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MOISTURE PENETRATION IN CONCRETE SUBJECTED TO
RAINFALL: EFFECT OF INTENSITY AND DURATION OF
EXPOSURE
Kaustav Sarkar a and Bishwajit Bhattacharjee b
a Research Scholar, Department of Civil Engineering, Indian Institute of Technology
Delhi, Hauz Khas, New Delhi110016, Email:srkrkaustav@gmail.com
b Professor, Department of Civil Engineering, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi110016, Email:bishwa@civil.i
itd.ac.in
Abstract: Moisture imbibed in structural concrete during the course of service plays a
critical role in the initiation and propagation of rebar corrosion in reinforced concrete
(RC) elements. The provision of an adequate cover depth is thus essential to restrain the
ingress of moisture up to the layer of embedded steel, mitigating thereby the evolution
of the corrosion process. A prediction of moisture penetration depth in concrete, under
the given conditions of exposure, facilitates the rational determination of cover
thickness. The present work relates to the numerical simulation of moisture distribution
in concrete subjected to rainfall exposure. Based on one dimensional nonlinear finite
element (FE) analysis of unsaturated flow in porous medium, the study investigates the
influence of rainfall intensity and duration on the extent of moisture penetration in
concrete. The study is extended to analyze the effect of intensityduration combinations
corresponding to a fixed quantity of incident moisture on the resulting state of moisture
uptake in exposed concrete. The findings of this study provide useful insight into the
phenomena of rain induced moisture ingress in concrete and facilitate identification of
critical intensityduration scenarios to be adopted for the estimation of cover thickness.
Keywords: Concrete, Moisture ingress, Rainfall exposure, FE analysis
Introduction
Corrosion of steel reinforcement is known to be the most prevalent cause of premature
distress in RC structures. Its widespread manifestation is an implication to the
inadequacy of currently followed prescriptive design practices which are deemed to
satisfy the requirements of durability. This in turn necessitates the constitution of
guidelines based on the rational comprehension of the hygrothermal behavior of
concrete subjected to specific conditions of exposure (Nilsson, 1996).
Under the influence of service environment, ambient fluids penetrate through the cover
zone of exposed RC elements and gradually disrupt the passivity of embedded steel.
This is subsequently followed by the onset of corrosion which results in the formation
of rust and gradually leads to the cracking and delamination of concrete cover. The
phenomena is critically influenced by the state of moisture distribution in near surface
concrete; it governs the rate of the physiochemical processes conjuring corrosion and
also limits the extent of their propagation to a depth amenable to moisture penetration.
The estimation of moisture distribution in exposed concrete thus becomes imperative in
enabling a reliable prediction of its durability performance.
Under tropical climatic conditions, structural concrete gets subjected to extended
periods of rainfall. The exposure causes conspicuous ingress of moisture in concrete and
aids the evolution of corrosion during the subsequent phase of drying. Despite of its
eminent significance, the investigation of rain induced moisture transport in concrete
has been very limited. In an early effort, Andrade et al. (1999) recorded the variation of
average relative humidity and temperature within the cover zone of concrete samples
exposed to natural rainfall. Ryu et al. (2011), in a recent study reported observations on
the evolution of humidity and saturation states at different depths of a concrete
specimen exposed to artificially simulated rainfall and summertime conditions. In a
more recent study on wetdry cycles, albeit not simulating a natural exposure condition,
Zhang et al. (2012) investigated the variation of pore humidity caused due to the action
of ponding and subsequent drying of specimen surface. These experimental studies have
provided a valuable impetus to the understanding of the hygrothermal behavior of
concrete under the action of wettingdrying cycles. However, the complexity of
controlling several influencing factors and the imprecision involved in the indirect
measurement of moisture render such experimental pursuits less lucrative for elaborate
investigations. A model based study, on the other hand has to rationally account for the
influence of dynamic ambient conditions and implement a robust numerical scheme to
address the inherent nonlinearity of moisture transport equations.
The present work relates to the numerical simulation of moisture penetration in an
ordinary concrete medium exposed to the action of low, medium and high intensity
rains taken to prevail over a range of time intervals. The study compares the relative
influence of rainfall intensity and duration on the extent of moisture penetration in
concrete. To achieve computational efficiency, the moisture transport phenomenon has
been represented using a modified form of Richards’ equation constituted using a set of
dimensionless terms corresponding to space, time and moisture variables. The modified
model has been analyzed using a one dimensional, nonlinear FE scheme. Material
proportions and associated hydraulic properties of concrete that constitute the input data
set for simulation have been adopted from published treatise of Wong et al. (2001). The
findings of the study substantiate the significance of rainfall duration over intensity in
causing the ingress of moisture in concrete.
Mathematical modeling of moisture movement in concrete
Governing equation
Moisture flow in an unsaturated porous medium is conventionally represented using the
extended Darcy's law, stated as,
()D
tx x
θ
θ
θ
∂∂ ∂
⎛⎞
=⎜⎟
∂∂ ∂
⎝⎠
(1)
with the term, ().Dx
θ
θ
∂
∂ representing a flux acting in the direction of outward normal
to the surface of the domain. Here, θ (m3/m3) is the volumetric moisture content of
concrete, t (s) is the time variable, x (m) is the space variable and D(θ) (m2/s) is the
moisture dependent hydraulic diffusivity function and has been successfully represented
using an exponential function of the form (Lin, 1992; Hall, 1994; Pel, 1995),
_
() er
n
rr dwet
DD
θ
θ
= (1a)
where, r
θ
is normalized moisture content as defined in Eq.(2a), Dd_wet (m2/s) is the
wetting diffusivity corresponding to totally dry state of the medium. The value of n in
the stated equation ranges between 68 for building materials (Hall, 1989) and for
concrete in an initially dry state a value of n=6 has been suggested (Leech et al., 2003).
The term, Dd_wet in Eq.(1a) can be estimated using the known values of parameter n,
saturation moisture content θs (m3/m3) and sorptivity S (m/√s) of concrete using the
relationship (Leech et al., 2003),
22
_
.( / )
(2 1) 1
s
dwet n
nS
Den n
θ
=
−
−+ (1b)
The strong dependence of hydraulic diffusivity on moisture content renders the
unsaturated flow problem highly nonlinear. A plausible analysis of the problem is
therefore dependent on the application of a robust numerical scheme. Being of first
order in time and second order in space, the solution of the problem relies on the
specification of an initial condition and two boundary conditions. The boundary
condition may either be provided as the value of moisture content θ (Dirichlet/Essential
boundary condition) or as the value of moisture flux stated as, () o
D
xV
θ
θ
∂∂=
(Neumann/Natural boundary condition) where, Vo (ms1) is boundary rain flux acting
opposite to the direction of outward normal to surface. The initial moisture content
across the physical domain of analysis is generally described by an initial moisture
profile, (, ) ()
ini
x
t0 x
θ
θ
== .
Modified governing equation
Since the parameters constituting the given problem range over several orders of
magnitude, restating Eq.(1) using the following dimensionless terms, aids in minimizing
the computing errors.
Reduced moisture,
()( )

roso
θ
θθ θ θ
= (2a)
Reduced distance, _
()
rodwet
x
VD x= (2b)
Reduced time, 2
_
()
rodwet
tVD t= (2c)
where, θo (m3/m3) and θs (m3/m3) are moisture contents corresponding to capillary dry
and saturated states of concrete. Restating Eq.(2) in terms of the nondimensional
parameters gives,
22
2
__
1() 1
.()
rrrr r
rr
r d wet r r d wet r
DD
tD x D x
θ
θθ θ
θ
θ
⎛⎞
∂∂∂ ∂
=+
⎜⎟
∂∂∂ ∂
⎝⎠
(3)
Equating the modified boundary flux term, _
()( ()/ ) /
os o rr dwet r r
VDD x
θ
θθ θ
∂
∂ to wetting
flux yields the following condition, 1 e/ ()
r
n
rr so
x
θ
θ
θθ
=∂∂ .
FE formulation
Using the governing differential equation stated in Eq.(3), the FE formulation can be
carried out using Galerkin's weighted residual technique (Reddy, 2005). For a linear
element of reduced length l, the element level governing equation can be obtained as
(Sarkar and Bhattacharjee, 2013),
0
1

21 11
{} e {}
12 1 1
6e
r
r
r
r
n
eso
x
e
rnr
rxl
x
ld d
tl
θ
θ
θ
θθ
=
=
∂
∂
⎧
⎫
⎛⎞
+
⎪
⎪
⎜⎟
⎝⎠
+
⎡⎤ ⎡ ⎤
∂
⎪
⎪
+=
⎨
⎬
⎢⎥ ⎢ ⎥
+
∂⎛⎞
⎣⎦ ⎣ ⎦
⎪
⎪
⎜⎟
⎪
⎪
⎝⎠
⎩⎭
(4)
Eq.(4) is semi discrete and can be represented in the matrix form as,
[]{}[]{}{}
ee
ddmk q+=
,where []m and []kare element level mass and diffusivity
matrices,{}
e
dand{ }
e
d
are the vectors of elemental degrees of freedom and their time
derivatives and{}qis the vector of elemental nodal fluxes. In order to obtain a fully
discretized system of equations, the time derivatives of the field variable in these
equations are to be further approximated using the method of finite difference. Adopting
the CrankNicolson scheme (Reddy, 2005), a completely discrete system of equations is
obtained as,
(
)
{
}
(
)
{
}
(
)
1
1 1
[]0.5 [] []0.5 [] 0.5 {} {}
nn
ne ne n n
rrr
mtkd mtkd tqq
+
+ +
+Δ = Δ +Δ + (4a)
where, the superscripts n and (n+1) denote the previous and present time levels.
Analysis of moisture transport
The analysis has been carried out for an ordinary concrete medium of 0.5 m length in an
initially dry state i.e., θr = 0 at tr = 0 and xr > 0. The FE mesh has been constituted using
linear elements of reduced size, l = 0.5. The reduced time step, Δtr has been augmented
in small increments up to a limit corresponding to 300 s. The mix proportion data and
hydraulic properties of concrete have been adopted from the published treatise of Wong
et al. (2001) and are furnished in Table 1 for reference.
Table 1. Concrete mix proportions and properties
w/c Cement
(kg/m3)
FA
(kg/m3)
CA
(kg/m3)
Water
(kg/m3)
Air
(%)
θs
(m3/m3)
S
(m/√s)
Dd_wet
(m2/s)
0.6 317 923 887 190 1.97 0.13 3.615 x 105 6.449 x 1010
The moisture content of concrete corresponding to the state of full saturation has been
assumed to be equal to its capillary porosity determined using the wellknown Power’s
model (Neville and Brooks, 1987) for a curing age of 28 days,
0.36
0.317
c
fc
fc
wa
h
cC
A
A
wa
CCcC
φ
ρρ
−+
=
+
+++
(5)
Here, c
φ
(m3/m3) is the capillary porosity of concrete, h is the degree of hydration of
cement, w/c is the water to cement ratio by mass, a (m3/m3) is the volume of entrapped
air in concrete, C, Af and Ac are the parts of cement, fine and coarse aggregates by mass,
ρf and ρc are the specific gravities of fine and coarse aggregate respectively. The degree
of hydration in Eq.(5) can be estimated for a curing temperature of tcure = 20°C using the
empirical expression proposed by Kondraivendhan and Bhattacharjee (2010),
(
)
(
)
.ln .ln
12cure3
hC wc C t C=++
(5a)
For OPC 43 (IS 12269:1989) grade cement the constant coefficients in Eq.(8b) have
been empirically determined and reported to be, 0.217, 0.07 and 0.591
12 3
CC C
=
==
.
The analysis has been carried out in two phases. The first phase studies the effect of
rainfall intensity on the extent of moisture penetration in concrete. The analysis has
been carried out for rainfall intensity values of 1.25 mm/h, 5 mm/h and 25 mm/h taken
to prevail for a period of 1 hour. The considered intensity values pertain to the
categories of light (< 2.5 mm/h), medium (2.57.5 mm/h) and heavy (> 7.5 mm//h) rains
respectively (Deodhar, 2008). Fig.1 presents the simulated moisture profiles for each of
the considered instances. It is evident that the medium and high intensity rains, despite
of the fivefold difference in their magnitude, result in practically similar moisture
penetration profiles. The light intensity rain on the other hand causes a relatively lower
ingress of moisture. It can thus be concluded that, the extent of moisture penetration in
concrete remains dependent on the intensity value only for light rains, whereas, for
higher intensities the ingress is governed by the duration of rainfall.
Fig.1 Moisture penetration profiles for concrete subjected to light, medium and high intensity rains
prevailing for a duration of one hour
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Reduced moisture content
Distance from exposed face (m)
1.25 mm/h
5mm/h
25 mm/h
exposure duration: 1 hr.
Second phase of the analysis has been carried out to estimate the state of moisture
penetration achieved in response to intensityduration combinations which cause the
same quantity of water to become incident on the exposed surface. The following
combinations have been adopted in the present study: (1.25 mm/h, 1 h), (5 mm/h, 0.25
h) and (25 mm/h, 0.05h). Fig.2 presents the simulated moisture profiles from which it
becomes evident that, for the same quantity of impinging rain (here 1.25 mm3/mm2),
higher intensity rains which have shorter spells result in lesser penetration of moisture
in concrete. The observation is of particular relevance to reallife conditions, where,
rainfall events manifesting with higher average intensities prevail over shorter durations
while those with lighter intensities linger over considerable periods.
Fig.2 Moisture penetration profiles for concrete subjected to light, medium and high intensity rains
prevailing for decreasing durations keeping the quantity of impinging water constant
Summary and Conclusions
The paper has discussed the issue of moisture penetration in concrete subjected to
rainfall exposure. A summary of the discourse is as follows:
• The study of rain induced moisture ingress in concrete bears a special
significance in the context of durability and service life assessment of RC
structures in tropics.
• A modified form of Richard’s equation has been implemented to describe the
phenomenon of moisture flow in unsaturated concrete. The model offers a better
computational efficiency to numerical treatment.
• To address the mathematical nonlinearity of the model, a one dimensional,
nonlinear FE scheme has been implemented for analysis. Simulation results for
the evolution of moisture distribution in concrete under different rainfall
intensity and duration scenarios have been presented.
• Rainfall events which manifest with lighter intensities and tend to span over
longer durations have been observed to result in higher moisture penetration in
concrete.
• For the same duration, rainfall events with medium and heavy intensities have
been found to result in similar moisture ingress patterns.
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Reduced moisture content
Distance from exposed face (m)
1.25 mm/h, 1 h
5 mm/h, 0.25 h
25 mm/h, 0.05 h
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