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

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.

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Drying eﬀect of polymer-modiﬁed cement for patch-repaired

mortar on constraint stress

a Division of Architecture and Ocean Space, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea

b 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 inves-tigated The moisture diffusion coefficient of the repair materials was determined by varying the drying temperature and the polymer-to-cement ratios of the polymer-modified polymer-to-cement mortar (PCM) in the experiment It is found that the diffusivity of PCM increases in propor-tion to the polymer-to-cement ratio up to 10% The constraint stresses due to drying at the repaired region were estimated by the couple-linear 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

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

dimen-sionally and electrochemically stable, resistant against

pen-etration 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,

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,

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-emul-siﬁcation-type polymer resin, the use of which is increasing rapidly as it is convenient to application

con-crete changes non-linearly with changes in relative water

moisture diﬀusivity and relative water content of concrete

deter-mined the moisture diﬀusivity of a specimen by either slic-ing the specimen and measurslic-ing its relative water content,

or monitoring the changes in relative humidity in the spec-imen 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,

doi:10.1016/j.conbuildmat.2007.11.003

*

Corresponding author Tel.: +82 10 5533 9443; fax: + 82 51 403 8841.

E-mail address: dcpark@hhu.ac.kr (D Park).

www.elsevier.com/locate/conbuildmat Construction and Building Materials 23 (2009) 434–447

Construction and Building

MATERIALS

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prediction analysis is easy, and the characteristics of the

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

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

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

condi-tions 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

exper-imental 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

struc-ture analysis was conducted on the mechanical property

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

moisture diﬀusion in porous materials such as those used

for patch repair and the concrete substrate, and a number

[18,19], which uses Boltzmann transform, or a method

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

used that involved slicing a specimen, drying it to an abso-lutely 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

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

deter-mined from the gradient of relative water content, and R (%) is relative water content, which is given by

con-tent 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

assumed in this study, the relative water content is expressed as a Boltzmann transfer variable:

t

p

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:

2

R

oR ok

ð4Þ

This equation can be used to determine the moisture dif-fusion 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

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2.2 Moisture diﬀusion coeﬃcient considering temperature

eﬀects

Moisture diﬀusivity D is a function of temperature and

esti-mated that the movement of water at normal temperature

was determined by the movement of water molecules along

cap-illary 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

move-ment of water molecules are determined not by the adhesion

To consider the eﬀects of temperature on moisture

which is a function of relative water content proposed by

tem-perature on moisture diﬀusivity at a relative humidity of

100%:

100

þ 1

293

R

1

where U (J/mol) is the activation energy; R (J/mol K) is the

gas constant; and m, n and N are material constants

deter-mined by the polymer-to-cement ratio

2.3 Initial and boundary conditions

The initial and boundary conditions used for the ﬁnite

element analysis are shown below

Initial conditions:

Boundary conditions:

ox

where f (cm/day) is the coeﬃcient of moisture transfer, and

dry-ing 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

The matrix expression of the moisture diﬀusion equation is:

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 relation-ship with relative water content R, the Newton–Raphson method was used in the ﬁnite element analysis

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

increase in time) is given as:

2

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

o

2

and organizing the equation gives:

1

fRðtÞg þ fF g

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

3 Overview of the experiment 3.1 Materials used

Ordinary Portland cement was used Fine aggregates were river sand from the Oigawa River in Japan, and its

re-emulsiﬁca-tion-type polymer resin was manufactured by N Co., and

3.2 Preparing the specimens Specimens of polymer-modiﬁed cement mortar (PCM) used for patch repair were prepared according to the test-ing methods stated in JIS A 1171 The mix proportion was a ﬁne aggregate-to-cement ratio of 1:3, a water-to-cement ratio of 1:1, and polymer/water-to-cement with 0%, 5%,

added at 0.7% of the polymer weight Flow and air content

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The specimens were molded in dimensions of

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

60% After 2, 4, and 8 weeks, a sample was chipped from

the drying surface, and changes in the mass of each element

days to absolute dryness condition

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 iso-thermal absorption curve needed to set the boundary condi-tions of ﬁnite element analysis and to correct analytical results The specimen was prepared as described for the

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 equi-librium The relative water content for each relative humid-ity value was determined from the weight diﬀerences

4 Results and discussion 4.1 Determining moisture diﬀusivity

As described above, the non-linear moisture diﬀusivity can be calculated from the relative water content using the

rela-tionship between the Boltzmann transfer variable k and

subjected to regression analysis using the following curve:

ð12Þ

where R (%) is the relative water content, a and b are con-stants determined by the shape of the curve The results are

oR

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

p

g

Table 1

Property values of ﬁne aggregates

Absolute dry density (g/cm3)

Surface dry density (g/cm3)

Absorption (%)

FM

Oigawa River sand

in Japan

Table 2

Properties of re-emulsiﬁcation-type polymer resin

VeoVa/acrylate

Solid content (determined by furnace

drying for 3 h at 105 °C)

99 (±1)%

Minimum ﬁlm-forming

temperature (MFT)

0 °C

Table 3

Mix proportion and property values of polymer-modiﬁed cement mortar

Polymer

(%)

Cement:ﬁne

aggregate

Water:

cement

Antifoaming agent (%)

Flow (mm)

Air content (%)

Fig 1 Dimensions of a specimen with one drying surface.

60 70 80 90 100

Data: P/C=20%

R2 = 0.95864

a 0.54 ±0.08

b 1.18 ±0.11

Data: P/C=10%

R2 = 0.97214

a 0.77 ±0.09

b 1.44 ±0.11

Data: P/C=5%

R2 = 0.97421

a 0.42 ±0.05

b 1.00 ±0.08

Data: P/C=0%

R 2 = 0.9695

a 0.23 ±0.03

b 0.75 ±0.07

=

λ ( x / t1/2)

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

Temp.=20°C, R.H.=60%

Y=100*(1-(a/( λ +b)^2))

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

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The movement of water at normal temperature is

deter-mined 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

showed this phenomenon and were in a non-linear

temperature during the drying process The higher the tem-perature, the greater the moisture diﬀusivity The eﬀects of

polymer content diﬀered from those in an earlier study

polymer-to-cement 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%

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

Table 4

Material constants determining the shape of Eq (12)

0 2 4 6 8 10 12

2 /d)

5 ° C, 60%

20 ° C, 60%

40 ° C, 60%

P/C=0%

0 2 4 6 8 10 12

2 /d)

5 ° C, 60%

20 ° C, 60%

40 ° C, 60%

P/C=5%

0 10 20 30 40 50 60 70 80 90 100 0

2 4 6 8 10 12

2 /d)

Relative Moisture Content (%)

0 10 20 30 40 50 60 70 80 90 100 Relative Moisture Content (%)

5 ° C, 60%

20 ° C, 60%

40 ° C, 60%

P/C=10%

0 2 4 6 8 10 12

2 /d)

5 ° C, 60%

20 ° C, 60%

40 ° C, 60%

P/C=20%

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

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temperature, the water content of a porous mass is in

equilib-rium with the ambient relative humidity The relationship

between the relative humidity and relative water content of

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

The relationships diﬀered slightly, depending on the

poly-mer-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

ver-tical direction from the drying surface was determined by

non-linear ﬁnite element analysis based on the values

above The elements were four-nodal isoparametric, and

the entire analytical length of 160 mm was divided into

and boundary conditions, respectively The relative water

content at a relative humidity of 60% in ambient

atmo-sphere, which was a boundary condition, was calculated

using the tryout method based on the isothermal

f was determined retrogressively using the experimental

values and repetitive calculation The relative water

con-tent at each temperature at a relative humidity of 60%,

which was a boundary condition, and the coeﬃcient of

coeﬃcient of moisture transfer on water movement

coeﬃcient of moisture transfer of 0.007 cm/day was used,

which resulted in a good correlation with experimental val-ues 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

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 trans-fer variable and relative water content The errors were lar-ger 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 with-out changing the water-to-cement ratio as described in

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

analysis that included data for a relative humidity of 60%

bound-ary conditions (relative water content) for the ﬁnite element analysis of relative humidity data in the real environment, which is described below:

where R is the relative water content (%), T the drying tem-perature (°C) and H is the relative humidity (%)

0

20

40

60

80

100

Relative Humidity (%)

P/C=0%

P/C=5%

P/C=10%

P/C=20%

Mean Value

Fig 4 Relationship between relative water content and relative humidity.

Table 5 Relative water content and coeﬃcient of moisture transfer corresponding

to 60% relative humidity

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4.4 Qualitative prediction of internal water content

distribution and stress generation under ﬁxed ambient

atmospheric conditions

content of 55%, which corresponds to a relative humidity of

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

diﬀusivity values of the substrate concrete reported in an

the element division of the analytical model The beam

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

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

changes in length caused by changes in water content were

min-imize 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 con-crete Since no measured data were available for the mois-ture 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

the isothermal absorption curves of the substrate concrete were analyzed using the measurements reported by

regions The repair material, interface and substrate con-crete were assumed to be perfectly united, and the mechan-ical 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

40 50 60 70 80 90 100

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

5 ° C, P/C=0%

40 50 60 70 80 90 100

5 ° C, P/C=5%

0 2 4 6 8 10 12 14 16 18 40

50 60 70 80 90 100

Depth from the Drying Surface (cm)

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

5 ° C, P/C=10%

40 50 60 70 80 90 100

5 ° C, P/C=20%

Temperature, 5 ° C; R.H., 60%

Fig 5 Measured and analytical relative water content.

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The distribution of relative water content on the

inter-face on the 30th day after the start of drying is shown in

Fig 9 The distribution of the main stress (rmax) generated

stress generated on the drying surface under the

constrain-ing conditions was compared between specimens with

dif-ferent polymer-to-cement ratios The stress near the

drying surface was predicted to be higher for a

polymer-to-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-to-cement ratio of 10%, in which relatively large stress was

generated by the eﬀects of the elasticity coeﬃcient and

vol-umetric changes

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 condi-tions were the mean of the meteorological data recorded over the past 10 years in Tokyo, Naha (Okinawa Prefec-ture) and Sapporo (Hokkaido PrefecPrefec-ture) The annual tem-perature and humidity in Tokyo, Okinawa, and Sapporo from March 2004 to February 2005 and the mean for the

coef-ﬁcients of the repair material and substrate concrete were corrected by considering the eﬀects of the drying tempera-ture The mechanical property values and the changes in

dry-ing period was from March until the followdry-ing February The relative water content gradient along the vertical

the start of the drying process, the relative water contents

of the surface and the inside diﬀered sharply, but the diﬀer-ence was less marked as time passed The drying speed was highest for the polymer-to-cement ratio of 10% and in Oki-nawa, 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

40 50 60 70 80 90 100

20 ° C, P/C=0%

40 50 60 70 80 90 100

20 ° C, P/C=5%

0 2 4 6 8 10 12 14 16 18 40

50 60 70 80 90 100

Depth from the Drying Surface (cm)

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

20 ° C, P/C=10%

40 50 60 70 80 90 100

20 ° C, P/C=20%

Temperature, 20 °C; R.H., 60%

Fig 5 (continued)

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are shown inFig 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 mois-ture 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

The stress was also larger in specimens of lower poly-mer-to-cement ratios in the real environment, as discussed

The changes in internal water content distribution and stress generation caused by changes in thickness of the

ratio analyzed was 5%, and the thickness of the patch-repaired region was 5, 7, and 10 cm The environmental data recorded in Tokyo were used as the boundary condi-tions 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

40 ° C, P/C=0%

40 50 60 70 80 90 100

40 ° C, P/C=5%

40 50 60 70 80 90 100

Depth from the Drying surface (cm)

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

Depth from the Drying surface (cm)

40 ° C, P/C=10%

40 50 60 70 80 90 100

40 ° C, P/C=20%

Temperature, 40 °C; R.H., 60%

Fig 5 (continued)

0

20

40

60

80

100

H : Relative Humidity (%)

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

R=17.36+0.263* T-0.00847*T 2

+2.303*H-0.0254*T*H-0.000016*T 2

*H -0.04175*H 2

+0.000258*T*H 2

+0.00027*H 3

Fig 6 Regression curve of the relationship between relative humidity and

relative water content during the drying process.

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Fig 7 Element division of the analytical model.

Table 6

Dimensions of analytical model

0.00 0.03 0.06 0.09 0.12 0.15 50

60 70 80 90 100

Depth from the Drying Surface (m)

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

Drying Time = 30 days

Fig 9 Distribution of relative water content along the vertical direction from the drying surface (A–A 0 ).

0.00 0.03 0.06 0.09 0.12 0.15 0

4 8 12 16 20 24

Depth from the Drying Surface (m)

P/C=0%

P/C=5%

P/C=10% P/C=20%

Fig 10 Main stress generated along the vertical direction from the drying surface (A–A 0 ).

Table 7

Input data of patch repair materials and substrate concrete

Water:

cement

Polymer (%)

Coeﬃcient

of elasticity (GPa)

Length change

by water absorption (10 6 %) Patch repair

material

Substrate

concrete

10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

6

7

8

2 /day)

Relative Water Content (%)

Fujiwara(W/C=0.52, T=10 °C)

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

Fig 8 Diﬀusion coeﬃcient of substrate concrete [29]

distribution and stress generation under ﬁxed ambient

atmospheric conditions

content of. .. start of drying is shown in

Fig The distribution of the main stress (rmax) generated

stress generated on the drying surface under the

constrain-ing conditions was... which corresponds to a relative humidity of

stress generation were compared for the polymer-to -cement

ratios The relative water content of the substrate concrete

before repair

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