Construction and Building Materials 25 (2011) 99–108

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Construction and Building Materials

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An analytical study on the water penetration and diffusion into concreteunder water pressure

Jo-Hyeong Yoo a, Han-Seung Lee a,*, Mohamed A. Ismail b

a School of Architecture & Architectural Engineering, Hanyang University, Ansan 425-791, Republic of Koreab Faculty of Civil Engineering, Universiti Teknologi Malaysia, Skudai 81310, Malaysia

a r t i c l e i n f o

Article history:Received 18 November 2009Received in revised form 26 May 2010Accepted 19 June 2010Available online 14 July 2010

Keywords:Darcy’s lawCoefficient of diffusionWater penetration of concreteFEM analysis

0950-0618/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2010.06.052

* Corresponding author. Tel.: +82 31 400 5181; faxE-mail address: ercleehs@hanyang.ac.kr (H.-S. Lee

a b s t r a c t

Because concrete is a type of porous material, water or air can permeate freely into the concrete and thatdecreases the durability of concrete. Therefore, it is possible to permeate some corrosion inhibitors fromthe surface of concrete to inside the concrete due to its porosity even the steel-frame location by applyingwater pressure.

The objective of this study is to investigate the depth of the water penetration in concrete forced underpressure. For achieving this purpose, the experiments for the depth of penetration were executed throughselecting related factors and levels, such as water pressure and water pressurizing time. The water flow inconcrete was examined theoretically and experimentally. As a result, in the case of the low water pres-sure approximately at 0.15 MPa or less, it was found that the flow showed a Darcy seepage flow and thesame flow as an ordinary sand stratum. However, in the case of the high water pressure, the flow wasdiffused as a seepage flow that is accompanied by an internal deformation of concrete. This studyattempts to develop a method that penetrates corrosion inhibitors to the location of steel bars and inves-tigate the penetration depth of corrosion inhibitors by verifying water penetration in concrete underapplied pressure.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background and objective of the study

Concrete is a type of porous material and can be physically andchemically damaged due to its exposure to various environmentsfrom the placing of concrete to its to the service life. In particular,some external hazardous elements, such as sulfate, chloride ion,and carbon dioxide, permeate in concrete over a long-term periodas a solution or a gaseous state and cause physical damage due tochemical reactions. These reactions affect the corrosion of steelbars applied in concrete and that decreases the durability lifeand strength of such steel bars. Thus, it is very important to insertcorrosion inhibitors into steel bars in the case of a deteriorationelement that exceeds the critical amount of corrosion in the loca-tion of steel bars [1]. However, it is very difficult to guarantee cor-rosion resistance at the location of steel bars using conventionaltechnology that applies corrosion inhibitors only on the surfaceof concrete [2,3]. This study attempts to develop a method thatpenetrates corrosion inhibitors up to the location of steel barsand investigate the penetration depth of corrosion inhibitors by

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verifying moisture migration in concrete under applied pressure.In the penetration of water in concrete, the penetration depthaccording to the passage of time can be estimated using the Darcy’slaw, which is also applicable to the penetration of sand stratumsunder low pressure conditions. Meanwhile, it is necessary toanalyze the penetrative diffusion flow accompanied by internaldeformation under high pressure conditions [4]. Under the circum-stances, this study applied the experiment on the penetrationdepth of water for reinforced concrete structures using the waterpressure applied to the holes in concrete as a variable. Based onthe results of this experiment, this study also calculated coeffi-cients of water penetration and diffusion and estimated the pene-tration depth for the concrete according to the water pressuringtime and pressure. In addition, this study attempts to provide thebasic data for the development of a diffusion method with highpressure penetration of corrosion inhibitors for penetrating theinhibitors to the location of steel bars through investigating thewater penetration mechanism in concrete using a FEM analysisthat reflects the interaction between solid and fluid [5,6].

1.2. Methods and scope of the study

Although studies on the water movement in general pur-posed concrete have been conducted through permeability and

100 J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108

water-proofing experiments, studies on the water penetrationand movement caused by water pressure and the mechanismon the water movement in concrete still have not been fullyachieved [7].

Thus, this study performed a basic study on pressured seepageflows [4] and evaluated the water movement in concrete by apply-ing time and pressure as variables through the pressured penetra-tion of water into the concrete that represents a regular strengthbased on the water flow in concrete as experimental and analyticalmanners. In addition, based on the results of this evaluation, thisstudy calculated the coefficient of diffusion as a quantitative waythrough the water movement mechanism and by comparing thedata obtained from its analysis and experiment and verified thewater movement and diffusion in concrete through experimentsand by applying a FEM analysis.

2. Literature survey

2.1. Considerations on the confining seepage theory

2.1.1. Darcy seepage flow [4]Because the Darcy’s flow velocity is constant over time and

space, the hydraulic gradient becomes linear. Eq. (1) is thereforerewritten as follows

u ¼ dvdt¼ k

Px0

v ð1Þ

where P: water pressure acting on the top of concrete; v: depth ofpenetration; v dv: (kP)/(x0)dt

By integrating this with the initial condition as t = 0, v = 0

v2

2¼ kP

x0t; v ¼

ffiffiffiffiffiffiffikPx0

st ð2Þ

By rewritten k as K when the measured average penetrationdepth, dm, is used and defining this as the permeability coefficient,Eq. (3) is written as follows

K ¼ x0

2Ptdm2 ð3Þ

where K: seepage coefficient, mm/s; P: water pressure, MPa; t: pres-suring time, s; dm: average seepage depth, mm

Fig. 1. High pressure seepage model.

2.1.2. Seepage diffusion flowA high-pressure seepage model is employed for the case of high

water pressure as the internal deformation (deformation of theconcrete body and water) becomes significant level (Fig. 1). In thiscase both the flow velocity and hydraulic gradient are variable overtime and space. Referring to the lower graph as shown in Fig. 1;

DQ ¼ Q I � Q II ¼ uðvÞAdt ð4Þ

uðvþ dvÞAdt ¼ @u@v dvAdt ð5Þ

where QI: quantity of inflow through Section I; QII: quantity of in-flow through Section II; DQ: quantity of water remaining betweenSections I and II; A: cross-section area of concrete

The pressure increment, dp, during time of dt due to the remain-ing DQ is

dp ¼ @p@t

dt ¼ EDQAdv ¼

@u@v Edt

@p@t¼ �E

@u@v ð6Þ

where E = volumetric modulus of elasticity when considered sub-stances of water and concrete are expressed as 1/E = m/Ec + (1 � m)/Ew; Ec: volumetric modulus of the elasticity of a concrete body;Ew: volumetric modulus of the elasticity of water; v: volumetric ra-tio of a concrete body

From the Darcy’s law

@u@v ¼ �

kx@2p@v2 ð7Þ

By substituting Eq. (6) into Eq. (7)

@p@t¼ kE

x0

@2p@v2 ¼ b2 @

2p@v2 ð8Þ

Eq. (8) is a fundamental equation concerning the pressure of aone-dimensional high-pressure seepage flow. As the high-pressureseepage flow conforms a diffusion type differential equation con-cerning pressure in this way, it will be called diffused seepage flowwith b2, which called a diffusion coefficient. The solution of Eq. (8) isa complementary error function (Eq. (9)) with the initial conditionp(v, 0) = 0, boundary condition, p(0, t) = P, and p(1, t) = 0. This indi-cates that the water pressure distribution follows the complemen-tary error function curve (refer to the graph as shown in Fig. 1).

pðv; tÞ ¼ Perfcv

2bffiffitp

� �¼ 2Pffiffiffiffi

pp

Z 1

v2bffitp

e�k2dk ð9Þ

Because Eq. (9) is also a solution to pressure P at distance v, andtime t, the diffusion coefficient can be determined by configuringthe pressure at the seepage front p = Pf using the measurementsof the penetration depth of v after a given time, t.

Table 1P � n relationships for assumed Pf value.

Assumed value of p(x, t) = Pf (MPa) Value of n m (=c0P1/m)Water pressure P (MPa)

0.49 0.98 1.47

0.001 2.182 2.324 2.403 11.40.01 1.640 1.817 1.914 7.070.05 1.156 1.380 1.499 4.190.10 0.898 1.156 1.290 3.000.12 0.822 1.091 1.231 2.690.14 0.755 1.036 1.180 2.430.15 0.734 1.010 1.156 2.310.16 0.694 0.986 1.134 2.210.18 0.637 0.940 1.092 2.010.20 0.585 0.898 1.054 1.83

J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108 101

Table 1 gives the relationship between P in Eq. (9) with differentassumed Pf values and the relative penetration depth nð¼ v=2b

ffiffitpÞ,

which represents the value of m in n = c0P1/m.If the difference between the theoretical and the measured

increasing gradient is caused by certain secondary factors, suchas those mentioned previously, then the diffusion coefficientcan be expressed by the following equation using a correctionfactor, a.

b20 ¼ a

dm2

4tn2 ð10Þ

where b20: initial diffusion coefficient, mm2/s; dm: average penetra-

tion depth; t: pressurizing time, s; a: correction factor for the pres-surizing time (a = t3/7, Table 2); n: coefficient for the water pressure(Pf = 0.15 MPa, Table 3)

Value of n determined from table of co-error functions or tableof normal distribution by assuming Pf = 0.15 MPa.

Table 2Value of correction coefficient a(a = t3/7).

Time t (s) 12 � 602 24 � 602 48 � 602 72 � 602

a 97.0 130.5 175.7 209.0

Table 3Value of n(Pf = 0.15 MPa).

Water pressure P (MPa) 0.3 0.5 1.0 1.5 2.0

n 0.477 0.733 1.018 1.163 1.259

Fig. 2. Schematic of a p

3. Seepage depth test

3.1. Experimental outline

Fig. 2 shows a schematic of the permeability tester. Cylindricalconcrete specimens 150 mm diameter and 300 mm long were castwith 20 mm diameter hollow cylindrical core at the center. It wascured in water for 28 days and dried at 20 �C and 65% humidity.Then, it was applied to the average water seepage depth test asillustrated using an internal pressured permeability tester by con-trolling time and pressure [8].

The test factors and levels were determined as compressivestrength, water pressure, and pressuring time. Table 4 demon-strates the factors and levels applied in this test.

3.2. Materials and methods

ASTM C 150 Type-I (Ordinary Portland Cement) cement was inall concrete specimens. Table 5 shows the chemical composition ofthe cement.

The coarse aggregate was 25 mm maximum size crushed lime-stone, with a bulk specific gravity of 2.5 g/cm3 and an averageabsorption of 2.45%. As fine aggregate, wash sand of gravity2.6 g/cm3 and an average absorption of 0.57% were used. All aggre-gates ware washed and dried when procured from the local sup-plier and were free fine dust, chloride and sulfate contamination.And a multi-component synthetic resin type of air entrainingadmixture was used in each specimen to increase the air contentof concrete from 1.5% for non-air entrained concrete to 5% for airentrained concrete.

Three concrete mixtures were prepared and used in this studyaccording to ACI 211.1-91 to investigate the penetration depth of

ermeability tester.

Table 4Test factors and levels.

Test factor Level

Compressive strength 16 MPa, 21 MPa, 27 MPaWater pressure 0.5 MPa, 1 MPa, 1.5 MPaPressuring time 48, 96, 144, 192 h

Table 5Chemical composition of the cement.

Compound (%) Cement

SiO2 20.5Al2O3 5.6Fe2O3 3.8MgO 2.1CaO 64.5Na2O 0.2K2O 0.2SO3 2.1Loss on ignition 0.8

102 J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108

concrete. Three W/C ratios were used in this study 0.4, 0.5 and 0.6.Details of concrete mixtures are presented in Table 6.

3.3. Test method

Fig. 3 illustrates the measurement of average seepage depthusing an internal pressured permeability tester according to waterpressure and pressuring time. The process of this test can be sum-marized as follows [10,11]:

(1) Set nitrogen pressure and water pressure in the water tankthe same level.

(2) Unlock the bolt to insert the specimen into the tank and sealit using rubber seals for both upper and lower parts.

(3) Tighten the bolt to fix the specimen and apply pressure tothe internal part of the specimen.

(4) Apply pressure until the desired time and separate the spec-imen from the tester.

(5) Fracture the separated specimen using an Universal TestingMachine (UTM) and measure the average seepage depth.

(6) Measure the seepage depth each three parts (Upper, Middle,Bottom area) and average the measured values.

3.4. Calculation of average seepage depth and initial diffusioncoefficient

Table 7 shows the results of the measurement of compressivestrength, slump, air, and average seepage depth in accordance withtest factors. The initial diffusion coefficient was obtained accordingto the compressive strength by substituting the average seepagedepth produced from a 48 h confining seepage test according tothe pressure in Eq. (10).

Table 6Proportions of concrete mixture according to the test factors and levels.

W/C(%)

Unit weight (kg/m3)

Water(kg)

Cement(kg)

Fine aggregate(kg)

Coarse aggregate(kg)

AE(kg)

60 168 280 1010 843 1.450 168 336 935 869 1.6340 168 411 841 880 2.06

AE = air entraining admixture.

4. Experimental result

4.1. Comparison of the Darcy’s seepage and seepage diffusion flow

Fig. 4 shows the average seepage depth produced from thetest based on the analysis of the Darcy’s seepage flow and seep-age diffusion flow. As illustrated in Fig. 4, the seepage depthshows an increase in both flows according to the passage oftime in both flows. However, the analysis of the seepage diffu-sion flow represented more precise results than that of theDarcy’s seepage flow. Existing literatures argued that it was nec-essary to analyze seepage diffusion flow under high pressureconditions. The reason for differences in the estimation curveand the test data is due to the analysis based on the initial dif-fusion coefficient. Thus, a correction process is necessary to ob-tain accurate results.

4.2. Relationship between the initial diffusion coefficient and time

Fig. 5 shows the diffusion coefficient according to the passageof time under 1.5 MPa of pressure. As shown in Fig. 5, the diffu-sion coefficient changed according to the passage of time becauseEq. (10) represented the initial diffusion coefficient for the initial72 h stage, and time was considered as a variable factor after72 h.

The reason for differences in the estimation value after 72 hwas also due to these results. It was assumed that there werechanges in internal deformations or expansion of apertures dueto high pressure after the passage of time. Then, the time depen-dent water diffusion coefficient was proposed by considering achange in diffusion coefficients based on this assumption. Thetime dependent moisture diffusion coefficient can be obtainedusing Eq. (11). D(t) is a time dependent moisture diffusion coeffi-cient according to the passage of time and can be expressed asfollows:

DðtÞ ¼ b20

t0

t

� �n

ð11Þ

D(t): time dependent water diffusion coefficient, mm2/s; b20: ini-

tial diffusion coefficient, mm2/s; t0: initial pressurizing time, h; t:measured time, h; n: change coefficient of the water diffusion coef-ficient to time.

Table 8 shows the water diffusion coefficient (n) according tothe passage of time, and Table 9 shows the time dependent waterdiffusion coefficient, D(t), based on the average value obtained inEq. (11) according to the compressive strength.

4.3. Calculation of the time dependent water diffusion coefficient

The average seepage depth can be calculated using the timedependent moisture diffusion coefficient as expressed in Eq. (12)in place of using the initial diffusion coefficient.

dm ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDðtÞ4tn2

a

sð12Þ

where D(t): time dependant water diffusion coefficient, mm2/s;dm: average penetration depth; t: pressurizing time, s; a: correc-tion factor for the pressurizing time; n coefficient for the waterpressure

Fig. 6 illustrates the comparison of the results between the esti-mation with the time dependent water diffusion coefficient, D(t),and the value obtained in this test. As shown in Fig. 6, the estima-tion value is similar to the value obtained in the test.

(b) Install specimen(a) Permeability tester

(c) Split specimen (d) Measured penetration depth (mm)

Fig. 3. Test method.

Table 7Test results.

W/C (%) Water pressure (MPa) Compressive strength (MPa) Slump (cm) Air (%) Average seepage depth (mm) RemarksPressuring time (h)48 96 144 192

60 0.5 16.54 20 6 19 – – – Average value of three specimens1.0 27 – – –1.5 31 40 48 55

50 0.5 21.13 18 6 15 – – –1.0 22 – – –1.5 26 33 42 47

40 0.5 27.92 15 5 11 – – –1.0 13 – – –1.5 19 24 27 32

J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108 103

5. Analysis of finite element method (FEM)

5.1. Fluid flow through porous media

A porous medium saturated with a fluid has very differentproperties compared to a pure fluid medium (see the followingfigure for a typical saturated porous medium). The porous do-main consists of both fluid and solid. In case of a rigid solid,the fluid flows depend only on the properties of the fluid regionthat is formed by many small holes of possibly different shapesand sizes. Although the Navier–Stokes equations are valid forflows through porous media, the simulation of fluid flowsthrough these regions of small scales is impractical and far be-yond the capacity of present day computers if a large domainis considered [6].

In order to determine the flow properties in porous media, themean (or average) velocity must be used. During the averagingprocedure, an important property of the porous medium, calledpermeability, is introduced.

Let us consider a simple example as shown in Fig. 7 where vis-cous fluid flows through a micro-circular hole are subjected to a

constant pressure drop. The equation that governs the flow canbe obtained from the momentum equation, Eq. (13).

dpdx¼ l@y

y@mm

@y

� �ð13Þ

where mm is the velocity of fluid in the hole. By imposing on the wall,the exact solution can be obtained as

mm ¼1

4l@p@x

y2 � R2� �

ð14Þ

Integrating the solution along the cross section of the hole, weobtain the average velocity through the hole as follows

m ¼ 1pR2

Z 2p

0

Z R

0mmydyd/ ¼ � R2

8l@p@x

ð15Þ

Considering that such holes are sparsely located in a porousmedium that has a porosity / (the ratio of volume occupied bythe fluid to the volume of the mixed medium), the average velocityin that medium is Eq. (16).

Fig. 4. Analysis of Darcy’s seepage and seepage diffusion flow.

Fig. 5. Difference in the diffusion coefficient according to the passage of time.

Table 8Water diffusion coefficient (n) according the passage of time.

Pressuring time Compressive strength

16 MPa 21 MPa 27 MPa

96 h �0.195 �0.230 �0.391144 h �0.193 �0.295 �0.198192 h �0.180 �0.226 �0.217Average �0.190 �0.251 �0.269

Table 9Time dependent water diffusion coefficient.

Time dependent water diffusion coefficient (mm2/s)Compressive strength

16 MPa 21 MPa 27 MPa

2.30 � 10�1 1.68 � 10�1 7.78 � 10�2

104 J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108

m ¼ /m ¼ � R2

8l@p@x

ð16Þ

The coefficient /R2/8 here is called the permeability of the por-ous medium discussed in the example. It is clear then that the per-meability has a unit of square length.

Of course, the actual permeability of a porous medium dependson the shape of the saturated region that shows difference in each

other even within the same porous medium. Furthermore, the per-meability may not be isotropic. Nevertheless, a more general formthat governs flows through the porous media can be expressed asEq. (17).

lj�1 � m ¼ rpþ f B ð17Þ

where

Fig. 6. Comparison of the results between the estimation with the time dependent water diffusion coefficient and the value obtained in this test.

Fig. 7. Illustration of the porous media model.

J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108 105

j ¼ jijEiEj ð18Þ

is the permeability tensor. Eq. (17) is call the Darcy’s law. It governsthe momentum conservation of fluid flows through the porousmedia.

The continuity equations obtained in all sections are valid forthe averaged velocity, which controls the mass conversation ofthe fluid in the porous medium as considered. In other words,the porous media flows can be assumed as different ways, suchas incompressible, slightly compressible and compressible.

The energy equation obtained in the previous and later sectionsare all valid as well, in both fluid and solid regions in the porousmedia. In order to obtain an average temperature solution, thematerial properties are averaged using fluid and solid properties.

qCv ¼ ðqf Cmf Þ þ ð1� /ÞðqsCmsÞj ¼ /kf þ ð1� /Þks ð19Þ

Regarding the continuity equation, Darcy’s law (replacing themomentum equation) and the energy equation (using averagedmaterial data) from the governing equation system for fluid flowthrough the porous media.

The Darcy’s law equation is different from the Navier–Stokesequations. For instance, there is no derivative of the velocity. Someconventional no-slip wall boundary conditions may not be appro-priate for the porous media flow. For example, considering a satu-rated porous medium in a pipe subjected again to a constantpressure drop as shown in Fig. 7. The size of the pipe here is also

much larger than that of the micro-holes discussed earlier. Therewould be no solution if a no-slip condition was applied on the wall.Instead, the Darcy’s law will give an exact solution if a slip wallcondition is applied.

Also note that Darcy’s law has no time derivatives. Therefore, ifthe body force fB is constant, it is unnecessary to perform transientanalyses. Many fluid flow problems in porous media are in factcoupled with temperature using the Boussinesq approximation tothe gravitational force. Finally, for a better understanding ofDarcy’s equation, let us apply the mass conservation condition toit [12],

r � j � rp ¼ r � j � f B ð20Þ

This is a type of Poisson equation for pressure. The pressure isthen very much like a velocity potential. The pressure in porousmedia sometimes is also called pressure. When the deformabilityof the solid in porous media is considered, the velocity in Darcy’sequation becomes the relative velocity v–w, where w is the veloc-ity of the structure.

5.2. Introduction of the analysis of fluid–structure interaction (FSI)

This study used a fluid structure interaction (FSI) module that isa commercial finite element analysis program in order to verify theamount of diffusion in the fluid in porous media according to ap-plied pressure [9]. The analyses on the fluid and structure wereperformed by assuming the structure as a rigid body in order toperform a fluid analysis in which the analysis of the structurewas applied by assuming the velocity of fluid as pressure. How-ever, these analyses represent a lack of accuracy in the analysisof structures, which show certain large deformation related tothe interaction between fluids and structures. The behaviors pre-sented in the fluid and structure show no specific independencybecause it affects the behaviors in each region. The FSI is an anal-ysis that reflects such behaviors to the analysis between fluidsand structures. Fig. 8 illustrates a numerical analysis that considersthe interaction between fluids and structures. This study analyzedthe movement of fluids by considering the pressure condition offluids and the boundary condition of structures. Then, this studyanalyzed the flow and diffusion of fluids in structures by consider-ing the effects of fluids in structures [13,14].

Fig. 8. FSI analysis procedure.

Fig. 9. Modeling of the concrete and fluid models.

Table 10Input data of the concrete and fluid models.

Porous media Concrete

Density 1 kg/m3 Density 2400 kg/m3

Viscosity 0.00179 kg/m s Poisson’s ratio 0.2Pressure 0.5 MPa Young’s Module 2.7 GPaPorosity 12.023% Diffusion coefficient 2.30 � 10�1 mm2/s

106 J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108

5.3. Mesh distribution and modeling

As shown in Fig. 9, some punching works were applied to themid section of the model in which the punched area that was mod-eled with some meshes where a specific water pressure was ap-plied to the meshed area was analyzed as a second dimensionalmanner. Then, a water penetration analysis was applied throughconsidering the interaction between fluids and solids by configur-ing a FSI boundary at their boundary [15].

5.3.1. Configuration of a concrete modelThe concrete model was configured by using compressive

strength as a variable. The compressive strength was determinedby 21 MPa, which is applied to general purposed concrete. In theanalysis, input variables were determined by the compressivestrength of concrete according to the modulus and Poisson’s ratioof concrete [9,14].

5.3.2. Configuration of a fluid (porous media) modelThe fluid model was configured by two different regions, such

as a porous model in concrete and a fluid model that plays a rolein pressuring. Also, the porosity, permeability, and coefficient ofpenetration that were obtained from the previous experiments

were applied as input data according to the configuration processof the FEM program. Table 10 shows input data of the concreteand fluid models.

5.4. Comparison of the results of the experiment and FEM analysis

Fig. 10 shows the comparison of the results of the experimentand FEM–FSI analysis. In the results of the analysis, the values ob-tained from the analysis represented a lot more penetration in theearly stage than other periods. In the case of the FEM analysis, itwas considered that although there was a lot of penetration inthe early stage, the penetration depth decreased significantlyaccording to time.

5.5. FEM analysis on the water penetration in concrete (case study)

Fig. 11 shows estimation of the penetration depth based on theresults of the FEM analysis. Based on the variable analysis, thisstudy estimated the depth of the water penetration according tothe compressive strength and water pressure. Also, this study per-formed the variable analysis by varying water pressure and pres-suring time through configuring variables in concrete accordingto strength based on the existing literature. Then, this study esti-mated the penetration depth according to the penetration depthcaused by the applied strength and water pressure through theanalysis of the penetration depth in concrete.

6. Conclusions

This study is a basic study that processes the development ofanti-corrosion methods with high pressured corrosion inhibitorsin order to penetrate the corrosion inhibitors into the location ofsteel bars in concrete. So we installed some holes in concrete andpenetrated water into the holes of concrete according to pressureusing the water with rust inhibitors. Then, we measured the pene-tration depth according to time and analyzed the results using the

Fig. 11. Estimation of the penetration depth based on the results of the FEM analysis.

Fig. 10. Comparison of the FEM Analysis and the value obtained in this test.

J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108 107

FEM. Based on the results of this study, the conclusions can besummarized as follows:

1. In the case of the penetration of water into concrete by pres-suring the water, it was possible to verify that the depth of thepenetration of water in concrete increased according to theincrease in water pressure and pressuring time and thedecrease in the strength of concrete through the results ofthe experiments.

2. In the results of the analysis that was performed using two dif-ferent characteristics of the pressured seepage, such as Darcy’sseepage and seepage diffusion flows, based on the coefficient ofwater diffusion obtained by the experiment, it was considered

that the analysis of the seepage diffusion flow was a moreproper way to analyze the movement of water in concrete thanother methods in the case of the high pressured condition.

3. Because the coefficient of the initial diffusion obtained from theexperiment represented no agreements between the values ofthe analysis and the experiment after 72 h based on the calcu-lation of it referenced by 72 h of the penetration time, this studyproposed the coefficient of time dependent water diffusion,D(t), as shown in Eq. (12) that evaluates the water penetrationas a general manner.

4. In the results of the FEM analysis using the coefficient of timedependent water diffusion obtained from the experiment ofwater penetration according to the pressure applied to

108 J.-H. Yoo et al. / Construction and Building Materials 25 (2011) 99–108

concrete, it was possible to estimate the depth of the water pen-etration in concrete according to water pressure using the FEManalysis because the results of the experiment showed almostthe same value as that of the analysis.

5. Furthermore, this study is to perform the experiments on thepenetration and diffusion of actual corrosion inhibitors in con-crete based on the results of this study.

Acknowledgement

This work is supported by Sustainable Building Research CenterHanyang University which is supported the SRC/ERC program ofMEST (#R11-2005-056-04003-0) and the Center for Concrete Cor-ea (05-CCT-D11), supported by Korea Institute of Construction andTransportation Technology Evaluation and Planning (KICTTEP) un-der the (MOCT).

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