Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 129787, 12 pages

http://dx.doi.org/10.1155/2015/129787

## A Novel Approach to Evaluate the Time-Variant System Reliability of Deteriorating Concrete Bridges

^{1}Zhejiang Scientific Research Institute of Transport, Hangzhou 310006, China^{2}State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China^{3}Zhejiang Institute of Communications, Hangzhou 311112, China^{4}Department of Bridge Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China

Received 8 October 2015; Revised 6 December 2015; Accepted 9 December 2015

Academic Editor: Egidijus R. Vaidogas

Copyright © 2015 Hao Tian 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

Bridge time-variant system reliability is a useful measure to evaluate the lifetime performance of deteriorating bridge structures under uncertainty and is an influential performance indicator in bridge maintenance management programs. This paper proposes a computational methodology based on the Monte Carlo simulations for evaluating the time-variant system reliability of concrete bridges under environmental attacks. Methods related to the reduction of concrete sections and the variation of the load effects acting on the components are investigated using a finite element-based computational program, CBDAS (Concrete Bridge Durability Analysis System), to perform the assessment of lifetime structural performance. With regard to system reliability, a practical technique for searching the structural failure mode is also presented and a program, SRMCS (System Reliability by Monte Carlo Simulations), based on the Monte Carlo simulations is written to calculate and evaluate the structural system reliability of deteriorating concrete bridges. Finally, three numerical examples are presented to display the CBDAS and SRMCS functions.

#### 1. Introduction

A large percentage of the bridges all over the world are constructed with concrete and reinforcing steel, because of their relatively low cost [1]. In recent years, however, significant distress and deterioration have been observed in many concrete bridges, mainly due to the environmental stressors such as concrete carbonation, chloride penetration, and freeze-thaw cycles. Thus, maintenance intervention to keep the structure healthy during its service life is necessary. The primary task in selecting and performing an appropriate maintenance strategy for a deteriorating concrete bridge is to evaluate and predict its lifetime structural performance [2]. To achieve this, the computational prediction should be probabilistic based, due to the inherent randomness reflected in the structural configuration, materials properties, live loads, and different environments. A comprehensive consideration of time-variant performance and uncertainty is a useful measure to assess the lifetime performance of a deteriorating bridge structure and is one of the key performance indicators in bridge maintenance management programs [3, 4]. However, though widely accepted and used, current techniques and methods may still not be accurate enough in measuring the time-variant reliability of bridges for the following reasons: () the effects of the aggressive environments on the structural performance have not been precisely simulated, () the structural failure mode (i.e., the relationship between the overall structural failure and the individual component failure) is hard to measure; and () the correlation coefficients among the individual components or failure modes are difficult to determine [5–7].

Because of the shortcomings of previous techniques and methods, a finite element- and Monte Carlo simulations-based computational methodology is proposed for evaluating the time-variant system reliability of deteriorating concrete bridges [8–10]. For time-variant performance, methods related to the reduction of concrete sections and the variation of structural load effect are discussed. For system reliability, a technique for searching the structural failure mode is presented, and a Monte Carlo simulations-based program, SRMCS, is presented. Finally, three numerical examples are illustrated to display the functions of CBDAS and SRMCS and of the combination of the two programs: () in the first example, the time-variant performance of a reinforced concrete continuous bridge under chloride-induced corrosion is evaluated by means of CBDAS; () in the second example, the procedure for computing the system reliability of a two-story truss is displayed in terms of SRMCS; and () in the third example, the time-variant system reliability of the same model as the first example is investigated by combining CBDAS with SRMCS.

#### 2. Time-Variant Performance

It is well known that the variation of structural performance with respect to the deteriorating concrete bridges may be significant during their entire service lifetime due to the environmental attacks [9, 10]. Also, because the resistances of the individual components are time variant, it is necessary to evaluate the time-variant structural performance in an effective way by selecting an appropriate maintenance schedule.

##### 2.1. Finite Element-Based Approach

The essential problems encountered in the assessment of lifetime performance are as follows: () the deterioration of the materials properties, () the reduction of sectional areas, and () the variation of the overall structural performance induced by the first two problems. Furthermore, the last two problems can be divided into the reductions of reinforcing steel and concrete sections, the deterioration of resistances of the individual components, and the variation of load effects acting on these components. The two main problems to be investigated in this paper are the reduction of concrete sections due to environmental attacks and the variation of the load effects acting on the individual components.

###### 2.1.1. Reduction of Concrete Sections

When considering the reduction of a concrete section, it is necessary to simulate the accurate shape of the section, as it is one of the critical factors related to measuring the actual reduction process. One way to accurately do this is to simulate the section by using the concrete edge as the basic unit because the reduced depths of the concrete edges in the same section are likely to be not identical due to the different values of the environmental parameters and other design variables among the concrete edges. It can be seen from Figure 1(a) that the number of the edges is equal to that of the nodes. Thus, the edge information can be obtained from the coordinates of the control nodes. The cross-sectional geometrical properties can be thus calculated associated with the node coordinates and the Triangle Partitioning Method [11, 12] and by using the edge as basic unit, the reduction process of concrete section can be described as the movement of the concrete edges. The specific steps are as follows: () the corrosion rate of the reinforcing steel related to each concrete edge is calculated by means of the corrosion numerical model, () the reduced depths of the two adjacent concrete edges are obtained in association with the corrosion rates of the reinforcing steels on the two edges, () each edge moves a distance equal to the respective reduced depth along its normal direction and a group of new control nodes are obtained as the intersections of the moved concrete edges, and () the remaining concrete section can be generated with the same method as the original one. The reduction process is shown in Figure 1(b), where the figure surrounded by solid lines is the original concrete section and the one encircled by dashed lines is the remaining section.