Maximum Isolator Displacement Research Articles

A critical assessment of the design displacements of friction pendulum systems

The equivalent linear static procedure suggested in seismic codes for determining the maximum displacements of seismic isolation systems is evaluated comprehensively for friction pendulum isolators with respect to the benchmark nonlinear response history analysis procedure for a set of radii of curvature and coefficients of friction. A large set of selected and scaled near field ground motions recorded on stiff and soft soils are employed in comparative evaluations. It has been observed that equivalent linear static procedure significantly overestimates the maximum isolator displacements for all practical combinations of radius of curvature and friction coefficient. Overestimation is larger for ground motions on soft soils. Alternatively, a practical description of inelastic displacement spectra is introduced where the hazard is defined in terms of the 1-second spectral acceleration accounting for the seismicity and soil class of the site, and friction pendulum isolation systems are characterized by their radius of curvature and nominal friction coefficient. Employing the proposed design spectra in design and production may lead to significant reductions of the isolator sizes. Moreover, realistic estimation of maximum isolator displacements also leads to realistic estimation of isolator stiffness, as well as the internal design forces of both the isolation system and the superstructure through response spectrum analysis under design spectrum.

Effects of rotational component of ground motions on seismic responses of asymmetric base-isolated structures

Asymmetric base-isolated structures installed on lead rubber bearings (LRBs) and laminated rubber bearings (LNRs) may suffer severe torsion due to the presence of the eccentricity ratio of the isolation system (eb/r). It is also recognized that the rotational component of ground motions can markedly increase torsional responses in structures, which may further amplify the adverse effect of torsion on asymmetric structures. Therefore, understanding how these rotational motions affect asymmetric base-isolated structures on LRBs and LNRs is crucial. Surprisingly, existing literature overlooks the impact of the structural parameter (eb/r) and the ground motion’s pulse period (Tp) on these effects. To fill this gap, numerical analyses are conducted on typical U-shaped planar asymmetric base-isolated structures. These structures, having 5 and 8 stories, are examined using MATLAB programming. Firstly, the translational and rotational responses of the selected cases under coupled rotational and translational components of ground motions are compared with those under the translational components. The responses are also compared to those of the associated, asymmetric fixed-base structures. Then, the role of eb/r in amplifying the negative effect of rotational excitations on selected cases is examined by varying eb/r from 0 to 0.3. The study compares the responses of selected cases subjected to coupled rotational and translational components of fourteen pulse-type ground motions (with Tp ranging from 0.728 to 8.043 s) to those subjected only to the translational components. The results reveal that seismic isolation effectively mitigates the adverse effects of the rotational component of ground motions on asymmetric structures. While rotational components can increase torsion in asymmetric base-isolated structures, the adverse effects are relatively minor and are not exacerbated by eb/r. However, when facing pulse-type ground motions with substantial Tp values, these structures exhibit at least a 200% increase in maximum interstory rotation and a 28% increase in maximum isolator displacement. These increases significantly exceed those observed for the structure subjected to non-pulse-type ground motions. Consequently, structural engineers should take these findings into account when designing and evaluating asymmetric base-isolated structures installed on LRBs and LNRs, particularly in regions where pulse-type ground motions are typical.

Effects of Building Height and Seismic Load on the Optimal Performance of Base Isolation System

AbstractSeismic isolation has been widely accepted as one of the techniques that can be used to protect structures during earthquake ground motions. However, some challenges still exist such as the optimal control of excessive isolator shear strains imposed by some ground motions. The main purpose of this study was to assess the effects of building height variation and earthquake ground motion type on the optimal performance of the seismic isolation using lead core rubber bearing (LCRB). Nonlinear time history analysis for building models of various storeys isolated by LCRB and exposed to different real earthquakes was performed. To achieve this, the equations governing the motion of the isolated three different building models were presented, and an approach for solving the equations while taking into consideration of the optimized mechanical properties of the LCRB was developed. The LCRB performance was measured in terms of elastomer shear strains, derived after an optimal criterion leading to reliable substructure and superstructure responses was reached. The results showed that the combined effects of the earthquake type and building height significantly affect the substructure responses (maximum isolator displacement, energy dissipation capacity, maximum isolator force) and the superstructure responses (storey shear forces, storey drifts, floor displacements, and floor accelerations), which in some cases lead to a need for adding a fluid damper. In this regard, an attempt to couple the LCRB with nonlinear fluid viscous damper was made, and the performance of the hybrid was assessed. It was generally found that the hybrid can positively improve the substructure responses, thereby reducing the unwanted large elastomer shear strains without adversely affecting the superstructure responses.

PREDICTION MODEL FOR BASE SHEAR INCREASE DUE TO VERTICAL GROUND MOTION IN FRICTION PENDULUM ISOLATED STRUCTURES

Seismic isolation is one of the most effective seismic hazard mitigation techniques, which has been implemented in many structures. Friction pendulum isolators are one of the most popular isolation devices to achieve energy dissipation and shear resistance that depends on the effective radius and instantaneous vertical force on them. So, the horizontal response of this type of isolators is coupled with the axial load on them, which could change due to vertical acceleration during ground shaking. Thus, it makes consideration of the vertical excitation in the design and analysis phase inevitable, especially for structures in those regions where vertical ground accelerations are more pronounced. In this study a model for the prediction of increase in base shear due to vertical motion for friction pendulum isolated structures is proposed. A simple single friction pendulum isolator system is utilized with the assumption of rigid superstructure on top and subjected to a hundred earthquake ground motions with different characteristics. A multi-layer perceptron model with three layers is utilized, and a simple computer program, which is open-source, is prepared to construct probability curves. With the help of the program, within the range of the considered structural parameters in the study, probability curves related to increase in base shear, maximum isolator displacement and residual isolator displacement can be constructed, and designers can have a rough estimation on modification of these parameters due to vertical ground motion.

Developing a simplified method for analysis and design of isolated structures with the novel quintuple friction pendulum system under bidirectional near-field excitations

Simplified analysis methods for seismically isolated structures proposed in recent structural codes and specifications are frequently used to reduce the computational effort and to simplify the design procedure, either directly for special cases or for checking the results of nonlinear response history analysis. Of the approximate methods, the equivalent lateral force procedure using the effective stiffness and effective damping is one of the best known. In this study, the simplified method is developed by combining the equivalent lateral force procedure with the capacity spectrum method and evaluated in terms of maximum isolator displacements and base shears for isolated structures with recently invented quintuple friction pendulum isolators , with different geometrical and frictional properties, under two different response spectra with corresponding two different sets of bidirectional near-field ground motions for stiff and soft soils site classes. In order to assess the accuracy of the simplified method, the delivered results of the ELF procedure are compared to those of nonlinear response history analysis, by modelling the quintuple friction pendulum isolator 3D element in OpenSees. Eventually, comments on the accuracy of the simplified method are given to make its applications more appropriate in practical design of base isolation systems.

Risk-targeted design of seismically isolated buildings

Seismic isolation has been used to improve the seismic performance of buildings for the last decades. However, it has been shown that the code-based displacement capacity of isolation members does not provide adequate collapse probabilities for different Risk Categories of ASCE 7–16. Seismic design codes stipulate to determine maximum isolator displacement at the Risk-Targeted Maximum Considered Earthquake (MCER) level. Although the code-based isolator displacement capacity is checked with the mean displacement of the MCER level nonlinear time history analysis results, extreme event effects and incorporating uncertainties into fragility curves create additional displacement demands. Therefore, there is a need to amplify the code-based displacement capacity of isolators to obtain sufficient collapse performance. A previous study, assumed elastic behavior and rigid mass model for the superstructure, proposes an iterative probabilistic approach. In the present study, seven different seismically isolated buildings are modeled, and the nonlinear behavior of isolators and superstructures is considered in the incremental dynamic analyses achieved for all models to obtain fragility curves. Although the seismic isolation considerably decreases the spectral accelerations of the superstructure, it is shown that the R-μ-T relations for diaphragm level accelerations, transferred accelerations from base to superstructure, become more sensitive to nonlinear behavior at the superstructure mode periods. The fragility curves of five case study buildings are obtained using the FEMA P695 procedure, and it is figured out that the collapse probability of isolation units is highly correlated with the required isolator displacement to code-based maximum isolator displacement (D/DM) ratio. Then, two simple equations with high correlation coefficients are acquired to estimate the required displacement capacity for prescribed risk-target levels. Further, the obtained equations are verified for two different isolated building models, and their results are compared with the Incremental Dynamic Analysis (IDA) results. The verification results show that the given equations can be used in the preliminary design phase of seismically isolated mid-rise reinforced concrete buildings.

Amplification in maximum isolator displacement of an LRB isolated building due to mass eccentricity

Amplification in maximum isolator displacement of an LRB isolated building due to mass eccentricity

Optimal Earthquake Intensity Measures for Probabilistic Seismic Demand Models of Base-Isolated Nuclear Power Plant Structures

The purpose of this study is to evaluate the optimal earthquake intensity measures (IMs) for probabilistic seismic demand models (PSDMs) of the base-isolated nuclear power plant (NPP) structures. The numerical model of NPP structures is developed using a lumped-mass stick model, in which a bilinear model is employed to simulate the force-displacement relations of base isolators. In this study, 20 different IMs are considered and 90 ground motion records are used to perform time-history analyses. The seismic engineering demand parameters (EDPs) are monitored in terms of maximum floor displacement (MFD), the maximum floor acceleration (MFA) of the structures, and maximum isolator displacement (MID). As a result, a set of PSDMs of the base-isolated structure is developed based on three EDPs (i.e., MFD, MFA, and MID) associated with 20 IMs. Four statistical parameters including the coefficient of determination, efficiency (i.e., standard deviation), practicality, and proficiency are then calculated to evaluate optimal IMs for seismic performances of the isolated NPP structures. The results reveal that the optimal IMs for PSDMs with respect to MFD and MID are velocity spectrum intensity, Housner intensity, peak ground velocity, and spectral velocity at the fundamental period. Meanwhile, peak ground acceleration, acceleration spectrum intensity, A95, effective peak acceleration, and sustained maximum acceleration are efficient IMs for PSDMs with respect to MFA of the base-isolated structures. On the other hand, cumulative absolute velocity is not recommended for determining the exceedance of the operating basis earthquake of base-isolated NPP structures.

Proposed minimum restoring force requirements for seismic isolated structures

In this research study, a new set of restoring force equations are proposed for seismic isolated structures subjected to far fault ground motions (FFGM) and near fault ground motions (NFGM). For this purpose, 110 FFGM and 49 NFGM are selected. Then, nonlinear time history analyses (NLTHA) of SDOF seismic isolated structures are performed using the selected ground motions to obtain their residual and maximum displacements. The analyses are repeated for an extensive range of parameters including peak ground acceleration, Ap, characteristic strength, Qd and post elastic period, Td, of the isolation system. Next, the variations of the residual and maximum displacements are plotted as functions of the various combinations of the parameters considered in the analyses. Then, nonlinear regression analyses are performed to formulate the residual and maximum displacements as functions of the parameters considered in the analyses. The developed equations are then used to formulate the upper limits of Td (restoring force equations) to ensure reasonable levels of residual and maximum isolator displacements. The developed restoring force equations are then compared with those of AASHTO and Eurocode-8 (EC-8) using the pool of residual and maximum displacement data obtained from NLTHA. It is observed that using the restoring force equations of AASHTO and EC-8 to check the design of seismic-isolated structures may, in some cases, produce unreasonably large levels of residual and maximum displacements. However, when the restoring force requirements proposed in this research study are applied, the residual and maximum displacements are observed to be within reasonable ranges.

Using maximum direction of a ground motion in a code-compliant analysis of seismically isolated structures

This study investigates the change in response of a seismically isolated structure as a function of ground motion orientation. Accordingly, a ground motion set composed of 11 records was clustered and each record was rotated by 10° increments through 90°. Both the original and rotated forms of ground motion records were scaled in order to perform code compliant nonlinear response history analyses (NRHA). Furthermore, the maximum directions (defined as the direction at which maximum isolator displacements are recorded) of each ground motion record was determined. Then, ground motion records rotated to their maximum directions were also scaled in accordance with code specifications and NRHA were repeated for the same seismically isolated structure. Parallel to code specifications related to the design of seismically isolated structures, averages of maximum isolator displacements (MIDs) and maximum floor accelerations (MFAs) were used to assess the analyses results. It is found that using the maximum direction of ground motions does not provide the maximum response compared to those obtained by considering different orientations of ground motions for both MIDs and MFAs.

Influence of superstructure modeling approach on the response prediction of buildings with LRBs considering heating effects

The aim of this study is to investigate the variation in response quantities of buildings seismically isolated by lead rubber bearings (LRBs), depending on how the superstructure is modeled in the analyses. For this purpose, two distinct seismically isolated structures with 4- and 9-stories are idealized by (i) a single-degree-of-freedom model (SDOF), (ii) a two-degree-of-freedom model (2DOF), (iii) a 3D model and subjected to near-fault earthquake excitations through nonlinear response history analyses (NRHA). In all of the structural models, the hysteretic behavior of LRBs is represented by a deteriorating force–displacement curve in which the strength of bearing decreases gradually during cyclic motion due to the lead core heating. Analyses are performed by OpenSees and the response quantities considered are floor drifts and floor accelerations for superstructures and maximum isolator displacements for isolation systems. In order to assess the influence of the superstructure modeling approach on selected response quantities, results of analyses with SDOF, 2DOF, and 3D models are compared with each other. Furthermore, in order to highlight the significance of hysteretic representation used to model LRBs, a non-deteriorating force–displacement curve, where lead core heating phenomenon is ignored, is also considered to idealize LRBs in the case of a 3D superstructural model. Results showed that the SDOF model overestimates the isolator displacements obtained from the 3D model and the 2DOF model is effective only in estimating mid-story response quantities of the 3D model.

Seismic Response Mitigation of Base-Isolated Buildings

Earthquake response mitigation of a base-isolated (BI) building equipped with (i) a single tuned mass damper at the top of the building, (ii) multiple tuned mass dampers (MTMDs) at the top of the building, and (iii) MTMDs distributed on different floors of the building (d-MTMDs) is studied. The shear-type buildings are modeled by considering only one lateral degree of freedom (DOF) at the floor level. Numerical approach of Newmark’s integration is adopted for solving the coupled, governing differential equations of motion of 5- and 10-story BI buildings with and without TMD schemes. A set of 40 earthquake ground motions, scaled 80 times to get 3200 ground motions, is used to develop simplified fragility curves in terms of the isolator maximum displacement. Incremental dynamic analysis (IDA) is used to develop simplified fragility curves for the maximum target isolator displacement. It is found that TMDs are efficient in reducing the bearing displacement, top floor acceleration, and base shear of the BI buildings. In addition, it was noticed that TMDs are efficient in reducing the probability of failure of BI building. Further, it is found that the MTMDs placed at the top floor and d-MTMDs on different floors of BI buildings are more efficient in decreasing the probability of failure of the BI building when compared with STMD.

Performance evaluation of bridges isolated with SMA-based friction pendulum system at low temperatures

This study investigates the performance of bridges isolated with the SMA (shape memory alloy) -based FPB (pendulum friction bearing) system at low temperatures. The SMA-based FPB system with Cu–Al–Be alloy wires is performed in OpenSees. The nonlinear time history analyses are conducted under near-fault ground motions. The optimum amount of the Cu–Al–Be wires with respect to isolation period is obtained by the proposed method. The effectiveness of the SMA-based FPB system for bridges at low temperatures is further investigated. Results show that the residual displacement can be effectively reduced without significantly increasing the base forces at low temperatures. The maximum isolator displacement can be effectively reduced when temperature is higher than −10 °C, whereas the reduction is limited below −20 °C. The energy dissipation capability of the side bearings can be improved at 20 °C, whereas limited improvement for the energy dissipation of the bearings can be provided at low temperatures. This study demonstrates that the SMA-based FPB system with Cu–Al–Be wires at low temperatures can provide reliable re-centering capability for bridges under near-fault ground motions.

Effects of temperature and lead core heating on response of seismically isolated bridges under near-fault excitations

Seismic responses of bridges isolated by lead rubber bearings under near-fault excitations are presented in this article. A bilinear force-deformation model is employed to represent the hysteretic behaviors of lead rubber bearings. The joint effects of ambient temperature, initial displacement, and lead core heating on the responses of seismically isolated bridges are investigated. Nonlinear time history analyses are conducted with the employed hysteretic models of lead rubber bearings. Comparisons of the responses with and without the joint effects are performed, in terms of maximum isolator displacements, maximum isolator forces, and base forces of the piers. Results show that ambient temperature, initial displacement, and lead core heating have significant joint effects on the responses of seismically isolated bridges. When such joint effects are ignored at low temperatures, the maximum isolator displacements could be overestimated, whereas the maximum isolator forces and the base forces could be underestimated. However, as for ambient temperatures above 20°C, the maximum isolator displacements could be underestimated, whereas the maximum isolator forces and the base forces could be overestimated with small maximum isolator displacements and underestimated with large maximum isolator displacements.

Assessment of proposed lateral load patterns in pushover analysis for base-isolated frames

The effectiveness of two proposed lateral load patterns (LLPs) to estimate the seismic demands of base-isolated building frames by the pushover analysis (POA) is assessed by comparing their estimates with the benchmark responses obtained by the nonlinear time history analysis (NTHA). The proposed LLPs include: (i) pattern derived from the square root of the sum of squares (SRSS) of first three mode shapes of BI frame; and (ii) two variants derived by the modification of the uniform force distribution load pattern. The conventional first mode shape LLP is also used in the POA for the purpose of comparison. A mid-rise (5-storey) and a high-rise (10-storey) base isolated (BI) reinforced concrete building frames are considered as illustrative examples for the analysis. An ensemble of five ground motion time-histories, each of far-field and near-field with forward directivity and fling-step effects are employed for NTHA. Target displacement-based comparison is performed by considering three target displacements, which cater to elastic, elastic to plastic and plastic states on the capacity curve of the building frames. The seismic demands namely, peak storey displacement, maximum inter-storey drift, number of plastic hinges, SRSS of plastic hinge rotations, maximum base shear and maximum isolator displacement are considered for comparison. The study reveals that (i) the errors in estimating the seismic demands by different LLPs depend on the state (elastic or elastic–plastic or plastic) of the building frame in which target displacement is considered; and (ii) the proposed LLP (modified uniform distribution) is found to best estimate the NTHA predictions.

Effects of vertical component of near-field ground motions on seismic responses of asymmetric structures supported on TCFP bearings

The effects of vertical component of earthquakes on torsional amplification due to mass eccentricity in seismic responses of base-isolated structures subjected to near-field ground motions are studied in this paper. 3-, 6- and 9-story superstructures and aspect ratios of 1, 2 and 3 have been modeled as steel special moment frames mounted on Triple Concave Friction Pendulum (TCFP) bearings considering different period and damping ratios. Three-dimensional linear superstructures resting on nonlinear isolators are subjected to both 2 and 3 component near-field ground motions. Effects of mass eccentricity and vertical component of 25 near-field earthquakes on the seismic responses including maximum isolator displacement and base shear as well as peak superstructure acceleration are studied. The results indicate that the effect of vertical component on the responses of asymmetric structures, especially on the base shear is significant. Therefore, it can be claimed that in the absence of the vertical component, mass eccentricity has a little effect on the base shear increase. Additionally, the impact of this component on acceleration is remarkable so the roof acceleration of a nine-story structure has been increased 1.67 times, compared to the case that the structure is subjected to only horizontal components of earthquakes.

USE OF BOUNDING ANALYSES TO ESTIMATE THE PREFORMANCE OF A SEISMICALLY ISOLATED STRUCTURE

Current design approach for seismic isolated structures is to perform bounding analyses. These analyses provide an envelope for the response of the seismic isolated structure rather than focusing on the actual performance. In this study, the success of bounding analyses to estimate performance of a seismic isolated structure, in which the isolation is provided by means of lead rubber bearings (LRBs), is evaluated in a comparative manner. For this purpose, nonlinear response history analyses were performed under the effect of bidirectional ground motion excitations. In bounding analyses, non-deteriorating hysteretic representations were used to model the hysteretic behavior of LRBs. On the other hand, to estimate the actual performance of both the superstructure and isolator units, deteriorating hysteretic idealizations were employed. The deterioration in strength of LRBs was defined as a function of temperature rise in the lead core. The analyzed structure is an existing seismically isolated hospital building and analytically modeled in accordance with its reported design properties for both isolation units and superstructure. Results obtained from analyses where LRBs are idealized by both deteriorating and non-deteriorating hysteretic representations are used in the comparisons. The response quantities used in the comparisons are maximum isolator displacement, maximum isolator force, maximum absolute floor acceleration, and maximum relative story displacements. In an average sense, bounding analyses is found to provide conservative estimates for the selected response quantities and fulfills its intended purpose. However, it is revealed that there may be individual cases where bounding analyses fails to provide a safe envelope.

Control of underground blast induced building vibration by shape-memory-alloy rubber bearing (SMARB)

Summary This paper focuses on the performance of shape-memory-alloy rubber bearings (SMARBs) compared to conventional lead-plug or New-Zealand (N-Z) bearings in control of building vibration due to underground blast induced ground motion (BIGM). The performance is evaluated with regard to maximum acceleration and isolator displacement obtained by nonlinear time history analysis. In doing so the Bouc–Wen's model is used to represent the nonlinear behaviour of the N-Z bearing and the superelastic behaviour of nickel–titanium-based shape-memory alloy is represented by the Graesser–Cozzarelli model. The underground BIGM input is modelled by exponentially decaying function. It is observed that though the N-Z bearing is fairly effective in controlling the structural accelerations due to BIGM without excessive bearing displacements, there remains a problem with the residual bearing displacements. The latter, however, is found to be dealt with very effectively by the SMARB. Furthermore, the procedure to obtain the optimum design parameters of the base isolators under study is obtained by optimizing two mutually conflicting objective functions, that is, the minimization of peak acceleration as well as peak bearing displacement by converting the multiobjective optimization problem to a single composite objective function. The improved and robust control performance of SMARB compared to N-Z bearing is elucidated through numerical study by considering a five-storied shear building frame.

Seismic responses of asymmetric steel structures isolated with the TCFP subjected to mathematical near-fault pulse models

In this paper, the effects of mass eccentricity of superstructure as well as stiffness eccentricity of isolators on the amplification of seismic responses of base-isolated structures are investigated by using mathematical near-fault pulse models. Superstructures with 3, 6 and 9 stories and aspect ratios equal to 1, 2 and 3 are mounted on a reasonable variety of Triple Concave Friction Pendulum (TCFP) bearings considering different period and damping ratio. Three-dimensional linear superstructure mounted on nonlinear isolators are subjected to simplified pulses including fling step and forward directivity while various pulse period (Tp) and Peak Ground Velocity (PGV) amounts as two crucial parameters of these pulses are scrutinized. Maximum isolator displacement and base shear as well as peak superstructure acceleration and drift are selected as the main engineering demand parameters. The results indicate that the torsional intensification of different demand parameters caused by superstructure mass eccentricity is more significant than isolator stiffness eccentricity. The torsion due to mass eccentricity has intensified the base shear of asymmetric 6-story model 2.55 times comparing to symmetric one. In similar circumstances, the isolator displacement and roof acceleration are increased 49 and 116 percent respectively in the presence of mass eccentricity. Furthermore, it is demonstrated that torsional effects of mass eccentricity can force the drift to reach the allowable limit of ASCE 7 standard in the presence of forward directivity pulses.

Seismic vibration control of bridges with excessive isolator displacement

The effectiveness of base isolation (BI) systems for mitigation of seismic vibration of bridges have been extensively studied in the past. It is well established in those studies that the performance of BI system is largely dependent on the characteristics of isolator yield strength. For optimum design of such systems, normally a standard nonlinear optimization problem is formulated to minimize the maximum response of the structure, referred as Stochastic Structural Optimization (SSO). The SSO of BI system is usually performed with reference to a problem of unconstrained optimization without imposing any restriction on the maximum isolator displacement. In this regard it is important to note that the isolator displacement should not be arbitrarily large to fulfil the serviceability requirements and to avoid the possibility of pounding to the adjacent units. The present study is intended to incorporate the effect of excessive isolator displacement in optimizing BI system to control seismic vibration effect of bridges. In doing so, the necessary stochastic response of the isolated bridge needs to be optimized is obtained in the framework of statistical linearization of the related nonlinear random vibration problem. A simply supported bridge is taken up to elucidate the effect of constraint condition on optimum design and overall performance of the isolated bridge compared to that of obtained by the conventional unconstrained optimization approach.