Water absorption and constraint stress analysis of polymer-modified cement mortar used as a patch repair material

Reinforced concrete structures are damaged by salt attack, concrete carbonation, and sulfate attack, etc. The expansion stress by the corrosion of reinforcing steel causes crack in the cover concrete. Patch repair method is commonly applied to deteriorated RC structures. Deterioration mechanism of a patch-repair method in reinforced concrete is investigated through the experiment and analysis. The repair material selected is polymer-modified cement mortar re-emulsified by polymer resin. Because the water absorption of the patch-repaired material varies, depending on the relative moisture content, the water-absorption coefficient was measured, which is obtained by the Boltzmann–Matano method. Two-dimensional coupled analysis (FEM) of water absorption, volume change, and mechanical properties were used to estimate qualitatively the factors responsible for the stress increment at the repair site, such as the nature of the repair materials and the substrate concrete, and conditions at the interface between the concrete and the repair material. The cracking mechanism after repair and the selection of repair materials are discussed.

Water absorption and constraint stress analysis of polymer-modified cement

mortar used as a patch repair material

Dogncheon Parka,⇑, Sooyong Parka, Youngkyo Seob, Takafumi Noguchic

a

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

b

Department of Ocean Engineering, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea

c

Department of Architecture, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

a r t i c l e i n f o

Article history:

Received 16 July 2007

Received in revised form 9 May 2011

Accepted 24 June 2011

Available online 10 November 2011

Keywords:

Patch repair materials

Water absorption coefficient

Polymer-modified cement mortar

Environmental boundary conditions

Constraint stress analysis (FEM)

a b s t r a c t

Reinforced concrete structures are damaged by salt attack, concrete carbonation, and sulfate attack, etc The expansion stress by the corrosion of reinforcing steel causes crack in the cover concrete Patch repair method is commonly applied to deteriorated RC structures Deterioration mechanism of a patch-repair method in reinforced concrete is investigated through the experiment and analysis The repair material selected is polymer-modified cement mortar re-emulsified by polymer resin Because the water absorp-tion of the patch-repaired material varies, depending on the relative moisture content, the water-absorp-tion coefficient was measured, which is obtained by the Boltzmann–Matano method Two-dimensional coupled analysis (FEM) of water absorption, volume change, and mechanical properties were used to esti-mate qualitatively the factors responsible for the stress increment at the repair site, such as the nature of the repair materials and the substrate concrete, and conditions at the interface between the concrete and the repair material The cracking mechanism after repair and the selection of repair materials are discussed

Ó 2011 Published by Elsevier Ltd

1 Introduction

The patch repair method is widely used in reinforced concrete

structures to repair the damage to deteriorated and exfoliated

lin-ing concrete, which has been caused by corrosion of the

reinforc-ing bars As the method is used for repairreinforc-ing small to large

sections, diverse factors have been reported to cause poor

func-tioning of the patch repair regions, such as: cracks attributable

to differences in volumetric changes between the patch materials

and the substrate concrete[1], macro-cell corrosion of the

rein-forcing bars caused by electrochemical reactions between the

patch material and the substrate[2], reactions with the substrate

concrete caused by chemical non-stability[3], and reduced

resis-tance against the penetration of deterioration factors[4] Of these,

cracks on the surface and at the boundaries of the repaired

regions damage the appearance and reduce the resistance to

pen-etration of deterioration factors, which are a major cause of early

re-deterioration of repaired regions

One possible cause of cracks on the repair regions is the drying

and shrinkage under constraint stress of the substrate concrete

The difference in volumetric changes between the two materials

produces tensile stress inside the patches and at the boundaries,

creating a condition in which cracks readily develop[5] The

devel-opment of cracks may be prevented by avoiding sudden volumetric changes through the use of shrinkage retardants and the addition

of inflating agents and polymers to the patch repair material Suf-ficient curing before exposure to the outdoor environment is also effective for ensuring stable, strong patches

Although initial cracks can be controlled by these methods, cracks can develop when moisture seeps from the surface into and near the patch repair regions during rain, since differences in volumetric expansion between the substrate concrete and patch repair regions may produce large stress constraints Even when the stress does not spontaneously produce cracks, repetitive con-straints act as fatigue stress and can result in cracks on the surface and/or at the boundaries Therefore, diffusion of absorbed water and resultant stresses should be assessed experimentally and ana-lytically to enable the identification of appropriate patch repair materials for selected environmental boundary conditions The water absorption coefficient (moisture diffusivity) of por-ous materials, such as patch repair materials and substrate con-crete, is difficult to determine, since chronological changes in water content at specific points are difficult to monitor The output method[6]and the input method[7], which both use permeability testing devices, have been used to determine the moisture diffusiv-ity of concrete The former gives the permeabildiffusiv-ity coefficient at saturation The latter considers seepage flow in which surface tension is superimposed on the external pressure, but the effects

of capillary diffusion are not included in the resulting moisture diffusivity values [8] Thus, both methods are inappropriate for 0950-0618/$ - see front matter Ó 2011 Published by Elsevier Ltd.

⇑ Corresponding author Tel.: +82 51 410 4587; fax: +82 51 403 8841.

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

Contents lists available atSciVerse ScienceDirect Construction and Building Materials

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / c o n b u i l d m a t

reproducing the diffusion of moisture in porous materials, and are

insufficient for producing input data to reproduce the diffusion of

moisture by numerical analysis

On the other hand, patch repair regions and substrate concrete

that are exposed to ordinary outdoor environments are in an

unsaturated state, in which the moisture diffusion is in a

non-linear relationship with the water content distribution Moisture

diffusion in such an unsaturated state should be investigated

sep-arately by Richard’s equation approach to liquid flow and vapor

diffusion However, IRS tests [9–11], which conform to British

Standard BS 3921, are widely used for assessing diffusion but can

only assess the total cumulative water absorption and not the

diffusion of water that depends on the water content

If the diffusion of water depends on Fick’s second law, time and

water content at a specific point should be monitored continuously

to determine the two-dimensional moisture diffusivity The use of

thec-ray attenuation method[12]and the nuclear magnetic

reso-nance method[13,14]started several years ago, but their precision

has not been verified and the equipment is difficult to use

With such a background, changes in mass were measured to

estimate the moisture diffusivity of non-saturated patch repair

materials, which was assumed to be a non-linear function of water

content Mass change measurement is believed to be an easy and

highly precise direct method[18] The distributions of diffusion

of absorbed water and chronological change of stress produced

by constraints were predicted using data for volumetric changes

by water absorption[15], which were determined using patch

re-pair materials which had the same mix as the specimen used for

analyzing moisture diffusion, and finite element analysis coupled

with the mechanical properties of the substrate concrete The

experimental and analytical results were used to investigate the

performance of patch repair materials appropriate for the

environ-mental conditions and the deterioration conditions of the concrete

region to be repaired

2 Theory of measurement and analytical methods

The moisture flux at unsaturated conditions can be divided into

liquid moisture flux and vapor moisture flux[16] The former can

be further subdivided into: (1) that by total potential at a uniform

temperature (Richard’s flow), (2) that by temperature differences

(such as temperature capillarity), and (3) that by differences in

solution concentration The vapor moisture flux can be divided

into: (1) that by temperature differences (vapor diffusion), and

(2) that by differences in chemical potential at a uniform

temper-ature (vapor diffusion at a uniform tempertemper-ature) Since uniform

temperature was assumed in this study, the dominant driving

forces for water diffusion were likely to be Richard’s flow and

va-por diffusion

Fig 1A is a diagram of thin-slice gravimetric analysis, which

determines the movement of water caused by total potential (/)

as the moisture diffusivity The upward diffusion of water by

cap-illary action is attenuated gradually, although the water source

continues to exist, and the movement of water finally stops when

the gradient of the total potential curve becomes zero This is

be-cause the capillary potential gradient (w) and the gravity potential

(z) have opposite signs If the gradients of the two potentials are

both negative, as the capillary potential gradient (w) which is

dom-inant at the initial stages decreases, the gradient of the gravity

po-tential (z) becomes dominant, showing a vertical cross-sectional

spread of water as shown inFig 1B[17]

The theoretical principles for determining the movement of

water through a non-saturated specimen and its moisture

diffusivity are discussed below using Richard’s capillary potential

theory and Cleuet’s diffusion equations

When there is a difference in total potential (/) between two points, water in the pores moves from regions of higher potential

to those of lower potential The phenomenon of diffusion is the same as that of a substance diffusing from areas of high concentra-tion to areas of low concentraconcentra-tion in a space of non-uniform con-centration[18]

Richard assumed that the coefficient K of proportionality is a function of water content (h) or of capillary potential (w) and that the flux can be calculated by:

The equation consists of both horizontal and vertical components The horizontal components are:

qx¼ K@w

The vertical components are:

qz¼ K@w

wherewis the capillary potential and z is the gravity potential The coefficient K is termed the hydraulic conductivity or capillary conductivity

Their continuous equation is:

@h

(r q is the divergence of vector q)

Substituting Eq.(5)into Eq.(1)gives:

@h

This general equation for unsaturated flow is known as Richard’s potential equation

When (w+ z) is used instead of total potential (/), the relation-ship can be expressed as:

@h

@t¼r ½KðwÞrðw þ zÞ ¼r ½KðwÞrw þ@KðwÞ

When the flow is horizontal (rz = 0) or whenrwis much smaller thanrz and is thus negligible, the second term can be omitted

@h

The relationship can be expressed in coordinates From Eq.(8), the horizontal one-dimensional equation is:

@h

@t¼

@

@x KðwÞ

@w

@x

ð9Þ

ψ

z

ψ

z

Fig 1 Schematic diagram of moisture diffusion (A) Moisture diffusion when the capillary (w) and gravity (z) potentials act in the opposite directions; (B) moisture diffusion when the capillary (w) and gravity (z) potentials act in the same direction.

From Eq.(10), the vertical one-dimensional equation is:

@w

@x¼

dw

dh

@h

@x¼

1 dh=dw

@h

@x¼

1 CðhÞ

@h

The resultant general equation, which is based on the capillary

potential theory, must be converted for practical use so that the

water content is the only independent variable on the right-hand

side of the equation Cleuet converted Richard’s equation into a

diffusion equation that can be analyzed numerically, by

convert-ing the variables on the right-hand side of the equation as

de-scribed below

Eq.(9)is converted into Eq.(11)by substituting K(h) for K(w):

@h

@t¼

@

@x KðhÞ

@w

@x

ð11Þ Then:

@w

@x¼

dw

dh

@h

@x¼

1 dh=dw

@h

@x¼

1 CðhÞ

@h

where C(h) is the specific moisture capacity and is a gradient at a

certainwon the moisture property curve Substituting this gives:

@h

@t¼

@

@x

KðhÞ

CðhÞ

@h

@x

¼ h

@x DðhÞ

@h

@x

ð13Þ DðhÞ ¼ KðhÞ dw

dhand is known as the moisture diffusivity

The vertical one-dimensional equation is processed similarly in

order to derive:

@h

@t¼

@

@z DðhÞ 

@h

@x

þdKðhÞ

@h @h

These equations can be solved numerically if the relationships of K–

hand D–h are given

When the moisture flux in a liquid converges under the

condi-tions shown inFig 1, the vapor diffuses due to the concentration

differences which it experiences

By combining the diffusion flux qvapof the vapor and the

contin-uous equation, the diffusion equation is:

@qvap

where Dvap is the diffusivity of vapor and qvap is the density of

vapor

Since the movement of the two phases is very difficult to

sepa-rate[19], a diffusion model that uses the apparent moisture

diffu-sivity D(h), which is the sum of the two, was used in this study to

analyze the movement of moisture The initial and boundary

con-ditions were:

h¼ hsx ¼ 0t P 0

Moisture diffusivity was determined from the changes in water

content of specimens in terms of time and position

The Boltzmann conversion[20–22]of the one-dimensional

dif-fusion equation (Eq.(13)) gives an ordinary differential equation:

b

2

dh

db

 

¼ d

dh DðhÞ

dh db

ð18Þ The moisture diffusivity at relative water content h is determined

by integrating Eq.(18):

DðhÞ ¼ 1

2

1

@h

 

Zh

3 Overview of the experiment 3.1 Materials used

Ordinary Portland cement and River sand from the Oigawa

Riv-er in Japan wRiv-ere used Its physical propRiv-erties are shown inTable 1 The re-emulsification-type polymer resin was manufactured by N

Co Its properties are shown inTable 2 3.2 Preparing the specimens

Specimens of polymer-modified cement mortar (PCM) to be used as patch repair materials were prepared according to the testing methods stated in JIS A 1171 The mix proportions were: cement/fine aggregate, 1:3; water/cement, 1:1; and polymer as 0%, 5%, 10% or 20% of the cement mortar (Table 3) An antifoaming agent was added at 0.7% of the polymer weight Flow and air content were measured as the performance of fresh specimens The results are shown inTable 3

The specimens were molded with dimensions of 40 mm 

40 mm  160 mm and were cured in 85% relative humidity at

20 °C for 2 days, under water at 20 °C for 5 days, and in 60% relative humidity at 20 °C for 21 days

3.3 Measurement methods 3.3.1 Measuring the diameter of pores using mercury porosimetry The distributions of pores in the PCM specimens were measured using a mercury porosimeter The specimens were first left in vacuo for 7 days to dehydrate, and the pore size distribution curves were determined from the relationship between pressure and the amount of mercury that penetrated at low pressure and at high pressure Since specimens with high polymer to cement ratios

Table 1 Property values of fine aggregates.

Absolute dry density (g/cm 3

) Surface dry density (g/cm 3

) Absorption (%) FM Oigawa River sand

in Japan

Fineness modulus (FM) is obtained by adding the total percentage of the sample of

an aggregate retained on each of a specified series of sieves, and dividing the sum by

100 The values shall be obtained by tests conducted in accordance with CRD-C 103.

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%

Apparent density (JIS K 5101) 0.5 ± 0.1 (g/cm 3 ) Glass transition temperature (T g ) 14 °C

Minimum film forming temperature (MFT) 0 °C

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

mortar (%)

Cement:fine aggregate

W/C (%) Antifoaming agent (%)

Flow (mm) Air content (%)

were of interest for changes in the properties on the cut surfaces

caused by frictional heat from the use of diamond cutters [4],

5 mm thick specimens were prepared and broken, and the

resultant fragments were used for measurements

3.3.2 Measuring the relative water content at each height

The relative water content at various depths and its

chronolog-ical changes were measured using 40 mm  40 mm  160 mm

specimens cut into 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm

thick slices(Fig 2) The relative water content is the amount of

water absorbed, expressed as a percentage of the water content

at saturation Epoxy resin coating was applied to the sides of the

specimens to prevent evaporation of water Changes in relative

water content with time were substituted into Eq.(20)to

deter-mine the water content at each depth (local volume)[23]:

hðx; tÞ ¼Wðx þ 10; tÞ  Wðx; tÞ

Vlocal

where h(x, t) is the water content (%) at depth x at time t, W(x, t) is

the amount of water absorbed (cm3) at depth x at time t, and Vlocalis

the local volume (mm3) of the region subjected to water content

measurement

4 Results and discussion

4.1 Pore diameter distribution measured by mercury porosimetry

The porosity of porous materials such as PCM can be assessed

by conducting water absorption tests and mercury porosimetry

However, these methods cannot determine precise total porosity

or distribution of porosity, and the results are characterized by

the measurement principles used[24] Mercury porosimetry can

measure pores with diameters of about 0.003–375.00lm Thus,

the results are not precise for total porosity and should be highly

correlated with capillary water absorption and diffusion, since

the results are determined from the relationship between the

injection pressure of mercury and the amount penetrated, and

are highly dependent on the capacity of the connected pores

Fig 3 shows the measurements of specimens using polymer to

cement ratio as the experimental variable In all mixtures, a peak

appeared between 0.01lm and 0.1lm, which was probably

attributable to pore connection As the polymer to cement ratio

in-creased, the center of the peak shifted toward the left (to smaller

pore diameters), suggesting that increases in polymer cement

con-tent, while maintaining a uniform water/cement ratio, reduced the

diameter of the necks that connected the pores

4.2 Determining moisture diffusivity

Changes in water absorption over time are shown inFig 4 The

results are the mean measurements of three specimens All 10 mm

thick specimens showed convergence of water absorption as time

passed However, diverse patterns of water absorption curves were

observed in specimens that were at least 20 mm thick Water

absorption was greatest in specimens with 5% polymer in the

cement, followed by polymer contents of 0%, 10%, and 20%, in that order The results differed from those of the previous test, which were smaller diameter necks that connected pores with higher polymer content, possibly because the pore structure of PCM was not known for diameters outside the range for estimation by mer-cury porosity Polymer content and air entraining during mixing probably require further investigation Specimens with high poly-mer content showed no difference above a certain thickness Thus,

it was decided that the water absorption curves of specimens with

a polymer content of 10% at thicknesses of 40 mm and 50 mm would be excluded from the assessment, since the curves were similar to those at a thickness of 30 mm Similarly, it was decided that the curves of specimens with a polymer content of 20% at thicknesses of 30 mm, 40 mm, and 50 mm would not be assessed The data ofFig 4were substituted in Eq.(19), and the resultant changes in water content at the assessment are shown inFig 5 The relationship between the measurements and Boltzmann trans-fer variables, which are functions of time and position, is shown in

Fig 6

Fig 6shows the relationship between water content and Boltz-mann transfer variable at each measurement depth The relation-ship was assessed by calculating the regression using Eq (21) The coefficient of correlation (R2) was at least 0.8, showing a high degree of correlation Moisture diffusivity (D(h)) as a function of water content (h) can be determined by substituting the regression formula in Eq.(18):

h¼ m  1  b

n

knþ bn

ð21Þ

where h is the water content, b is the Boltzmann transfer variable, and k and n are material constants

The relationship between moisture diffusivity and water con-tent in PCM is shown inFig 7 The moisture diffusivity values were in a non-linear relationship with the water content, and showed a U-shaped curve with large values at both low and high water contents This trend agreed with the results reported by

Fig 2 Schematic diagram of the test for determining moisture diffusivity.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Pore Diameter (μm)

P/C=0%

P/C=5%

P/C=10%

P/C=20%

Fig 3 Pore distribution in polymer-modified cement mortar.

1

2

3

4

5

6

7

H=10mm H=20mm H=30mm H=40mm H=50mm

0

1

2

3

4

5

6

7

P/C=10%

Time (h)

P/C=20%

Time (h)

Fig 4 Chronological changes in water absorption for each height and each polymer resin content.

0

2

4

6

8

10

12

14

X=0~10mm X=10~20mm X=20~30mm X=30~40mm X=40~50mm

P/C=0%

P/C=5%

0

2

4

6

8

10

12

14

P/C=10%

Time (h)

P/C=20%

Time (h)

Benazzouk et al.[25], Chichimatsu et al.[26], Taketuchi et al.[27]

and Nakano et al.[28] As with the pore distribution

measure-ments, moisture diffusivity was smaller for higher polymer

con-tents The results are illustrated in Fig 9 The diffusion of

moisture by total potential (/) can be classified into diffusion of

liquid water and diffusion of vapor Diffusion of vapor was

prob-ably dominant in sections of low water content, and diffusion of

liquid water was probably dominant in sections of high water

content.Fig 8shows the relationship inFig 7but with the

sorbed volumetric water content converted into the relative

ab-sorbed volumetric water content, which is the percentage of

water content relative to the water content at saturation This

experiment was conducted to determine the moisture diffusivity

at unsaturated states using unsaturated specimens that were cured at 20 °C and 60% relative humidity Thus, a relative absorbed volumetric water content of 0% does not mean absolute dryness but rather the water content when moisture diffusion started For some polymer contents, vapor diffusivity showed greater changes com-pared to liquid water diffusivity

4.3 Verifying the experimental results (moisture diffusivity) by non-linear finite element analysis

The moisture diffusivity values determined in the experiment were verified by conducting non-linear finite element analysis and comparing the analytical and measured relationships between

0 2 4 6 8 10 12 14

Y=m*(1-((Xn)/((kn)+(Xn))))

P/C=0%

m:13.83, k:2.58, n:2.22

R2 = 0.833 P/C=5%

0 2 4 6 8 10 12 14

m:11.27, k:0.995, n:5.34

R2 = 0.858

m:11.21, k:1.43, n:2.405

R2 = 0.883

m:10.1, k:3.16, n:2.08

R2 = 0.839

Boltzmann Transfer Variable (b=x/t1/2)

P/C=10%

Boltzmann Transfer Variable (b=x/t1/2)

P/C=20%

Fig 6 Relationship between water content and Boltzmann transfer variable at each height.

0.1

1

10

100

1000

P/C=0%

P/C=5%

P/C=10%

P/C=20%

2 /h)

Absorbed Volumic Water Content (%) Fig 7 Relationship between moisture diffusivity and absorbed volumetric water

content.

0.1 1 10 100

1000

P/C=0%

P/C=5%

P/C=10%

P/C=20%

2 /h)

Relative Absorbed Volumic Water Content (%) Fig 8 Relationship between moisture diffusivity and relative absorbed volumetric water content.

moisture diffusivity and duration of water absorption Four-nodal

isoparametric elements were used, and the entire length of

160 mm was divided into 40 equal parts

A matrix expression of the moisture diffusivity equation is:

½Dfhg þ ½L @h

@t



where [D] is the moisture diffusion matrix, [L] is the water capacity

matrix, {F} is the external moisture flux vector, and {h} is the total

nodal water content vector

The specimen was assumed to not have absorbed any water The boundary conditions of the water-absorbing surfaces exposed

to rain were assumed to have a water content that gave 100% rel-ative water content for the specimen The boundary conditions used for each specimen are shown inTable 4

Since the moisture diffusivity (D) has a non-linear relationship with the water content (h), the Newton–Raphson method was used for the analysis The matrix of moisture diffusivity equation (Eq

(14)) was discrete in space but not in time To discretize it in time, the Crank–Nicolson finite difference method[29]was used

A comparison between the experimentally measured water content values and the analytically determined water content curves is shown inFig 10 Although there were some errors, over-all the analytical and measured values correlated well However, there was little data for the specimens with polymer contents of 10% and 20%, since water only diffused to their lower sections, and thus the data were not fully reliable The large errors for deep sections may be attributable to the use of 10 mm thick specimens, whose final diffusion points could not be measured precisely, and the inclusion of errors in the Boltzmann transfer variable and water content in the regression formula

5 Qualitative estimation of stress generation under swelling and constraint conditions

5.1 Analytical model When rainwater diffuses from exposed surfaces into patch re-pair regions, differences in swelling occur depending on the con-stituent materials, and stress is generated by the constraints of the substrate concrete When the stress exceeds the limit crack strength, cracks develop in the patch and cause early deterioration

( l)

D θ

( ) ( v) ( l)

D θ =D θ +D θ

D (θ)

θ

D (θv)

Fig 9 Schematic diagram of moisture diffusivity depending on water content.

Table 4

Water content of polymer-modified cement mortar at boundary conditions (100%

relative water content).

Water content at boundary conditions (%) 10.10 13.83 10.21 11.27

0 2 4 6 8 10 12

P/C=0%

0 10 20 30 40 50 60 70 0

2 4 6 8 10 12

Depth from Absorption Surface (mm)

Measured Value (3.25 H) Measured Value (26.5 H) Measured Value (50 H) Measured Value (95 H) Measured Value (3.25 H) Measured Value (26.5 H) Measured Value (50 H) Measured Value (95 H)

Depth from Absorption Surface (mm)

0 10 20 30 40 50 60 70

Even when the stress is smaller than the limit crack strength,

repetitive water absorption and drying act as fatigue stresses,

and the patch repair region becomes prone to cracks The cracks

accelerate the penetration of deteriorating factors and produce

an environment that causes macro-cell corrosion of the reinforcing

bars

A two-dimensional finite element analysis of full-scale patch

re-pair materials was conducted The dimensions of the rere-paired

member and the element division are shown inFig 11andTable

5 The beam was assumed to be fixed at both ends InTable 5, TI

denotes the thickness of the interface, CH is the thickness of the

re-pair 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

material The temperature during rain was assumed to be uniform

at 20 °C, and the effects of temperature on the moisture diffusion

were disregarded Moisture diffusion was analyzed using the

mois-ture diffusivity of the patch repair materials determined in the

experiment and the moisture diffusivity values determined in

ear-lier studies for the substrate concrete [30] (Fig 12) To predict

stress generation, a linear structural analysis was conducted using

the relationship between changes in water content and length[15],

which was determined by monitoring the changes for 35 days

The input data used for the analyses are shown inTable 6 Since

data on dimensional changes caused by water absorption were not

available for the substrate concrete, an assumed value was used in

order to evaluate the patch repair materials under constraining

conditions Changes in length caused by changes in water content

were measured by soaking a thin rectangular specimen (5 mm 

40 mm  160 mm) in water This procedure was devised so as to

minimize the inner constraint of the materials The moisture

diffu-sivity of the interface between the repair material and the

sub-strate concrete was assumed to be 1/1000 of the diffusivity of

the repair material by assuming that primer was applied and the

water movement was almost zero The patch repair material,

inter-face, and substrate concrete elements were assumed to adhere

tightly to each other, and the mechanical properties of the adhered

surface were assumed to be the same as those of the repair

mate-rial The repair material and substrate concrete before the analysis

were assumed to be stable in an environment with 60% relative

humidity Rain was assumed to have continued for a period of

48 h, and no water was assumed to seep from surfaces other than

the surface exposed to rain The boundary conditions of the surface exposed to rain were assumed to be the water content of the sub-strate concrete and the repair material at saturation

5.2 Distribution of water content formed by moisture diffusion

An example of the distribution of water content in a patch re-pair region exposed to rain is shown inFig 13 The analytical con-ditions were: (1) patch repair material was cement only (no polymer); (2) substrate concrete with a water/cement ratio of 1:1; and (3) a period of 24 h after exposure to rain Since the mois-ture diffusivity of the patch repair was relatively small, the water front reached only half the patch depth of 7 cm However, the water front in the substrate concrete exceeded the depth of the re-pair patch The water content differed sharply between the regions

Table 5 Dimensions of the analytical model.

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 material.

0.1 1 10 100

1000

W/C=30%

W/C=50%

W/C=70%

2 /sec)

Relative Volumic Water Content (%) Fig 12 Moisture diffusivity of substrate concrete [30]

separated by the interface, which had been coated with polymer

resin

The distribution of water in the substrate concrete and

verti-cally in the repair material at 24 h and 48 h after exposure to rain

is shown inFig 14 The distribution of moisture diffusion was

clo-sely correlated to the water/cement ratio of the concrete In

spec-imens having a water/cement ratio of 70% and 50%, the water front

had exceeded the repair depth (7 cm in this analysis) at 24 h On

the other hand, in specimens having a water/cement ratio of 30%,

the water front was only 4–5 cm from the surface even at 48 h

Since the diffusivity of liquid water in the PCM was similar to or

slightly smaller than that of vapor, as shown inFig 7, the water

distribution pattern differed from that of the substrate concrete,

in which the diffusivity of vapor dominated Regions of high water

content were observed in the substrate concrete, but regions of low

water content were spread over a large area in the PCM repair

material In the repair materials that contained 0% or 5% polymer,

water reached the bottom of the repair within 24 h of exposure to

rain On the other hand, repair materials that contained 10% or 20%

polymer were highly resistant to moisture diffusion, and water did not reach below 2 cm

5.3 Vertical stress on the interface (rxx) Chronological changes in the distribution of vertical stress (rxx)

at the interface are shown inFig 15in terms of depth from the absorptive surface (A–A0inFig 11) A steep compression stress gra-dient formed near the absorptive surface immediately after expo-sure to rain but this leveled off gradually as moisture diffused inward The stress generated on the surface was predicted to be the largest for repair material that contained 20% polymer, and the smallest for repair material with no added polymer The stress

on the bottom interface was distributed similarly, and the 20% polymer/cement repair material showed the greatest increase in stress compared to the other repair materials The substrate con-crete with a water to cement ratio of 1:1 showed a water front exceeding the repair depth of 7 cm within 24 h of the start of anal-ysis, and then swelled Thus, the stress in the substrate concrete was probably larger than that in the repair material with 10% or 20% polymer, which showed almost no increase in volume by water absorption The repair material with 20% polymer showed the largest stress, probably because of Hooke’s law of elasticity, which states that greater stress is generated under uniform dis-placement when the difference in the elasticity coefficient is larger Chronological changes in stress at the interface (A–A0 in

Fig 11), which depend on the properties of the substrate con-crete, are shown inFig 16 The substrate concrete was more por-ous and had a greater moisture diffusivity when prepared with a larger water/cement ratio In this analysis, the specimen with a water/cement ratio of 70% started to show compression stress

at the interface at the bottom of the repair patch in 6 h due to

Table 6

Input data of patch repair materials and substrate concrete.

Water/cement ratio (%), polymer/

cement ratio (%)

Coefficient of elasticity (GPa)

Length change by water absorption (10 6

/%)

Fig 13 Predicted water content distribution 24 h after exposure to rain.

0.00 0.04 0.08 0.12 0.16 0

2 4 6 8 10 12 14 16 18 20

0.00 0.02 0.04 0.06 0.08 0.10

Depth from the Adsorptive Surface (m)

W/C=30%_24 hours W/C=30%_48 hours W/C=50%_24 hours W/C=50%_48 hours W/C=70%_24 hours W/C=70%_48 hours

Repair materials

Interface

& Concrete

Depth from the Adsorptive Surface (m)

P/C=0%_24 hours P/C=0%_48 hours P/C=5%_24 hours P/C=5%_48 hours P/C=10%_24 hours P/C=10%_48 hours P/C=20%_24 hours P/C=20%_48 hours

swelling of the substrate concrete On the other hand, with a

water/cement ratio of 30%, moisture did not reach the interface

at the bottom of the repair patch, and almost no stress was

observed, even after 48 h

5.4 Shear stress on the interface at the bottom of the patch repair

region (sxy)

The chronological changes in shear stress (sxy) at the interface

(B–B0inFig 11) at the bottom of the repair region are shown in

Fig 17 The results are for the repair material with 20% polymer,

which showed the largest vertical stress (r ) at the interface

Although the shear stress was small up to 6 h, it increased with time, and the water content of the substrate concrete increased When the repair patch was applied to substrate concrete with a water/cement ratio of 30%, which had a low moisture diffusivity, all repair materials showed a small shear stress (sxy) at the inter-face at the bottom of the patch, and the stress was unlikely to cause cracks (Fig 19) On the other hand, in substrate concrete with a water/cement ratio of 50% or 70%, which had a large moisture dif-fusivity, the moisture diffusion was much more dominant than that in the repair materials, and very large shear stresses were gen-erated, as shown inFigs 18 and 19 Increases in the polymer con-tent of the repair materials also caused slight increases in the stress generated at the interface

-80 -60 -40 -20 0

Repair: P/C=20%

Concrete: W/C=50%

Repair: P/C=10%

Concrete: W/C=50%

Repair: P/C=5%

Concrete: W/C=50%

σxx

0.2 hours

6 hours

12 hours

24 hours

48 hours

Repair: P/C=0%

Concrete: W/C=50%

0.00 0.02 0.04 0.06 0.08 0.10 0.12 -80

-60 -40 -20 0

σxx

Depth from the Absorptive Surface(m) Depth from the Absorptive Surface(m)

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Fig 15 Chronological changes in stress generated on interface (A–A 0 ).

-80 -60 -40 -20 0

Repair: P/C=5%

Concrete: W/C=70%

0.2 hours

6 hours

12 hours

24 hours

48 hours

σxx

Depth from the Absorptive Surface(m)

Repair: P/C=5%

Concrete: W/C=30%

Depth from the Absorptive Surface(m) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.00 0.02 0.04 0.06 0.08 0.10 0.12

Fig 16 Changes in stress distribution on the interface due to differences in properties of substrate concrete (patch repair materials having a polymer/cement ratio of 5%, A–

A 0 ).