International Journal of Corrosion

Volume 2016 (2016), Article ID 6392702, 5 pages

http://dx.doi.org/10.1155/2016/6392702

## Simulation of the Ill-Posed Problem of Reinforced Concrete Corrosion Detection Using Boundary Element Method

^{1}Department of Mechanical Engineering, Syiah Kuala University, Jalan Tgk Syech Abdul Rauf 7, Banda Aceh 23111, Indonesia^{2}Tsunami & Disaster Mitigation Research Center (TDMRC), Syiah Kuala University, Jalan Tgk Abdul Rahman, Gp. Pie, Meuraxa District, Banda Aceh 23111, Indonesia^{3}Department of Mechanical and Materials Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 21 January 2016; Accepted 24 March 2016

Academic Editor: Jerzy A. Szpunar

Copyright © 2016 Syarizal Fonna 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

Many studies have suggested that the corrosion detection of reinforced concrete (RC) based on electrical potential on concrete surface was an ill-posed problem, and thus it may present an inaccurate interpretation of corrosion. However, it is difficult to prove the ill-posed problem of the RC corrosion detection by experiment. One promising technique is using a numerical method. The objective of this study is to simulate the ill-posed problem of RC corrosion detection based on electrical potential on a concrete surface using the Boundary Element Method (BEM). BEM simulates electrical potential within a concrete domain. In order to simulate the electrical potential, the domain is assumed to be governed by Laplace’s equation. The boundary conditions for the corrosion area and the noncorrosion area of rebar were selected from its polarization curve. A rectangular reinforced concrete model with a single rebar was chosen to be simulated using BEM. The numerical simulation results using BEM showed that the same electrical potential distribution on the concrete surface could be generated from different combinations of parameters. Corresponding to such a phenomenon, this problem can be categorized as an ill-posed problem since it has many solutions. Therefore, BEM successfully simulates the ill-posed problem of reinforced concrete corrosion detection.

#### 1. Introduction

Rebar corrosion is one of the main causes of reinforced concrete (RC) premature failures [1–3]. Reports of these premature failures can be found in various publications. The failures include the collapse of Silver Bridge in USA, 1967 [4], the collapse of highway overpass in Canada, 2006 [5], and the collapse of Atlantis Water Adventure,* Taman Impian Jaya Ancol* in Indonesia, 2011 [6]. Recent failure due to corrosion was reported in March 2015: the porch of a building collapsed in Albany, USA [7]. Thus, It is important to conduct periodic evaluation, monitoring and early detection for RC corrosion [8–10].

The half-cell potential technique is among the conventional methods that are used in the field to detect or evaluate the RC corrosion [11, 12]. This technique follows the procedure as described in ASTM C876 to evaluate corrosion of an RC structure. However, the method only provides the probability of corrosion [13, 14] and needs a considerable amount of measurement data to generate an accurate potential map [11, 15]. Therefore, it is important to understand the nature of the RC corrosion problem before the development of other methods and/or improvement of conventional techniques to detect RC corrosion. Many workers have proposed methods based on inverse analysis to detect RC corrosion [13, 15, 16] since the nature of RC corrosion implies an ill-posed problem. However, it is difficult to prove the ill-posed problem of RC corrosion via experiments. Thus, using a numerical method to prove the ill-posed problem of RC corrosion is very promising.

Many researchers have explored a numerical method termed the Boundary Element Method (BEM) to simulate the corrosion phenomenon. The corrosion was modeled by the Laplace equation in BEM [16–18]. Thus, BEM can potentially be utilized to simulate the ill-posed problem of RC corrosion. The purpose of this paper is to simulate the ill-posed problem of RC corrosion problem by using BEM.

#### 2. Basic Idea to Simulate the Ill-Posed Problem of RC Corrosion

The ill-posed problem is a problem that has one of the following criteria; that is, the problem has no unique solution or many solutions, and small error would give high disturbance to the solution [19]. The motivation for utilizing BEM to simulate the ill-posed problem of RC corrosion came from the actual condition that interpretation of the half-cell potential technique is merely based on electrical potential data on the RC surface, as mentioned in ASTM C876. Previous researchers have pointed out that the electrical potential on the RC surface is influenced not only by rebar corrosion but also by other parameters [20].

Furthermore, it has been suggested that the variation of some parameters could give similar electrical potential profiles on the RC surface, which should indicate an ill-posed problem. By simulating similar electrical potentials resulting from different parameter combinations, the ill-posed problem of RC corrosion can be proven. This ill-posed problem might lead to misleading conclusions in the detection of RC corrosion by the half-cell potential technique.

Since BEM has the capability of obtaining electrical potential and current density within an evaluated domain, it is proposed in this paper that BEM is also capable to be used to simulate the ill-posed problem of RC corrosion. The basic idea for this purpose was to compare the electrical potential on an RC surface obtained by BEM, which came from various combinations of parameters.

#### 3. RC Corrosion Modeling in BEM

The RC model with single reinforcing steel as given in Figure 1(a) was considered. There is corrosion located in the reinforcing steel. This RC model was simplified into a 2D model, as shown in Figure 1(b), which also displays the boundary conditions for the model.