Dynamics of inelastic base‐isolated structures subjected to analytical pulse ground motions

Structural design code provisions worldwide prescribe relatively small seismic force reduction factors for seismically base‐isolated structures, making their response to design‐level earthquake excitation essentially elastic. This paper uses the method of dimensional analysis to prove that; in most cases, this is not a conservative design approach but a necessity that emerges from the dynamics of base‐isolated structures. It is shown that allowing typical base‐isolated structures to yield results in large displacement ductility demands for the structure. This phenomenon is caused by the change in the nature of the ground motion excitation as it is transmitted to the structure through the seismic base isolation system as well as by the change in the distribution of displacements between the structure and the isolation bearings caused by yielding of the isolated structure. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Effect of viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Direct estimation of seismic response in reduced-degree-of-freedom isolation and energy dissipation systems

A methodology for the development of design tools for direct estimation of peak inelastic response in reduced-degree-of-freedom (RDOF) isolation and energy dissipation systems is presented. The suggested procedure is an extension of an earlier method addressing purely hysteretic isolation systems. Herein, the dynamic equation of motion is first normalised to reduce the number of design parameters that significantly affect the response. The sensitivity of normalised response quantities to the amplitude of the ground motion is then investigated through extensive parametric nonlinear dynamic analyses of isolated single-degree-of-freedom (SDOF) systems with linear viscous damping using code-based target spectra. Regression analysis is subsequently employed to develop generalised design equations (GDEs) suitable for design. Further investigations are made to address nonlinear viscous damping and the effect of the transverse component of seismic action in two-degree-of freedom (2DOF) systems under bidirectional excitation, making the procedure applicable to common bridge isolation schemes. GDEs constitute an alternative to equivalent linearisation approaches commonly adopted by codes, informing the selection among alternative isolation and energy dissipations schemes without requiring iterative analysis. The approach is incorporated in the Deformation-Based Design methodology for seismically isolated bridges in a forthcoming paper.     

Effect of variation of normal force on seismic performance of resilient sliding isolation systems in highway bridges

In this study, a series of shaking table tests are carried out on scaled models of two seismically isolated highway bridges to investigate the effect of rocking motion and vertical acceleration on seismic performance of resilient sliding isolators. In addition, performance of RSI is compared with system having solely natural rubber bearings. Test results show that variation of normal force on sliders due to rocking effect and vertical acceleration makes no significant difference in response of RSI systems. In addition, analytical response of prototype isolated bridge and the model used in experiments is obtained analytically by using non‐linear model for isolation systems. It is observed that for seismically isolated bridges, dynamic response of full‐scale complex structures can be predicted with acceptable accuracy by experiments using a simple model of the structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Base isolation for near‐fault motions

Three analytical studies of base‐isolated structures are carried out. First, six pairs of near‐fault motions oriented in directions parallel and normal to the fault were considered, and the average of the response spectra of these earthquake records was obtained. This study shows that in addition to pulse‐type displacements, these motions contain significant energy at high frequencies and that the real and pseudo‐velocity spectra are quite different. The second analysis modelled the response of a model of an isolated structure with a flexible superstructure to study the effect of isolation damping on the performance of different isolation systems under near‐fault motion. The results show that there exists a value of isolation system damping for which the superstructure acceleration for a given structural system attains a minimum value under near‐fault motion. Therefore, although increasing the bearing damping beyond a certain value may decrease the bearing displacement, it may transmit higher accelerations into the superstructure. Finally, the behaviour of four isolation systems subjected to the normal component of each of the near‐fault motions were studied, showing that EDF type isolation systems may be the optimum choice for the design of isolated structures in near‐fault locations. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimum viscous damper for connecting adjacent SDOF structures for harmonic and stationary white‐noise random excitations

The dynamic behaviour of two adjacent single‐degree‐of‐freedom (SDOF) structures connected with a viscous damper is studied under base acceleration. The base acceleration is modelled as harmonic excitation as well as stationary white‐noise random process. The governing equations of motion of the connected system are derived and solved for relative displacement and absolute acceleration responses of connected structures. The response of structures is found to be reduced by connecting with a viscous damper having appropriate damping. For undamped SDOF structures, the closed‐form expressions for optimum damping of viscous damper for minimum steady state as well as minimum mean square relative displacement and absolute acceleration of either of the connected SDOF structures are derived. The optimum damper damping is found to be functions of mass and frequency ratio of two connected structures. Further, numerical results had indicated that the damping of the connected structures does not have noticeable effects on the optimum damper damping and the corresponding optimized response. This implies that the derived closed‐form expressions for optimum damper damping of undamped structures can also be used in practical applications for damped structures. Copyright © 2006 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.     

Response spectrum analysis for non-classically damped linear system with multiple-support excitations

A new response spectrum method, which is named complex multiple-support response spectrum (CMSRS) method in this article, is developed for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-supported ground motion. The CMSRS method is based on fundamental principles of random vibration theory and properly accounts for the effect of correlation between the support motions as well as between the modal displacement and velocity responses of structure, and provides an reasonable and acceptable estimate of the peak response in term of peak seismic ground motions and response spectra at the support points and the coherency function. Meanwhile, three new cross-correlation coefficients or cross covariance especially for the non-classically damped linear structures with multiple-supports excitations are derived under the same assumptions of the MSRS method of classically damped system. The CMSRS method is examined and compared to the results of time history analyses in two numerical examples of non-classically damped structures in consideration of the coherences of spatially variable ground motion. The results show that for non-classically damped structure, the cross terms representing the cross covariance between the pseudo-static and dynamic component are also quite small just as same as classically damped system. In addition, it is found that the usual way of neglecting all the off-diagonal elements in transformed damping matrix in modal coordinates in order to make the concerned non-classically damped structure to become remaining proportional damping property will bring some errors in the case of subjected to spatially excited inhomogeneous ground motion.     

Optimal damping between two adjacent elastic structures

The optimal values for the distribution of passive dampers interconnecting two adjacent structures of different heights are determined. The dampers are selected to minimize the seismic response in the first and second modes of the taller of the two structures. For simplicity, the structures are represented as uniform damped shear beams subjected to a common ground motion. Under certain conditions, apparent damping ratios as high as 12 and 15 per cent can be achieved in the first and second modes of lightly damped structures by the introduction of interconnection dampers. The largest reduction of the response in the first mode is achieved when the taller structure is about twice the height of the second structure. © 1998 John Wiley & Sons, Ltd.     

Response of seismically isolated buildings considering poundings

Numerical simulations and parametric studies have been used to investigate the influence of potential poundings of seismically isolated buildings with adjacent structures on the effectiveness of seismic isolation. Poundings are assumed to occur at the isolation level between the seismically isolated building and the surrounding moat wall. After assessing some common force‐based impact models, a variation of the linear viscoelastic impact model is proposed to avoid tensile impact forces during detachment, while enabling the consideration of permanent plastic deformations at the vicinity of the impact. A large number of numerical simulations of seismically isolated buildings with different characteristics have been conducted under six earthquake excitations in order to investigate the influence of various design parameters and conditions on the peak floor accelerations and interstorey deflections during poundings. The numerical simulations demonstrate that poundings may substantially increase floor accelerations, especially t the base floor where impacts occur. Higher modes of vibration are excided during poundings, increasing the interstorey deflections, instead of retaining an almost rigid‐body motion of the superstructure, which is aimed with seismic isolation. Impact stiffness seems to affect significantly the acceleration response at the isolation level, while the displacement response is more insensitive to the variation of the impact stiffness. Finally, the results indicate that providing excessive flexibility at the isolation system to minimize the floor accelerations may lead to a building vulnerable to poundings, if the available seismic gap is limited. Copyright © 2007 John Wiley & Sons, Ltd.     

Response of seismically isolated structures to rocking‐type excitations

In this paper, the origin of rocking‐type excitations and their effects on the response of base isolated structures are studied. In particular, the role of kinematic interaction in the determination of the rocking excitation is highlighted. The cases of surface foundations subjected to horizontally propagating waves, as well as of embedded foundations under vertically incident shear waves are examined. The validity of the kinematic interaction based on the rigid base mat assumption is discussed. It is shown that, in the case of classical horizontal isolation, rocking input may amplify significantly the response of the lower non‐isolated modes. The examination of full three‐dimensional isolation and active and semi‐active control methods demonstrates the efficacy of these methods to improve the performance of seismically isolated structures subjected to rocking excitations. Copyright © 2009 John Wiley & Sons, Ltd.     

On selection and scaling of ground motions for analysis of seismically isolated structures

A broader consensus on the number of ground motions to be used and the method of scaling to be adopted for nonlinear response history analysis (RHA) of structures is yet to be reached. Therefore, in this study, the effects of selection and scaling of ground motions on the response of seismically isolated structures, which are routinely designed using nonlinear RHA, are investigated. For this purpose, isolation systems with a range of properties subjected to bidirectional excitation are considered. Benchmark response of the isolation systems is established using large sets of unscaled ground motions systematically categorized into pulse-like, non-pulse-like, and mixed set of motions. Different subsets of seven to 14 ground motions are selected from these large sets using (a) random selection and (b) selection based on the best match of the shape of the response spectrum of ground motions to the target spectrum. Consequences of weighted scaling (also commonly referred to as amplitude scaling or linear scaling) as well as spectral matching are investigated. The ground motion selection and scaling procedures are evaluated from the viewpoint of their accuracy, efficiency, and consistency in predicting the benchmark response. It is confirmed that seven time histories are sufficient for a reliable prediction of isolation system displacement demands, for all ground motion subsets, selection and scaling procedures, and isolation systems considered. If ground motions are selected based on their best match to the shape of the target response spectrum (which should be preferred over randomly selected motions), weighted scaling should be used if pulse-like motions are considered, either of weighted scaling or spectral matching can be used if non-pulse-like motions are considered, and an average of responses from weighted-scaled and spectrum-matched ground motions should be used for a mixed set of motions. On the other hand, the importance of randomly selected motions in representing inherent variability of response is recognized and it is found that weighted scaling is more appropriate for such 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.     

Earthquake response of a multiblock nuclear reactor graphite core: Experimental model vs simulations

The complex dynamics of a quarter‐scale model of a graphite nuclear reactor core, representative of the second generation of British advanced gas‐cooled nuclear reactors, is investigated numerically and experimentally. Advanced gas‐cooled nuclear reactor cores are polygonal, multilayer, arrays of graphite bricks, with each brick allowed to rock by design relative to each other in accordance with the boundary conditions. A 35 000 DOF, nonlinear finite element model of the core created by Atkins Nuclear, was analysed on a high performance computing facility at the University of Bristol, and a corresponding 8 t physical model, equipped with 3200 data acquisition channels, was built and tested on the University of Bristol 6‐DOF shaking table. In this paper, the two models are subjected to a series of (1) synthetic earthquake and (2) idealised harmonic input motions. The experimental data are used to compare and verify the two models and explore the dynamics of the core. A kinematic model of the response is also developed based solely on geometric constraints. The results are presented in the form of response maps and graphs. Important conclusions are drawn as to the dynamics and earthquake response of such systems, which inform numerical model validation. It is found that contrary to the case of a small number of rocking blocks that exhibit highly complex response patterns, the behaviour of the model at hand is both smooth and repeatable. An analogy between the response of the core and that of dense granular matter exhibiting particle interlocking and dilatancy is highlighted.     

近断层脉冲型地震动作用下高层摩擦摆基础隔震结构的减震性能研究

近断层地震动中长周期、短持时和高能量的加速度脉冲将对高层摩擦摆基础隔震结构的减震性能产生不利影响,考虑土-结构相互作用（SSI效应）后的隔震结构将产生动力耦合效应,可能进一步放大隔震结构地震响应。为此,通过一幢框架-核心筒高层摩擦摆基础隔震结构的非线性地震响应分析,考察近断层脉冲型地震动作用下框架-核心筒摩擦摆基础隔震结构的层间位移角、楼层加速度和隔震层变形等响应规律,揭示隔震体系的损伤机理。基于集总参数SR （sway-rocking）模型,分析不同场地类别与不同地震动类型对隔震体系动力响应影响规律。结果表明:高层摩擦摆基础隔震结构在近断层脉冲型地震动作用下的减震效果相比普通地震动减震效果变差,楼层剪力、层间位移角和隔震层变形等超越普通地震动作用下的1.5倍;对于Ⅲ和Ⅳ类场地类别,考虑SSI效应使隔震结构的地震响应进一步放大,弹塑性层间位移角随着土质变软增大尤为明显。     

Spatial seismic modeling of base‐isolated buildings pounding against moat walls: effects of ground motion directionality and mass eccentricity

Structural impact between adjacent buildings may induce local and, in some extreme cases, severe damage, especially in the case of seismically isolated buildings. This study parametrically investigates in the three‐dimensional domain the effect of pounding on the peak response of base‐isolated buildings, which are simulated as nonlinear three‐dimensional multi‐degree‐of‐freedom systems. Firstly, it is shown that considering unidirectional, instead of bidirectional, excitations may lead to underestimation of the base drift demands. Subsequently, the peak responses of seismically isolated buildings utilizing lead rubber bearings are studied while varying important parameters, such as the incidence angle of seismic excitations, the available seismic clearance, and mass eccentricities, under the action of bidirectional horizontal excitations. A large number of numerical simulations are performed using a specially developed software that implements an efficient approach to model impacts, taking into account arbitrary locations of contact points. It is found that the peak interstory drift ratio is significantly influenced by the directionality of the ground motion. Therefore, the seismic performance of structures should ideally be assessed examining the peak structural response while bidirectional ground motions are imposed at various incident angles. Furthermore, it is also observed that the interstory drift ratios increase while decreasing the available gap size, up to a certain value. Finally, the parametric analyses indicate that the effects of impact are more severe for structures with mass eccentricities, and in which case, the estimation of the critical incidence angle becomes more laborious. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic response of 20‐story base‐isolated and fixed‐base reinforced concrete structural wall buildings at a near‐fault site

This paper investigates numerically the seismic response of six seismically base‐isolated (BI) 20‐story reinforced concrete buildings and compares their response to that of a fixed‐base (FB) building with a similar structural system above ground. Located in Berkeley, California, 2 km from the Hayward fault, the buildings are designed with a core wall that provides most of the lateral force resistance above ground. For the BI buildings, the following are investigated: two isolation systems (both implemented below a three‐story basement), isolation periods equal to 4, 5, and 6 s, and two levels of flexural strength of the wall. The first isolation system combines tension‐resistant friction pendulum bearings and nonlinear fluid viscous dampers (NFVDs); the second combines low‐friction tension‐resistant crosslinear bearings, lead‐rubber bearings, and NFVDs. The designs of all buildings satisfy ASCE 7‐10 requirements, except that one component of horizontal excitation, is used in the 2D nonlinear response history analysis. Analysis is performed for a set of ground motions scaled to the design earthquake and to the maximum considered earthquake (MCE). At both the design earthquake and the MCE, the FB building develops large inelastic deformations and shear forces in the wall and large floor accelerations. At the MCE, four of the BI buildings experience nominally elastic response of the wall, with floor accelerations and shear forces being 0.25 to 0.55 times those experienced by the FB building. The response of the FB and four of the BI buildings to four unscaled historical pulse‐like near‐fault ground motions is also studied. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental validation of a simplified model for rolling isolation systems

Rolling isolation systems (RISs) protect mission‐critical equipment and valuable property from earthquake hazards by decoupling the dynamic responses of vibration‐sensitive objects from horizontal floor motions. These responses involve the constrained rolling of steel balls between bowl‐shaped surfaces. The light damping of steel balls rolling between steel plates can be augmented by adhering thin rubber sheets to the plates, thereby increasing the rolling resistance and decreasing the displacement demand on the RIS. An assessment of the ability of lightly‐ and heavily‐damped RISs to mitigate the hazard of seismically induced failures requires high‐fidelity models that can adequately capture the systems' intrinsic nonlinear behavior. The simplified model presented in this paper is applicable to RISs with any potential energy function, is amenable to both lightly‐ and heavily‐damped RISs, and is validated through the successful prediction of peak responses for a wide range of disturbance frequencies and intensities. The validated model can therefore be used to compute the spectra of peak floor motions for which displacement demands equal capacity. These spectra are compared with representative floor motion spectra provided by the American Society of Civil Engineers 7–10. The damping provided by rolling between thin viscoelastic sheets increases the allowable floor motion intensity by a factor of 2–3, depending on the period of motion. Acceleration responses of isolation systems with damping supplied in this fashion do not grow with increased damping, even for short‐period excitations. Copyright © 2013 John Wiley & Sons, Ltd.     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.