various combinations of vertical load and shear deformation were performed to identify the mechanical characteristics of bearings. The test results indicate that bearing rotational stiffness increases with increasing vertical load but decreases with increasing shear deformation. Simulation analyses were conducted to validate the new mechanical model. The results of analyses using the new model show very good agreement with experimental observations. A series of seismic response analyses were performed to demonstrate the dynamic behavior of top‐of‐column isolated structures, a configuration where the end rotations of isolation bearings are typically expected to be larger. The results suggest that the end rotations of elastomeric bearings used in practical top‐of‐column isolated structures do not reduce the stability limit of isolation system. Copyright © 2016 John Wiley & Sons, Ltd.     

A mathematical hysteretic model for elastomeric isolation bearings

An analytical model for high damping elastomeric isolation bearings is presented in this paper. The model is used to describe mathematically the damping force and restoring force of the rubber material and bearing. Ten parameters to be identified from cyclic loading tests are included in the model. The sensitivity of the ten parameters in affecting the model is examined. These ten parameters are functions of a number of influence factors on the elastomer such as the rubber compound, Mullins effect, scragging effect, frequency, temperature and axial load. In this study, however, only the Mullins effect, scragging effect, frequency and temperature are investigated. Both material tests and shaking table tests were performed to validate the proposed model. Based on the comparison between the experimental and the analytical results, it is found that the proposed analytical model is capable of predicting the shear force–displacement hysteresis very accurately for both rubber material and bearing under cyclic loading reversals. The seismic response time histories of the bearing can also be captured, using the proposed analytical model, with a practically acceptable precision. Copyright © 2002 John Wiley & Sons, Ltd.     

Improved numerical analysis for ultimate behavior of elastomeric seismic isolation bearings

Elastomeric isolation bearings consist of multiple rubber layers with their top and bottom surfaces bonded to steel plates to restrict compressive deformation. Deformation constraints result in a variation of elastic modulus over the cross section of the rubber layers. In this paper, we describe a normalized compression modulus distribution on a circular rubber pad. The compressive and bending moduli of the rubber pad can be reproduced by applying the distribution to a series of axial springs. We also present a mechanical model for predicting the behavior of elastomeric seismic isolation bearings subject to large shear deformation and high compressive load. The mechanical model consists of a series of multiple shear springs at midheight and a series of axial springs at the top and bottom interfaces of the bearing. Simulation analyses of bearing tests were conducted to validate the proposed model. The analyses demonstrated that a model for circular lead-rubber bearings can successfully capture the influence of the axial load magnitude on the bearing shear behavior. The new model can simulate much more realistic behavior than prior models based on a uniform modulus assumption.     

A mechanical model for elastomeric seismic isolation bearings including the influence of axial load

For the purpose of predicting the large‐displacement response of seismically isolated buildings, an analytical model for elastomeric isolation bearings is proposed. The model comprises shear and axial springs and a series of axial springs at the top and bottom boundaries. The properties of elastomeric bearings vary with the imposed vertical load. At large shear deformations, elastomeric bearings exhibit stiffening behavior under low axial stress and buckling under high axial stress. These properties depend on the interaction between the shear and axial forces. The proposed model includes interaction between shear and axial forces, nonlinear hysteresis, and dependence on axial stress. To confirm the validity of the model, analyses are performed for actual static loading tests of lead–rubber isolation bearings. The results of analyses using the new model show very good agreement with the experimental results. Seismic response analyses with the new model are also conducted to demonstrate the behavior of isolated buildings under severe earthquake excitations. The results obtained from the analyses with the new model differ in some cases from those given by existing models. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of the seismic response of high‐rise buildings supported on tension‐resistant elastomeric isolation bearings

In many applications of seismic isolation, such as in high‐rise construction, lightweight construction, and structures with large height‐to‐width aspect ratios, significant tension forces can develop in bearings, raising concerns about the possible rupture of elastomeric bearings and the uplift of sliding bearings. In this paper, a novel tension‐resistant lead plug rubber bearing (TLRB) with improved tension‐resisting capabilities is developed and experimentally and numerically assessed. This TLRB consists of a common lead plug rubber bearing (LRB) and several helical springs. After describing the theory underlying the behavior of the TLRB, the mechanical properties of reduced‐scale prototype bearings are investigated through extensive horizontal and vertical loading tests. The test results indicate that TLRBs can improve the shear stiffness and tension resistance capacity even under significant tensile loads. A series of shaking table tests on scaled models of high‐rise buildings with different aspect ratios were conducted to investigate the dynamic performance of the TLRB and the seismic responses of base‐isolated high‐rise buildings. Three different cases were considered in the shaking table tests: a fixed base condition and the use of TLRB and LRB isolation systems. The results of the shaking table test show that (a) base‐isolated systems are effective in reducing the structural responses of high‐rise buildings; (b) an isolated structure's aspect ratio is an important factor influencing its dynamic response; (c) TLRBs can endure large tensile stresses and avoid rupture on rubber bearings under strong earthquakes; and (d) the experimental and numerical results of the responses of the models show good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental and analytical studies on the performance of hybrid isolation systems

This paper presents experimental and analytical results on the seismic response of a rigid structure supported on isolation systems that consist of either lead rubber or sliding bearings. Shake table tests are conducted with various levels of isolation damping that is provided from the bearings and supplemental viscous fluid dampers. The table motions originated from recorded strong ground motions that have been compressed to the extent that the mass of the model structure corresponds to the mass of a typical freeway overcrossing. Experimental data are used to validate mechanical idealizations and numerical procedures. The study concludes that supplemental damping is most effective in suppressing displacements of rigid structures with moderately long isolation periods (T_I≤3 sec) without affecting base shears. Friction damping is most effective in suppressing displacement amplifications triggered by long duration pulses—in particular, pulses that have duration close to the isolation period. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparison of fundamental properties of new types of fiber‐mesh‐reinforced seismic isolators with conventional isolators

New types of fiber‐reinforced rubber‐based seismic isolators have been a research interest for a number of engineers in the past decade. These new types of isolators can have similar seismic performances compared with the conventional ones. In most of the previous researches, the fiber‐reinforced rubber‐based isolators is usually manufactured with placing fiber sheets between precut rubber layers with the use of a bonding agent. This research differs from the previous researches in terms of manufacturing process, use of fiber mesh instead of fiber sheets, and use of lead in the core for some of the bearings. The aim of this research is to provide comparisons in fundamental seismic response properties of the new type of fiber mesh reinforced isolators and conventional isolators. In this scope, four pairs of fiber mesh reinforced elastomeric bearings and four pairs of steel‐reinforced elastomeric bearings are subjected to various levels of compression stresses and cyclic shear strains under constant vertical pressure. The tested types of isolators are fiber mesh reinforced elastomeric bearing, fiber mesh reinforced elastomeric bearing with lead core, steel‐reinforced elastomeric bearings, and steel‐reinforced elastomeric bearings with lead core. In this research, steel‐reinforced bearings are called conventional isolators. The major advantage for fiber mesh reinforced bearings observed during the tests is that these isolators can develop a considerable low horizontal stiffness compared with the conventional isolators. The damping characteristics of the new and conventional types are similar to each other. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic performance of highway bridges with fusing bearing components for quasi‐isolation

Modern highway bridges in Illinois are often installed with economical elastomeric bearings that allow for thermal movement of the superstructure, and steel fixed bearings and transverse retainers that prevent excessive movement from service‐level loadings. In the event of an earthquake, the bearing system has the potential to provide a quasi‐isolated response where failure of sacrificial elements and sliding of the bearings can cause a period elongation and reduce or cap the force demands on the substructure. A computational model that has been calibrated for the expected nonlinear behaviors is used to carry out a parametric study to evaluate quasi‐isolated bridge behavior. The study investigates different superstructure types, substructure types, substructure heights, foundation types, and elastomeric bearing types. Overall, only a few bridge variants were noted to unseat for design‐level seismic input in the New Madrid Seismic Zone, indicating that most structures in Illinois would not experience severe damage during their typical design life. However, Type II bearing systems, which consist of an elastomeric bearing and a flat PTFE slider, would in some cases result in critical damage from unseating at moderate and high seismic input. The sequence of damage for many bridge cases indicates yielding of piers at low‐level seismic input. This is caused by the high strength of the fixed bearing element, which justifies further calibration of the quasi‐isolation design approach. Finally, the type of ground motion, pier height, and bearing type were noted to have significant influence on the global bridge response. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of mechanical degradation of laminated elastomeric bearings and shear keys upon seismic behaviors of small-to-medium-span highway bridges in transverse direction

Laminated elastomeric bearings have been widely used for small-to-medium-span highway bridges in China, in which concrete shear keys are set transversely to prohibit large girder displacement. To evaluate bridge seismic responses more accurately, proper analytical models of bearings and shear keys should be developed. Based on a series of cyclic loading experiments and analyses, rational analytical models of laminated elastomeric bearings and shear keys, which can consider mechanical degradation, were developed. The effect of the mechanical degradation was investigated by examining the seismic response of a small-to-medium-span bridge in the transverse direction under a wide range of peak ground accelerations (PGA). The damage mechanism for small-to-medium-span highway bridges was determined, which can explain the seismic damage investigation during earthquakes in recent years. The experimental results show that the mechanical properties of laminated elastomeric bearings will degrade due to friction sliding, but the degree of decrease is dependent upon the influencing parameters. It can be concluded that the mechanical degradation of laminated elastomeric bearings and shear keys play an important role in the seismic response of bridges. The degradation of mechanical properties of laminated elastomeric bearings and shear keys should be included to evaluate more precise bridge seismic performance.     

An advanced numerical model of elastomeric seismic isolation bearings

The nuclear accident at Fukushima Daiichi in March 2011 has led the nuclear community to consider seismic isolation for new large light water and small modular reactors to withstand the effects of beyond design basis loadings, including extreme earthquakes. The United States Nuclear Regulatory Commission is sponsoring a research project that will quantify the response of low damping rubber (LDR) and lead rubber (LR) bearings under loadings associated with extreme earthquakes. Under design basis loadings, the response of an elastomeric bearing is not expected to deviate from well‐established numerical models, and bearings are not expected to experience net tension. However, under extended or beyond design basis shaking, elastomer shear strains may exceed 300% in regions of high seismic hazard, bearings may experience net tension, the compression and tension stiffness will be affected by isolator lateral displacement, and the properties of the lead core in LR bearings will degrade in the short‐term because of substantial energy dissipation. New mathematical models of LDR and LR bearings are presented for the analysis of base isolated structures under design and beyond design basis shaking, explicitly considering both the effects of lateral displacement and cyclic vertical and horizontal loading. These mathematical models extend the available formulations in shear and compression. Phenomenological models are presented to describe the behavior of elastomeric isolation bearings in tension, including the cavitation and post‐cavitation behavior. The elastic mechanical properties make use of the two‐spring model. Strength degradation of LR bearing under cyclic shear loading due to heating of lead core is incorporated. The bilinear area reduction method is used to include variation of critical buckling load capacity with lateral displacement. The numerical models are coded in OpenSees, and the results of numerical analysis are compared with test data. The effect of different parameters on the response is investigated through a series of analyses. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic response of torsionally coupled base isolated structures

An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent.     

Coupled horizontal–vertical stability of bearings under dynamic loading

In this study, the coupled horizontal–vertical behavior of elastomeric bearings subjected to dynamic loading is studied in detail. Under extreme dynamic loading, elastomeric bearings exhibit unstable behavior and an instantaneous loss of horizontal stiffness that is recoverable. Building on an earlier study where the authors developed an analytical model for the horizontal behavior of bearings under dynamic loads, in this study, a new analytical model for the coupled horizontal–vertical behavior of the bearings is developed. The coupled behavior of the bearing is first studied for quasi‐static loading, and later, the behavior of the bearings under dynamic loading is studied. A clear distinction is made between different types of deformation the bearing undergoes in the vertical direction. Based on experimental results, it is observed that the behavior of the bearings under dynamic loading differs markedly from that observed under static loading. A new analytical model is proposed that can account for the coupled horizontal–vertical behavior of the bearings under dynamic loading. The proposed analytical model for predicting the post‐stability vertical behavior of the bearings is verified using experimental results. The model proposed is found to successfully predict the coupled horizontal–vertical behavior of elastomeric bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic response of base isolated buildings including p-Δ effects of isolation bearings

In order to achieve a low isolation frequency, elastomeric bearings used for base isolation of buildings usually have low shear rigidity which leads to a significant reduction in the buckling load. The effects of compression load on the bearing behaviour are therefore an important consideration. A study of seismic response of base isolated buildings is presented in this paper, fully accounting for the P-Δ effects of isolation bearings. An analytical procedure is formulated that treats separately the superstructure and the supporting bearings and assembles the governing equations via the interaction forces at the base deck. The resulting equations are then solved step-by-step numerically. Numerical results obtained for a base isolated five-storey shear building show that neglecting the P-Δ effects can lead to considerable errors in the computed seismic response when the buckling safety factor of bearings is low.     

Shaking table test and analysis method on ultimate behavior of slender base‐isolated structure supported by laminated rubber bearings

This paper describes the results of shaking table tests to ascertain the ultimate behavior of slender base‐isolated buildings and proposes a time history response analysis method, which can predict the ultimate behavior of base‐isolated buildings caused by buckling fracture in laminated rubber bearings. In the tests, a base‐isolated structure model weighing 192 kN supported by four lead rubber bearings is used. The experimental parameters are the aspect ratio of height‐to‐distance between the bearings and the shape of and the axial stress on the bearings. The test results indicate that the motion types of the superstructure at large input levels can be classified into three types: the sinking type; the uplift type; and the mixed type. These behaviors depend on the relationship between the static ultimate lateral uplifting force on the superstructure and the lateral restoring characteristics of the base‐isolated story. In the analysis method, bearing characteristics are represented by a macroscopic mechanical model that is expanded by adding an axial spring to an existing model. Nonlinear spring characteristics are used for its rotational, shear, and axial spring. The central difference method is applied to solve the equation of motion. To verify the validity of the method, simulation analysis of the shaking table tests are carried out. The results of the analysis agree well with the test results. The proposed model can express the buckling behavior of bearings in the large deformation range. Copyright © 2010 John Wiley & Sons, Ltd.     

Aseismic roof isolation system: analytic and shake table studies

Presented are the features of a roof isolation system that is proposed as a device to reduce the seismic response of buildings. Presented also are the details of and results from analytical and experimental studies conducted with a small-scale laboratory model to assess the feasibility and effectiveness of such a device. The roof isolation system entails the insertion of flexible laminated rubber bearings between a building’s roof and the columns that support this roof, and the installation of viscous dampers that are connected to the roof and a structural element below the roof. It is based on the concept of a damped vibration absorber and on the idea of making the roof, rubber bearings, and viscous dampers respectively constitute the mass, spring, and dashpot of such an absorber. The model considered in the analytical and experimental studies is a 2·44-m high, five-storey, moment-resisting steel frame, with a fundamental natural frequency of 2·0 Hz. In the experimental study the frame is tested with and without the proposed roof isolation system on a pair of shaking tables under a truncated version of one of the accelerograms from the 1985 Mexico City earthquake. In the analytical study, the frame is also analysed with and without such a system and under the same ground motion except that the ground motion accelerations are properly magnified to study the effec tiveness of the roof isolation system when the frame is stressed beyond its linear range of behavior. It is found that the suggested device effectively reduces the seismic response of the frame, although the extent of this reduction depends on how large its non-linear deformations are. Based on these findings, it is concluded that the proposed roof isolation system has the potential to become a practical and effective way to reduce earthquake damage in low- and medium-rise buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

An advanced analytical model for high damping rubber bearings

Base‐isolation technologies have been developed over the years in attempts to mitigate the effects of earthquakes on structures and potentially vulnerable contents in earthquake prone areas of the world. The high damping rubber bearing (HDRB) is a relatively recent and evolving technology of this kind. The isolator shifts the fundamental period of the base‐isolated structure to a value beyond the range of the plentiful energy‐containing periods of earthquake motions and supplies significant damping to dissipate energy caused by motions. Nevertheless, the highly non‐linear mechanical behaviour of the HDRB is so complex, especially at large strains, that it is difficult to model it analytically. In this paper, an extensive study of experimental tests for identifying the mechanical characteristics of the HDRB is presented. By modifying the Wen's model to include the rate‐dependent effects, an advanced analytical model in an incremental form for the HDRB is also proposed. A very good agreement between the analytical and experimental results has been obtained. It is illustrated that the proposed mathematical model can predict well the mechanical behaviour of HDRB bearings, even at large shear strain. Copyright © 2003 John Wiley & Sons, Ltd.     

滑移摩擦隔震系统在多向地面运动作用下的试验研究

基础隔震通常只考虑隔离水平地面运动，而对竖向地面运动的影响注意不够，本文进行了滑移摩擦隔震系统的振动台房屋模型试验，研究多向地面运动输入时上部结构反应和隔震系统的性能，试验中分别对模型输入了不同方向的地震动，其中包括水平单向、水平双向、水平和竖向及三向地震动输入，对试验结果进行了分析比较，结果表明竖向地震动输入对上部结构的水平地震反应有显著影响，同时在橡胶隔震支座中产生了竖向拉力。     

Shaking table test and numerical simulation of an isolated cylindrical latticed shell under multiple-support excitations

In order to study the influence of the ground motion spatial effect on the seismic response of large span spatial structures with isolation bearings, a single-layer cylindrical latticed shell scale model with a similarity ratio of 1/10 was constructed. An earthquake simulation shaking table test on the response under multiple-support excitations was performed with the high-position seismic isolation method using high damping rubber(HDR) bearings. Small-amplitude sinusoidal waves and seismic wave records with various spectral characteristics were applied to the model. The dynamic characteristics of the model and the seismic isolation effect on it were analyzed at varying apparent wave velocities, namely infinitely great, 1000 m/s, 500 m/s and 250 m/s. Besides, numerical simulations were carried out by Matlab software. According to the comparison results, the numerical results agreed well with the experimental data. Moreover, the results showed that the latticed shell roof exhibited a translational motion as a rigid body after the installation of the HDR bearings with a much lower natural frequency, higher damping ratio and only 1/2～1/8 of the acceleration response peak values. Meanwhile, the structural responses and the bearing deformations at the output end of the seismic waves were greatly increased under multiple-support excitations.     

A modal procedure for seismic analysis of non-linear base-isolated multistorey structures

A modal procedure for non-linear analysis of multistorey structures with high-damping base-isolation systems was proposed. Two different isolation devices were considered in the analysis: an high-damping laminated rubber bearing and a lead-rubber bearing. Starting from deformational properties verified by tests, the isolation systems were characterized using three different analytical models (an Elastic Viscous, a Bilinear Hysteretic and a Wen's Model) with parameters depending from maximum lateral strain. After non-linear modelling of isolation and lateral-force-resisting systems, the effects of material non-linearities were considered as pseudo-forces applied to the equivalent linear system (Pseudo-Force Method) and the formally linearized equations of motion were uncoupled by the transformation defined by the complex mode shapes. The modal responses were finally obtained with an extension of Nigam–Jennings technique to non-linear and non-classically damped systems, in conjunction with an iterative technique searching for non-linear contributions satisfying equations of motion and constitutive laws. Since the properties of the isolated structure usually change with maximun lateral strain of isolation bearings, the integration of a new set of governing equations was required for each design-displacement value. The procedure proposed was described in detail and then applied for the determination of modal and total seismic responses in some real cases. At first, a very good agreement between non-linear responses obtained with the proposed mode superposition and with a direct integration method was observed. Then a comparison of results obtained with the three different analytical models of the isolation bearings was carried out. At last, the exact modal response obtained with analytical models depending from the design displacement of the isolation bearings was compared with two different approximated solutions, evaluated using mode shapes and isolation properties, respectively, calculated under simplified hypothesis.© 1998 John Wiley & Sons, Ltd.