Regional Confe
rence on Engineering Mathematics, Mechanics, Manufacturing & Architecture (EM
3
ARC) 2007
2007
Computational & Experimental Mechanics Research Group
Editors:
A. K. Ariffin, N. A. N. Mohamed and S. Abdullah
APPLICATION OF BEM T
O EVALUATE THE
POTENTIAL MAPPING
TECHNIQUE FOR CORROS
ION
MONITORING
M
.
Ridha
1
and S.
Aoki
2
1
Department of
Mechanical Engineering
Syiah Kuala University
Darussalam, Banda Aceh (23111)
,
Indonesia
2
Department of Computational Science
and Engineering
Toyo University
2100 Kujirai, Kawagoe, Saitama, Japan
ABSTRACT
Potential mapping technique has been extensively used in the field for diagnosing
the corrosion of reinforced concrete structure.
H
owever, the method can not be
used to ac
curately identify the corrosion of steel in concrete.
The purpose of this
study is to apply the boundary element method
to analysize the
influence
of some
factors such as corrosion intensity,
electrical
resistivity of concrete and the
thickness of concrete
cover to the potential reading on the concrete surface. In
this study,
Laplace’s equation is used to model the potential in the concrete
structure.
Boundary element method i
s
employed t
o solve the Laplace’s
equation
.
H
ence the potential
on the
concrete
su
rface
can be determined.
To simulate the
influence of some factors to the potential value on the concrete surface, a model
of prismatic concrete block with embedded steel was used. A small corroded area
was existed on the steel. The numerical analysis resu
lt shows that the potential
values on the concrete surface are subject to change when
the
factors such as
corrosion intensity of the corroding steel, the concrete conductivity
and the
concrete cover depth were changed.
Keywords:
p
otential
ma
pping
t
echniqu
e
;
r
einforced
c
oncrete
c
orrosion
;
c
orrosion
m
onitoring
;
B
EM
INTRODUCTION
Corrosion of steel reinforcement is a major factor in the deterioration of
infrastructures such as highway and bridge
.
It is important to have an easy, cost

effective and reliable
method
for identifying
the corrosion of reinforcement
without having to remove the concrete cover
(
Broomfield
1998
)
.
A. K. Ariffin, N. A. N. Mohamed and S. Abdullah
2
Potential mapping technique
has been
applied in the fields
since the early
1970’s (Van Daveer
1975).
In this method, the map of potential
on the surface of
the concrete structure is used to evaluate the corrosion of the reinforcing steel.
However, w
hen the surface potentials are taken, they are essentially remote the
reinforcement due to the concrete cover. The potentials thereby measured a
re, in
fact, mixed potentials
(
Elsener
et
al
.
1990
).
Nowadays, the use of numerical method such as boundary element method
(BEM)
(Brebbia 1992) becomes popular among researchers
and corrosion
engineer
for modeling and solving various corrosion problems (A
dey et
al.
1992
,
Aoki et al.1998,
DeGiorgi 1997
and Ridha 2000).
The purpose of this study is to apply the boundary element method (BEM)
for
evaluating the effectiveness of the potential mapping technique for monitoring
the corrosion of steel in concrete s
tructure. The
influence
s
of
corrosion intensity
on the steel
,
the
conductivity of the
concrete
and the
depth of the
concrete cover
to the potential value on the surface of the concrete structure
are
analyzed
.
POTENTIAL MAPPING TE
CHNIQUE
Figure 1 shows
the schematic of potential mapping technique, also called half

cell potential measurement
(
Anonymous
2000)
.
This technique is the
simplest
way to assess the severity of steel corrosion by measuring the corrosion potential,
since it is qualitatively associa
ted with the steel corrosion rate. One can measure
the
potential difference between a standard half

cell such as copper/copper
sulfate (Cu/CuSO
4
) standard reference electrode placed on the surface of the
concrete with
the
steel reinforcement underneath (Pi
ng Gu et al. 1998).
The readings are plotted automatically or manually and lines drawn between
points of equal potential. The anodic areas (where the corrosion risk is high) and
cathodic areas (where the risk is less) are indicated by these ‘contour lines
’.
ASTM C867
(1991)
present criteria, developed in the USA mainly in relation to
bridges, for interpreting the potentials reading in field.
A simple comparison of the half

cell potential data with the ASTM guideline
on steel reinforcement corrosion proba
bility could prove meaningless. For
FIGURE 1
Schematic of half

cell
potential
techn
ique
and mapping of
potential on the concrete surface
.
Application of BEM to Evaluate the
Potential Mapping Technique for
Monitoring of
Reinforced Concrete
3
instance, a more
negative
reading of potential is generally considered to indicate
a higher probability of corrosion. This general
“
rule
”
may not always be valid;
many factors can shift the half

cell potential readings t
owards more positive or
negative values but these shifts may not necessarily be related to the severity of
the steel corrosion.
MATHEMATICAL MODELIN
G
Suppose that the concrete domain (
) is surrounded by the surface of the
concrete structure (
s) and t
he surface of the steel
s
(
m
) as shown in Fig
ure 1
, the
electrical conductivity (
) is uniform in the whole concrete domain and there is
no accumulation or loss of ions in the bulk of the domain.
The potential
in
can
be
modeled by
the L
aplace's equation,
(Aoki 1998)
0
2
in
(
1
)
The density of current
(
i
)
across the boundary
is given by
n
i
(
2
)
where
is the electrical conductivity and
/
n is the outward normal derivati
ve.
The boundary condition on surface of the concrete,
s
is defined as:
0
i
on
s
(
3)
On the surface of corroded and non corroded steel
(
m
)
,
is defined
as
,
(i)
m1
1
f
m
on
m
1
(
4
)
(i)
m2
2
f
m
on
m
2
(
5
)
where
f
m1
(
i
)
and
f
m2
(
i
) are the non

linear functions representing the
experimentally determined polarization curves for corroded and non

corroded
parts, respectively.
It is noted that the potential
is defined with referring to the
metal and has the inverse sign of the employed usually in the corrosion science
.
The potential within the steels has been imposed as the reference potential (i.e.
zero
volts) for the numerical calculations
.
Boundary element method can be used to solve
the Laplace's equation in
Eq
uation
(
1
)
if
the boundary
conditions
in Equation
s
(
2
) to (
5
)
are known. Hence,
and
i
on the whole concrete
surface
can be determined.
A. K. Ariffin, N. A. N. Mohamed and S. Abdullah
4
MO
DEL OF CONCRETE SPEC
IMEN
To study the influence of some factors that have significant effect on the potential
value on the concrete surface, a model of concrete specimen shown in Figure 1
was considered. . The specimen size was 500x100x100 mm. An embedded
steel,
16 mm in diameter, was cast in concrete at location of y=0.375 m. A
single
corroded area (5 mm in length) was exist on the reinforcing steel and located at
x=0.25 m from the left

end of the concrete specimen.
The polarization curve 2 (see Figure 2
), the steel which was immerse in 10%
sodium chloride (NaCl) solution for 45 days as reported by Wheat et al. (1985),
was used to represent the polarization curve of the non

corroded area of the steel.
In this study, the analy
sis was limited only to simulate the
influence
s of
polarization
curves of the corroded steel, the conductivity (inverse resistivity) of
the concrete and the thickness of the concrete cover.
In
boundary
element calculation, the concrete specimen was discre
tized into
192 constant rectangular elements. The steel was discretized into 10 constant
pipe

elements. The total number of node was 237. Since all boundary condition
in Eq
uation
s
(2) to (5) are known, then BEM can be used to solve the Laplace
’
s
Equation
in Eq
uation
(1), then the potential on the concrete surface can be
obtained.
RESULTS AND DISCUSSI
ON
The influence of corrosion intensity
To study the effect of corrosion intensity, three
polarization
curves which were
immersed in 10% NaCl solution for
60, 75 and 90 days (polarization curve 3, 4, 6
in Figure 2) was used. The conductivity of the concrete
and the thickness of
F
IGURE
2
Polarization curve of steel which was immerse in 10% NaCl
solution for various days (Wheat et al
.
1985).
Application of BEM to Evaluate the
Potential Mapping Technique for
Monitoring of
Reinforced Concrete
5
concrete cover (t) were prescribed, i.e,
=
0.001 (1/
.m) and t
=
22mm,
respectively.
Figure 3 shows the boundary element calc
ulation when difference polarization
curves are employed to represent the corrosion intensity of the corroded area.
It
can be seen from Figure
3
that the potential value around the corroded area on the
concrete surface become bigger when the corrosion inte
nsity of the corroded steel
increases.
The
influence
of concrete conductivity
To study the effect of concrete conductivity, four different values of the concrete
conductivity were chosen. They are
(= 0.1, 0.01, 0.001 and
0.0001) 1/
.m.
Two polarization curves of the steel in concrete which were immerse in 10%
sodium chloride (NaCl) solution for 45 and 60 days (polarization curves 2 and 4
in Figure 2), were used to represent the polarization curve of the non

corroded
and c
orroded areas of the steel,
respectively
. The concrete cover (t) was 22 mm.
Figure
4
shows the
influence
of concrete conductivity to the potential on the
concrete surface. It can be seen form Figure 4 that the potential along the steel on
the concrete
surface almost has the same potential values when the
con
ductivity
of the concrete
is high.
In other words, when the concrete conductivity is low, the
location of corroded area becomes difficult to identify from the potential values
on the concrete surface
.
FIGURE
3
T
he influence of corrosion intensity to potent
ial on the surface of
the concrete structure
A. K. Ariffin, N. A. N. Mohamed and S. Abdullah
6
FIGURE
4
T
he influence of concrete
conductivity
to the potential on the concrete
surface
The influence of concrete cover
depth
To study the effect of concrete
cover depth
,
six
different
thickness of
the concrete
co
ver t were pres
cribed, i.e. t
(=
20
,
30
,
40, 50, 60
and
70
)
mm
. T
he polarization
curve 2 and 4 in Figure 2, were chosen to represents
the polarization curve of the
non

corroded and corroded areas of the steel, respectively.
= 0.01 1/
.m.
Figure 5 shows
influence
of t
he concrete cover depth to the potential value on
the concrete surface as a result of boundary element calculation for various
concrete cover depth. With increasing the concrete cover, the potential values of
active corroding and passive corroding become s
imilar. Thus, the location of
small corrosion spots gets more difficult with increasing cover depth.
FIGURE
5
the influence of concrete cover
depth
to the potential on the concrete
surface
CONCLUSIONS
Application of BEM to Evaluate the
Potential Mapping Technique for
Monitoring of
Reinforced Concrete
7
BEM
was
applied to
evaluate the effectiveness of potential mapping technique
for diagnosing the corrosion of reinforced concrete structure.
The potential in the concrete domain was modeled using the
Laplace’s
equation. The polarization curve represents the corros
ion intensity of the
reinforcing steel.
BEM was used to solve the Laplace
’
s equation. Hence,
the
potential on the concrete surface
can be determined.
The result of boundary element simulation
using a model of prismatic
concrete block with embedded steel
sh
ows that the potential values on the
concrete surface were subject to change when the factors such as the
corrosion
intensity
of the corroding steel, the
conductivity of the concrete and the depth of
the
concrete cover depth were changed.
NOTATIONS
i
Cu
rrent Density
A/m
2
Potential
V
C
onductivity
1/
m
t
Thickness of Concrete Cover mm
ACKNOWLEDGEMENTS
The authors would like to thank
Professor Sakamoto and Mr. Kondo, Research
Institute of Industrial Technology, Toyo Univ
ersity Japan for their assistance and
support. This study was conducted at Toyo University, Japan.
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&
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.
Computer Modeling of Corrosion Using the
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Computer Modeling in Corrosion
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115
4, pp. 248

264
Anonymous
2000
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, 1998
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Boundary Element Analysis on
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