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.
Construction and Building Materials 28 (2012) 819–830 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat Water absorption and constraint stress analysis of polymer-modified cement mortar used as a patch repair material Dogncheon Park a,⇑, Sooyong Park a, Youngkyo Seo b, Takafumi Noguchi c a Department of Architecture and Ocean Space, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea 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 b a r t i c l e i n f o Article history: Received 16 July 2007 Received in revised form 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 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 Ó 2011 Published by Elsevier Ltd Introduction The patch repair method is widely used in reinforced concrete structures to repair the damage to deteriorated and exfoliated lining concrete, which has been caused by corrosion of the reinforcing bars As the method is used for repairing small to large sections, diverse factors have been reported to cause poor functioning 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 reinforcing 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 resistance 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 penetration 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- ⇑ Corresponding author Tel.: +82 51 410 4587; fax: +82 51 403 8841 E-mail address: dcpark@hhu.ac.kr (D Park) 0950-0618/$ - see front matter Ó 2011 Published by Elsevier Ltd doi:10.1016/j.conbuildmat.2011.06.081 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 Sufficient 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 constraints 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 analytically to enable the identification of appropriate patch repair materials for selected environmental boundary conditions The water absorption coefficient (moisture diffusivity) of porous materials, such as patch repair materials and substrate concrete, 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 diffusivity of concrete The former gives the permeability 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 820 D Park et al / Construction and Building Materials 28 (2012) 819–830 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 nonlinear relationship with the water content distribution Moisture diffusion in such an unsaturated state should be investigated separately 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 the c-ray attenuation method [12] and the nuclear magnetic resonance 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 repair 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 environmental conditions and the deterioration conditions of the concrete region to be repaired ψ ψ z z Fig 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 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 concentration to areas of low concentration in a space of non-uniform concentration [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: q ẳ Kwịr/ The equation consists of both horizontal and vertical components The horizontal components are: qx ¼ ÀK @w @x 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 temperature (vapor diffusion at a uniform temperature) Since uniform temperature was assumed in this study, the dominant driving forces for water diffusion were likely to be Richard’s flow and vapor 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 capillary 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 because 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 dominant at the initial stages decreases, the gradient of the gravity potential (z) becomes dominant, showing a vertical cross-sectional spread of water as shown in Fig 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 ð2Þ The vertical components are: @w ÀK @z */ ẳ w ỵ z qz ẳ K Theory of measurement and analytical methods ð1Þ ð3Þ ð4Þ where w is 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 ¼ Àr Á q @t ð5Þ (r Á q is the divergence of vector q) Substituting Eq (5) into Eq (1) gives: @h ¼ r ẵKwịr/ @t 6ị This general equation for unsaturated ow is known as Richard’s potential equation When (w + z) is used instead of total potential (/), the relationship can be expressed as: @h @Kwị ẳ r ẵKwịrw ỵ zị ẳ r ẵKwịrw ỵ @t @z 7ị When the flow is horizontal (rz = 0) or when rw is much smaller than rz and is thus negligible, the second term can be omitted @h ẳ r ẵKwịrw @t ð8Þ The relationship can be expressed in coordinates From Eq (8), the horizontal one-dimensional equation is: ! @h @ @w ẳ Kwị @t @x @x 9ị 821 D Park et al / Construction and Building Materials 28 (2012) 819–830 From Eq (10), the vertical one-dimensional equation is: @w dw @h @h @h ¼ Á ¼ Á ¼ Á @x dh @x dh=dw @x CðhÞ @x Overview of the experiment ð10Þ 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 converting the variables on the right-hand side of the equation as described below Eq (9) is converted into Eq (11) by substituting K(h) for K(w): ! @h @ @w ẳ Khị @t @x @x 11ị Then: @w dw @h @h @h ¼ Á ¼ Á ¼ Á @x dh @x dh=dw @x CðhÞ @x ð12Þ where C(h) is the specific moisture capacity and is a gradient at a certain w on the moisture property curve Substituting this gives: ! ! @h @ KðhÞ @h h @h ẳ ẳ Dhị @t @x Chị @x @x @x 13ị dw dh Dhị ẳ Khị and is known as the moisture diffusivity The vertical one-dimensional equation is processed similarly in order to derive: ! @h @ @h dKhị @h ẳ Dhị ỵ @t @z @x @h @z ð14Þ These equations can be solved numerically if the relationships of K– h and D–h are given When the moisture flux in a liquid converges under the conditions shown in Fig 1, the vapor diffuses due to the concentration differences which it experiences By combining the diffusion flux qvap of the vapor and the continuous equation, the diffusion equation is: @ qv ap ¼ Dv ap Á r2 qv ap @t ð15Þ 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 separate [19], a diffusion model that uses the apparent moisture diffusivity D(h), which is the sum of the two, was used in this study to analyze the movement of moisture The initial and boundary conditions were: 16ị h ẳ h0 x > 0t ¼ 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 diffusion equation (Eq (13)) gives an ordinary differential equation: b ¼ xtÀ1=2 b dh d dh ¼ DðhÞ À db dh db 1 À@hÁ @b 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 in Table The specimens were molded with dimensions of 40 mm  40 mm  160 mm and were cured in 85% relative humidity at 20 °C for days, under water at 20 °C for 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 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 Property values of fine aggregates Oigawa River sand in Japan Absolute dry density (g/cm3) Surface dry density (g/cm3) Absorption (%) FM 2.54 2.59 2.03 2.65 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 Properties of re-emulsification type polymer resin ð18Þ h bdh Protection colloid Solid content (determined by furnace drying for h at 105 °C) Apparent density (JIS K 5101) Glass transition temperature (Tg) Minimum film forming temperature (MFT) Monomer base vinyl acetate/ VeoVa/acrylate Polyvinyl alcohol 99 ± 1% 0.5 ± 0.1 (g/cm3) 14 °C $0 °C ð17Þ The moisture diffusivity at relative water content h is determined by integrating Eq (18): Dhị ẳ Ordinary Portland cement and River sand from the Oigawa River in Japan were used Its physical properties are shown in Table The re-emulsification-type polymer resin was manufactured by N Co Its properties are shown in Table Polymer h ¼ hs x ¼ 0t P Z 3.1 Materials used ð19Þ Table Mix proportion and property values of polymer-modified cement mortar Polymer/cement mortar (%) Cement:fine aggregate W/C (%) Antifoaming agent (%) Flow (mm) Air content (%) 10 20 1:3 50 0.7 160 185 190 195 6.2 7.5 8.2 8.9 822 D Park et al / Construction and Building Materials 28 (2012) 819–830 Fig Schematic diagram of the test for determining moisture diffusivity were of interest for changes in the properties on the cut surfaces caused by frictional heat from the use of diamond cutters [4], mm thick specimens were prepared and broken, and the resultant fragments were used for measurements hx; tị ẳ Wx þ 10; tÞ À Wðx; tÞ Â 100 V local ð20Þ 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 Vlocal is the local volume (mm3) of the region subjected to water content measurement 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 0.003–375.00 lm 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 shows the measurements of specimens using polymer to cement ratio as the experimental variable In all mixtures, a peak appeared between 0.01 lm and 0.1 lm, which was probably attributable to pore connection As the polymer to cement ratio increased, the center of the peak shifted toward the left (to smaller pore diameters), suggesting that increases in polymer cement content, while maintaining a uniform water/cement ratio, reduced the diameter of the necks that connected the pores P/C=0% P/C=5% P/C=10% P/C=20% 1.4 Porosity (ml/ml) 3.3.2 Measuring the relative water content at each height The relative water content at various depths and its chronological 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 determine the water content at each depth (local volume) [23]: 1.6 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.01 0.1 10 Pore Diameter (μm) Fig Pore distribution in polymer-modified cement mortar 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 mercury porosity Polymer content and air entraining during mixing probably require further investigation Specimens with high polymer 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 of Fig were substituted in Eq (19), and the resultant changes in water content at the assessment are shown in Fig The relationship between the measurements and Boltzmann transfer variables, which are functions of time and position, is shown in Fig Fig shows the relationship between water content and Boltzmann transfer variable at each measurement depth The relationship 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): h¼m 1À n b n k þb n ð21Þ 4.2 Determining moisture diffusivity Changes in water absorption over time are shown in Fig 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 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 content in PCM is shown in Fig 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 823 P/C=5% P/C=0% Volume of Absorbed Water (cm ) D Park et al / Construction and Building Materials 28 (2012) 819–830 P/C=10% Volume of Absorbed Water (cm ) P/C=20% H=10mm H=20mm H=30mm H=40mm H=50mm 0 50 100 150 200 250 50 100 150 200 250 Time (h) Time (h) 14 P/C=0% 12 10 14 X=0~10mm X=10~20mm X=20~30mm X=30~40mm X=40~50mm P/C=10% Volume of Absorbed Water (cm ) Volume of Absorbed Water (cm ) Fig Chronological changes in water absorption for each height and each polymer resin content 12 P/C=5% P/C=20% 10 0 50 100 150 Time (h) 200 250 50 100 150 Time (h) Fig Changes in water content at each height 200 250 824 D Park et al / Construction and Building Materials 28 (2012) 819–830 Volumic Water Content (%) 14 P/C=0% 12 P/C=5% Y=m*(1-((Xn)/((kn)+(Xn)))) m:13.83, k:2.58, n:2.22 R2 = 0.833 10 m:10.1, k:3.16, n:2.08 R2 = 0.839 Volumic Water Content (%) 14 P/C=20% P/C=10% 12 m:11.27, k:0.995, n:5.34 R2 = 0.858 m:11.21, k:1.43, n:2.405 R2 = 0.883 10 0 20 40 60 80 100 1/2 Boltzmann Transfer Variable (b=x/t ) 20 40 60 80 100 1/2 Boltzmann Transfer Variable (b=x/t ) Fig Relationship between water content and Boltzmann transfer variable at each height 1000 Hydraulic Diffusivity (mm /h) 100 P/C=0% P/C=5% P/C=10% P/C=20% P/C=0% P/C=5% P/C=10% P/C=20% Hydraulic Diffusivity (mm /h) 1000 10 100 10 0.1 0.1 10 12 14 Absorbed Volumic Water Content (%) Fig Relationship between moisture diffusivity and absorbed volumetric water content Benazzouk et al [25], Chichimatsu et al [26], Taketuchi et al [27] and Nakano et al [28] As with the pore distribution measurements, moisture diffusivity was smaller for higher polymer contents The results are illustrated in Fig The diffusion of moisture by total potential (/) can be classified into diffusion of liquid water and diffusion of vapor Diffusion of vapor was probably dominant in sections of low water content, and diffusion of liquid water was probably dominant in sections of high water content Fig shows the relationship in Fig but with the absorbed volumetric water content converted into the relative absorbed 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 20 40 60 80 100 Relative Absorbed Volumic Water Content (%) Fig Relationship between moisture diffusivity and relative absorbed volumetric water content 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 compared to liquid water diffusivity 4.3 Verifying the experimental results (moisture diffusivity) by nonlinear 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 825 D Park et al / Construction and Building Materials 28 (2012) 819–830 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% relative water content for the specimen The boundary conditions used for each specimen are shown in Table 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 in Fig 10 Although there were some errors, overall 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 D (θ ) = D (θ v ) + D (θ l ) D (θ ) D ( θ v) D (θ l ) θ Fig Schematic diagram of moisture diffusivity depending on water content Table Water content of polymer-modified cement mortar at boundary conditions (100% relative water content) Polymer/cement ratio (%) Water content at boundary conditions (%) 10.10 13.83 10 10.21 20 11.27 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: & ' @h ẳ fFg ẵDfhg ỵ ẵL @t Qualitative estimation of stress generation under swelling and constraint conditions 5.1 Analytical model ð22Þ When rainwater diffuses from exposed surfaces into patch repair regions, differences in swelling occur depending on the constituent 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 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 Volumic Water Content (%) 14 P/C=5% P/C=10% P/C=20% 12 10 14 Volumic Water Content (%) P/C=0% 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) 12 10 0 10 20 30 40 50 60 70 Depth from Absorption Surface (mm) 10 20 30 40 50 60 70 Depth from Absorption Surface (mm) Fig 10 Comparison between experimental and analytical values D Park et al / Construction and Building Materials 28 (2012) 819–830 Table Dimensions of the analytical model Symbol CW CH RW RH TI Length (m) 1.5 0.3 0.25 0.07 0.005 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 W/C=30% W/C=50% W/C=70% 1000 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 repair materials was conducted The dimensions of the repaired member and the element division are shown in Fig 11 and Table The beam was assumed to be fixed at both ends In Table 5, 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 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 moisture diffusivity of the patch repair materials determined in the experiment and the moisture diffusivity values determined in earlier 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 in Table 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 diffusivity of the interface between the repair material and the substrate 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, interface, 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 material 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 Hydraulic Diffusivity (m /sec) 826 100 10 0.1 20 40 60 80 100 Relative Volumic Water Content (%) Fig 12 Moisture diffusivity of substrate concrete [30] the surface exposed to rain The boundary conditions of the surface exposed to rain were assumed to be the water content of the substrate 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 repair region exposed to rain is shown in Fig 13 The analytical conditions 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 moisture diffusivity of the patch repair was relatively small, the water front reached only half the patch depth of cm However, the water front in the substrate concrete exceeded the depth of the repair patch The water content differed sharply between the regions Fig 11 Element division of the analytical model 827 D Park et al / Construction and Building Materials 28 (2012) 819–830 Table Input data of patch repair materials and substrate concrete Water/cement ratio (%), polymer/ cement ratio (%) Coefficient of elasticity (GPa) Length change by water absorption (Â10À6/%) Patch repair materials W/C = 50, W/C = 50, W/C = 50, W/C = 50, 25.71 23.65 21.39 18.25 23.7 25.3 27.1 31.3 Substrate concrete W/C = 30 W/C = 50 W/C = 70 50.00 40.00 30.00 130.0 140.0 150.0 P/C = P/C = P/C = 10 P/C = 20 polymer were highly resistant to moisture diffusion, and water did not reach below cm 5.3 Vertical stress on the interface (rxx) Fig 13 Predicted water content distribution 24 h after exposure to rain separated by the interface, which had been coated with polymer resin The distribution of water in the substrate concrete and vertically in the repair material at 24 h and 48 h after exposure to rain is shown in Fig 14 The distribution of moisture diffusion was closely correlated to the water/cement ratio of the concrete In specimens 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 in Fig 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% 20 18 Moisture Content (%) 16 W/C=30%_24 hours W/C=50%_24 hours W/C=70%_24 hours Chronological changes in the distribution of vertical stress (rxx) at the interface are shown in Fig 15 in terms of depth from the absorptive surface (A–A0 in Fig 11) A steep compression stress gradient formed near the absorptive surface immediately after exposure 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 concrete with a water to cement ratio of 1:1 showed a water front exceeding the repair depth of cm within 24 h of the start of analysis, 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 displacement 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 concrete, are shown in Fig 16 The substrate concrete was more porous 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 h due to W/C=30%_48 hours W/C=50%_48 hours W/C=70%_48 hours 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 14 12 10 Repair materials Interface & Concrete 0.00 0.04 0.08 0.12 0.16 Depth from the Adsorptive Surface (m) 0.00 0.02 0.04 0.06 0.08 0.10 Depth from the Adsorptive Surface (m) Fig 14 Water content distribution in substrate concrete and patch repair materials (left: substrate concrete, right: patch repair materials) 828 D Park et al / Construction and Building Materials 28 (2012) 819–830 -20 σxx (N/mm ) -40 -60 -80 Repair: P/C=0% Concrete: W/C=50% 0.2 hours hours 12 hours 24 hours 48 hours Repair: P/C=5% Concrete: W/C=50% σxx (N/mm ) -20 -40 -60 -80 Repair: P/C=10% Concrete: W/C=50% 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Depth from the Absorptive Surface(m) Repair: P/C=20% Concrete: W/C=50% 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Depth from the Absorptive Surface(m) Fig 15 Chronological changes in stress generated on interface (A–A0 ) σxx (N/mm ) -20 -40 -60 0.2 hours hours 12 hours 24 hours 48 hours Repair: P/C=5% Concrete: W/C=30% Repair: P/C=5% Concrete: W/C=70% 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 -80 Depth from the Absorptive Surface(m) Depth from the Absorptive Surface(m) 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– A0 ) 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–B0 in Fig 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 (rxx) at the interface Although the shear stress was small up to 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 interface 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 diffusivity, the moisture diffusion was much more dominant than that in the repair materials, and very large shear stresses were generated, as shown in Figs 18 and 19 Increases in the polymer content of the repair materials also caused slight increases in the stress generated at the interface 829 D Park et al / Construction and Building Materials 28 (2012) 819–830 15 12 Concrete & Repair materials Interface Repair: P/C=20% Concrete: W/C=50% τxy (N/mm ) After 6 0.2 hours hours 12 hours 24 hours 48 hours -3 -6 0.0 Interface 0.1 0.2 0.3 After 48 0.4 Distance from the Interface (m) Fig 17 Chronological changes in shear stress on the interface beneath the patch repair region (B–B0 ) 15 Concrete & Repair materials Interface After 48 hours 12 P/C=5%, W/C=30% P/C=5%, W/C=50% P/C=5%, W/C=70% τxy (N/mm ) -3 -6 Interface 0.0 0.1 0.2 0.3 0.4 Distance from Adsorptive Surface (m) Fig 18 Changes in shear stress on the interface beneath the patch repair region (B– B0 ) due to differences in physical properties of substrate concrete 5.5 Selecting patch repair materials The choice of patch repair material should take into account the deterioration of the part to be repaired and the environmental conditions, but no guidelines have been proposed The patch repair material to be used on deteriorated parts that are frequently exposed to rain should be chosen following thorough consideration 15 Interface Interface After 48 hours After 48 hours P/C=0%, W/C=70% P/C=5%, W/C=70% P/C=10%, W/C=70% P/C=20%, W/C=70% P/C=0%, W/C=30% P/C=5%, W/C=30% P/C=10%, W/C=30% P/C=20%, W/C=30% 12 τxy (N/mm ) of the interactions among: moisture diffusivity, changes in volume caused by changes in water content, mechanical properties and adhesion properties of both the repair material and the substrate concrete, since they interact and affect stress generation In this study, methods for selecting patch repair materials were investigated on the basis of experimental results and finite element analysis The study showed that when water was absorbed from the repair region, volumetric changes caused by changes in water content were greater in repair materials with higher polymer to cement ratios, and large stresses was generated when there was a large difference in the coefficients of elasticity of the repair material and the substrate concrete The stress at the bottom of the repair region was mainly affected by the moisture diffusion resistance of the substrate concrete, which was much larger than that of the repair material The performance of patch repair materials was investigated with a focus on moisture diffusivity For substrate concrete with a high diffusion resistance, the repair material should have moisture diffusivity and mechanical properties similar to those of the substrate concrete For substrate concrete with a high water/ cement ratio in which moisture diffuses easily, highly adhesive patch repair material should be used, since moisture may penetrate from the substrate concrete into the repair region and produce large stresses after extended exposure to rain Besides rain, which was considered in this study, there are other factors that could cause cracks to develop in patch repair regions, such as: evaporation of moisture, repetitive heating and cooling, -3 -6 0.0 0.1 0.2 0.3 0.4 Distance from the Interface (m) 0.0 0.1 0.2 0.3 0.4 Distance from the Interface (m) Fig 19 Effects of polymer cement ratio of patch repair materials on the stress distribution on the interface (B–B0 ) (left: W/C = 30%, right: W/C = 70%) 830 D Park et al / Construction and Building Materials 28 (2012) 819–830 repetitive freezing and thawing, and loading The analytical results of this study may not represent actual phenomena in the real environment, since stress relaxation caused by the development of minute cracks and creep also affects stress However, the repair materials, the substrate concrete and the environmental conditions are diverse in practice, and proposing a qualitative guideline for selecting optimum patch repair materials by testing and analyzing re-deterioration mechanisms should be more effective than determining properties that only satisfy the required performance under certain conditions Conclusions The moisture diffusivity of patch repair regions on a deteriorated reinforced concrete structure during rain and the resultant internal stress were investigated, and a series of experiments and finite element analysis were conducted to determine the optimum repair material The following knowledge was acquired: (1) The moisture diffusivity of the PCM used in this study as patch repair material was a non-linear function of the absorbed water content, and showed a U-shaped distribution curve of high moisture diffusivity at both low and high water content This was probably due to the dominant movement of vapor at low water content and the dominant movement of liquid water at high water content (2) Moisture diffusivity was lower for PCM with a higher polymer to cement ratio The trend was more apparent for vapor diffusivity than for liquid water diffusivity (3) Stresses generated in patch repair regions by rain were predicted to increase with an increase in the polymer content in the PCM (4) Since, in most cases the moisture diffusivity of substrate concrete is much higher than that of the repair material, the stress generated at the interface beneath the repair region is largely affected by moisture diffusion in the substrate concrete and the resultant increase in volume The stress in a patch repair region was predicted to be larger for PCM with a higher polymer content, for which the coefficient of elasticity differs greatly from that of the substrate concrete (5) A patch repair material with moisture diffusivity and mechanical properties similar to that of the substrate concrete is likely to be appropriate for substrate concrete with high diffusion resistance For substrate concrete with a high water/cement ratio in which moisture diffuses easily, a highly adhesive patch repair material should be used, since moisture may penetrate from the substrate concrete into the patch repair region through the interface after extended exposure to rain References [1] Fujimura Toshiyoki, Kunieda Minoru, Nakamura Hikaru, Lee Sanghun Analytical approach on volumetric stability of patch repair materials Proc Jpn Concr Inst 2005;27(1):1597–602 [2] Emmons Peter H, Vaysburd Alexander M The total system concept – necessary for improving the performance of repaired structures Concr Int 1995:31–7 [3] Sugihasi Naoyuki Compatibility between substrate concrete and patch repair materials Concr J 1997;35(2):46–50 [4] Park Dongcheon, Kanematsu Manabu, 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Yanagi Hirofumi, Hukuhara Teruyuki, Matsuoka Sigeru Effects of the water– cement ratio on moisture absorption in unsaturated concrete J Construct Manage Eng 2001;683(52):65–73 ... 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, interface, and substrate concrete... 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 material The repair material and substrate... than that in the repair materials, and very large shear stresses were generated, as shown in Figs 18 and 19 Increases in the polymer content of the repair materials also caused slight increases