Geology Reference
In-Depth Information
Table 1. Summary of modification factors used for the estimation of chloride diffusion coefficient
Formulation
Parameters
Assigned values
log
D
Cl ref
= +
a
b
log
( / )
w c
a
,
b
: empirical coefficients
a
= -10.6,
b
= 1.9
,
E
: activation energy for diffusion process
R
: gas constant
T
ref
: reference temperature
E
= 44.6 ± 4.3 (kJ/mol)
R
= 8.314 (kJ/mol. °K)
T
ref
= 296 (°K)
E
R T
1
1
( )
=
F T
exp
−
2
T
ref
4
−
−
h
h
c
1
1
( )
=
F h
+
1
/
1
h
c
: critical humidity level
h
c
= 0.75
3
t
ref
: reference time
m
: empirical age factor
t
ref
= 28 (day)
m
= 0.04
m
4
( )
=
t
ref
F t
e
t
(
)
= −
(
)
n
F C
κ
C
1
k, n
: empirical parameters
k
= 8.366,
n
= 0.5
5
f
f
tion can be fit very well to that. The temperature
at the
j
-th day of the year can be found from
Equation 5:
methods. In the current study, a finite difference
algorithm is developed to evaluate the chloride
diffusion process at different time steps by con-
stant updating of the diffusion coefficient. This
algorithm considers the effects of all influential
parameters and provides a more accurate estima-
tion of chloride content in the concrete.
For the numerical solution, it is assumed that
the free chloride content in the concrete is zero
at the initial condition. This value will gradually
increase by the intrusion of chloride ions over the
time. On the other hand, the free chloride content
is always constant at the concrete surface. The
surface chloride content,
C
s
, depends on various
parameters, such as the composition of the con-
crete, location of the structure, orientation of its
surface, chloride concentration in the environment,
and general conditions of exposure with regard to
rain and wind (Bertolini, 2008). A range of 2.95
kg.m
-3
(McGee, 1999) to 7.00 kg.m
-3
(Val, 2004)
has been suggested for the surface chloride content
at bridges located near coastlines. In this study
the average value of 5.00 kg.m
-3
is assigned to
C
s
.
(
)
T K
(
° =
)
291
−
15
sin
π
2
j
/
365
(5)
Similar to the ambient temperature, the local
humidity information is needed for
F
2
(
h
). The
average monthly relative humidity data for the
Los Angeles area has been obtained from NOAA
to find the annual trend of humidity. The relative
humidity is periodic in nature and is repeated
throughout the years. Hence, it can be simulated
for the
j
-th day by a half-sinusoidal function as
below:
( )
=
h
%
0 65
.
+
0 13
.
sin
π
(
j
/
365
)
(6)
A review of Table 1 shows that the chloride dif-
fusion coefficient is a nonlinear parameter which
varies over the time. Hence, the governing partial
differential equation given by Equation 2 cannot
be solved without using appropriate numerical
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