Advances in Civil Engineering

Volume 2018, Article ID 4517940, 21 pages

https://doi.org/10.1155/2018/4517940

## Seismic Response Analysis of Fully Base-Isolated Adjacent Buildings with Segregated Foundations

Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

Correspondence should be addressed to Khaled Ghaedi; moc.oohay@ideahqdelahk and Zainah Ibrahim; ym.ude.mu@haniaz

Received 27 August 2017; Accepted 26 November 2017; Published 12 March 2018

Academic Editor: Chiara Bedon

Copyright © 2018 Khaled Ghaedi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In populous cities, construction of multistorey buildings close to each other due to space limitation and increased land cost is a dire need. Such construction methods arise several problems during earthquake excitation. The aim of this study is to investigate the bidirectional seismic responses of fully base-isolated (FBI) adjacent buildings having different heights and segregated foundations. Therefore, two scenarios, namely, (a) investigation of the responses of FBI adjacent buildings compared to those with fixed base (FFB) and (b) the effects of separation distance on FBI adjacent buildings, were studied. Based on these investigations, the results showed that isolation system significantly enhances the overall responses of the BI buildings. Spectacularly, the base isolation system was further efficient to decrease displacement rather than the acceleration. In addition, increase of the seismic gap changed the acceleration, pounding, base shear, base moment, and storey drift, as well as the force-deformation performance of the isolators. Therefore, it seems a need to focus on the effect of the separation distances for the design of base isolators for FBI adjacent buildings in future works.

#### 1. Introduction

Adjacent buildings are constructed without any structural link connected to surrounding buildings. However, in few cases, they are rarely connected at the foundation level. As a matter of fact, engineers have taken serious concerns about structural damages caused by devastating earthquakes [1–3]. Therefore, the structural pounding phenomenon will usually occur in adjacent buildings during earthquake excitations [4]. Consequently, the buildings with inadequate seismic gap suffer from damages due to the pounding force. Mexico City, 1985, and Northern California, 1989, are good examples to signify the importance of seismic gap between adjacent buildings. It is good enough to flashback both events where pounding effect has been seen by 132 demolished adjacent buildings in the Mexico City and 200 collapsed buildings in Northern California [5, 6]. In this regard, many researchers have studied the structural responses of either the base-isolated (BI) building in adjacent with a conventional fixed supported building [7–9], FFB adjacent buildings, or adjacent building equipped with other dissipative devices [6, 10–18].

Structural responses of adjacent buildings have been investigated by means of nonlinear techniques which demonstrated that collapse of structures has a significant influence on the performance of light and flexibility of buildings mainly in the pounding direction [11, 19–22]. Penzien [23] used the complete quadratic mode combination (CQC) approach, whilst Kasai et al. [24] used the spectral difference (SPD) method to calculate the required gap between two FB adjacent buildings. Both techniques were able to predict the structural responses concerning building vibration. Moreover, the square root of the sum of the squares (SRSS) approach has been governed by the international buildings codes (IBC), and consequently, the required distances between buildings were provided [25]. Shrestha [26] offered a minimum required gap for buildings to prevent pounding by means of double difference combination (DDC) and SRSS techniques. The obtained results exhibited that the DDC method assessed the required separation gap to hold pounding up. Furthermore, structural responses of FFB adjacent buildings have been numerically analyzed [26, 27]. Khatiwada et al. [28] proposed the Hunt–Crossley model. The precise calculation of damping constant was presented in that model. The efficiency of Hunt–Crossley model in linear and nonlinear analysis for pounding simulation of concrete structures was compared with nonlinear viscoelastic, linear viscoelastic, and modified linear viscoelastic models. The nonlinear Hunt–Crossley model was capable to predict the contact force between FB adjacent buildings.

From the literature review, it was found that the seismic responses of FBI adjacent buildings have not been studied thoroughly. In this paper, an attempt was thoroughly made by dividing the scenarios into two cases comprising (i) investigate the seismic response characteristics of FBI adjacent building comparing to FFB buildings (Scenario 1) and (ii) investigate the gap size effect on seismic pounding of FBI adjacent buildings (Scenario 2) having different heights. For this aim, lead rubber bearings (LRB) were designed based on the NEHRP provisions [29]. Afterwards, a comparative analysis of two FFB and BI adjacent buildings under bidirectional seismic excitations was carried out.

#### 2. Methodology

##### 2.1. Nonlinear Dynamic Analysis

In the present study, nonlinear dynamic analysis was done using a typical bidirectional seismic recorded and a finite element (FE) analysis package. That is, SAP2000 was selected as an appropriate tool for aiding the purpose. The main equations of motion were taken deliberating equilibrium of forces at each DOF. The motion equations for superstructure and base isolation were written asin which [*M*] is the mass matrix, [*C*] and [*K*] are damping and stiffness matrix of the superstructure, respectively, and is the superstructure displacement. Displacement and acceleration corresponding to the ground are nominated by and . The earthquake effect coefficient matrix is given by .

All nonlinearities are only restricted to the elements of the base isolator. In the above dynamic equilibrium equation, the base isolator and superstructure are considered as nonlinear and elastic, respectively. Therefore, (1) is written aswhere *K*_{L} is the stiffness matrix for superstructure as the linear elastic and is the force vectors due to nonlinear degrees of freedom related to isolator elements. The displacement, velocity, and acceleration corresponding to ground is determined by , and , respectively; and the vector of imposed loads is defined by . At nonlinear DOF, the effective stiffness is arbitrary, but it changes between zero and the utmost stiffness of that DOF. The equation of equilibrium could be rewritten asin whichwhere is the stiffness matrix for all nonlinear DOFs.

##### 2.2. Gap Elements

The gap distance between the buildings was represented by the link element in SAP2000. It is remarkable that the gap (link) element is active only in a compression state. The function of the link element (gap element) is to transfer pounding force through itself only at the moment of the impact of buildings. The force-deformation correlation in nonlinearity form was expressed as follows:in which *k* is the constant of spring, *d* represents the displacement, and the initial gap opening (has to be zero or positive) is defined by open. For gap element in nonlinear analysis cases, its stiffness was defined as one to two orders stiffer than surrounding columns and beams in each level. The gap element stiffness was selected to be 10^{2} times larger than the stiffness of adjacent attached element. Hence, in this study, the stiffness of the gap elements was determined asin which *A* is the cross-sectional area of the element, *E* is Young’s modulus of the element, and *L* is the element length in perpendicular direction to the contact surface. Furthermore, dissipating energy during collision can be determined by damping. The linear effective stiffness effect and damping were included in the gap element to achieve favourable contact behaviour.

##### 2.3. Nonlinear Time History Analysis

The finite element software SAP2000 was implemented to investigate the response of adjacent buildings under different seismic loads by modelling two adjacent ordinary moment-resisting concrete frame (OMRCF) buildings considering FFB adjacent buildings and FBI adjacent buildings subjected to bidirectional earthquake excitations. Nonlinear dynamic time history analysis was carried out through bilateral seismic recorded of Cape (PGA 2.85 m/s^{2}), Los Angeles Century City, LACC-North (PGA 3.85 m/s^{2}), Santa Monica (PGA 1.20 m/s^{2}), and El-Centro (PGA 3.20 m/s^{2}), as shown in Figure 1.