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.     

Low cyclic fatigue and hysteretic behavior of U‐shaped steel dampers for seismically isolated buildings under dynamic cyclic loadings

Energy dissipation devices are necessary for base‐isolated buildings to control the deformation in the isolation system and to dissipate the earthquake‐induced energy. U‐shaped steel dampers (also known as U‐dampers) dissipate energy through plastic deformation of specially designed U‐shaped steel elements. This type of device can be installed at several locations in the isolation system. U‐dampers have been widely used in Japan for different types of isolated structures, such as hospitals, plants and residential buildings, since the 1995 Kobe Earthquake. Previous research has used static tests to estimate the performance of U‐dampers. However, the ultimate plastic deformation capacities and hysteretic behaviors of full‐scale U‐dampers under dynamic excitations still remain unclear. In addition, it is unclear whether the initial temperature has an effect on the hysteretic behavior and plastic deformation capacity of U‐dampers. In this paper, two series of dynamic loading tests of U‐dampers were conducted to evaluate the issues described earlier. The major findings of the study are (i) the loading speed has little effect on the plastic deformation capacity of U‐dampers; (ii) method to evaluate the ultimate plastic deformation capacities of U‐shaped steel dampers of different sizes is established using a Manson–Coffin relation‐based equation that is based on the peak‐to‐peak horizontal shear angle γ_t, which is defined as the lateral deformation amplitude (peak‐to‐peak amplitude) divided by the height of the dampers; (iii) the loading rate and the initial temperature have a minimal effect on the hysteretic behavior of the U‐dampers; and (iv) a bilinear model is proposed to simulate the force‐deformation relationships of the U‐dampers. Copyright © 2014 John Wiley & Sons, Ltd.     

Second‐mode tuned mass dampers in base‐isolated structures for reduction of floor acceleration

To reduce floor acceleration of base‐isolated structures under earthquakes, a tuned mass damper (TMD) system installed on the roof is studied. The optimal tuning parameters of the TMD are analyzed for linear base isolation under a generalized ground motion, and the performance of the TMD is validated using a suite of recorded ground motions. The simulation shows that a TMD tuned to the second mode of a base‐isolated structure reduces roof acceleration more effectively than a TMD tuned to the first mode. The reduction ratio, defined as the maximum roof acceleration with the TMD relative to that without the TMD, is approximately 0.9 with the second‐mode TMD. The higher effectiveness of the second‐mode TMD relative to the first‐mode TMD is attributed primarily to the unique characteristics of base isolation, ie, the relatively long first‐mode period and high base damping. The modal acceleration of the second mode is close to or even higher than that of the first mode in base‐isolated structures. The larger TMD mass ratio and lower modal damping ratio of the second‐mode TMD compared to the first‐mode TMD increases its effect on modal acceleration reduction. The reduction ratio with the second‐mode TMD improves to 0.8 for bilinear base isolation. Because of the detuning effect caused by the change in the first‐mode period in bilinear isolation, the first‐mode TMD is ineffective in reducing roof acceleration. Additionally, the displacement experienced by the second‐mode TMD is considerably smaller than that of the first‐mode TMD, thereby reducing the installation space for the TMD.     

Independent component regression for predicting the responses of biaxial base‐isolated buildings

This paper presents a regression model to predict the base displacement responses of biaxial base‐isolated buildings using independent component analysis. The model proposed utilizes multiple ground motion intensity measures from North American and Japanese earthquakes as inputs, and transforms them into an independent component space using independent component regression (ICR). Unlike other latent variable methods, such as principal component regression, ICR does not readily allow for dimensionality reduction of the components that do not contribute significantly to the explained variance of the original data set. Hence, a whitening‐step to transform the correlated variables into uncorrelated ones is introduced prior to performing ICR. Prediction results are presented and compared with the simulation results for two building models with increasing degree of complexity. The results show that the model based on ICR results in good estimates for the base displacement responses, and the standard errors remain relatively small and constant across a range of isolation periods. Copyright © 2009 John Wiley & Sons, Ltd.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental study on the bidirectional inelastic deformation capacity of U‐shaped steel dampers for seismic isolated buildings

Hysteretic dampers are used to dissipate earthquake‐induced energy in base‐isolated structures by acquiring inelastic deformations, rendering their hysteretic behavior of vital importance. The present paper focuses on investigating the behavior of U‐shaped steel dampers under bidirectional loading; this is significantly different from their corresponding uniaxial behavior. Two main sets of loading tests on full‐scale specimens are conducted in this regard: (i) quasi‐static tests with simple histories and (ii) dynamic tests with realistic loading histories. Based on the results obtained in the quasi‐static tests, an interaction curve that accounts for the reduction of the cyclic deformation capacity is proposed. However, the fidelity of this relation must be assessed under loading conditions similar to those of a seismically isolated structure subjected to an earthquake, which represents the goal of the second set of tests. The results of the dynamic tests validate the proposed interaction curve for estimating the deformation capacity of U‐shaped steel dampers under bidirectional loading. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance of base‐isolated reinforced concrete buildings under bidirectional seismic excitation considering pounding with retaining walls including friction effects

Seismic pounding of base‐isolated buildings has been mostly studied in the past assuming unidirectional excitation. Therefore, in this study, the effects of seismic pounding on the response of base‐isolated reinforced concrete buildings under bidirectional excitation are investigated. For this purpose, a three‐dimensional finite element model of a code‐compliant four‐story building is considered, where a newly developed contact element that accounts for friction and is capable of simulating pounding with retaining walls at the base, is used. Nonlinear behavior of the superstructure as well as the isolation system is considered. The performance of the building is evaluated separately for far‐fault non‐pulse‐like ground motions and near‐fault pulse‐like ground motions, which are weighted scaled to represent two levels of shaking viz. the design earthquake (DE) level and the risk‐targeted maximum considered earthquake (MCE_R) level. Nonlinear time‐history analyses are carried out considering lower bound as well as upper bound properties of isolators. The influence of separation distance between the building and the retaining walls at the base is also investigated. It is found that if pounding is avoided, the performance of the building is satisfactory in terms of limiting structural and nonstructural damage, under DE‐level motions and MCE_R‐level far‐fault motions, whereas unacceptably large demands are imposed by MCE_R‐level near‐fault motions. In the case of seismic pounding, MCE_R‐level near‐fault motions are found to be detrimental, where the effect of pounding is mostly concentrated at the first story. In addition, it is determined that considering unidirectional excitation instead of bidirectional excitation for MCE_R‐level near‐fault motions provides highly unconservative estimates of superstructure demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental and analytical study on pounding reduction of base‐isolated highway bridges using MR dampers

Pounding between adjacent superstructures has been a major cause of highway bridge damage in the past several earthquakes. This paper presents an experimental and analytical study on pounding reduction of highway bridges subjected to earthquake ground motions by using magnetorheological (MR) dampers. An analytical model, which incorporates structural pounding and MR dampers, is developed. A series of shaking table tests on a 1:20 scaled base‐isolated bridge model are performed to investigate the effects of pounding between adjacent superstructures on the dynamics of the structures. Based on the test results, the parameters of the linear and the nonlinear viscoelastic impact models are identified. Performance of the semiactive system for reducing structural pounding is also investigated experimentally, in which the MR dampers are used in conjunction with the proposed control strategy, to verify the effectiveness of the MR dampers. Structural responses are also simulated by using the established analytical model and compared with the shaking table test results. The results show that pounding between adjacent superstructures of the highway bridge significantly increases the structural acceleration responses. For the base‐isolated bridge model considered here, the semiactive control system with MR dampers effectively precludes pounding. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparative response assessment of minimally compliant low‐rise conventional and base‐isolated steel frames

In this study, the multi‐intensity seismic response of code‐designed conventional and base‐isolated steel frame buildings is evaluated using nonlinear response history analysis. The results of hazard and structural response analysis for three‐story braced‐frame buildings are presented in this paper. Three‐dimensional models for both buildings are created and seismic response is assessed for three scenario earthquakes. The response history analysis results indicate that the design objectives are met and the performance of the isolated building is superior to the conventional building in the design event. For the Maximum Considered Earthquake, isolation leads to reductions in story drifts and floor accelerations relative to the conventional building. However, the extremely high displacement demands of the isolation system could not be accommodated under normal circumstances, and creative approaches should be developed to control displacements in the MCE. Copyright © 2010 John Wiley & Sons, Ltd.     

Simplified inelastic seismic analysis of base‐isolated structures using the N2 method

In the paper a simplified nonlinear method has been applied to the analysis of base‐isolated structures. In the first part, a three‐linear idealization of the capacity curve is proposed. The initial stiffness is defined based on the first yielding point in the superstructure, whereas the secondary slope depends on the failure mechanism of the superstructure. A consequence is a much more pronounced secondary slope, which does not correspond to the presumptions used in the originally proposed N2 method. A parametric nonlinear dynamic study of single degree of freedom systems with different hardening slopes and damping has been performed for an ensemble of seven EC8 spectrum‐compatible artificial accelerograms. It was concluded that, in the long‐period range, the equal displacement rule could be assumed also for the proposed systems with non‐zero post‐yield stiffness. In the second part, the proposed idealization was used for the analysis of isolated RC frame buildings that were isolated with different (lead) rubber‐bearing isolation systems. The stiffness of the isolators was selected for three different protection levels and for three different ground motion intensities, which have resulted in elastic as well as moderately and fully damaged superstructure performance levels. Three different lateral load distributions were investigated. It was observed that a triangular distribution, with an additional force at the base, works best in the majority of practical cases. It was concluded that the N2 method can, in general, provide a reasonably accurate prediction of the actual top displacement, as well as of the expected damage to the superstructure. Copyright © 2009 John Wiley & Sons, Ltd.     

Development and experimental evaluation of a passive gap damper device to prevent pounding in base‐isolated structures

Studies have shown the effectiveness of providing supplemental energy dissipation in base‐isolated structures to reduce displacements at the isolation level. A previous analytical study demonstrated the benefits of providing this energy dissipation at a specified gap larger than the design displacement. The gap before engagement allows the base isolation system to meet performance criteria in varying levels of ground excitation. Use of this ‘gap damper’ device eliminates undesirable effects often exhibited with large amounts of supplemental damping at lower intensity motions. Using results from an analytical study, the primary purpose of this research was to develop devices for practical implementation. Development of the devices demanded simplicity, feasibility, economy, and reliability to be an effective option in building design and construction. Multiple designs were proposed, and a final design was chosen based on selection criteria and finite element analyses. The device was designed and tested in Auburn University's Structural Research Lab. Experimental results were compared with theoretical models to verify behavior and make necessary adjustments for a shake table experiment. The design parameters were selected to accommodate re‐use of the device for the shake table test. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic reliability‐based ductility demand evaluation for inelastic base‐isolated structures with friction pendulum devices

The aim of this work is to propose seismic reliability‐based relationships between the strength reduction factors and the displacement ductility demand of nonlinear structural systems equipped with friction pendulum isolators (FPS) depending on the structural properties. The isolated structures are described by employing an equivalent 2dof model characterized by a perfectly elastoplastic rule to account for the inelastic response of the superstructure, whereas, the FPS behavior is described by a velocity‐dependent model. An extensive parametric study is carried out encompassing a wide range of elastic and inelastic building properties, different seismic intensity levels and considering the friction coefficient as a random variable. Defined a set of natural seismic records and scaled to the seismic intensity corresponding to life safety limit state for L'Aquila site (Italy) according to NTC08, the inelastic characteristics of the superstructures are designed as the ratio between the average elastic responses and increasing strength reduction factors. Incremental dynamic analyses (IDAs) are developed to evaluate the seismic fragility curves of both the inelastic superstructure and the isolation level assuming different values of the corresponding limit states. Integrating the fragility curves with the seismic hazard curves related to L'Aquila site (Italy), the reliability curves of the equivalent inelastic base‐isolated structural systems, with a design life of 50 years, are derived proposing seismic reliability‐based regression expressions between the displacement ductility demand and the strength reduction factors for the superstructure as well as seismic reliability‐based design (SRBD) abacuses useful to define the FPS properties. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of FPS bearing properties on the seismic performance of base‐isolated structures

The paper analyzes the influence of friction pendulum system (FPS) isolator properties on the seismic performance of base‐isolated building frames. The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the FPS isolator behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. The uncertainty in the seismic input is taken into account by considering a set of natural records with different characteristics scaled to increasing intensity levels. The variation of the statistics of the response parameters relevant to the seismic performance is investigated through the nondimensionalization of the motion equation and an extensive parametric study carried out for different isolator and system properties. The proposed approach allows to explore a wide range of situations while limiting the required nonlinear response history analyses. Two case studies consisting of base‐isolated building frames described as shear‐type systems are finally investigated in order to demonstrate the capabilities of the proposed simplified model in unveiling the essential characteristics of the performance of buildings isolated with FPS bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

黏滞阻尼器对高层钢结构地震易损性的影响

为研究黏滞阻尼器对高层钢结构地震易损性的影响,基于Open SEES有限元分析平台,建立一个25层钢框架结构以及同尺寸附着黏滞阻尼器的钢框架结构,对两个钢框架结构以地震动峰值加速度(PGA)作为地震动强度指标,以结构最大层间位移角θmax为工程需求参数,从太平洋地震工程研究中心(PEER)中选取了15条地震动记录,分别对两个结构进行增量动力分析(Incremental Dynamic Analysis,IDA),建立结构的IDA曲线簇。结合地震易损性分析,对分析结果进行对数拟合,构筑两个结构的连续易损性曲线,并进一步提出用贝塔分布函数将结果转化为地震动参数-震害指数概率密度函数的概率表达方式,可以更加直观简便地观察到黏滞阻尼器显著的减震效果。该表达方法具有直观性,研究成果可为既有结构的地震灾害风险评估等提供简明且有力的分析方法。     

Horizontal floor response spectra of base‐isolated buildings due to vertical excitation

A mechanism of horizontal floor response spectra amplification in the vicinity of higher modes' frequencies is investigated. It is demonstrated, by means of a simple two‐degrees‐of‐freedom model, that in the case of unsymmetrical superstructure, such amplification may occur because of the coupling between vertical excitation and horizontal response of the non‐isolated modes. This phenomenon is further illustrated by the results of analyses of a model of a nuclear plant. Copyright © 2011 John Wiley & Sons, Ltd.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of semi‐active tuned mass dampers to base‐excited systems

A continuously variable semi‐active damper is used in a tuned mass damper (TMD) to reduce the level of vibration of a single‐degree‐of‐freedom system subjected to harmonic base excitations. The ground hook dampers as have been used in the auto‐industry are being studied here. Using these dampers a new class of tuned mass dampers, named as ground hook tuned mass dampers (GHTMD) is being introduced. In order to generalize the design properties of the GHTMDs, they are defined in terms of non‐dimensional parameters. The optimum design parameters of GHTMDs for lightly damped systems are obtained based on the minimization of the steady‐state displacement response of the main mass. These parameters are computed for different mass ratios and main system damping ratios. Frequency responses of the resulting systems are compared to that of equivalent TMDs using passive dampers. In addition, other characteristics of this system as compared to the passive TMDs are discussed. A design guide to obtain the optimum parameters of GHTMD using the developed diagrams in this paper based on non‐dimensional values is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Full‐scale shaking table test of a base‐isolated medical facility subjected to vertical motions

Base isolation is a well known technology that has been proven to reduce structural response to horizontal ground accelerations. However, vertical response still remains a topic of concern for base‐isolated buildings, perhaps more so than in fixed‐base buildings as isolation is often used when high performance is required. To investigate the effects of vertical response on building contents and nonstructural components, a series of full‐scale shaking table tests were conducted at the E‐Defense facility in Japan. A four‐story base‐isolated reinforced concrete building was outfitted as a medical facility with a wide variety of contents, and the behavior of the contents was observed. The rubber base isolation system was found to significantly amplify vertical accelerations in some cases. However, the damage caused by the vertical ground motions was not detrimental when peak vertical floor accelerations remained below 2 g with three exceptions: (1) small items placed on shelves slid or toppled; (2) objects jumped when placed on nonrigid furniture, which tended to increase the response; and (3) equipment with vertical eccentricities rocked and jumped. In these tests, all equipment and nonstructural components remained functional after shaking. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental and computational verification of reasonable design formulae for base‐isolated structures

It is clear that base isolation is a sensible strategic design in attenuating the responses of a structural system induced by ground motions. The design of seismically isolated structures is mainly governed by the Uniform Building Code (UBC) published by the International Conference of Building Officials. The UBC code emphasizes a simple, statically equivalent design method that displacements of an isolated structure are concentrated at the isolation level. Therefore, the superstructure nearly moves as a rigid body and the design forces of elements above isolators are based on the behaviour of isolators at the design displacement. However, in the UBC code, the distribution of inertial (or lateral) forces over the height of the superstructure above isolation has been found to be too conservative for most isolated structures. In view of this, two simple and reasonable design formulae for the lateral force distribution on isolated structures have been proposed in this paper. Results obtained from a full‐scale isolated structure tested on the shaking table and numerical analyses of two additional examples verify the suitability of design formulae. It is illustrated that the proposed formulae can predict well the lateral force distribution on isolated structures during earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

The applicability of the N2 method to the estimation of torsional effects in asymmetric base‐isolated buildings

The paper deals with the applicability of the extended N2 method to base‐isolated plan‐asymmetric building structures. The results obtained by the usual pushover analysis of a 3D structural model are further combined with the aid of linear dynamic (spectral) analysis to account for the dynamic effects caused by structural asymmetry. In the paper, the method has been applied to the seismic analysis of a mass‐eccentric four‐storeyed RC frame building isolated with lead rubber bearings. Three different positions of the center of isolation system (CI) with respect to the center of mass (CM) and the center of stiffness of the superstructure (CS) were considered. The response was analyzed for three different eccentricities, three different torsional to lateral frequency ratios of the superstructure, and two ground motion intensities. The stiffness of the isolators was selected for three different protection levels, which resulted in elastic as well as moderately to excessively damaged superstructure performance levels. The results are presented in terms of the top, base and relative displacements, as well as the stiff/flexible side amplification factors. A more detailed insight into the nonlinear behavior of the superstructure is given in a form of ductility factors for the flexible and stiff side frames. The results of the extended N2 method for selected lateral load distributions are compared with the average results of nonlinear dynamic analyses. It was concluded that the extended N2 method could, with certain limitations, provide a reasonable prediction of the torsional influences in minor to moderately asymmetric base‐isolated structures. Copyright © 2010 John Wiley & Sons, Ltd.