COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Identification of Electric Conductivity and Impedance of Reinforced
Concrete by Boundary Element Inverse Analysis
Masato Yoshida 1*, Kazuhiro Suga 2, M. Ridha 3, Kenji Amaya 4 , Shigeru Aoki 5
1
2
3
4
5
GraduateSchool of Engineering, Toyo University, Japan
Center for Computational Mechanics Research, Toyo University,2-36-5 Hakusan, Bunkyo-ku Tokyo, Japan
Department of Mechanical Engineering, Syiah Kuala University, Banda Aceh, Indonesia
Department of Mechanical and Enviromental Informatics Tokyo Institute of Technology, 2-12-1 Ookayama,
Meguroku Tokyo 152-8552, Japan
Department of Computational science and Engineering, Toyo University, Japan
Email: [email protected]
Abstract A new method is introduced for identifying the electrical conductivity of concrete and the impedance of
steel-concrete interface by using some potential data which are measured on the concrete surface. The identification is
based on the boundary element inverse analysis. The inverse analysis was carried out by minimizing the cost function,
which is the different between measured and calculated potential in the concrete surface. Laplace equation, which is
solved by boundary element method, is used to describe the potential on the concrete domain. An experiment using a
concrete block with an embedded rebar is used to demonstrate the effectiveness of the proposed method. The
alternative current is impressed into the concrete domain at one point on the concrete surface and the potential is
measured at several points on the concrete surface.
Key words: Electric Conductivity, Impedance, Reinforced Concrete, Boundary Element Method, Inverse Analysis
INTRODUCTION
Corrosion of steel bars in concrete is a major cause of failure of the reinforced concrete structures. It is desired to
prevent it effectively based on the corrosion analysis of steel bar in concrete structures [1]. In order to do corrosion
analysis, it is necessary to know the electric conductivity of concrete and the impedance between a steel bar and
concrete. A new method is introduced in this study for identifying the conductivity and impedance. These are
identified from the potential data measured at some points on a concrete surface. The identification method is based on
a boundary element inverse analysis.
MODEL
Figure 1: Concrete model
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Fig. 1 shows the steel bar embedded in a concrete block used in this study. An alternative current (amplitude = 0.1 mA , frequency
= 1Hz) was impressed into the concrete from a counter electrode on the concrete surface. In boundary element calculation, the
surface of the concrete and steel was discretized into 190 rectangular constant elements.
SIMULATION
Before applying the identification method using experimental data, a numerical simulation was performed to confirm
the validity of several points on the concrete surface shown in Figure 2. Direct analysis of boundary element method
was used the calculated the potential on the concrete surface. The calculated potential values were rounded off into
three digits to take into account the measurement error. The complex electrical conductivity of the concrete (k = kre + i
kim) and the complex impedance of steel-concrete interface, (z = zre + i zim) were identified using these simulated
potential data in the inverse analysis.
Figure 2: Measurement part of model
Fig. 3 shows the inverse analysis Algorithm. Firstly, The value of complex electric conductivity and impedance are
assumed. Next, the complex values of potential on the concrete surface are calculated by using the boundary element
direct analysis. Then, he cost function c(kre, kim, zre, zim), which is shown in Fig. 3 and a measure of the difference
between the measured and calculated potential values is evaluated. To minimize the cost function , the values of kre,
kim, zre and zim are modified by using the downhill simplex method. This procedure is repeated until the cost function
becomes less than a prescribed small value, ε = 0.1 × 10−4.
Figure 3: Boundary element inverse analysis algorithm
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Fig. 4 shows the shows the accuracy of the identification of kre, kim, zre and zim. It is found that the relative error
decreases with increase in the number of measurement points.
kre
kim
zre
zim
Figure 4: Relative error
EXPERIMENT FOR IDENTIFICATION
Fig. 5 shows the experimental set up for identification of complex conductivity of concrete and the impedance between
a steel bar and concrete. Three electrodes arrangement, bar and concrete. Three electrodes arrangement, namely
working electrode, reference electrode and counter electrode are used. An alternative current was impressed into the
concrete domain from counter electrode. The real and imaginary parts of potentials were measured 20 points on the
concrete surface using reference electrodes (saturated calomel electrode). These data were used as input data for the
inverse analysis. The identification results are as follows :
kre = 0.18181 Ω−1m
kim = −0.00018 Ω−1m
zre = 0.839393 Ωm2
zim = −0.828813 Ωm2
Figure 5: Experimental setup
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EFFICIENT IDENTIFICATION
Accuracy of identification differs depending on measurement location. Fig. 6 shows the ranking in order of high
accuracy [3]. Identification was carried out using the potential data measured at (1) 20 points shown in the shadowed
part in Fig. 6, (2) 4 points (ranking 7, 4, 6, 8, this set will be referred to as 4 points A) or (3) other 4 points (ranking 24,
19, 14, 13, this set will be is referred to as 4 points B).
Figure 6: A 3D model with spherical particles
Fig. 7 and Fig. 8 show the real and imaginary parts of the electric potential distributions on the concrete surface. The
distributions were calculated by the boundary element direct analysis using the values of kre, kim, zre and zim which
were estimated by the inverse analysis with the input data measured at (1) 20 points, (2) 4points A or (3) 4points B. It
is found that the result for (1) 20 points agree well with those for (2) 4 points A, but differ from those for (3) 4 points
B. This means that an effective identification can be made with a small number of input data measured at the high
ranking location shows in Fig. 6
Figure 7: Potential real
Figure 8: Potential imaginary
CONCLUSIONS
A new method for identifying the complex electric conductivity of concrete and the impedance between a steel bar and
the concrete were introduced using the boundary element inverse analysis are the electric potentials measured at some
points on the concrete surface. It is show that an elective identification can be made by selecting appropriate measuring
points.
REFERENCES
1. Ridha M, Amaya K, Aoki S. Multistep genetic algorithm for detecting corrosion of reinforceing steels in
concrete. Corrosion, 2001; 57: 791-801.
2. Ridha M, Amaya K, Aoki S. Improvement of AC impedance method for monitoring corrosion of rebar structure
by boundary element inverse analysis. Zairyo-to-Kankyo, 1999; 48: 654-659.
3. Suga K, Ridha M, Aoki S. Optimization of observation condition on inverse analysis for identifying corrosion of
steel in concrete. to appear in the proceedings of EPMESC X, 2006.
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