Conference PaperPDF Available

MOISTURE PENETRATION IN CONCRETE SUBJECTED TO RAINFALL: EFFECT OF INTENSITY AND DURATION OF EXPOSURE

Abstract and Figures

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 intensity-duration 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 intensity-duration scenarios to be adopted for the estimation of cover thickness.
Content may be subject to copyright.
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 Delhi-110016, Email:srkrkaustav@gmail.com
b Professor, Department of Civil Engineering, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi-110016, 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 intensity-duration 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 intensity-duration 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 hygro-thermal 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 wet-dry 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 hygro-thermal behavior of
concrete under the action of wetting-drying 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 6-8 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 non-linear. 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
xV
θ
θ
∂∂=
(Neumann/Natural boundary condition) where, Vo (ms-1) 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 non-dimensional
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 1-1
{} e {}
12 -1 1
6-e
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 Crank-Nicolson 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 + (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 10-5 6.449 x 10-10
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 well-known 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 (2.5-7.5 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 intensity-duration 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 real-life 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
References
1. Andrade, C., Sarria, J. and Alonso, C. (1999), “Relative humidity in the interior
of concrete exposed to natural and artificial weathering”, Cement Concrete Res.,
29(8), 1249-1259.
2. Deodhar, M.J. (2008), “Elementary Engineering Hydrology”, Pearson.
3. Hall, C. (1989), “Water sorptivity of mortars and concretes: a review”, Mag.
Concrete Res., 41 (147), 51-61.
4. Leech, C., Lockington, D. and Dux, P. (2003), “Unsaturated diffusivity
functions for concrete derived from NMR images”, Mater. and Struct., 36 (6),
413-418.
5. Neville, A.M. and Brooks, J.J. (1987), “Concrete Technology”, Pearson, New
Delhi.
6. Nilsson, L. (1996), “Interaction between microclimate and concrete - a
prerequisite for deterioration”, Const. and Build. Mater., 10 (5), 301-308.
7. Reddy, J.N. (2005), “An Introduction to the Finite Element Method (3rd ed.)”,
TMH, New Delhi.
8. Ryu, D.W., Ko, J.W. and Noguchi, T. (2011), “Effects of simulated
environmental conditions on the internal relative humidity and relative moisture
content distribution of exposed concrete”, Cement Concrete Comp. 33 (1), 142-
153.
9. Sarkar, K and Bhattacharjee, B. (2013), “Finite element modelling of moisture
distribution in concrete subjected to wetting-drying exposure” Proc. of
international conference on Innovations in Concrete Construction, UKIERI
Concrete Congress held at NIT Jalandhar, 1713-1723.
10. Wong, S.F., Wee, T.H., Swaddinwudhipong, S. and Lee, S.L. (2001), “Study of
water movement in concrete”, Mag. Concrete Res. 53 (3), 205-220.
11. Zhang, J., Gao, Y. and Han, Y. (2012), “Interior humidity of concrete under dry-
wet cycles”, J. Mater. in Civil Engg., 24(3), 289-298.
ResearchGate has not been able to resolve any citations for this publication.
Article
The dry-wet cycle is one of the aggressive environmental conditions suffered by concrete. This paper focuses on the experimental study and theoretical simulation of water distribution in normal- and high-strength concrete through dry-wet cycles. The experimental results show that under dry-wet cycles, the variation in the interior humidity of concrete occurs mainly within a certain depth from the drying/wetting face. This depth is called the influencing depth under dry-wet cycles. The interior relative humidity of concrete within the influencing region periodically changes under dry-wet cycles. As concrete undergoes wetting, a fast rise in interior humidity occurs in a short time, and finally the relative humidity reaches approximately 100%. By contrast, as concrete undergoes drying, the interior relative humidity does not drop immediately, but in a more gradual manner. In the modeling, a model taking both cement hydration and moisture diffusion into account synchronously is used to simulate the moisture distribution in concrete under dry-wet cycles. A comparison between model and experimental results concludes that the model can predict the moisture distribution in concrete, as well as its variations, through dry-wet cycles.
Article
An investigation on the movement of water in 100% Portland cement concretes is presented. The water diffusion and sorptivity tests, together with the accelerated water permeability test, are performed to determine the transport parameters that characterise the mechanisms of water diffusion, sorptivity and permeability in concrete respectively. The effects of pore humidity, ambient temperature, environmental relative humidity, applied hydrostatic pressure gradient and water-cement ratio are also explored. The results obtained from the tests on water diffusion, sorptivity and permeability show good agreement with those reported in the literature. The study of water movement has practical implications on the prediction of transport and distribution of aggressive chemical agents in concrete, as well as on the development of rational and quantitative durability assessment for concrete structures exposed to different climatic and environmental conditions.
Article
The sorptivity is an easily measured material property which characterizes the tendency of a porous material to absorb and transmit water by capillarity. Its theoretical basis in unsaturated flow theory is reviewed, together with methods of measurement suitable for cement-based materials. Available data on mortars and concretes are included. The dependence of the sorptivity on initial water content, temperature and fluid properties is also described. Other test methods (the initial surface absorption, the Figg water absorption and the Covercrete absorption tests) are discussed in terms of the sorptivity.
Article
This paper gives an overview of the present knowledge regarding the interaction between the climatic conditions at the concrete surface and the corresponding conditions inside the concrete. The phenomena dealt with are those involved in frost damage, frost and salt scaling and reinforcement corrosion, such as temperature and moisture conditions in the near surface regions, carbonation and chloride penetration. Data on the intensity, duration and frequency of the microclimatic conditions should be included. The interaction depends on material properties concerning various flow processes and binding of heat and substances transported in the concrete. It is of decisive importance to choose simplifications carefully depending on the required accuracy, available information and the effort to be put into the task.
Book
1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
Article
The moisture content is a crucial parameter for most of the degradation processes suffered by concrete. Thus, a certain water content is needed to develop alkali-silica reaction, frost attack, or steel corrosion, while in contrast carbonation can only progress if the concrete is relatively dry. The importance of the concrete moisture state has been studied for many years in the concrete literature, and the internal relative humidity has been addressed mainly by those researchers interested in creep and shrinkage. However, despite the numerous works on the subject, almost no data can be found on the monitoring of the moisture content or of the internal relative humidity in structures subjected to real weathering conditions. In general the extensive studies have been made in the laboratory in well-controlled chambers to examine water isotherms. In addition, modelling has been developed assuming general isothermic conditions. However, natural weathering usually implies irregular changes of temperature and relative humidity, which induce continuous nonsteady-state conditions in the interior of the concrete. In the present paper, values of the internal relative humidity of concretes submitted to natural and artificial weathering are presented. From these, it is possible to deduce that the temperature is the main factor influencing the concrete internal relative humidity in samples sheltered from rain, while rain periods are the main factor in unsheltered samples. In the environment tested, two kinds of temperature cycles are acting: the day-night cycle and the seasonal cycle. The paper discusses the phenomenological features of the observed evolution of the internal relative humidity and presents some interpretations on the mechanisms of water transport induced by the external environment.
Article
Simultaneous measurement of the relative moisture content (RM) within concrete by the electrode method and the relative humidity (RH) within concrete using humidity sensors was conducted to elucidate the effects of cyclic daily changes in the environmental conditions (temperature and RH) and rainfall on the internal RH and RM distribution within exposed concrete.The effects of the presence of cracking in concrete were also experimentally investigated in comparison with uncracked concrete. As a result, the changes of the internal RH and RM distribution within concrete due to external temperature/RH changes were found to occur only in the surface region of concrete, while moisture was found to decrease extremely slowly deeper inward. As for the effect of cracking on the RM distribution within concrete, a larger crack width tended to lead to a slightly higher drying rate. In regard to the effect of rainfall, the duration of rainfall and whether or not the concrete is directly exposed to rainwater were found to be more important than the amount of rainfall.
Article
Deterioration of concrete or reinforcing steel through excessive contaminant concentration is often the result of repeated wetting and drying cycles. At each cycle, the absorption of water carries new contaminants into the unsaturated concrete. Nuclear Magnetic Resonance (NMR) is used with large concrete samples to observe the shape of the wetting profile during a simple one-dimensional wetting process. The absorption of water by dry concrete is modelled by a nonlinear diffusion equation with the unsaturated hydraulic diffusivity being a strongly nonlinear function of the moisture content. Exponential and power functions are used for the hydraulic diffusivity and corresponding solutions of the diffusion equation adequately predict the shape of the experimental wetting profile. The shape parameters, describing the wetting profile, vary little between different blends and are relatively insensitive to subsequent re-wetting experiments allowing universal parameters to be suggested for these concretes.
  • M J Deodhar
Deodhar, M.J. (2008), " Elementary Engineering Hydrology ", Pearson.
Finite element modelling of moisture distribution in concrete subjected to wetting-drying exposure
  • Sarkar
  • B Bhattacharjee
Sarkar, K and Bhattacharjee, B. (2013), "Finite element modelling of moisture distribution in concrete subjected to wetting-drying exposure" Proc. of international conference on Innovations in Concrete Construction, UKIERI Concrete Congress held at NIT Jalandhar, 1713-1723.