# APPLICATION OF BEM TO EVALUATE THE POTENTIAL MAPPING TECHNIQUE FOR CORROSION MONITORING

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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
-
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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&
Niku, S.M. 1992
.

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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-
Cell Potential Surveys of Reinforced Concrete Structures,
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-
45.

Aoki, S
.,
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, 1998
.

Boundary Element Analysis on
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, Tokyo.

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8

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