Spherical sliding isolation bearings with adaptive behavior: Theory

The principles of operation and force–displacement relationships of three novel spherical sliding isolation bearings are developed in this paper. These bearings are completely passive devices, yet exhibit adaptive stiffness and adaptive damping. That is, the stiffness and damping change to predictable values at calculable and controllable displacement amplitudes. The primary benefit of adaptive behavior is that a given isolation system can be separately optimized for multiple performance objectives and/or multiple levels of ground shaking. With the devices presented here, this is accomplished using technology that is inherently no more complex than what is currently used by the civil engineering profession. The internal construction consists of various concave surfaces and behavior is dictated by the different combinations of surfaces upon which sliding can occur over the course of motion. As the surfaces upon which sliding occurs change, the stiffness and effective friction change accordingly. A methodology is presented for determining which surfaces are active at any given time based on the effective radius of curvature, coefficient of friction and displacement capacity of each sliding surface. The force–displacement relationships and relevant parameters of interest are subsequently derived based on the first principles. Copyright © 2007 John Wiley & Sons, Ltd.     

Behaviour of the double concave Friction Pendulum bearing

The double concave Friction Pendulum (DCFP) bearing is an adaptation of the well‐known single concave Friction Pendulum bearing. The principal benefit of the DCFP bearing is its capacity to accommodate substantially larger displacements compared to a traditional FP bearing of identical plan dimensions. Moreover, there is the capability to use sliding surfaces with varying radii of curvature and coefficients of friction, offering the designer greater flexibility to optimize performance. This paper describes the principles of operation of the bearing and presents the development of the force–displacement relationship based on considerations of equilibrium. The theoretical force–displacement relationship is then verified through characterization testing of bearings with sliding surfaces having the same and then different radii of curvature and coefficients of friction. Lastly, some practical considerations for analysis and design of DCFP bearings are presented. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental study of the effect of restraining rim design on the extreme behavior of pendulum sliding bearings

While the performance of sliding isolators has been extensively validated under typical levels of ground motion, there have been very few experimental studies on the extreme behavior of sliding isolation bearings when the displacement limit is reached. However, to appropriately design isolated systems, from selecting the displacement capacity of the bearing to sizing the superstructure members, the behavior of the bearing as it reaches, and in some cases exceeds, the displacement limit should be well understood. A series of shake table tests to investigate the extreme behavior of double pendulum sliding bearings under strong ground motions were conducted at McMaster University. One major difference in sliding bearings around the world is how the motion of the bearing is restrained at the bearing's displacement capacity. Scaled bearings with four different types of restraining rim designs were included, representing typical sliding restraining rims found in Europe, Japan, and the United States. Experimental observation shows that the restraining rim has a significant influence on the extreme behavior of sliding isolation bearing. Key response parameters such as impact force and uplift are evaluated and compared between the different sliding bearing designs. While the bearing with no rim bearing imparts the lowest forces to the superstructure, it loses its functionality at a lower amplitude input than all the other rim types. For the other rim designs, the impact forces are significantly higher but they remained operational although damaged.     

Experimental and analytical study of the bi‐directional behavior of the triple friction pendulum isolator

This paper presents a non‐linear, kinematic model for triple friction pendulum isolation bearings. The model, which incorporates coupled plasticity and circular restraining surfaces for all sliding surfaces, is capable of capturing bi‐directional behavior and is able to explicitly track the movement of each internal component. The model is general so that no conditions regarding bearing properties, which effect the sequence of sliding stages, are required for the validity of the model. Controlled‐displacement and seismic‐input experiments were conducted using the shake table at the University of California, Berkeley to assess the fidelity of the proposed model under bi‐directional motion. Comparison of the experimental data with the corresponding results of the kinematic model shows good agreement. Additionally, experiments showed that the performance of TFP bearings is reliable over many motions, and the behavior is repeatable even when initial slider offsets are present. Copyright © 2011 John Wiley & Sons, Ltd.     

The existence of ‘complete similarities’ in the response of seismic isolated structures subjected to pulse‐like ground motions and their implications in analysis

In this paper the seismic response of isolated structures supported on bearings with bilinear and trilinear behavior is revisited with dimensional analysis in an effort to better understand the relative significance of the various parameters that control the mechanical behavior of isolation systems. An isolation system that consists of lead rubber bearings or of single concave spherical sliding bearings exhibits bilinear behavior; whereas, when a double concave configuration is used the behavior is trilinear. For the case of bilinear behavior it is well known that the value of the normalized yield displacement is immaterial to the response of the isolated superstructure—or, in mathematical terms, that the response of the bilinear oscillator exhibits complete similarity in the dimensionless yield displacement. Similarly, for the case of trilinear behavior the paper shows that the presence of the intermediate slope is immaterial to the peak response of most isolated structures—a finding that shows the response of the trilinear oscillator exhibits a complete similarity in the difference between the coefficients of friction along the two sliding surfaces as well as in the ratio of the intermediate to the final slope. This finding implies that even when the coefficients of friction of the two sliding surfaces are different, the response of isolated structures for most practical configurations can be computed with confidence by replacing the double concave spherical bearings with single concave spherical bearings with an effective radius of curvature and an effective coefficient of friction. Copyright © 2010 John Wiley & Sons, Ltd.     

A model of triple friction pendulum bearing for general geometric and frictional parameters

Current models describing the behavior for the triple friction pendulum (TFP) bearing are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply as a direct consequence of equilibrium. This paper presents a revised model of behavior of the TFP bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact. To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces. Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior. The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity and temperature can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made. This paper presents (a) the development of the revised TFP bearing model, (b) the analytic solution for the force–displacement relations of two configurations of the TFP bearing, (c) a model that incorporates inertia effects of the TFP bearing components and other effects that are useful in advanced response history analysis, and (d) examples of implementation of the features of the presented model. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid simulation of a multi‐span RC viaduct with plain bars and sliding bearings

This paper deals with the seismic response assessment of an old reinforced concrete viaduct and the effectiveness of friction‐based retrofitting systems. Emphasis was laid on an old bridge, not properly designed to resist seismic action, consisting of 12 portal piers that support a 13‐span bay deck for each independent roadway. On the basis of an OpenSEES finite element frame pier model, calibrated in a previous experimental campaign with cyclic displacement on three 1:4 scale frame piers, a more complex experimental activity using hybrid simulation has been devised. The aim of the simulation was twofold: (i) to increase knowledge of non‐linear behavior of reinforced concrete frame piers with plain steel rebars and detailing dating from the late 1950s; and (ii) to study the effectiveness of sliding bearings for seismic response mitigation. Hence, to explore the performance of the as built bridge layout and also of the viaduct retrofitted with friction‐based devices, at both serviceability and ultimate limit state conditions, hybrid simulation tests were carried out. In particular, two frame piers were experimentally controlled with eight‐actuator channels in the as built case while two frame piers and eight sliding bearings were controlled with 18‐actuator channels in the isolated case. The remaining frame piers were part of numerical substructures and were updated offline to accurately track damage evolution. Copyright © 2015 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.     

Frictional Behavior of Steel-PTFE Interfaces for Seismic Isolation

The widespread use of sliding bearings for the seismic isolation of structures requires detailed knowledge of their behavior and improved modeling capability under seismic conditions. The paper summarizes the results of a large experimental investigation on steel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure, air temperature and state of lubrication on the mechanical behavior of steel-PTFE sliding bearings. Based on the experimental outcomes, two different mathematical models have been calibrated, which are capable of accounting for the investigated parameters in the evaluation of the sliding friction coefficient. The first model is basically an extension of the model proposed by Constantinou et al. (1990)Journal of Earthquake Engineering, 116(2), 455–472, while the second model is derived from the one proposed by Changet al. (1990)Journal of Engineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a function of bearing pressure and air temperature are presented for lubricated and non-lubricated sliding surfaces. Predicted and experimental results are finally compared.     

Further results on the heating of single and multi-core lead-rubber bearings and dampers

Single-core and to a certain extent multi-core lead-rubber bearings have been extensively used in seismic isolation. Yet their behavior is not well understood and experimentation is required to obtain their mechanical properties. A recently developed and validated theory contributed to the understanding of the effects of heating of the lead core on the characteristic strength and ability to dissipate energy of these bearings. Additional results on the theory of heating of lead-rubber bearings are presented in this paper, including readily useable data on the rise of temperature in the steel shim and end plates of these bearings. The results may be used in the assessment of the validity of the theory of lead core heating in single and multi-core lead-rubber bearings and in recently developed multi-core lead-rubber dampers. Examples are presented (including some experimental data) to illustrate the application of the theory. The utility of the presented theory is to reduce the requirements for physical testing of lead-rubber bearings and dampers.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Seismic performance of cable-sliding friction bearing system for isolated bridges

During past strong earthquakes, highway bridges have sustained severe damage or even collapse due to excessive displacements and/or very large lateral forces. For commonly used isolation bearings with a pure friction sliding surface, seismic forces may be reduced but displacements are often unconstrained. In this paper, an alternative seismic bearing system, called the cable-sliding friction bearing system, is developed by integrating seismic isolation devices with displacement restrainers consisting of cables attached to the upper and lower plates of the bearing. Restoring forces are provided to limit the displacements of the sliding component. Design parameters including the length and stiffness of the cables, friction coefficient, strength of the shear bolt in a fixed-type bearing, and movements under earthquake excitations are discussed. Laboratory testing of a prototype bearing subjected to vertical loads and quasi-static cyclic lateral loads, and corresponding numerical finite element simulation analysis, were carried out. It is shown that the numerical simulation shows good agreement with the experimental force-displacement hysteretic response, indicating the viability of the new bearing system. In addition, practical application of this bearing system to a multi-span bridge in China and its design advantages are discussed.     

Multiple‐slider surfaces bearing for seismic retrofitting of frame structures with soft first stories

A new isolation interface is proposed in this study to retrofit existing buildings with inadequate soft stories as well as new structures to be constructed with soft first story intended for architectural or functional purposes. The seismic interface is an assembly of bearings set in parallel on the top of the first story columns: the multiple‐slider bearings and rubber bearings. The multiple‐slider bearing is a simple sliding device consisting of one horizontal and two inclined plane sliding surfaces based on polytetrafluoroethylene and highly polished stainless steel interface at both ends set in series. A numerical example of a five‐story reinforced concrete shear frame with soft first story is considered and analyzed to demonstrate the efficiency of the proposed isolation system in reducing the ductility demand and damage in the structure while maintaining the superstructure above the bearings to behave nearly in the elastic range with controlled bearing displacement. Comparative study with the conventional system as well as various isolation systems such as rubber bearing interface and resilient sliding isolation is carried out. Moreover, an optimum design procedure for the multiple‐slider bearing is proposed through the trade‐off between the maximum bearing displacement and the first story ductility demand ratio. The results of extensive numerical analysis verify the effectiveness of the multiple‐slider bearing in minimizing the damage from earthquake and protecting the soft first story from excessively large ductility demand. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

弹性滑移支座力学性能的试验研究

介绍了弹性滑移支座的原理、构造和特点;通过对其在不同工况下的性能试验,研究了竖向荷载、位移幅值以及加载频率对弹性滑移支座力学性能的影响,并给出了试验值与理论计算值之间的对比。研究结果表明：弹性滑移支座具有良好的工作性能,滞回曲线饱满,耗能能力强;竖向荷载和加载频率对弹性滑移支座的力学性能有一定的影响,而位移幅值对其影响较小;弹性滑移支座的恢复力模型,可以用考虑速度的指数摩擦力模型来描述,并且模拟得较为准确。     

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。     

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.     

Extreme behavior in a triple friction pendulum isolated frame

While isolation can provide significantly enhanced performance compared to fixed‐base counter parts in design level or even maximum considered level earthquakes, there is still uncertainty over the performance of isolation systems in extreme events. Researchers have looked at component level stability of rubber bearings and on the effect of moat impact on behavior of structures isolated on general bilinear isolators. However, testing of triple friction pendulum (TFP) sliding bearings has not been done dynamically or incorporated into a building system. Here, one‐third scale laboratory tests were conducted to on a 2‐story 2‐bay TFP‐isolated structure. Input motions were increasingly scaled until failure occurred at the isolation level. As the superstructure was designed with a yield force equivalent to the force of the bearing just at their ultimate displacement capacity, there was minimal yielding. A numerical model is presented to simulate the isolated building up to and including bearing failure. Forces transferred to the superstructure in extreme motions are examined using both experimental and numerical data. Additionally, the effect of the hardening stage of the TFP bearing is evaluated using the numerical model, finding slight benefits.     

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.