Seismic response of base-isolated structures with vertical-rocking coupling

A base-isolated building is liable to have a small horizontal eccentricity between the centre of mass of the superstructure and the centre of rigidity of the supporting bearings. In seismic analysis, the structure is modelled as a rigid block with tributary masses supported on massless elastomeric rubber bearings placed at a constant elevation below the centre of mass. This simplified system has three degrees of freedom: two translations and one rotation in the vertical plane. The investigation of the dynamic behaviour of a base-isolated building is carried out for both the detuned and the perfectly tuned cases. In the detuned case, the natural frequencies of the system are assumed to be well separated. In the perfectly tuned case, the uncoupled rocking frequency is assumed to be identical to the vertical translational frequency, which may result from an unusual mass distribution and/or an extreme aspect ratio of the superstructure. Perturbation methods are implemented in finding the dynamic characteristics for both cases. However, the dynamic response of the perfectly tuned case is the major concern in this investigation. The Green's functions for the displacement response of the three-degree-of-freedom system are derived for both the undamped and damped conditions. The response spectrum modal superposition method is used in estimating the maximum acceleration response. A simple method, accounting for the effect of closely spaced modes, is proposed for combining modal maxima and results in an approximate solution corresponding to a single-degree-of-freedom system. This approximate solution may be used for the preliminary design of a base-isolated structure. Numerical results for a base-isolated building subjected to the vertical component of the El Centro earthquake of 1940 were carried out for comparison with these analytical results. The proposed modal combination method showed superiority over the conventional Square Root of the Sum of the Squares method in estimating maximum responses. The results also indicated that the approximate single-degree-of-freedom system yields accurate estimations. It is shown that the effect of rocking coupling on the vertical response of base-isolated structures subjected to transient loadings, such as earthquake motions, can generally be neglected as a result of the combined effects of the time lag between the maximum translational and rotational responses and the influence of damping in the isolation system, which for elastomeric bearings can be as high as 8 to 10 per cent of critical.     

AN ANALYTICAL HYSTERESIS MODEL FOR ELASTOMERIC SEISMIC ISOLATION BEARINGS

For the purpose of accurately predicting the seismic response of base-isolated structures, an analytical hysteresis model for elastomeric seismic isolation bearings is proposed. An extensive series of experimental tests of four types of seismic isolation bearings—two types of high-damping rubber bearings, one type of lead-rubber bearing and one type of silicon rubber bearing—was carried out with the objective of fully identifying their mechanical characteristics. The proposed model is capable of well-predicting the mechanical properties of each type of elastomeric bearing into the large strain range. Earthquake simulator tests were also conducted after the loading tests of the individual bearings. In order to show the validity of the proposed model, non-linear dynamic analyses were conducted to simulate the earthquake simulator test results. Good agreement between the experimental and analytical results shows that the model can be an effective numerical tool to predict not only the peak response value but also the force–displacement relationship of the isolators and floor response spectra for isolated structures. © 1997 by 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.     

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.     

组合基础隔震在建筑工程中的应用

隔震作为一种新的抗震技术,已广泛应用于新建和加固的建筑工程,同时,许多新型式的支座得到了开发和应用。组合基础隔震是一种新的隔震设计思想,能充分应用不同类型隔震支座的特性,有效降低上部结构地震反应。本文介绍了组合基础隔震在某一工程中的应用,工程中使用的支座包括普通橡胶隔震支座、铅芯橡胶隔震支座和弹性滑板支座三种类型,对全部使用支座进行了常规检测,结构计算采用等效线性法、能量包络法和时程反应分析等方法,计算结果表明:组合基础隔震能有效降低上部结构的反应,隔震层的变形控制在安全范围之内。     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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 response of light internal equipment in base-isolated structures

The seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system. The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base-isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment-structure interaction need not be considered and multiple support response analysis is rendered unnecessary. Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead-rubber hysteretic bearings, having a force-displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead-rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment. The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.     

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility

The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil.However,it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper,seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom(SDOF) and multi degree-of-freedom(MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted.The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis,a large number of parametric studies for different earthquake excitations with three different peak ground acceleration(PGA) levels,different natural periods of the building models,and different shear wave velocities in the soil are considered.For the isolation system,laminated rubber bearings(LRBs) as well as high damping rubber bearings(HDRBs) are used.Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions:(1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures;(2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs;(3) although the peak response is affected by the incorporation of soil flexibility,it appears insensitive to the variation of shear wave velocity in the soil;(4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building,indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions,base isolations and shear wave velocities;(5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories,especially for earthquakes with low and moderate PGA levels;and(6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications,especially at the level of the lower stories.     

不对称大底板多塔楼隔震结构的地震响应分析

针对不对称大底板多塔楼隔震结构体系,通过建立地震响应的动力分析简化模型,推导出不对称大底板多塔楼隔震结构体系地震作用下的运动方程。对一实际的不对称大底板多塔楼隔震结构进行地震响应仿真分析,探讨塔楼质量偏心率和塔楼质量比对结构周期比、位移比和层剪力比的影响。结果显示,不对称大底板多塔楼隔震结构扭转角主要由隔震层产生;与不隔震结构相比,不对称大底板多塔楼隔震体系的扭转角减小,可取得较好的减震效果;塔楼与底板的位置分布和质量分布会影响体系的扭转效应和减震效果,应尽量使塔楼的质心与底板质心重合,塔楼质量分布均匀,以减小结构的扭转效应,提高减震效果。     

Pseudodynamic tests on rubber base isolators with numerical substructuring of the superstructure and strain‐rate effect compensation

A pseudodynamic testing procedure has been applied by which the seismic response of a base‐isolated building is obtained by using as specimen the isolators, while the superstructure is numerically simulated. The procedure also takes advantage of the continuous pseudodynamic testing capabilities of the ELSA laboratory, which increase the accuracy of the results and reduce the strain‐rate effect of the rubber bearings. A simple proportional correction of the measured forces compensates the remaining strain‐rate effect due to the unrealistic speed of the test. The correction factor is obtained by means of a characterizing test on the specific rubber isolators. The developed method has been successfully applied to the prediction of the seismic response of a base‐isolated four‐storey building submitted to several specified accelerograms. The results for those earthquakes as well as the effects of some changes of the parameters of the system are discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

近断层地震动破裂向前方向性与滑冲效应对隔震建筑结构抗震性能的影响

选择台湾集集地震和美国北岭地震的近断层地震动记录作为输入,考察了近断层地震动破裂向前方向性与滑冲效应引起的两种不同速度脉冲运动对单自由度体系和长周期橡胶支座隔震建筑结构抗震性能的影响.反应谱分析表明,破裂向前方向性与滑冲效应对工程结构地震响应的影响是随结构周期变化的.在中短周期段,含破裂向前方向性效应地震动的谱加速度值大于含滑冲效应地震动的谱加速度值;而在长周期段,含滑冲效应地震动的谱加速度大于含破裂向前方向性效应的谱加速度值.并且,与无脉冲地震动作用相比,含破裂向前方向性与滑冲效应脉冲的近断层地震动作用下隔震建筑的地震响应显著增大.滑冲效应引起的速度脉冲使隔震建筑底部的层间变形和楼层剪力明显增大,这意味着滑冲效应脉冲比向前方向性效应脉冲对长周期建筑结构的破坏更具危害性.     

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.     

Finite‐element analysis of laminated rubber bearing of building frame under seismic excitation

Finite element analysis is carried out for a building frame supported by laminated rubber bearings to simultaneously investigate global displacement and local stress responses under seismic excitation. The frame members and the rubber bearings are discretized into hexahedral solid elements with more than 3 million degrees of freedom. The material property of rubber is represented by the Ogden model, and the frame is assumed to remain in elastic range. It is shown that the time histories of non‐uniform stress distribution and rocking behavior of the rubber bearings under a frame subjected to seismic excitation can be successfully evaluated, and detailed responses of base and frame can be evaluated through large‐scale finite element analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Sensitivity analysis of carbon fiber-reinforced elastomeric isolators based on experimental tests and finite element simulations

Conventional steel-based rubber bearings are being replaced by fiber reinforced elastomeric isolators (FREI) due to their high weight and manufacturing cost. Compared to existing rubber bearings, FREIs have superior performance and as a result can control the seismic response of structures more efficiently. This study aims to simulate the performance of rectangular carbon FREIs (C-FREIs) produced through a simple and cost-effective manufacturing process. Additionally, the effect of different factors including the number and the thickness of rubber layers, as well as the thickness of carbon fiber reinforced sheets are investigated on the performance of C-FREIs through sensitivity analyses based on the results obtained from finite element simulations. The results show that by increasing the number and thickness of rubber layers, the efficiency of C-FREIs degrades in terms of vertical strength and damping capacity, however, the performance improves in terms of lateral flexibility. Another important observation is that the increasing thickness of fiber-reinforced layers can increase the vertical rigidity of the base isolator. The vertical stiffness has the most sensitivity to the thickness of elastomeric layers and the thickness of CFR sheets while, when the number of rubber layers increases, the effective lateral stiffness is mostly affected.     

Dynamic parameter identification for non-linear isolation systems in response spectrum analysis

The response spectrum method has been widely used in earthquake engineering design, but cannot be directly applied to non-linear systems such as the lead-filled rubber bearing used in base isolation systems. An appraoch to determine the equivalent linearized stiffness and damping coefficient of the lead-filled rubber bearing by use of the results of shaking table tests is developed. Comparisons of time histories for the equivalent linear systems and the actual model show the method gives accurate maxima for displacement and acceleration and at the appropriate times. It is found that the identified parameters vary with the maximum deformation and the simplified formulae that can optimally describe the variations are derived. Using these formulae, an iterative algorithm using the response spectrum method to calculate the dynamic response of buildings isolated by lead-filled rubber bearings is also presented.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental Investigations on Laminated Rubber Bearings

Increasing application of base isolation as a seismic protection method has subsequently increased its analytical and experimental studies. Being the most critical part of the base isolated buildings, accurate evaluation of structural properties and precise modeling of isolation devices is of utmost importance in predicting the response of the buildings during the earthquakes. This technical note is concerned with experimental study on laminated rubber bearings. Free vibration and harmonic base excitation tests are performed on a three-storey building model to evaluate the properties of the structure, efficiency of the system, and effect of base excitations. It is found that these experimental methods can effectively be used for this purpose.