Computational Intelligence and Neuroscience

Volume 2015, Article ID 495042, 7 pages

http://dx.doi.org/10.1155/2015/495042

## Analysis of the Seismic Performance of Isolated Buildings according to Life-Cycle Cost

^{1}Key Laboratory of Concrete and Prestressed Concrete Structure, Ministry of Education, Nanjing 210096, China^{2}School of Civil Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 19 August 2014; Accepted 19 December 2014

Academic Editor: Carlos M. Travieso-González

Copyright © 2015 Yu Dang 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

This paper proposes an indicator of seismic performance based on life-cycle cost of a building. It is expressed as a ratio of lifetime damage loss to life-cycle cost and determines the seismic performance of isolated buildings. Major factors are considered, including uncertainty in hazard demand and structural capacity, initial costs, and expected loss during earthquakes. Thus, a high indicator value indicates poor building seismic performance. Moreover, random vibration analysis is conducted to measure structural reliability and evaluate the expected loss and life-cycle cost of isolated buildings. The expected loss of an actual, seven-story isolated hospital building is only 37% of that of a fixed-base building. Furthermore, the indicator of the structural seismic performance of the isolated building is much lower in value than that of the structural seismic performance of the fixed-base building. Therefore, isolated buildings are safer and less risky than fixed-base buildings. The indicator based on life-cycle cost assists owners and engineers in making investment decisions in consideration of structural design, construction, and expected loss. It also helps optimize the balance between building reliability and building investment.

#### 1. Introduction

The life-cycle cost of a building is the entire cost over its expected life time, including initial investment, maintenance, and repair costs. It also covers loss in occasional cases, such as that incurred during earthquakes. The optimum seismic performance of a building can be considered “the reasonable balance between the initial investment cost of improving seismic performance and the prospective loss as a result of earthquakes” [1]. Life-cycle cost can be regarded as an indicator of structural seismic performance because the cost of earthquake damage can be quantified.

Many of the following studies determine the optimal seismic design by minimizing life-cycle cost. Nathwani et al. [2], Pandey and Nathwani [3], and Rackwitz [4] developed optimal designs simply by minimizing the expected life-cycle cost based on its magnitude of uncertainty. Liu et al. [5] suggested a two-objective optimization procedure to design steel moment-resisting frame buildings within a performance-based seismic design framework. In this procedure, the initial material and life time costs of seismic damage are treated as two separate objectives. Lagaros et al. [1] adopted the limit-state cost to compare descriptive and performance-based design procedures. Frangopol and Liu [6] reviewed the recent developments in life-cycle maintenance and management planning for deteriorating civil infrastructures, especially bridges. Kappos and Dimitrakopoulos [7] implemented decision-making tools, namely, cost-benefit and life-cycle cost analyses, to determine the feasibility of strengthening reinforced-concrete buildings. Pei and van de Lindt [8] also proposed a probabilistic framework to estimate long-term, earthquake-induced economic loss related to wood-frame structures.

Several studies have analyzed the life-cycle cost of isolated buildings. Lee et al. [9] studied the life-cycle cost of a structure with base isolation. The results of life-cycle cost analysis indicate that isolators reduced the life-cycle cost by approximately 16%. Moreover, Sarkisian et al. [10] designed a 12-story structure for the Administrative Office of the Courts. Life-cycle cost analysis assisted in informed decision making and system selection, and the final design featured a steel-framed superstructure with an isolation system. Chatzidaki [11] optimized the design of and economically evaluated reinforced-concrete (RC) isolated structures. Generally, the researchers have a similar conclusion: the life-cycle cost of isolated buildings is less than that of the fixed-base buildings.

In the current study, structural seismic performance is measured according to indicator-based life-cycle cost. This cost can synthesize all factors, including structural design, construction, and expected loss from earthquakes. The indicator of an isolated building is analyzed in detail in comparison with that of a fixed-base building in the following sections. Practical construction complexity, important but difficult to be included in initial cost analysis, is taken into due account by a proposed diversity index as another objective, this approximation data is best used for the preliminary design stage, and the large pools of alternatives leave to a design maker much freedom to select the one that best meets his/her goals.

#### 2. Indicator-Based Life-Cycle Cost of Structural Seismic Performance

##### 2.1. Life-Cycle Cost of Structures

The life-cycle cost of a structure may refer either to the design life of a new structure or to the remaining life of an existing or retrofitted structure. This cost can be expressed as a function of time and of the design vector [1]: where is the total cost of a structure; is the initial cost of a new or retrofitted structure; is expected loss; is the time period; is the design vector corresponding to the design loads, resistance, and material properties that influence the performance of the structural system; and is the constant annual discount rate and is usually equal to 3% [1].

can be written as [1] where is the conditional probability of failure, which can be obtained through dynamic reliability analysis. is fortification intensity; is the probability of seismic hazard; and denotes the three seismic design levels, namely, minor , moderate , and major earthquakes . The cumulative distribution function of fortification intensity is a type III extreme value distribution during the design reference period in Mainland China. Thus, , , and are approximately equal to 70%, 25.2%, and 4.5%, respectively [12].

represents structural damage and can be divided into five levels, that is, none, slight, moderate, severe, and collapsed. These structural damage states are defined by specific quantities. Interstory drift can be a reliable limit-state criterion according to which expected damage can be determined. Thus, maximum interstory drift is considered the response parameter that best characterizes structural damage. The damage index limits of isolated superstructures are similar to those of fixed-base buildings; however, these limits have not been determined for the isolated layer. The damage states are quantitatively defined in terms of interstory drift given that the isolator may be damaged when its shear strain exceeds the acceptable value as shown in Table 1.