Seismic response of the superstructure and attached equipment in a base-isolated building

Base isolation can be used both to protect the structure and simultaneously to reduce the response of internal equipment. The seismic response of a base-isolated structure has been studied through the shaking table test or numerical calculation before. The object of this paper is to analyse a base-isolated structure by a different analytical approach—perturbation analysis. Recognizing that the horizontal stiffness of an isolation system is much smaller than that of the superstructure, the mathematical expressions of the modal properties of base-isolated structures are derived by the perturbation method in terms of the modal properties of the superstructure and used to study the dynamic response of superstructure and attached equipment in the base-isolated building. This study shows that the first base-isolated mode not only controls the superstructural response but also dominates the response of high-frequency attachment. The contribution of higher modes to the response of base-isolated structures, which is proportional to the horizontal stiffness of isolation system, is very small.     

Study of the earthquake response of the base-isolated Law and Justice Center in Rancho Cucamonga

The recorded earthquake response of a base-isolated building—the Foothill Communities Law and Justice Center in Rancho Cucamonga—shaken by the 1985 Redlands earthquake (M_L 4–8) is discussed and analysed by employing system identification techniques. The calculated response of one-dimensional and three-dimensional linear structural models is fitted to the recorded motions of the superstructure using the ‘modal minimization method’ for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the building. Simple one-dimensional analyses are used to identify also the effective values of key parameters (e.g. damping) of the isolation system. Furthermore, the recorded motions obtained from the densely instrumented foundation (i.e. below the isolation bearings) of the structure and from the free-field station located 330 ft

1 1 ft =0.3048 m; 1 mile=1.609 km.

from the building show how the presence of the structure affects the incoming seismic waves. It is observed that the transverse component of motion (i.e. the component which is perpendicular to the long dimension of the plan of the building) is affected by the presence of the structure considerably more than the longitudinal component. Factors contributing to this effect are the extreme length of the structure (414 ft) and the rotational motions of the superstructure caused by the spatial variability of ground motion. It is pointed out that, despite the fact that the shift in the effective frequency of the structure induced by the isolation was very small, the elastomeric bearings were very effective in reducing the accelerations transmitted to the structure. This is attributed to the damping capacity of the isolation. Based on the observed response of the building to this small earthquake it can be stated with confidence that the structure performed according to expectations.     

Seismic response of torsionally coupled base isolated structures

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

Response of a nuclear power plant on aseismic bearings to horizontally propagating waves

The nuclear island of Koeberg with a large basemat, a non-linear base isolation effective in the horizontal direction only, founded on rock, is analysed for inclined body waves and for a combination of surface and body waves associated with prescribed horizontal and vertical components of the control motion. When compared to vertical incidence, an additional rocking component arises, generated by the horizontally propagating vertical component. As the aseismic bearings do not isolate against this rocking component, the corresponding horizontal response bears comparison with that of a conventional structure. The ratio of the response for horizontally propagating waves and that for vertically incident waves is thus considerably larger for the base-isolated structure than for a conventional one. However, the actual design incorporating other loading cases is affected much less.     

Application of fractional derivatives to seismic analysis of base-isolated models

The concept of fractional derivatives is employed in the formulation of a stress-strain relationship for elastomers. An oscillator consisting of a mass and a ‘fractional’ Kelvin element is used to model elastomeric bearings used in base isolation systems. Efficient numerical multi-step schemes are developed for the dynamic analysis of a single-degree-of-freedom ‘fractional oscillator’ in the time domain. Numerical examples show that these multi-step schemes are in good agreement with the Laplace and Fourier solutions. When applied to shaking table tests of a base-isolated bridge deck, the fractional derivative model is found to agree well with the experimental results.     

Seismic response of segmental buildings

This paper proposes an aseismic design concept in which the superstructure of a base-isolated building is divided into several segments. Each segment may comprise a few storeys and is interconnected by additional vibrational isolation systems. The dynamic characteristics of the segmental buildings are investigated. The optimum parameters of the vibration isolation systems are determined by minimizing the mean square acceleration response. The seismic response of a typical segmental building subjected to the N—S component of the 1940 El Centro earthquake input is evaluated and compared with the responses of the corresponding fixed-base and conventional base-isolated buildings. The comparisons show that, when the superstructure is segmented, while the acceleration response in the superstructure remains as small as that in the conventional base-isolated building, the displacement across the base isolation system at foundation level is substantially reduced.     

Seismic response of heavily damped base isolation systems

The development of an efficient energy-dissipating mechanism that works in conjunction with laminated elastomeric bearings in order to reduce the lateral deformation of the isolation system has always been a goal of base isolation research. Theoretically, this deformation will be reduced to the minimum if damping augmentation of the isolation system can reach a critical value. However, augmenting the isolation damping may cause some unwanted side effects. The purpose of this paper is to study the influence of isolation damping on the seismic response of heavily damped base-isolated buildings. The base isolation system is assumed to be linearly viscoelastic and is analysed using the complex mode method. Solutions derived by using perturbation techniques for a two-degree-of-freedom system and the computer simulation for a multiple-degree-of-freedom system reveal that augmenting the isolation damping can reduce efficiently the deformation of the isolation system, but at the price of increasing the high-frequency vibration in the superstructure. When the damping ratio of the isolation system is beyond some level, increasing the isolation damping will enlarge the extreme values of the base and superstructural accelerations. It is also found that approximate solutions derived from the use of classical damping and classical modes of vibration in the seismic analysis of heavily damped base isolation systems can be substantially in error.     

某框架结构基础隔震地震反应对比分析

基于结构动力学原理和有限元基本理论,利用SAP2000有限元分析软件,以某框架结构基础隔震楼和与其相近的非隔震楼为研究对象分别建立分析模型,运用动力时程分析法对两种模型进行水平地震反应分析。结果表明:基础隔震楼的水平向地震反应远小于非隔震楼,其上部结构的自振周期明显大于非隔震楼,其层间剪力和基底剪力、楼层相对位移和加速度低于非隔震楼。总体来说,隔震支座可以显著降低水平向地震对于结构的不良反应,值得推广应用。     

RIGIDITY–PLASTICITY–VISCOSITY: CAN ELECTRORHEOLOGICAL DAMPERS PROTECT BASE-ISOLATED STRUCTURES FROM NEAR-SOURCE GROUND MOTIONS?

The concept of seismic protection by lengthening the fundamental period of the structure has been implemented through a number of isolation systems. While flexible isolation systems can effectively protect structures from earthquakes containing high frequencies and sharp accelerations, they might amplify the response of the structure when subjected to rapid, long-period motions. In this case of long period excitations the stiff superstructure should be ‘locked’ to the ground, rather than be supported on flexible bearings. This paper shows through a comprehensive analytical study that a practical solution to this problem is to provide additional rigidity to the structure using a friction-type mechanism (rigid-plastic behaviour). The presence of friction-type forces reduce substantially the relative displacements of a single-degree-of-freedom structure by keeping accelerations at low levels; however, they are responsible for the presence of permanent displacements. Accordingly, the use of controllable fluid dampers is proposed and it is shown that they can be a practical solution to the problem. The response of a single-degree-of-freedom base-isolated structures is investigated, and the feasibility of a proposed electrorheological damper to deliver the required forces is discussed. © 1997 by John Wiley & Sons, Ltd.     

Optimal cost‐effective topology of column bearings for reducing vertical acceleration demands in multistory base‐isolated buildings

Base‐isolation is regarded as one of the most effective methods for protecting the structural and nonstructural building elements from design level horizontal earthquake ground shaking. However, base‐isolation as currently practiced does not offer unlimited protection for these buildings, especially when the ground shaking includes a strong vertical component. The vulnerability of nonstructural systems in a base‐isolated building was made evident during recent shake table testing of a full‐scale five‐story base‐isolated steel moment frame where nonstructural system damage was observed following tests including vertical excitation. Past research efforts have attempted to achieve 3D isolation of buildings and nuclear structures by concentrating both the horizontal and vertical flexibility at the base of the building that are either quite limited or not economically viable. An approach whereby the vertical flexibility is distributed up the height of the building superstructure to passively reduce vertical acceleration demands in base‐isolated buildings is presented. The vertical flexibility is achieved by placing laterally restrained elastomeric ‘column’ bearings at one or more floor levels along the height of the building. To broadly investigate the efficacy of the vertically distributed flexibility concept and the trade‐off between mitigation and cost, a multi‐objective optimization study was conducted considering 3‐story, 9‐story, and 20‐story archetype buildings that aimed to minimize the median peak vertical floor acceleration demands and to minimize the direct cost of column bearings. Based on the results of the optimization study, a practical rule for determining the number of levels and locations of column bearings is proposed and evaluated. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solution of seismic response of base-isolated structure with supplemental inerter

Closed-form solutions are derived for the modal characteristics and seismic response of a base-isolated structure equipped with additional inerters. By simplifying the structure-isolator-inerter system in terms of the two-degree-of-freedom (2DOF) model, the modal frequencies, mode shapes, damping ratios, and participation factors of the system are derived. Consequently, analytical seismic response solutions are formulated by the modal superposition method. Utilizing these analytical solutions, an extensive parametric study has been carried out to investigate the effect of supplement inerters on both the modal characteristics and seismic response of the structure-isolator-inerter system. There is a critical inertance leading to the zero second modal participation factor (ie, the disappearance of the second modal response). The associated critical inertance ratio is derived in closed form as well. Moreover, it is observed that the reduction of deformation of isolators by increasing the inertance may be offset by the increase in relative displacements of the superstructure. To circumvent this adverse effect, an optimal range of inertance is identified whereby both the deformation of isolators and the relative displacement of the superstructure are mitigated concurrently.     

Seismic response evaluation of base-isolated reinforced concrete buildings under bidirectional excitation

This paper reports on an investigation of the seismic response of base-isolated reinforced concrete buildings, which considers various isolation system parameters under bidirectional near-fault and far-fault motions. Three-dimensional models of 4-, 8-, and 12-story base-isolated buildings with nonlinear effects in the isolation system and the superstructure are investigated, and nonlinear response history analysis is carried out. The bounding values of isolation system properties that incorporate the aging effect of isolators are also taken into account, as is the current state of practice in the design and analysis of base-isolated buildings. The response indicators of the buildings are studied for near-fault and far-fault motions weight-scaled to represent the design earthquake (DE) level and the risk-targeted maximum considered earthquake (MCE_R) level. Results of the nonlinear response history analyses indicate no structural damage under DE-level motions for near-fault and far-fault motions and for MCE_R-level far-fault motions, whereas minor structural damage is observed under MCE_R-level near-fault motions. Results of the base-isolated buildings are compared with their fixed-base counterparts. Significant reduction of the superstructure response of the 12-story base-isolated building compared to the fixed-base condition indicates that base isolation can be effectively used in taller buildings to enhance performance. Additionally, the applicability of a rigid superstructure to predict the isolator displacement demand is also investigated. It is found that the isolator displacements can be estimated accurately using a rigid body model for the superstructure for the buildings considered.     

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.     

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.     

Seismic response of light equipment in torsional buildings

This paper attempts to study the response of light equipment items attached to a multi-storey building that may be subjected to large torsional deformations during the earthquake excitation. To account for the effect of torsion and translation, each storey of the building is modelled as two degrees of freedom (DOFs), with one DOF for translation and the other for torsion. Perturbation techniques are employed to find closed-form expressions for the modal properties of the combined system in terms of the properties of the individual subsystems. The interaction between the equipment and building is studied for both tuned and detuned modes of vibration. Modal synthesis results obtained using the present technique based on the complete quadratic combination (CQC) method are compared with solutions obtained by other methods.     

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.     

Non-classical damping in dynamic analysis of base-isolated structures with internal equipment

It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response.     

Seismic response of base-isolated buildings including soil–structure interaction

This study investigates the effect of soil–structure interaction (SSI) on the response of base-isolated buildings. The equations of motion are formulated in the frequency domain, assuming frequency-independent soil stiffness and damping constants. An equivalent fixed-base system is developed that accounts for soil compliance and damping characteristics of the base-isolated building. Closed-form expressions are derived, followed by a thorough parametric study involving the pertinent system parameters. For preliminary design, the methodology can serve as a means to assess effective use of base isolation on building structures accounting for SSI. This study concludes that the effects of SSI are more pronounced on the modal properties of the system, especially for the case of squat and stiff base-isolated structures.     

Approximate soil–structure interaction analysis by a perturbation approach: The case of soft soils

An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.     

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.