ACI MATERIALS JOURNAL
TECHNICAL PAPER
Title No. 117-M50
Chloride Diffusion Models for Type V and Silica Fume
Cement Concretes
by M. M. Al-Zahrani, K. A. Alawi Al-Sodani, M. Maslehuddin, O. S. Baghabra Al-Amoudi, and
S. U. Al-Dulaijan
One of several methods used to minimize reinforcement corrosion
is the use of service-life prediction models to calculate mixture
design and construction variables for the desired service life of a
structure. Although several models are available for this purpose,
very few incorporate the effect of environmental temperature on
chloride diffusion. Moreover, most of the earlier studies were
conducted under laboratory conditions and they are not based on
actual field data. In the reported study, chloride diffusion in Type V
and silica fume cement concretes was evaluated under laboratory
and field conditions. Large-size concrete specimens were exposed
in the tidal zone of a marine exposure site for 1, 2, 5, and 10 years
while the laboratory specimens were exposed to a chloride solution
maintained at 22, 35, 50, and 60°C (71.6, 95, 122, and 140°F) for
1 year. The coefficient of chloride diffusion (Da) for Type V cement
concrete specimens placed in the field was noted to be much more
than that of silica fume cement concrete specimens at all exposure
periods. However, the Da for both Type V and silica fume cement
concrete specimens decreased by 1.3 to 3 times with increasing
period of exposure. The Da for the laboratory concrete specimens
increased by 2.2 to 3.8 times as the exposure temperature was
increased from 22 to 60°C (71.6 to 140°F). Furthermore, the Da
for Type V cement concrete specimens was 2.9 to 5 times more than
that of silica fume cement concrete specimens. Empirical models
correlating the field and laboratory data were developed. These
models could be useful for calculating the Da for field conditions
from the laboratory data.
Keywords: activation energy; coefficient of chloride diffusion; exposure temperature; field and laboratory exposure; silica fume; tidal zone;
Type V cement.
INTRODUCTION
Corrosion of reinforcing steel in concrete is mainly
attributed to the diffusion of chloride ions to the steel surface.
In addition to concrete quality, severity of exposure, and so
on, the chloride diffusion is also influenced by the exposure temperature.1,2 Therefore, exposure temperature must
be taken into consideration for predicting the service life of
reinforced concrete structures exposed to chloride-bearing
environments. In earlier research, the effect of temperature
on chloride diffusion was mostly conducted on cement paste
specimens.3-6 Moreover, the chloride diffusion in conventional concrete did not consider the effect of temperature.7-10
Also, limited data were reported on the effect of low and
high exposure temperature (5 to 50°C [41 to 122°F]) on
chloride diffusion in concrete.11-13
Due to the importance of chloride diffusion coefficient
(Da) in service-life prediction, several chloride diffusion
models have been reported by several researchers.14,15 Fick16
suggested a simple model, which expresses the chloride
ACI Materials Journal/May 2020
concentration as a function of both distance and time under
non-steady-state condition. This model, known as a Fick’s
Second Law of Diffusion, shown as Eq. (1), is commonly
used to calculate the coefficient of chloride diffusion.
∂C
∂
=D
∂t
∂X
 ∂C 


∂X 
(1)
The boundary and initial conditions for Eq. (1) are given
in Eq. (1a) to (1c)
Initial conditions: C (x, 0) = 0
(1a)
Boundary conditions: C (0, t) = Cs
(1b)
C (x → ∞, t) = 0
(1c)
Crank proposed a mathematical solution of Fick’s Second
Law of Diffusion by assuming chloride diffusion coefficient
(Da) as a constant, as shown in Eq. (2)

Cx ,t = Cs 1 − erf

 x 


 2 Da t 
(2)
where Cx,t is chloride concentration at depth x (%) at time
t in seconds; Cs is chloride concentration at the concrete
surface, %; x is depth from the concrete surface (m); t is time
(seconds); and Da is apparent diffusion coefficient (m2/s).
The values of Cs and Da are calculated using the least
squares method and the time-dependent changes in Da are
ignored in this approach.17
An alternative chloride diffusion model that takes into
consideration the influence of time dependence of the relevant diffusion coefficient and temperature was developed by
Mangat and Molloy18 and Maage et al. 19 The effect of time
is chosen as
t 
Dt = D28  28 
 t 
m
(3)
where Dt is the diffusion coefficient at time t (m2/s); D28 is the
diffusion coefficient at time t28 (28 days); and m is constant.
ACI Materials Journal, V. 117, No. 3, May 2020.
MS No. M-2018-307.R2, doi: 10.14359/51724589, received May 19, 2019, and
reviewed under Institute publication policies. Copyright © 2020, American Concrete
Institute. All rights reserved, including the making of copies unless permission is
obtained from the copyright proprietors. Pertinent discussion including author’s
closure, if any, will be published ten months from this journal’s date if the discussion
is received within four months of the paper’s print publication.
11