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Drying effect of polymer-modified cement for patch-repaired mortar on constraint stress

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Construction
and Building

MATERIALS

Construction and Building Materials 23 (2009) 434–447

www.elsevier.com/locate/conbuildmat

Drying effect of polymer-modified cement for patch-repaired
mortar on constraint stress
DongCheon Park a,*, JaeCheol Ahn b, SangGyun Oh c, HwaCheol Song a, Takafumi Noguchi b
a
b

Division of Architecture and Ocean Space, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea
Department of Architecture, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
c
Division of Architecture, Doneui University, Pusan 614-714, Republic of Korea
Received 8 June 2007; received in revised form 8 November 2007; accepted 13 November 2007
Available online 3 January 2008

Abstract
Deterioration mechanism due to drying and shrinkage of patch-repaired regions in reinforced concrete structures is analytically investigated. The moisture diffusion coefficient of the repair materials was determined by varying the drying temperature and the polymer-tocement ratios of the polymer-modified cement mortar (PCM) in the experiment. It is found that the diffusivity of PCM increases in proportion to the polymer-to-cement ratio up to 10%. The constraint stresses due to drying at the repaired region were estimated by the couplelinear finite element analysis with respect to volumetric change, moisture diffusivity, water content and mechanical properties of the repair
material. Based on the distributions of relative water contents and stresses, the effects of these parameters are discussed. The stress generated
by drying and shrinkage was affected by substrate concrete, environmental condition and the properties of PCM. Of the repaired PCM
tested, it is demonstrated that the CPM with 10% polymer-to-cement ratio generates the highest constraint stress.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Patch repair material; Moisture diffusion coefficient; Polymer-modified cement mortar; Real environmental boundary conditions; Constraint


stress analysis

1. Introduction
The patch method used to repair deteriorated reinforced
concrete structures should produce patches that are dimensionally and electrochemically stable, resistant against penetration of deterioration factors, and mechanically strong
[1–4]. Today, the patch repair materials that are widely
used contain admixtures, such as silica fume and polymers,
to improve the performance of cement mortar [5,6].
The admixtures are used to improve the workability and
performance of the hardened repair material. Material
compaction has been thought to cause reduced moisture
diffusivity due to changes in water content and the resultant
changes in the dimensions of the repair patch. However,

*

Corresponding author. Tel.: +82 10 5533 9443; fax: + 82 51 403 8841.
E-mail address: dcpark@hhu.ac.kr (D. Park).

0950-0618/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.conbuildmat.2007.11.003

there is insufficient quantitative data available for a proper
analysis. In particular, there have been very few studies of
the behavior of patch repair materials that contain re-emulsification-type polymer resin, the use of which is increasing
rapidly as it is convenient to application.
Bazant et al. [7] reported that moisture diffusion in concrete changes non-linearly with changes in relative water
content and relative humidity. In Japan, Sakata et al. [8]
and Akita et al. [9,10] determined the relationship between
moisture diffusivity and relative water content of concrete

and mortar, Takiguchi et al. [11] derived a function of
evaporable water quantity, and Hashida et al. [12] determined the moisture diffusivity of a specimen by either slicing the specimen and measuring its relative water content,
or monitoring the changes in relative humidity in the specimen to examine the decrease in water content caused by
hydration. Both methods have some physical inconsistency
but are widely used today as plenty of data is available,


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

prediction analysis is easy, and the characteristics of the
parameters are relatively well understood [13].
When deterioration in a reinforced concrete structure is
repaired by the patch method, the resultant structure is a
composite of the substrate concrete and the repair material
[14], and stress is generated at the repair site by volumetric
changes that accompany changes in water content. A major
cause of volumetric changes in patch-repaired materials is
evaporation of moisture, which causes tensile, compression
and shear stresses in the patch and the substrate concrete,
and/or their interface, depending on the constraints
imposed by the substrate concrete. When the stresses
exceed the crack-allowable stress, cracks develop that allow
the egress of water, which accelerates corrosion of the
metal reinforcing bars in the concrete.
The development of cracks may be attributed to the
selection of patch repair materials and designation of
repair zones without giving thorough consideration to the
surrounding environmental conditions, the conditions of
application, and the extent of deterioration. To prevent
cracks forming, prediction on the basis of preliminary

experiments and simulation analysis is indispensable, and
possible causes for stress generation after a repair need to
be understood by investigating each parameter.
Several studies [15,16] involving finite element analyses
have been conducted with the same objectives as in this
study, but the basic properties of the repair material were
ambiguous, the material properties and boundary conditions were only assumed, and the correlation between the
predicted results and the actual phenomena was low.
To prevent early re-deterioration and to ensure that the
repaired structure maintains the required performance over
its intended lifetime, it is important to be able predict the
stresses generated between the substrate concrete and the
patch-repaired material, to select the appropriate repair
material, to determine the appropriate region to repair,
and to cure repair patches appropriately.
With such a background, a series of experiments and finite
element analysis were conducted using the properties of the
repair materials and environmental conditions as the experimental parameters. The repair material was cement mortar
modified by the addition of a re-emulsification-type polymer
resin. The moisture diffusivity of the repair material was
determined by analyzing the effects of temperature. Using
the results of moisture diffusivity analysis, a coupled structure analysis was conducted on the mechanical property
and changes in volume [17] to calculate stress generation in
the repair material and the interface between the repair patch
and the structure. The results were used to assist in guiding
the selection of the optimum patch repair material.
2. Estimating moisture distribution in patch-repaired
material using a non-linear diffusion equation
Bazant et al. [7] have demonstrated the non-linearity of
moisture diffusion in porous materials such as those used

for patch repair and the concrete substrate, and a number

435

of studies were carried out on the basis of that principle [8–
12]. Most of these studies used either the Matano method
[18,19], which uses Boltzmann transform, or a method
involving inverse analysis of measured data [20]. In this
study, the Matano method was used to determine moisture
diffusivity, which required the monitoring of changes in
water content with the passage of time. Water content
can be monitored by slicing specimens and using a relative
humidity probe [21], or by measuring the nuclear magnetic
resonance [22]. In this study, a monitoring method was
used that involved slicing a specimen, drying it to an absolutely dry state, and measuring the change in weight before
and after drying. This method may cause a slight reduction
in the water content when specimens are cut, but requires
no correction and is simple, direct and precise [23,24].
Two-dimensional finite element analysis was conducted
to predict changes in water distribution in a patch-repaired
region caused by various environmental factors. A coupled
structural analysis of volume changes caused by changes in
water content was done to predict the stress generated
under the constraints imposed by the substrate concrete.
2.1. Calculating moisture diffusivity by the Boltzmann
transform
The unidimensional, non-linear diffusion equation is:
oR
¼ rðDrRÞ
ot


ð1Þ

where D (cm2/d) is the moisture diffusion coefficient determined from the gradient of relative water content, and R
(%) is relative water content, which is given by
R ¼ ðw=w0 Þ Â 100

ð2Þ

where w is the water content (%) and w0 is the water content at saturation (%).
The movement of moisture during the drying process
can be expressed by a diffusion equation, and a non-linear
diffusion equation can be derived from the monitored
water content distribution using the Boltzmann transform
[18]. For moisture movement in one direction, which was
assumed in this study, the relative water content is
expressed as a Boltzmann transfer variable:
pffi
k ¼ x= t
ð3Þ
where x (cm) is the distance from the drying surface and t
(day) is the drying period.
By applying the Boltzmann transform under boundary
conditions, the moisture diffusivity D(R) can be expressed as:
0 
Z Rs
1
oR
k dR
ð4Þ

DðRÞ ¼ À
2 R
ok
where Rs = 100%, from Eq. (1).
This equation can be used to determine the moisture diffusion coefficient at an arbitrary relative water content R.
To calculate the equation, relative water content must be
expressed as a function of the Boltzmann transfer variable.


436

D. Park et al. / Construction and Building Materials 23 (2009) 434–447

2.2. Moisture diffusion coefficient considering temperature
effects
Moisture diffusivity D is a function of temperature and
relative water content or relative humidity. Powers [25] estimated that the movement of water at normal temperature
was determined by the movement of water molecules along
adsorption surfaces. Bazant et al. [7] proposed that the
movement of water below 100 °C is not determined by capillary flow. But it is determined by the minimum pore
cross-sectional area of the neck of pores, since capillary space
is discontinuous, and the effects of temperature on the movement of water molecules are determined not by the adhesion
of the liquid or vapor, but by the activation energy (Q) [25].
To consider the effects of temperature on moisture diffusivity, Eq. (5) was developed by adding moisture diffusivity,
which is a function of relative water content proposed by
Akita et al. [10], to the temperature equations described by
Bazant et al. [7] and Mihashi et al. [26].
In Eq. (5), D1 represents the diffusivity at the standard
temperature (T = 20 °C) at saturation (h = 1.0). The term
f1(R) represents the effects of relative water content on

moisture diffusivity, and f2(T) represents the effects of temperature on moisture diffusivity at a relative humidity of
100%:
DðT ; RÞ ¼ D1 Á f1 ðRÞ Á f2 ðT Þ
1
À
Á
Én
f1 ðRÞ ¼ È
R
m  1 À 100
þ1

N

!
T þ 273
U
1
1
À
f2 ðT Þ ¼
exp
293
R 293 T þ 273

ð5Þ

where U (J/mol) is the activation energy; R (J/mol K) is the
gas constant; and m, n and N are material constants determined by the polymer-to-cement ratio.


The matrix expression of the moisture diffusion equation
is:

& '
oR
¼ fF g
½DŠfRg þ ½LŠ
ot

ð8Þ

where [D] is the moisture diffusion matrix, [L] the water
capacity matrix, {F} the external moisture flux vector,
and {R} is the relative water content vector.
Since moisture diffusivity D has a non-linear relationship with relative water content R, the Newton–Raphson
method was used in the finite element analysis.
The matrix of the moisture diffusion equation (Eq. (8)) is
discrete in space but not in time. Thus, the Crank–Nicolson
difference method was used to discretize the equation from
time.
In the Crank–Nicolson difference method, the nodal relative water content [27] vector at t + Dt/2 (Dt is a small
increase in time) is given as:
& 
'
Dt
1
¼ ðfRðt þ DtÞg þ fRðtÞgÞ
ð9Þ
R tþ
2

2
When the nodal relative water content vector at t + Dt/2 is
differentiated by time:
&

'
o
Dt
fRðt þ DtÞg À fRðtÞg
R tþ
¼
ð10Þ
ot
2
Dt
Substituting Eqs. (9) and (10) for {R} and foR
g in Eq. (8),
ot
and organizing the equation gives:




1
1
1
1
½DŠ þ ½LŠ fRðt þ DtÞg ¼ À ½DŠ þ ½LŠ fRðtÞg þ fF g
2
Dt

2
Dt
ð11Þ
Since {R(t)} on the right-hand side of the equation is
known, the equation for the finite element analysis of nonsteady moisture diffusion can be calculated.

2.3. Initial and boundary conditions
3. Overview of the experiment
The initial and boundary conditions used for the finite
element analysis are shown below.
Initial conditions:
Rðx; y; 0Þ ¼ 100%
Boundary conditions:
 
oR
DðRÞ
¼ f ðRen À Rs Þ
ox

ð6Þ

ð7Þ

where f (cm/day) is the coefficient of moisture transfer, and
Ren (%) and Rs (%) are the relative water content at the drying surface and in ambient air, respectively.
2.4. Non-linear finite element analysis
Non-linear finite element analysis was conducted using
experimentally determined moisture diffusion coefficients,
and initial and boundary conditions to calculate the water
content distribution in the repair material.


3.1. Materials used
Ordinary Portland cement was used. Fine aggregates
were river sand from the Oigawa River in Japan, and its
physical properties are given in Table 1. The re-emulsification-type polymer resin was manufactured by N Co., and
its properties are given in Table 2.
3.2. Preparing the specimens
Specimens of polymer-modified cement mortar (PCM)
used for patch repair were prepared according to the testing methods stated in JIS A 1171. The mix proportion
was a fine aggregate-to-cement ratio of 1:3, a water-tocement ratio of 1:1, and polymer/cement with 0%, 5%,
10%, and 20% polymer (Table 3). Antifoaming agent was
added at 0.7% of the polymer weight. Flow and air content
were measured and are given in Table 3.


D. Park et al. / Construction and Building Materials 23 (2009) 434–447
Table 1
Property values of fine aggregates

Oigawa River sand
in Japan

Absolute dry
density (g/cm3)

Surface dry
density
(g/cm3)

Absorption

(%)

FM

2.54

2.59

2.03

2.65

Table 2
Properties of re-emulsification-type polymer resin
Polymer
Protection colloid
Solid content (determined by furnace
drying for 3 h at 105 °C)
Apparent density (JIS K 5101)
Glass transition temperature (Tg)
Minimum film-forming
temperature (MFT)

Monomer base vinyl acetate/
VeoVa/acrylate
Polyvinyl alcohol
99 (±1)%
0.5 (±0.1)g/cm3
14 °C
$0 °C


437

3.3.2. Water content test at equilibrium
Water content at equilibrium was tested to determine the
relationship between RH and water content, which is the isothermal absorption curve needed to set the boundary conditions of finite element analysis and to correct analytical
results. The specimen was prepared as described for the
moisture diffusivity test (Table 3) and then cut into slices
about 0.5 cm thick to speed the establishment of equilibrium.
The humidity was controlled at a constant value using a
desiccator (0%) containing silica gel and a hygrostat (20%,
40%, and 80%). After four weeks, the mass showed no
change, and the specimen was judged to have reached equilibrium. The relative water content for each relative humidity value was determined from the weight differences.
4. Results and discussion
4.1. Determining moisture diffusivity

Polymer
(%)

Cement:fine
aggregate

Water:
cement

Antifoaming
agent (%)

Flow
(mm)


Air content
(%)

0
5
10
20

1:3

1:1

0.7

160
185
190
195

6.2
7.5
8.2
8.9

The specimens were molded in dimensions of
40 mm  40 mm  160 mm, cured in a humid atmosphere
(20 °C, 85% RH) for 2 days, under water (at 20 °C) for 5
days, and in a dry atmosphere (20 °C, 60% RH) for 21
days, and prepared in a saturated state of 100% relative

water content.
3.3. Experimental methods
3.3.1. Moisture diffusivity test
Unidimensional moisture movement was induced in
order to determine the moisture diffusivity. As shown in
Fig. 1, surfaces other than the drying surface were covered
with wrapping film and then sealed tightly with adhesive
tape to prevent water transpiration. Specimens were dried
at 5 °C, at 20 °C and at 40 °C, with a relative humidity of
60%. After 2, 4, and 8 weeks, a sample was chipped from
the drying surface, and changes in the mass of each element
were measured immediately and air-dried at 105 °C for 4
days to absolute dryness condition.

As described above, the non-linear moisture diffusivity
can be calculated from the relative water content using the
Boltzmann transform proposed by Matano [18,19]. The relationship between the Boltzmann transfer variable k and relative water content was determined (Fig. 2), and was
subjected to regression analysis using the following curve:
(
)
a
ð12Þ
R ¼ 100 1 À
2
ðk þ bÞ
where R (%) is the relative water content, a and b are constants determined by the shape of the curve. The results are
summarized in Table 4 for each drying condition.
Differentiation of Eq. (12) by the Boltzmann transfer
variable gives Eq. (13). Moisture diffusivity can be calculated by substituting Eqs. (13) and (14) in Eq. (4):
oR

200 Á a
¼
ok ðb þ kÞ3

ð13Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:5fÀb Á ðÀ200 þ 2RÞ À 20 100a À a Á Rg

À100 þ R
Temp.=20°C, R.H.=60%

ð14Þ
P/C=0%
P/C=5%
P/C=10%
P/C=20%

100
Relative Water Content (%)

Table 3
Mix proportion and property values of polymer-modified cement mortar

90
Y=100*(1-(a/(λ+b)^2))
80

Data: P/C=0%
2

= 0.9695
R
a
0.23 ±0.03
b
0.75 ±0.07

Data: P/C=5%
2
= 0.97421
R
a
0.42±0.05
b
1.00±0.08

70

Data: P/C=10%
2
= 0.97214
R
a
0.77 ±0.09
b
1.44 ±0.11

Data: P/C=20%
2
= 0.95864

R
a
0.54 ±0.08
b
1.18 ±0.11

60
0

Fig. 1. Dimensions of a specimen with one drying surface.

1

2

3

λ=(x/t

1/2

4

5

)

Fig. 2. Relationship between the Boltzmann transfer variable k and
relative water content (example: at 20 °C).



D. Park et al. / Construction and Building Materials 23 (2009) 434–447

Table 4
Material constants determining the shape of Eq. (12)

40

b

R2

0
5
10
20
0
5
10
20
0
5
10
20

0.093
0.144
0.224
0.158
0.228

0.418
0.769
0.534
0.612
0.950
1.310
1.060

0.430
0.556
0.717
0.619
0.750
1.000
1.440
1.182
0.974
1.255
1.510
1.309

0.991
0.996
0.992
0.986
0.970
0.974
0.972
0.959
0.942

0.948
0.966
0.968

The movement of water at normal temperature is determined by the smallest sectional area at the neck of capillary
pore space. Water movement at the neck is the movement
of water molecules within an absorbed water layer, which
becomes thinner as the moisture level decreases [7,25].
The moisture diffusivity measurements (Fig. 3) in this study
showed this phenomenon and were in a non-linear relationship with relative water content. Fig. 3 shows the effects of

10

2

Diffusion Coefficient (cm /d)

12

4.2. Water content at equilibrium
The water content of porous materials, such as patch
repair materials and substrate concrete, fluctuates with
the relative humidity of the ambient atmosphere. At a fixed

12

P/C=0%
5°C, 60%
20°C, 60%
40°C, 60%


8
6
4
2

2

Diffusion Coefficient (cm /d)

10

P/C=5%
5°C, 60%
20°C, 60%
40°C, 60%

8
6
4
2
0

0

12

10

2


20

a

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

Relative Moisture Content (%)

Relative Moisture Content (%)

12

P/C=10%
5°C, 60%
20°C, 60%
40°C, 60%

8
6
4
2
0

10

2


5

Polymer content (%)

Diffusion Coefficient (cm /d)

Temperature (°C)

temperature during the drying process. The higher the temperature, the greater the moisture diffusivity. The effects of
temperature were quantified using Eq. (5). The effects of
polymer content differed from those in an earlier study
[23], which reported that specimens of higher polymer-tocement ratios were more compact, had smaller capillary
pore sizes, and thus had lower moisture diffusivity. This
was because in the earlier study, the polymer-to-cement
ratio was first decided and then the water-to-cement ratio
was reduced so as to compensate for increases in fluidity
caused by the increase in polymer content. However, in
the present study, which was aimed at understanding the
effects of polymer content, the water-to-cement ratio was
fixed at 50% and the polymer-to-cement ratio was used
as the experimental variable. Up to a polymer-to-cement
ratio of 10%, moisture diffusivity increased, but dropped
slightly at a ratio of 20%.

Diffusion Coefficient (cm /d)

438

P/C=20%
5°C, 60%

20°C, 60%
40°C, 60%

8
6
4
2
0

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

Relative Moisture Content (%)

Relative Moisture Content (%)

Fig. 3. Moisture diffusivity for each drying temperature and polymer/cement ratio.


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

temperature, the water content of a porous mass is in equilibrium with the ambient relative humidity. The relationship
between the relative humidity and relative water content of
the specimen is called the sorption isotherm [28]. In this
experiment, which aimed to assess changes in water content
when the repair material dried, the desorption isotherm was
determined experimentally by decreasing the relative water
content until it reached equilibrium, as shown in Fig. 4.
The relationships differed slightly, depending on the polymer-to-cement ratio, but the difference was small and could

not be quantified. Thus, the mean was determined and used
to correct the boundary conditions of the non-linear finite
element analysis, as described in the following section.
4.3. Comparison between analytical and experimentally
measured relative water contents
The distribution of relative water content along the vertical direction from the drying surface was determined by
non-linear finite element analysis based on the values determined by the experiments described in Sections 4.1 and 4.2
above. The elements were four-nodal isoparametric, and
the entire analytical length of 160 mm was divided into
30 equal parts. Eqs. (6) and (7) were used as the initial
and boundary conditions, respectively. The relative water
content at a relative humidity of 60% in ambient atmosphere, which was a boundary condition, was calculated
using the tryout method based on the isothermal absorption curve shown in Fig. 4 for 20 °C and the experimental
results for 5 and 40 °C. The coefficient of moisture transfer
f was determined retrogressively using the experimental
values and repetitive calculation. The relative water content at each temperature at a relative humidity of 60%,
which was a boundary condition, and the coefficient of
moisture transfer are shown in Table 5. The effects of the
coefficient of moisture transfer on water movement analysis are reported to be small [10]. In this study, a uniform
coefficient of moisture transfer of 0.007 cm/day was used,

Relative Water Content (%)

100
P/C=0%
P/C=5%
P/C=10%
P/C=20%
Mean Value


80

60

40

20

439

Table 5
Relative water content and coefficient of moisture transfer corresponding
to 60% relative humidity
Drying temperature (°C)
Relative water content (%)
Coefficient of moisture transfer (m/d)

5
60
0.007

20
55
0.007

40
32
0.007

which resulted in a good correlation with experimental values. The coefficient of moisture transfer is not an intrinsic

property of patch repair materials; it changes depending
on the ambient conditions and the state of the surface of
the specimen. The coefficient of moisture transfer is rarely
measured accurately, and most analyses use fixed values.
Experimental and analytical relative water content values of a specimen are compared in Fig. 5. As a whole,
the correlation was good, but slight errors were observed
on the 56th day and at a depth more than 6 cm below
the drying surface. The errors were probably produced
because, although the Matano method, which was used
to determine the moisture diffusivity characteristically
requires that the surface opposite the drying surface has
a relative humidity of 100%, the specimen was already
dry on the 28th day of the experiment even at the element
furthest (14 cm) from the drying surface and, thus, small
errors were already present in the regression analysis for
determining the relationship between the Boltzmann transfer variable and relative water content. The errors were larger at higher temperatures.
Both experimentally and analytically, the drying speed
was faster at higher drying temperatures. It was fastest
for specimens with a polymer-to-cement ratio of 10%
and slowed gradually as the polymer-to-cement ratio
increased. The results differed from the widely accepted
belief that increases in polymer-to-cement ratio make
the inner structure of PCM compact. This is probably
because the polymer-to-cement ratio was adjusted without changing the water-to-cement ratio as described in
Section 4.1 [28].
The results of the regression analysis of the relationship
between the relative humidity and relative water content
during the drying process, determined by inverse analysis
using experimental values and the finite element analysis
method, are shown in Fig. 6. The results of the regression

analysis that included data for a relative humidity of 60%
and drying temperatures of 5 and 40 °C are expressed by
Eq. (15). The relationship was used to convert the boundary conditions (relative water content) for the finite element
analysis of relative humidity data in the real environment,
which is described below:
R ¼ 17:36 þ 0:263T À 0:00847T 2 þ 2:303H
À 0:0254TH À 0:000016T 2 H À 0:04175H 2

0
0

20

40
60
Relative Humidity (%)

80

100

Fig. 4. Relationship between relative water content and relative humidity.

þ 0:000258TH 2 þ 0:00027H 3

ð15Þ

where R is the relative water content (%), T the drying temperature (°C) and H is the relative humidity (%).



440

D. Park et al. / Construction and Building Materials 23 (2009) 434–447

4.4. Qualitative prediction of internal water content
distribution and stress generation under fixed ambient
atmospheric conditions
Under fixed drying conditions of 20 °C and relative water
content of 55%, which corresponds to a relative humidity of
60% (determined using Eq. (15)), moisture diffusion and
stress generation were compared for the polymer-to-cement
ratios. The relative water content of the substrate concrete
before repair was assumed to be 60%. The moisture diffusion
coefficients of the repair material (see Section 4.1) and the
diffusivity values of the substrate concrete reported in an
earlier study [29] were used in the analysis. Fig. 7 shows
the element division of the analytical model. The beam
was assumed to be fixed at both ends. In Fig. 7, TI denotes
the thickness of the interface, CH is the thickness of the
repair material, CW is the width of the substrate concrete,
RW is the width of the repair region, and RH is the thickness
of the repair region. The dimensions of the analytical model
are shown in Table 6. Structural analysis was conducted by
coupling the data for the volumetric changes caused by
changes in water content and the results of the internal water
content distribution analysis in order to predict the chrono-

logical changes in stress generation. Data related to changes
in length caused by changes in water content and the coefficient of elasticity [17] are given in Table 7. The data on the
changes in length caused by changes in water content were

measured by dyeing a thin rectangular specimen
5 mm  40 mm  160 mm, which had been devised to minimize the internal constraining force of the materials in a
desiccator. Primer resin was assumed to be applied to the
interface between the repair material and the substrate concrete. Since no measured data were available for the moisture diffusivity of primer resin, it was assumed to be
1/1000 of that of the patch-repaired materials. The input
moisture diffusion coefficients to the substrate concrete are
shown in Fig. 8. The moisture diffusion coefficients and
the isothermal absorption curves of the substrate concrete
were analyzed using the measurements reported by Fujiwara et al. [29]. The structural analysis is that for linear elastic
regions. The repair material, interface and substrate concrete were assumed to be perfectly united, and the mechanical properties of the interface were assumed to be the same
as those of the repair material in the analysis. The repair
regions were assumed to start drying after they were
cured-sealed over a period of 28 days.
100

90
80
70

5°C, P/C=0%

60

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days


50
40
0

2

4

6

Relative Water Content (%)

Relative Water Content (%)

100

90
80
70
5°C, P/C=5%
60
50
40

8 10 12 14 16 18

0

Depth from the Drying Surface (cm)


2

4

6

8 10 12 14 16 18

Depth from the Drying Surface (cm)

100

90
80
70
5°C, P/C=10%
60

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40
0

2


4

6

8 10 12 14 16 18

Depth from the Drying Surface (cm)

Relative Water Content (%)

100
Relative Water Content (%)

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

90
80
70
5°C, P/C=20%
60

14days
28days
56days

Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40
0

2

4

6

8 10 12 14 16 18

Depth from the Drying Surface (cm)

Temperature, 5°C; R.H., 60%
Fig. 5. Measured and analytical relative water content.


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

The distribution of relative water content on the interface on the 30th day after the start of drying is shown in
Fig. 9. The distribution of the main stress (rmax) generated
along with volumetric changes is shown in Fig. 10. The
stress generated on the drying surface under the constraining conditions was compared between specimens with different polymer-to-cement ratios. The stress near the
drying surface was predicted to be higher for a polymerto-cement ratio of 0% than that for the other ratios,
although the changes in volume caused by changes in water

content were small. The reduction in relative water content
inside the repair region was greatest at a polymer-tocement ratio of 10%, in which relatively large stress was
generated by the effects of the elasticity coefficient and volumetric changes.
4.5. Qualitative prediction of internal water content
distribution and stress generation under real environmental
conditions
Changes in the relative water content inside the repair
material and stress generation under real environmental

conditions were predicted. The boundary ambient conditions were the mean of the meteorological data recorded
over the past 10 years in Tokyo, Naha (Okinawa Prefecture) and Sapporo (Hokkaido Prefecture). The annual temperature and humidity in Tokyo, Okinawa, and Sapporo
from March 2004 to February 2005 and the mean for the
10 years are shown in Fig. 11. The moisture diffusion coefficients of the repair material and substrate concrete were
corrected by considering the effects of the drying temperature. The mechanical property values and the changes in
volume were the same as those used in Section 4.3. The drying period was from March until the following February.
The relative water content gradient along the vertical
direction from the drying surface is shown in Fig. 12. At
the start of the drying process, the relative water contents
of the surface and the inside differed sharply, but the difference was less marked as time passed. The drying speed was
highest for the polymer-to-cement ratio of 10% and in Okinawa, where the mean annual ambient temperature was the
highest.
The distribution of the relative water content along the
vertical direction and the main stress at the end of August
100

80
70
20°C, P/C=0%
60


14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40

0

2

4

6

Relative Water Content (%)

Relative Water Content (%)

100
90

90
80
70
20°C, P/C=5%
60


40

8 10 12 14 16 18

0 2 4 6 8 10 12 14 16 18
Depth from the Drying Surface (cm)

100

100

80
70
20°C, P/C=10%
60

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40
0

2


4

6

Relative Water Content (%)

Relative Water Content (%)

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50

Depth from the Drying Surface (cm)

90

441

90
80
70
20°C, P/C=20%
60

14days

28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40

8 10 12 14 16 18

Depth from the Drying Surface (cm)

0

2

Temperature, 20 °C; R.H., 60%
Fig. 5 (continued)

4

6

8 10 12 14 16 18

Depth from the Drying Surface (cm)


442


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

100

90
80
70
40°C, P/C=0%

60

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40

Relative Water Content (%)

Relative Water Content (%)

100

90
80

70

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40

0 2 4 6 8 10 12 14 16 18
Depth from the Drying surface (cm)

0 2 4 6 8 10 12 14 16 18
Depth from the Drying surface (cm)

100

100

90
80
70
40°C, P/C=10%

60

14days

28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days

50
40

Relative Water Content (%)

Relative Water Content (%)

40°C, P/C=5%

60

90
80
70
40°C, P/C=20%

60

14days
28days
56days
Analysis Curve of 14days
Analysis Curve of 28days
Analysis Curve of 56days


50
40

0 2 4 6 8 10 12 14 16 18
Depth from the Drying surface (cm)

0 2 4 6 8 10 12 14 16 18
Depth from the Drying surface (cm)

Temperature, 40 °C; R.H., 60%
Fig. 5 (continued)

R : Relative Water Content (%)

100
Temp.=5°C
Temp.=20°C
Temp.=40°C
Measured Value

80

60

40
2

20


R=17.36+0.263* T-0.00847*T
2
+2.303*H-0.0254*T*H-0.000016*T *H
2
2
3
-0.04175*H +0.000258*T*H +0.00027*H

0
0

20

40

60

80

100

H : Relative Humidity (%)
Fig. 6. Regression curve of the relationship between relative humidity and
relative water content during the drying process.

are shown in Fig. 13. The distribution and stress generation
of specimens of different polymer-to-cement ratios and
regions were compared. The gradient of the relative water

content caused by drying was steeper in Okinawa than in

Tokyo. Thus, the main stress was predicted to be larger
in Tokyo than in Okinawa, although the amount of moisture to be lost by drying was smaller in Tokyo. Thus, the
high stress generated near the drying surface probably
depended on the gradient of relative water content between
the drying surface and the inside of the patch repair, which
is the same as that of plastic cracks in concrete [30].
The stress was also larger in specimens of lower polymer-to-cement ratios in the real environment, as discussed
in Section 4.4.
The changes in internal water content distribution and
stress generation caused by changes in thickness of the
repair region are shown in Fig. 14. The polymer-to-cement
ratio analyzed was 5%, and the thickness of the patchrepaired region was 5, 7, and 10 cm. The environmental
data recorded in Tokyo were used as the boundary conditions. Regardless of the thickness of the patch, a very steep
stress gradient was observed between the drying surface
and the inside of the region at the end of March, which
was soon after drying started. The overall stress increased
as time passed. At the end of August the rate of change


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

443

Fig. 7. Element division of the analytical model.
Table 6
Dimensions of analytical model
CW

CH


RW

RH

TI

1.5

0.3

0.25

0.07

0.005

Table 7
Input data of patch repair materials and substrate concrete

Patch repair
material

Substrate
concrete

Water:
cement

Polymer
(%)


Coefficient
of elasticity
(GPa)

Length change
by water absorption
(Â10À6 %)

1:1
1:1
1:1
1:1
1:1

0
5
10
20


25.71
23.65
21.39
18.25
40.00

23.7
25.3
27.1

31.3
20.0

Relative Water Content (%)

Dimension (m)

100

Drying Time = 30 days

P/C=0%
P/C=5%
P/C=10%
P/C=20%

90
80
70
60
50
0.00

0.03

0.06

0.09

0.15


Fig. 9. Distribution of relative water content along the vertical direction
from the drying surface (A–A0 ).

24

8

Fujiwara(W/C=0.52, T=10°C)
Fujiwara(W/C=0.52, T=20°C)
Fujiwara(W/C=0.52, T=40°C)

7
6
5
4
3
2
1

16
12
8
4
0
0.00

0
10


20

30

40

50

60

70

P/C=0%
P/C=5%
P/C=10%
P/C=20%

20
Principal Stress (MPa)

Diffusion Coefficient (cm 2 /day)

0.12

Depth from the Drying Surface (m)

80

90 100


Relative Water Content (%)
Fig. 8. Diffusion coefficient of substrate concrete [29].

0.03

0.06

0.09

0.12

0.15

Depth from the Drying Surface (m)
Fig. 10. Main stress generated along the vertical direction from the drying
surface (A–A0 ).


444

D. Park et al. / Construction and Building Materials 23 (2009) 434–447
Temp. & R.H. of Tokyo
latitude 35.4 north and longitude 139.4 east

Avg. temp. of day('04-'05)
Avg. temp. of month('95-'04)

Avg. R.H. of day('04-'05)
Avg. R.H. of month('95-'04)


80

90

70

80

60

70

50

60

40

50

30

40

20

30

10


20

0

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Jan.

Feb.

Relative Humidity (%)


Temperature (°C)

100

10
0

-10

0

50

100

150

200

250

300

350

Time (Day & Month)
Temp. & R.H. of Okinawa
latitude 26.12 north and longitude 127.4 east

Avg. temp. of day('04-'05)

Avg. temp. of month('95-'04)

Avg. R. H. of day('04-'05)
Avg. R. H. of month('95-'04)

80

90

70

80

60

70

50

60

40

50

30

40

20


30

10

20

0

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Jan.


Feb.

-10

Relative Humidity (%)

Temperature (°C)

100

10
0

0

50

100

150

200

250

300

350


Time (Day & Month)
Temp. & R.H. of Sapporo
latitude 43 north and longitude 141.2 east

Avg. temp. of day('04-'05)
Avg. temp. of month('95-'04)

Avg. R.H. of day('04-'05)
Avg. R.H. of month('95-'04)

80

90

70

80

60

70

50

60

40

50


30

40

20

30

10

Dec.

0

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.


Jan.

Feb.

20

Relative Humidity (%)

Temperature (°C)

100

10

Nov.

0

-10
0

50

100

150

200

250


300

350

Time (Day & Month)
Fig. 11. Meteorological data used as the boundary conditions (mean annual temperature and relative humidity in Tokyo, Okinawa and Sapporo for 10
years).

of both relative water content and stress were smaller than
those in March. Thick specimens (10 cm) needed more time
than thin specimens (5 cm) for the relative water content

near the drying surface to decrease, since a larger amount
of water had to be removed from the inside. The thinner
specimens dried faster and showed increases in stress


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

Tokyo P/C=0%

80
70
Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)
Jan.(After 11 m)


60
50

100

Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)

Relative Water Content (%)

90

0.00

Relative Water Content (%)

100

70
Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)
Jan.(After 11 m)


50
0.00

0.02

0.04

80
70

Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)

0.06

Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)
Jan.(After 11 m)

60
50


100

80

60

90

0.08

70
Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)
Jan.(After 11 m)

60
50

60
50
0.00

Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)

Jan.(After 11 m)

0.02

0.04

Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)

0.06

0.08

Depth from the Drying Surface (m)

0.02

0.04

Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)


0.06

0.08

Depth from the Drying Surface (m)

Relative Water Content (%)

Relative Water Content (%)

70

0.08

80

100

80

0.06

90

0.00

Okinawa P/C=5%

90


0.04

Tokyo P/C=20%

Depth from the Drying Surface (m)

100

0.02

Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)

Depth from the Drying Surface (m)

Tokyo P/C=10%

90

Tokyo P/C=5%

0.00

0.02
0.04
0.06

0.08
Depth from the Drying Surface (m)

Relative Water Content (%)

Relative Water Content (%)

100

445

Sapporo P/C=5%

90
80
70
Mar.(After 1 m)
May(After 3 m)
Jul.(After 5 m)
Sep.(After 7 m)
Nov.(After 9 m)
Jan.(After 11 m)

60
50
0.00

0.02

0.04


Apr.(After 2 m)
Jun.(After 4 m)
Aug.(After 6 m)
Oct.(After 8 m)
Dec.(After 10 m)
Feb.(After 12 m)

0.06

0.08

Depth from the Drying Surface (m)

Fig. 12. Changes in water content (1 year) in patch repair PCM along the vertical direction from the surface (A–A0 ).

sooner. The phenomenon affected stress generation at the
interface with the substrate concrete, and the main stress
on the interface was greater in thinner specimens.
The analysis of stress generation and changes over time
are important when considering how a repair material will
perform under specific environmental conditions. However, this linear structural analysis could not predict the
stress generated at the repair region in the field, and further

analytical models need to be developed to reproduce microcracks, creep and interface properties.
5. Conclusions
The mechanism underlying the deterioration caused by
drying and shrinkage of patch repairs made to deteriorated
reinforced concrete structures was studied by measuring



446

D. Park et al. / Construction and Building Materials 23 (2009) 434–447

Tokyo P/C=0%
Tokyo P/C=10%
Okinawa P/C=5%

24

Tokyo P/C=5%
Tokyo P/C=20%
Spporo P/C=5%

Tokyo P/C=0%
Tokyo P/C=5%
Tokyo P/C=10%
Tokyo P/C=20%
Okinawa P/C=5%
Sapporo P/C=5%

20

90

Principal Stress (N/mm2 )

Relative Water Content (%)


100

80
70
60

16
12
8
4

50
0.00

0.03

0.06

0.09

0.12

0
0.00

0.15

Depth from the Drying Surface (m)

0.03 0.06 0.09 0.12 0.15

Depth from the Drying Surface (m)

Fig. 13. Relative water content and main stress at the interface along the vertical direction (A–A0 ) at the end of August (A–A0 ).

85

16

80
12

75

Depth=5cm
Depth=7cm
Depth=10cm

8

70
65
60

4

Depth=5cm
Depth=7cm
Depth=10cm

20


Depth=5cm
Depth=7cm
Depth=10cm

2

90

24

Principal Stress (N/mm )

Depth=5cm
Depth=7cm
Depth=10cm

20

95

0.03

0.06

0.09

0.12

50

0.15

Depth from the Drying surface (m)
(Mar.(After 1 m))

95
90
85

16

80
12

75
70

8

65
60

4

55
0
0.00

100


Relative Water Content (%)

2

100
Relative Water Content (%)

Principal Stress (N/mm )

24

55
0
0.00

0.03

0.06

0.09

0.12

50
0.15

Depth from the Drying surface (m)
(Aug.(After 6 m))

Fig. 14. Changes in relative water content and main stress caused by the difference in thickness of the patch repair region (A–A0 ).


the moisture diffusion coefficients of the repair material,
with drying temperature and polymer-to-cement ratio as
experimental parameters. The stress produced at the repair
regions by drying was predicted through linear structural
analysis by inputting moisture diffusivity, volumetric
changes caused by changes in water content, and mechanical properties. Fixed environmental conditions and real
environmental data (Tokyo, Okinawa and Hokkaido) were
used as boundary conditions. The chronological changes in
relative water content in repair regions and stress distribution were determined analytically, and the principal physical parameters involved in stress generation were
investigated. The following knowledge was acquired from
the experiments and analyses described here:
(1) The moisture diffusivity of the repair material (PCM)
investigated in this study increased in proportion to
the polymer-to-cement ratio, up to a ratio of 10%
and dropped slightly thereafter. Moisture diffusivity
was greater at higher drying temperatures. An equation for predicting the phenomenon was developed.

(2) Stress produced by drying and shrinkage was
affected by the differences in moisture diffusivity
between the repair material and the substrate concrete, as well as by volumetric changes caused by
changes in water content and the coefficient of elasticity. Of the repair materials tested in this study, the
polymer/cement mix with 10% polymer produced
the greatest stress.
(3) As drying proceeded, a gradient of relative water content was produced between the drying surface and the
inside of the repair region, and considerable stress
was generated in the vertical direction in this region.
The speed of stress mitigation by further drying varied, depending on the thickness of the repair region.
The thicker the region, the slower the stress generation by drying and, thus, the lower the risk of generating initial defects.
(4) An analysis using recorded environmental data as the

boundary conditions showed that the steepest stress
gradient was produced with the environment at
Tokyo.


D. Park et al. / Construction and Building Materials 23 (2009) 434–447

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