On the effect of near-field excitations on the reliability-based performance and design of base-isolated structures
Introduction
The recent improvements in isolation system products have led to the design and construction of an increasing number of seismically isolated structures worldwide [1], [2], [3], [4]. Similarly, seismic isolation has been extensively used for seismic retrofitting of existing buildings [5], [6]. In addition, base isolation concepts are utilized for the protection from shock and vibration of sensitive components of critical facilities such as hospitals, nuclear reactors, industrial and data center facilities. One of the difficulties in the analysis and design of base-isolated systems has been the explicit consideration of the non-linear behavior of the isolators. Another challenge has been the efficient prediction of the dynamic response under future ground motions considering their potential variability as well as the efficient control of competing objectives related to the protection of the superstructure and the minimization of the base displacement. In particular, the response of this class of systems under near-field ground motions has been recognized to be one of the current challenges for the analysis and design of base-isolated systems. In fact, the study of the effects of near-field ground motions on engineering structures is an active research topic in earthquake engineering [7], [8], [9], [10]. Near-field ground motions frequently include a strong long period pulse that has important implications for flexible structures such as base-isolated systems. For these systems near-field ground motions may lead to excessive base deformations and superstructure deformations with important implications for the integrity of the combined structural system (isolation system and superstructure).
The current work presents a framework for studying the effect of near-field excitations on the reliability-based performance and design of base-isolated systems. In particular, the case of large scale building models is considered in this work. The proposed study explicitly takes into account all non-linear characteristics of the combined structural system, and the variability of future excitations including near-field ground motions. Isolation systems composed by rubber bearings are used in the present formulation. The non-linear behavior of these devices is characterized by a biaxial hysteretic model which is calibrated with experimental data. A probabilistic logic approach is adopted for addressing the variability of future excitations. In the approach, probability is interpreted as a means of describing the incomplete information about the problem under consideration. This is established by characterizing the relative plausibility of future excitations by probabilistic models. A realistic stochastic model for the description of ground motions with high and low frequency components is considered in this work [11]. The model, which belongs to the class of point-source models, establishes a nexus between the knowledge about the characteristics of the seismic hazard in the structural site and future ground motions. First excursion probabilities are used as measures of the system reliability. In this setting, reliability is quantified as the probability that the response quantities of interest (base displacements and superstructure interstory drifts and absolute accelerations) will not exceed acceptable performance bounds within a particular reference period. Such probabilities are estimated by an adaptive Markov Chain Monte Carlo procedure [12].
In summary the novelty of this work is based on the integration of several independent tools in order to evaluate the effect of near-field excitations on the reliability-based performance and design of base-isolated systems. In particular, the following tools are integrated into the proposed methodology: a realistic stochastic model for the description of near-field ground motions; an accurate model for the nonlinear behavior of the isolators; and an advanced simulation technique for estimating high dimensional probability integrals. These tools allow to study the effect of near-field excitations on seismic isolated systems in a stochastic setting, e.g. from a reliability point of view.
The organization of the paper is as follows. Section 2 introduces the structural model for the superstructure and base platform. The stochastic model for the excitation is examined in Section 3. Section 4 deals with the characterization of the isolator elements. The reliability assessment and the structural response of base-isolated buildings are discussed in 5 Reliability measures, 6 Structural response, respectively. The effect of near-field excitations on the reliability-based performance and design of two large finite element building models are presented in 7 Application problem 1, 8 Application problem 2. The paper closes with some final remarks.
Section snippets
Structural model
Finite element building models with a large number of degrees of freedom are considered for modeling the superstructure, i.e. the structure above the isolation system. For illustration purposes a schematic representation of a base-isolated finite element building model is shown in Fig. 1. The corresponding base platform with isolators is illustrated in Fig. 2. In general, base-isolated buildings are designed such that the superstructure remains elastic. Hence, the superstructure is modeled as a
General description
The uncertain earthquake excitation is modeled as a non-stationary stochastic process with uncertain model parameters. In particular, a point source model characterized by the moment magnitude M and epicentral distance r is considered in this work [11], [13]. The methodology, which was initially developed for generating synthetic ground motions, has been reinterpreted to form a stochastic model for earthquake excitation [14], [15]. According to this approach high-frequency and low-frequency
Isolators description
Rubber bearings are considered for modeling the isolation system. Such devices have been used over many years in a number of seismically isolated buildings worldwide [3], [22], [23]. They require minimal initial cost and maintenance compared to other passive, semi-active and active energy absorption devices. A rubber bearing consists of layers of rubber and steel, with the rubber being vulcanized to the steel plates. Rubber bearing systems are able, in principle, to support the superstructure
Reliability measures
The performance of base-isolated structural systems is assumed to be characterized by means of a set of response functions , , where y is the vector of isolation system parameters, is the vector of uncertain variables that characterizes the stochastic excitation model, and Ih is a set of indices. Recall that the vector consists of the white noise sequence , the seismological parameters M and r, and the parameters for the near-fault pulse fp, Ap, γp and νp. The isolator
Structural response
The response of base-isolated structural systems is obtained from the solution of the equation of motion that characterizes the combined system (isolation system and superstructure). The solution of the equation of motion (3) is obtained in an iterative manner due to the nonlinearity of the isolators forces. The solution scheme is implemented as follows:
- (1)
At the beginning of the iteration (l=0) within the time interval it is assumed that , and
Description
The structural system shown in Fig. 11 is considered for analysis. It consists of a height floor three-dimensional reinforced concrete building model with base isolation. The system represents a standard structural configuration in terms of its flexibility. Material properties of the reinforced concrete structure have been assumed as follows: Young׳s modulus ; Poisson ratio ; and mass density . The total mass of all floors is except the first one which
Structural system
The goal of the second application problem is to analyze the effect of near-field motions on the performance and design of an isolation system for a stiff superstructure. The consideration of stiff superstructures is important since critical facilities such as nuclear reactors, data centers, etc, belong to this type of structures. For the purpose of this study a three-dimensional two story reinforced concrete building model with more than 7000 degrees of freedom is considered. The isometric
Conclusions
The effect of near-field ground motions on the reliability-based performance and design of large scale base-isolated building models has been investigated. The importance of the study lies in the fact that near-field ground motions frequently include strong long period pulses that have important implications for flexible structures such as base-isolated systems. Isolation systems composed by rubber bearings are considered in the present formulation. The non-linear behavior of these devices is
Acknowledgments
The research reported here was supported in part by CONICYT under grant number 1110061 which is gratefully acknowledged by the authors.
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