Deterioration mechanism due to drying and shrinkage of patch-repaired regions in reinforced concrete structures is analytically investigated. The moisture diffusion coefficient of the repair materials was determined by varying the drying temperature and the polymer-tocement ratios of the polymer-modified cement mortar (PCM) in the experiment. It is found that the diffusivity of PCM increases in proportion to the polymer-to-cement ratio up to 10%. The constraint stresses due to drying at the repaired region were estimated by the couplelinear finite element analysis with respect to volumetric change, moisture diffusivity, water content and mechanical properties of the repair material. Based on the distributions of relative water contents and stresses, the effects of these parameters are discussed. The stress generated by drying and shrinkage was affected by substrate concrete, environmental condition and the properties of PCM. Of the repaired PCM tested, it is demonstrated that the CPM with 10% polymer-to-cement ratio generates the highest constraint stress.
Available online at www.sciencedirect.com Construction and Building MATERIALS Construction and Building Materials 23 (2009) 434–447 www.elsevier.com/locate/conbuildmat Drying effect of polymer-modified cement for patch-repaired mortar on constraint stress DongCheon Park a,*, JaeCheol Ahn b, SangGyun Oh c, HwaCheol Song a, Takafumi Noguchi b a b Division of Architecture and Ocean Space, Korea Maritime University, Dongsam-Dong, Yeongdo-Ku, Pusan 606-791, Republic of Korea Department of Architecture, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan c Division of Architecture, Doneui University, Pusan 614-714, Republic of Korea Received June 2007; received in revised form November 2007; accepted 13 November 2007 Available online January 2008 Abstract Deterioration mechanism due to drying and shrinkage of patch-repaired regions in reinforced concrete structures is analytically investigated The moisture diffusion coefficient of the repair materials was determined by varying the drying temperature and the polymer-tocement ratios of the polymer-modified cement mortar (PCM) in the experiment It is found that the diffusivity of PCM increases in proportion to the polymer-to-cement ratio up to 10% The constraint stresses due to drying at the repaired region were estimated by the couplelinear finite element analysis with respect to volumetric change, moisture diffusivity, water content and mechanical properties of the repair material Based on the distributions of relative water contents and stresses, the effects of these parameters are discussed The stress generated by drying and shrinkage was affected by substrate concrete, environmental condition and the properties of PCM Of the repaired PCM tested, it is demonstrated that the CPM with 10% polymer-to-cement ratio generates the highest constraint stress Ó 2007 Elsevier Ltd All rights reserved Keywords: Patch repair material; Moisture diffusion coefficient; Polymer-modified cement mortar; Real environmental boundary conditions; Constraint stress analysis Introduction The patch method used to repair deteriorated reinforced concrete structures should produce patches that are dimensionally and electrochemically stable, resistant against penetration of deterioration factors, and mechanically strong [1–4] Today, the patch repair materials that are widely used contain admixtures, such as silica fume and polymers, to improve the performance of cement mortar [5,6] The admixtures are used to improve the workability and performance of the hardened repair material Material compaction has been thought to cause reduced moisture diffusivity due to changes in water content and the resultant changes in the dimensions of the repair patch However, * Corresponding author Tel.: +82 10 5533 9443; fax: + 82 51 403 8841 E-mail address: dcpark@hhu.ac.kr (D Park) 0950-0618/$ - see front matter Ó 2007 Elsevier Ltd All rights reserved doi:10.1016/j.conbuildmat.2007.11.003 there is insufficient quantitative data available for a proper analysis In particular, there have been very few studies of the behavior of patch repair materials that contain re-emulsification-type polymer resin, the use of which is increasing rapidly as it is convenient to application Bazant et al [7] reported that moisture diffusion in concrete changes non-linearly with changes in relative water content and relative humidity In Japan, Sakata et al [8] and Akita et al [9,10] determined the relationship between moisture diffusivity and relative water content of concrete and mortar, Takiguchi et al [11] derived a function of evaporable water quantity, and Hashida et al [12] determined the moisture diffusivity of a specimen by either slicing the specimen and measuring its relative water content, or monitoring the changes in relative humidity in the specimen to examine the decrease in water content caused by hydration Both methods have some physical inconsistency but are widely used today as plenty of data is available, D Park et al / Construction and Building Materials 23 (2009) 434–447 prediction analysis is easy, and the characteristics of the parameters are relatively well understood [13] When deterioration in a reinforced concrete structure is repaired by the patch method, the resultant structure is a composite of the substrate concrete and the repair material [14], and stress is generated at the repair site by volumetric changes that accompany changes in water content A major cause of volumetric changes in patch-repaired materials is evaporation of moisture, which causes tensile, compression and shear stresses in the patch and the substrate concrete, and/or their interface, depending on the constraints imposed by the substrate concrete When the stresses exceed the crack-allowable stress, cracks develop that allow the egress of water, which accelerates corrosion of the metal reinforcing bars in the concrete The development of cracks may be attributed to the selection of patch repair materials and designation of repair zones without giving thorough consideration to the surrounding environmental conditions, the conditions of application, and the extent of deterioration To prevent cracks forming, prediction on the basis of preliminary experiments and simulation analysis is indispensable, and possible causes for stress generation after a repair need to be understood by investigating each parameter Several studies [15,16] involving finite element analyses have been conducted with the same objectives as in this study, but the basic properties of the repair material were ambiguous, the material properties and boundary conditions were only assumed, and the correlation between the predicted results and the actual phenomena was low To prevent early re-deterioration and to ensure that the repaired structure maintains the required performance over its intended lifetime, it is important to be able predict the stresses generated between the substrate concrete and the patch-repaired material, to select the appropriate repair material, to determine the appropriate region to repair, and to cure repair patches appropriately With such a background, a series of experiments and finite element analysis were conducted using the properties of the repair materials and environmental conditions as the experimental parameters The repair material was cement mortar modified by the addition of a re-emulsification-type polymer resin The moisture diffusivity of the repair material was determined by analyzing the effects of temperature Using the results of moisture diffusivity analysis, a coupled structure analysis was conducted on the mechanical property and changes in volume [17] to calculate stress generation in the repair material and the interface between the repair patch and the structure The results were used to assist in guiding the selection of the optimum patch repair material Estimating moisture distribution in patch-repaired material using a non-linear diffusion equation Bazant et al [7] have demonstrated the non-linearity of moisture diffusion in porous materials such as those used for patch repair and the concrete substrate, and a number 435 of studies were carried out on the basis of that principle [8– 12] Most of these studies used either the Matano method [18,19], which uses Boltzmann transform, or a method involving inverse analysis of measured data [20] In this study, the Matano method was used to determine moisture diffusivity, which required the monitoring of changes in water content with the passage of time Water content can be monitored by slicing specimens and using a relative humidity probe [21], or by measuring the nuclear magnetic resonance [22] In this study, a monitoring method was used that involved slicing a specimen, drying it to an absolutely dry state, and measuring the change in weight before and after drying This method may cause a slight reduction in the water content when specimens are cut, but requires no correction and is simple, direct and precise [23,24] Two-dimensional finite element analysis was conducted to predict changes in water distribution in a patch-repaired region caused by various environmental factors A coupled structural analysis of volume changes caused by changes in water content was done to predict the stress generated under the constraints imposed by the substrate concrete 2.1 Calculating moisture diffusivity by the Boltzmann transform The unidimensional, non-linear diffusion equation is: oR ẳ rDrRị ot 1ị where D (cm2/d) is the moisture diffusion coefficient determined from the gradient of relative water content, and R (%) is relative water content, which is given by R ẳ w=w0 ị 100 2ị where w is the water content (%) and w0 is the water content at saturation (%) The movement of moisture during the drying process can be expressed by a diffusion equation, and a non-linear diffusion equation can be derived from the monitored water content distribution using the Boltzmann transform [18] For moisture movement in one direction, which was assumed in this study, the relative water content is expressed as a Boltzmann transfer variable: p k ẳ x= t 3ị where x (cm) is the distance from the drying surface and t (day) is the drying period By applying the Boltzmann transform under boundary conditions, the moisture diffusivity D(R) can be expressed as: Z Rs oR k dR ð4Þ DRị ẳ R ok where Rs = 100%, from Eq (1) This equation can be used to determine the moisture diffusion coefficient at an arbitrary relative water content R To calculate the equation, relative water content must be expressed as a function of the Boltzmann transfer variable 436 D Park et al / Construction and Building Materials 23 (2009) 434–447 2.2 Moisture diffusion coefficient considering temperature effects Moisture diffusivity D is a function of temperature and relative water content or relative humidity Powers [25] estimated that the movement of water at normal temperature was determined by the movement of water molecules along adsorption surfaces Bazant et al [7] proposed that the movement of water below 100 °C is not determined by capillary flow But it is determined by the minimum pore cross-sectional area of the neck of pores, since capillary space is discontinuous, and the effects of temperature on the movement of water molecules are determined not by the adhesion of the liquid or vapor, but by the activation energy (Q) [25] To consider the effects of temperature on moisture diffusivity, Eq (5) was developed by adding moisture diffusivity, which is a function of relative water content proposed by Akita et al [10], to the temperature equations described by Bazant et al [7] and Mihashi et al [26] In Eq (5), D1 represents the diffusivity at the standard temperature (T = 20 °C) at saturation (h = 1.0) The term f1(R) represents the effects of relative water content on moisture diffusivity, and f2(T) represents the effects of temperature on moisture diffusivity at a relative humidity of 100%: DðT ; Rị ẳ D1 f1 Rị f2 T Þ À Á Én f1 ðRÞ ¼ È R m 100 ỵ1 N ! T ỵ 273 U 1 f2 T ị ẳ exp 293 R 293 T ỵ 273 5ị where U (J/mol) is the activation energy; R (J/mol K) is the gas constant; and m, n and N are material constants determined by the polymer-to-cement ratio The matrix expression of the moisture diffusion equation is: & ' oR ¼ fF g ẵDfRg ỵ ẵL ot 8ị where [D] is the moisture diffusion matrix, [L] the water capacity matrix, {F} the external moisture flux vector, and {R} is the relative water content vector Since moisture diffusivity D has a non-linear relationship with relative water content R, the Newton–Raphson method was used in the finite element analysis The matrix of the moisture diffusion equation (Eq (8)) is discrete in space but not in time Thus, the Crank–Nicolson difference method was used to discretize the equation from time In the Crank–Nicolson difference method, the nodal relative water content [27] vector at t + Dt/2 (Dt is a small increase in time) is given as: & ' Dt ẳ fRt ỵ Dtịg þ fRðtÞgÞ ð9Þ R tþ 2 When the nodal relative water content vector at t + Dt/2 is differentiated by time: & ' o Dt fRt ỵ Dtịg fRtịg R tỵ ẳ 10ị ot Dt Substituting Eqs (9) and (10) for {R} and foR g in Eq (8), ot and organizing the equation gives: 1 1 ẵD ỵ ẵL fRt ỵ Dtịg ẳ ẵD ỵ ẵL fRtịg ỵ fF g Dt Dt ð11Þ Since {R(t)} on the right-hand side of the equation is known, the equation for the finite element analysis of nonsteady moisture diffusion can be calculated 2.3 Initial and boundary conditions Overview of the experiment The initial and boundary conditions used for the finite element analysis are shown below Initial conditions: Rðx; y; 0Þ ¼ 100% Boundary conditions: oR DðRÞ ¼ f ðRen À Rs Þ ox ð6Þ ð7Þ where f (cm/day) is the coefficient of moisture transfer, and Ren (%) and Rs (%) are the relative water content at the drying surface and in ambient air, respectively 2.4 Non-linear finite element analysis Non-linear finite element analysis was conducted using experimentally determined moisture diffusion coefficients, and initial and boundary conditions to calculate the water content distribution in the repair material 3.1 Materials used Ordinary Portland cement was used Fine aggregates were river sand from the Oigawa River in Japan, and its physical properties are given in Table The re-emulsification-type polymer resin was manufactured by N Co., and its properties are given in Table 3.2 Preparing the specimens Specimens of polymer-modified cement mortar (PCM) used for patch repair were prepared according to the testing methods stated in JIS A 1171 The mix proportion was a fine aggregate-to-cement ratio of 1:3, a water-tocement ratio of 1:1, and polymer/cement with 0%, 5%, 10%, and 20% polymer (Table 3) Antifoaming agent was added at 0.7% of the polymer weight Flow and air content were measured and are given in Table D Park et al / Construction and Building Materials 23 (2009) 434–447 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 Table Properties of re-emulsification-type polymer resin Polymer 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 437 3.3.2 Water content test at equilibrium Water content at equilibrium was tested to determine the relationship between RH and water content, which is the isothermal absorption curve needed to set the boundary conditions of finite element analysis and to correct analytical results The specimen was prepared as described for the moisture diffusivity test (Table 3) and then cut into slices about 0.5 cm thick to speed the establishment of equilibrium The humidity was controlled at a constant value using a desiccator (0%) containing silica gel and a hygrostat (20%, 40%, and 80%) After four weeks, the mass showed no change, and the specimen was judged to have reached equilibrium The relative water content for each relative humidity value was determined from the weight differences Results and discussion 4.1 Determining moisture diffusivity Polymer (%) Cement:fine aggregate Water: cement Antifoaming agent (%) Flow (mm) Air content (%) 10 20 1:3 1:1 0.7 160 185 190 195 6.2 7.5 8.2 8.9 The specimens were molded in dimensions of 40 mm  40 mm  160 mm, cured in a humid atmosphere (20 °C, 85% RH) for days, under water (at 20 °C) for days, and in a dry atmosphere (20 °C, 60% RH) for 21 days, and prepared in a saturated state of 100% relative water content 3.3 Experimental methods 3.3.1 Moisture diffusivity test Unidimensional moisture movement was induced in order to determine the moisture diffusivity As shown in Fig 1, surfaces other than the drying surface were covered with wrapping film and then sealed tightly with adhesive tape to prevent water transpiration Specimens were dried at °C, at 20 °C and at 40 °C, with a relative humidity of 60% After 2, 4, and weeks, a sample was chipped from the drying surface, and changes in the mass of each element were measured immediately and air-dried at 105 °C for days to absolute dryness condition As described above, the non-linear moisture diffusivity can be calculated from the relative water content using the Boltzmann transform proposed by Matano [18,19] The relationship between the Boltzmann transfer variable k and relative water content was determined (Fig 2), and was subjected to regression analysis using the following curve: ( ) a 12ị R ẳ 100 k ỵ bị where R (%) is the relative water content, a and b are constants determined by the shape of the curve The results are summarized in Table for each drying condition Differentiation of Eq (12) by the Boltzmann transfer variable gives Eq (13) Moisture diffusivity can be calculated by substituting Eqs (13) and (14) in Eq (4): oR 200 Á a ẳ ok b ỵ kị3 13ị p 0:5fb 200 ỵ 2Rị 20 100a a Rg kẳ 100 ỵ R Temp.=20C, R.H.=60% 14ị P/C=0% P/C=5% P/C=10% P/C=20% 100 Relative Water Content (%) Table Mix proportion and property values of polymer-modified cement mortar 90 Y=100*(1-(a/(λ+b)^2)) 80 Data: P/C=0% = 0.9695 R a 0.23 ±0.03 b 0.75 ±0.07 Data: P/C=5% = 0.97421 R a 0.42±0.05 b 1.00±0.08 70 Data: P/C=10% = 0.97214 R a 0.77 ±0.09 b 1.44 ±0.11 Data: P/C=20% = 0.95864 R a 0.54 ±0.08 b 1.18 ±0.11 60 Fig Dimensions of a specimen with one drying surface λ=(x/t 1/2 ) Fig Relationship between the Boltzmann transfer variable k and relative water content (example: at 20 °C) D Park et al / Construction and Building Materials 23 (2009) 434–447 Table Material constants determining the shape of Eq (12) 40 b R2 10 20 10 20 10 20 0.093 0.144 0.224 0.158 0.228 0.418 0.769 0.534 0.612 0.950 1.310 1.060 0.430 0.556 0.717 0.619 0.750 1.000 1.440 1.182 0.974 1.255 1.510 1.309 0.991 0.996 0.992 0.986 0.970 0.974 0.972 0.959 0.942 0.948 0.966 0.968 The movement of water at normal temperature is determined by the smallest sectional area at the neck of capillary pore space Water movement at the neck is the movement of water molecules within an absorbed water layer, which becomes thinner as the moisture level decreases [7,25] The moisture diffusivity measurements (Fig 3) in this study showed this phenomenon and were in a non-linear relationship with relative water content Fig shows the effects of 10 Diffusion Coefficient (cm /d) 12 4.2 Water content at equilibrium The water content of porous materials, such as patch repair materials and substrate concrete, fluctuates with the relative humidity of the ambient atmosphere At a fixed 12 P/C=0% 5°C, 60% 20°C, 60% 40°C, 60% 2 Diffusion Coefficient (cm /d) 10 P/C=5% 5°C, 60% 20°C, 60% 40°C, 60% 0 12 10 20 a 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Relative Moisture Content (%) Relative Moisture Content (%) 12 P/C=10% 5°C, 60% 20°C, 60% 40°C, 60% 10 Polymer content (%) Diffusion Coefficient (cm /d) Temperature (°C) temperature during the drying process The higher the temperature, the greater the moisture diffusivity The effects of temperature were quantified using Eq (5) The effects of polymer content differed from those in an earlier study [23], which reported that specimens of higher polymer-tocement ratios were more compact, had smaller capillary pore sizes, and thus had lower moisture diffusivity This was because in the earlier study, the polymer-to-cement ratio was first decided and then the water-to-cement ratio was reduced so as to compensate for increases in fluidity caused by the increase in polymer content However, in the present study, which was aimed at understanding the effects of polymer content, the water-to-cement ratio was fixed at 50% and the polymer-to-cement ratio was used as the experimental variable Up to a polymer-to-cement ratio of 10%, moisture diffusivity increased, but dropped slightly at a ratio of 20% Diffusion Coefficient (cm /d) 438 P/C=20% 5°C, 60% 20°C, 60% 40°C, 60% 0 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Relative Moisture Content (%) Relative Moisture Content (%) Fig Moisture diffusivity for each drying temperature and polymer/cement ratio D Park et al / Construction and Building Materials 23 (2009) 434–447 temperature, the water content of a porous mass is in equilibrium with the ambient relative humidity The relationship between the relative humidity and relative water content of the specimen is called the sorption isotherm [28] In this experiment, which aimed to assess changes in water content when the repair material dried, the desorption isotherm was determined experimentally by decreasing the relative water content until it reached equilibrium, as shown in Fig The relationships differed slightly, depending on the polymer-to-cement ratio, but the difference was small and could not be quantified Thus, the mean was determined and used to correct the boundary conditions of the non-linear finite element analysis, as described in the following section 4.3 Comparison between analytical and experimentally measured relative water contents The distribution of relative water content along the vertical direction from the drying surface was determined by non-linear finite element analysis based on the values determined by the experiments described in Sections 4.1 and 4.2 above The elements were four-nodal isoparametric, and the entire analytical length of 160 mm was divided into 30 equal parts Eqs (6) and (7) were used as the initial and boundary conditions, respectively The relative water content at a relative humidity of 60% in ambient atmosphere, which was a boundary condition, was calculated using the tryout method based on the isothermal absorption curve shown in Fig for 20 °C and the experimental results for and 40 °C The coefficient of moisture transfer f was determined retrogressively using the experimental values and repetitive calculation The relative water content at each temperature at a relative humidity of 60%, which was a boundary condition, and the coefficient of moisture transfer are shown in Table The effects of the coefficient of moisture transfer on water movement analysis are reported to be small [10] In this study, a uniform coefficient of moisture transfer of 0.007 cm/day was used, Relative Water Content (%) 100 P/C=0% P/C=5% P/C=10% P/C=20% Mean Value 80 60 40 20 439 Table Relative water content and coefficient of moisture transfer corresponding to 60% relative humidity Drying temperature (°C) Relative water content (%) Coefficient of moisture transfer (m/d) 60 0.007 20 55 0.007 40 32 0.007 which resulted in a good correlation with experimental values The coefficient of moisture transfer is not an intrinsic property of patch repair materials; it changes depending on the ambient conditions and the state of the surface of the specimen The coefficient of moisture transfer is rarely measured accurately, and most analyses use fixed values Experimental and analytical relative water content values of a specimen are compared in Fig As a whole, the correlation was good, but slight errors were observed on the 56th day and at a depth more than cm below the drying surface The errors were probably produced because, although the Matano method, which was used to determine the moisture diffusivity characteristically requires that the surface opposite the drying surface has a relative humidity of 100%, the specimen was already dry on the 28th day of the experiment even at the element furthest (14 cm) from the drying surface and, thus, small errors were already present in the regression analysis for determining the relationship between the Boltzmann transfer variable and relative water content The errors were larger at higher temperatures Both experimentally and analytically, the drying speed was faster at higher drying temperatures It was fastest for specimens with a polymer-to-cement ratio of 10% and slowed gradually as the polymer-to-cement ratio increased The results differed from the widely accepted belief that increases in polymer-to-cement ratio make the inner structure of PCM compact This is probably because the polymer-to-cement ratio was adjusted without changing the water-to-cement ratio as described in Section 4.1 [28] The results of the regression analysis of the relationship between the relative humidity and relative water content during the drying process, determined by inverse analysis using experimental values and the finite element analysis method, are shown in Fig The results of the regression analysis that included data for a relative humidity of 60% and drying temperatures of and 40 °C are expressed by Eq (15) The relationship was used to convert the boundary conditions (relative water content) for the finite element analysis of relative humidity data in the real environment, which is described below: R ẳ 17:36 ỵ 0:263T 0:00847T ỵ 2:303H 0:0254TH 0:000016T H 0:04175H 0 20 40 60 Relative Humidity (%) 80 100 Fig Relationship between relative water content and relative humidity ỵ 0:000258TH ỵ 0:00027H 15ị where R is the relative water content (%), T the drying temperature (°C) and H is the relative humidity (%) 440 D Park et al / Construction and Building Materials 23 (2009) 434–447 4.4 Qualitative prediction of internal water content distribution and stress generation under fixed ambient atmospheric conditions Under fixed drying conditions of 20 °C and relative water content of 55%, which corresponds to a relative humidity of 60% (determined using Eq (15)), moisture diffusion and stress generation were compared for the polymer-to-cement ratios The relative water content of the substrate concrete before repair was assumed to be 60% The moisture diffusion coefficients of the repair material (see Section 4.1) and the diffusivity values of the substrate concrete reported in an earlier study [29] were used in the analysis Fig shows the element division of the analytical model The beam was assumed to be fixed at both ends In Fig 7, TI denotes the thickness of the interface, CH is the thickness of the repair material, CW is the width of the substrate concrete, RW is the width of the repair region, and RH is the thickness of the repair region The dimensions of the analytical model are shown in Table Structural analysis was conducted by coupling the data for the volumetric changes caused by changes in water content and the results of the internal water content distribution analysis in order to predict the chrono- logical changes in stress generation Data related to changes in length caused by changes in water content and the coefficient of elasticity [17] are given in Table The data on the changes in length caused by changes in water content were measured by dyeing a thin rectangular specimen mm  40 mm  160 mm, which had been devised to minimize the internal constraining force of the materials in a desiccator Primer resin was assumed to be applied to the interface between the repair material and the substrate concrete Since no measured data were available for the moisture diffusivity of primer resin, it was assumed to be 1/1000 of that of the patch-repaired materials The input moisture diffusion coefficients to the substrate concrete are shown in Fig The moisture diffusion coefficients and the isothermal absorption curves of the substrate concrete were analyzed using the measurements reported by Fujiwara et al [29] The structural analysis is that for linear elastic regions The repair material, interface and substrate concrete were assumed to be perfectly united, and the mechanical properties of the interface were assumed to be the same as those of the repair material in the analysis The repair regions were assumed to start drying after they were cured-sealed over a period of 28 days 100 90 80 70 5°C, P/C=0% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 Relative Water Content (%) Relative Water Content (%) 100 90 80 70 5°C, P/C=5% 60 50 40 10 12 14 16 18 Depth from the Drying Surface (cm) 10 12 14 16 18 Depth from the Drying Surface (cm) 100 90 80 70 5°C, P/C=10% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 10 12 14 16 18 Depth from the Drying Surface (cm) Relative Water Content (%) 100 Relative Water Content (%) 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 90 80 70 5°C, P/C=20% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 10 12 14 16 18 Depth from the Drying Surface (cm) Temperature, 5°C; R.H., 60% Fig Measured and analytical relative water content D Park et al / Construction and Building Materials 23 (2009) 434–447 The distribution of relative water content on the interface on the 30th day after the start of drying is shown in Fig The distribution of the main stress (rmax) generated along with volumetric changes is shown in Fig 10 The stress generated on the drying surface under the constraining conditions was compared between specimens with different polymer-to-cement ratios The stress near the drying surface was predicted to be higher for a polymerto-cement ratio of 0% than that for the other ratios, although the changes in volume caused by changes in water content were small The reduction in relative water content inside the repair region was greatest at a polymer-tocement ratio of 10%, in which relatively large stress was generated by the effects of the elasticity coefficient and volumetric changes 4.5 Qualitative prediction of internal water content distribution and stress generation under real environmental conditions Changes in the relative water content inside the repair material and stress generation under real environmental conditions were predicted The boundary ambient conditions were the mean of the meteorological data recorded over the past 10 years in Tokyo, Naha (Okinawa Prefecture) and Sapporo (Hokkaido Prefecture) The annual temperature and humidity in Tokyo, Okinawa, and Sapporo from March 2004 to February 2005 and the mean for the 10 years are shown in Fig 11 The moisture diffusion coefficients of the repair material and substrate concrete were corrected by considering the effects of the drying temperature The mechanical property values and the changes in volume were the same as those used in Section 4.3 The drying period was from March until the following February The relative water content gradient along the vertical direction from the drying surface is shown in Fig 12 At the start of the drying process, the relative water contents of the surface and the inside differed sharply, but the difference was less marked as time passed The drying speed was highest for the polymer-to-cement ratio of 10% and in Okinawa, where the mean annual ambient temperature was the highest The distribution of the relative water content along the vertical direction and the main stress at the end of August 100 80 70 20°C, P/C=0% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 Relative Water Content (%) Relative Water Content (%) 100 90 90 80 70 20°C, P/C=5% 60 40 10 12 14 16 18 10 12 14 16 18 Depth from the Drying Surface (cm) 100 100 80 70 20°C, P/C=10% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 Relative Water Content (%) Relative Water Content (%) 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 Depth from the Drying Surface (cm) 90 441 90 80 70 20°C, P/C=20% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 10 12 14 16 18 Depth from the Drying Surface (cm) Temperature, 20 °C; R.H., 60% Fig (continued) 10 12 14 16 18 Depth from the Drying Surface (cm) 442 D Park et al / Construction and Building Materials 23 (2009) 434–447 100 90 80 70 40°C, P/C=0% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 Relative Water Content (%) Relative Water Content (%) 100 90 80 70 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 10 12 14 16 18 Depth from the Drying surface (cm) 10 12 14 16 18 Depth from the Drying surface (cm) 100 100 90 80 70 40°C, P/C=10% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 Relative Water Content (%) Relative Water Content (%) 40°C, P/C=5% 60 90 80 70 40°C, P/C=20% 60 14days 28days 56days Analysis Curve of 14days Analysis Curve of 28days Analysis Curve of 56days 50 40 10 12 14 16 18 Depth from the Drying surface (cm) 10 12 14 16 18 Depth from the Drying surface (cm) Temperature, 40 °C; R.H., 60% Fig (continued) R : Relative Water Content (%) 100 Temp.=5°C Temp.=20°C Temp.=40°C Measured Value 80 60 40 20 R=17.36+0.263* T-0.00847*T +2.303*H-0.0254*T*H-0.000016*T *H 2 -0.04175*H +0.000258*T*H +0.00027*H 0 20 40 60 80 100 H : Relative Humidity (%) Fig Regression curve of the relationship between relative humidity and relative water content during the drying process are shown in Fig 13 The distribution and stress generation of specimens of different polymer-to-cement ratios and regions were compared The gradient of the relative water content caused by drying was steeper in Okinawa than in Tokyo Thus, the main stress was predicted to be larger in Tokyo than in Okinawa, although the amount of moisture to be lost by drying was smaller in Tokyo Thus, the high stress generated near the drying surface probably depended on the gradient of relative water content between the drying surface and the inside of the patch repair, which is the same as that of plastic cracks in concrete [30] The stress was also larger in specimens of lower polymer-to-cement ratios in the real environment, as discussed in Section 4.4 The changes in internal water content distribution and stress generation caused by changes in thickness of the repair region are shown in Fig 14 The polymer-to-cement ratio analyzed was 5%, and the thickness of the patchrepaired region was 5, 7, and 10 cm The environmental data recorded in Tokyo were used as the boundary conditions Regardless of the thickness of the patch, a very steep stress gradient was observed between the drying surface and the inside of the region at the end of March, which was soon after drying started The overall stress increased as time passed At the end of August the rate of change D Park et al / Construction and Building Materials 23 (2009) 434–447 443 Fig Element division of the analytical model Table Dimensions of analytical model CW CH RW RH TI 1.5 0.3 0.25 0.07 0.005 Table Input data of patch repair materials and substrate concrete Patch repair material Substrate concrete Water: cement Polymer (%) Coefficient of elasticity (GPa) Length change by water absorption (Â10À6 %) 1:1 1:1 1:1 1:1 1:1 10 20 – 25.71 23.65 21.39 18.25 40.00 23.7 25.3 27.1 31.3 20.0 Relative Water Content (%) Dimension (m) 100 Drying Time = 30 days P/C=0% P/C=5% P/C=10% P/C=20% 90 80 70 60 50 0.00 0.03 0.06 0.09 0.15 Fig Distribution of relative water content along the vertical direction from the drying surface (A–A0 ) 24 Fujiwara(W/C=0.52, T=10°C) Fujiwara(W/C=0.52, T=20°C) Fujiwara(W/C=0.52, T=40°C) 16 12 0.00 10 20 30 40 50 60 70 P/C=0% P/C=5% P/C=10% P/C=20% 20 Principal Stress (MPa) Diffusion Coefficient (cm /day) 0.12 Depth from the Drying Surface (m) 80 90 100 Relative Water Content (%) Fig Diffusion coefficient of substrate concrete [29] 0.03 0.06 0.09 0.12 0.15 Depth from the Drying Surface (m) Fig 10 Main stress generated along the vertical direction from the drying surface (A–A0 ) 444 D Park et al / Construction and Building Materials 23 (2009) 434–447 Temp & R.H of Tokyo latitude 35.4 north and longitude 139.4 east Avg temp of day('04-'05) Avg temp of month('95-'04) Avg R.H of day('04-'05) Avg R.H of month('95-'04) 80 90 70 80 60 70 50 60 40 50 30 40 20 30 10 20 Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Relative Humidity (%) Temperature (°C) 100 10 -10 50 100 150 200 250 300 350 Time (Day & Month) Temp & R.H of Okinawa latitude 26.12 north and longitude 127.4 east Avg temp of day('04-'05) Avg temp of month('95-'04) Avg R H of day('04-'05) Avg R H of month('95-'04) 80 90 70 80 60 70 50 60 40 50 30 40 20 30 10 20 Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb -10 Relative Humidity (%) Temperature (°C) 100 10 0 50 100 150 200 250 300 350 Time (Day & Month) Temp & R.H of Sapporo latitude 43 north and longitude 141.2 east Avg temp of day('04-'05) Avg temp of month('95-'04) Avg R.H of day('04-'05) Avg R.H of month('95-'04) 80 90 70 80 60 70 50 60 40 50 30 40 20 30 10 Dec Mar Apr May Jun Jul Aug Sep Oct Jan Feb 20 Relative Humidity (%) Temperature (°C) 100 10 Nov -10 50 100 150 200 250 300 350 Time (Day & Month) Fig 11 Meteorological data used as the boundary conditions (mean annual temperature and relative humidity in Tokyo, Okinawa and Sapporo for 10 years) of both relative water content and stress were smaller than those in March Thick specimens (10 cm) needed more time than thin specimens (5 cm) for the relative water content near the drying surface to decrease, since a larger amount of water had to be removed from the inside The thinner specimens dried faster and showed increases in stress D Park et al / Construction and Building Materials 23 (2009) 434–447 Tokyo P/C=0% 80 70 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 60 50 100 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) Relative Water Content (%) 90 0.00 Relative Water Content (%) 100 70 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 50 0.00 0.02 0.04 80 70 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) 0.06 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 60 50 100 80 60 90 0.08 70 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 60 50 60 50 0.00 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 0.02 0.04 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) 0.06 0.08 Depth from the Drying Surface (m) 0.02 0.04 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) 0.06 0.08 Depth from the Drying Surface (m) Relative Water Content (%) Relative Water Content (%) 70 0.08 80 100 80 0.06 90 0.00 Okinawa P/C=5% 90 0.04 Tokyo P/C=20% Depth from the Drying Surface (m) 100 0.02 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) Depth from the Drying Surface (m) Tokyo P/C=10% 90 Tokyo P/C=5% 0.00 0.02 0.04 0.06 0.08 Depth from the Drying Surface (m) Relative Water Content (%) Relative Water Content (%) 100 445 Sapporo P/C=5% 90 80 70 Mar.(After m) May(After m) Jul.(After m) Sep.(After m) Nov.(After m) Jan.(After 11 m) 60 50 0.00 0.02 0.04 Apr.(After m) Jun.(After m) Aug.(After m) Oct.(After m) Dec.(After 10 m) Feb.(After 12 m) 0.06 0.08 Depth from the Drying Surface (m) Fig 12 Changes in water content (1 year) in patch repair PCM along the vertical direction from the surface (A–A0 ) sooner The phenomenon affected stress generation at the interface with the substrate concrete, and the main stress on the interface was greater in thinner specimens The analysis of stress generation and changes over time are important when considering how a repair material will perform under specific environmental conditions However, this linear structural analysis could not predict the stress generated at the repair region in the field, and further analytical models need to be developed to reproduce microcracks, creep and interface properties Conclusions The mechanism underlying the deterioration caused by drying and shrinkage of patch repairs made to deteriorated reinforced concrete structures was studied by measuring 446 D Park et al / Construction and Building Materials 23 (2009) 434–447 Tokyo P/C=0% Tokyo P/C=10% Okinawa P/C=5% 24 Tokyo P/C=5% Tokyo P/C=20% Spporo P/C=5% Tokyo P/C=0% Tokyo P/C=5% Tokyo P/C=10% Tokyo P/C=20% Okinawa P/C=5% Sapporo P/C=5% 20 90 Principal Stress (N/mm2 ) Relative Water Content (%) 100 80 70 60 16 12 50 0.00 0.03 0.06 0.09 0.12 0.00 0.15 Depth from the Drying Surface (m) 0.03 0.06 0.09 0.12 0.15 Depth from the Drying Surface (m) Fig 13 Relative water content and main stress at the interface along the vertical direction (A–A0 ) at the end of August (A–A0 ) 85 16 80 12 75 Depth=5cm Depth=7cm Depth=10cm 70 65 60 Depth=5cm Depth=7cm Depth=10cm 20 Depth=5cm Depth=7cm Depth=10cm 90 24 Principal Stress (N/mm ) Depth=5cm Depth=7cm Depth=10cm 20 95 0.03 0.06 0.09 0.12 50 0.15 Depth from the Drying surface (m) (Mar.(After m)) 95 90 85 16 80 12 75 70 65 60 55 0.00 100 Relative Water Content (%) 100 Relative Water Content (%) Principal Stress (N/mm ) 24 55 0.00 0.03 0.06 0.09 0.12 50 0.15 Depth from the Drying surface (m) (Aug.(After m)) Fig 14 Changes in relative water content and main stress caused by the difference in thickness of the patch repair region (A–A0 ) the moisture diffusion coefficients of the repair material, with drying temperature and polymer-to-cement ratio as experimental parameters The stress produced at the repair regions by drying was predicted through linear structural analysis by inputting moisture diffusivity, volumetric changes caused by changes in water content, and mechanical properties Fixed environmental conditions and real environmental data (Tokyo, Okinawa and Hokkaido) were used as boundary conditions The chronological changes in relative water content in repair regions and stress distribution were determined analytically, and the principal physical parameters involved in stress generation were investigated The following knowledge was acquired from the experiments and analyses described here: (1) The moisture diffusivity of the repair material (PCM) investigated in this study increased in proportion to the polymer-to-cement ratio, up to a ratio of 10% and dropped slightly thereafter Moisture diffusivity was greater at higher drying temperatures An equation for predicting the phenomenon was developed (2) Stress produced by drying and shrinkage was affected by the differences in moisture diffusivity between the repair material and the substrate concrete, as well as by volumetric changes caused by changes in water content and the coefficient of elasticity Of the repair materials tested in this study, the polymer/cement mix with 10% polymer produced the greatest stress (3) As drying proceeded, a gradient of relative water content was produced between the drying surface and the inside of the repair region, and considerable stress was generated in the vertical direction in this region The speed of stress mitigation by further drying varied, depending on the thickness of the repair region The thicker the region, the slower the stress generation by drying and, thus, the lower the risk of generating initial defects (4) An analysis using recorded environmental data as the boundary conditions showed that the steepest stress gradient was produced with the environment at Tokyo D Park et al / Construction and Building Materials 23 (2009) 434–447 References [1] Emmons PH, Vaysburd AM, McDonald JE Concrete repair in the future turn of the century-any problem? Concr Int 1994:42–9 [2] Emmons Peter H, Vaysburd Alexander M The total system conceptnecessary 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] Cusson Daniel, Mailvaganam Noel Durability of repair materials Concr Int 1996:34–9 [5] Gao JM, Qian CX, Wang B, Morino K Experimental study on properties of polymer-modified cement mortars with silica fume Cement Concr Res 2002;32:41–5 [6] Ohama Yoshihiko Handbook of polymer-modified concrete and mortars Noyers Publications; 1995 [7] Bazant ZP, Najjar LJ Nonlinear water diffusion in nonsaturated concrete Mater Construct 1972;5(25):3–20 [8] Sakata Kenji A study on moisture diffusion in drying and drying shrinkage of concrete Cement Concr Res 1983;13:216–24 [9] Fujiwara Tadashi, Ishida Hiroshi, Sato Kaichiro, Konishi Toshiyori Influence of curing condition on diffusion and mix proportion on water movement within concrete Proc Jpn Concr Inst 1989;11(1):223–8 [10] Akita Hiroshi, Fujiwara Tadashi, Ozaka Yoshio Water movement within mortar due to drying and wetting J Jpn Soc Civil Eng 1990;13(420):61–9 [11] Takiguchi Katsuki, Hotta Hisato, Morita Shuhei A study on distribution of water in young cement mortar under drying condition J Struct Construct Eng: AIJ 1992;434:13–20 [12] Hashida Hiroshi, Tanaka Kyoji, Koike Michio Drying on moisture behavior in concrete substrate for finishing layers – Part J Struct Construct Eng: AIJ 1990;412:1–8 [13] Japan Concrete Institute Repair methods for the deteriorated concrete structure Japan Concrete Institute; 1994 [14] Emmons Peter H, Emmons Brandon W Concrete repair and maintenance illustrated: problem analysis, repair strategy Techniques R.S Means Company; 1994 [15] Asad M, Baluch MH, Al-Gadhib AH Drying shrinkage stresses in concrete patch repair systems Mag Concr Res 1997;49(181):283–93 447 [16] Granger L, Torrenti JM, Acker P Thoughts about drying shrinkage: experimental results and quantification of structural drying creep Mater Struct 1997;30:588–98 [17] Park Dongcheon Study on the relationship between moisture content and length change of PCM J Architect Inst Korea 2007;23(8): 131–8 [18] Matano Jpn J Phys 1932;8:109–13 [19] Crank J The mathematics of diffusion Oxford: Clarendon Press; 1975 [20] Kim Jin-Keun, Lee Chil-Sung Moisture diffusion of concrete considering self-desiccation at early ages Cement Concr Res 1999;29(12):1921–7 [21] Anderade C, Sarria J, Alonso C Relative humidity in the interior of concrete exposed to natural and artificial weathering Cement Concr Res 1999;29:1249–59 [22] Cappenter TA, Davies ES, Hall C, Hall LD, Hoff WD, Wilson MA Capillary water migration in rock: process and material properties examined by NMR imaging Mater Struct 1993;26:286–92 [23] Jo Young-Kug, Soh Yang-Seob A study on the water diffusion of polymer-modified mortars in drying process J Korea Concr Inst 1996;8(5):51–9 [24] Akita Hiroshi, Fujiwara Tadashi, Ozawa Yoshio An analytical method of moisture transfer within concrete due to drying J Jpn Soc Civil Eng 1994;23(490):101–10 [25] Powers TC, Brownyard TL Studies of the physical properties of hardened cement paste Research Department Bulletin, No 22, Portland Cement Association, Chicago; 1948 [26] Mihashi Hirozo, Numao Tatsuya Influence of curing condition on diffusion process of concrete at elevated temperature Proc Jpn Concr Inst 1989;11:229–34 [27] Yagawa Genki, Miyazaki Noriyuki Thermal stress, creep, and thermal conduction analysis by FEM Science Press; 1991 [28] Bazant ZP, Wittmann FH Creep and shrinkage in concrete structures John Wiley & Sons; 1982 [29] Fujihara Tadashi, Kayaba Masakazu, Akita Hiroshi Water movement within concrete due to drying under various temperature conditions JCA Proc Cement Concr 1992;46:428–33 [30] Architectural Institute of Japan Shrinkage cracking in reinforced concrete structures-mechanism and practice of crack control Architectural Institute of Japan; 2003 ... surrounding environmental conditions, the conditions of application, and the extent of deterioration To prevent cracks forming, prediction on the basis of preliminary experiments and simulation analysis... direction in this region The speed of stress mitigation by further drying varied, depending on the thickness of the repair region The thicker the region, the slower the stress generation by drying. .. Najjar LJ Nonlinear water diffusion in nonsaturated concrete Mater Construct 1972;5(25):3–20 [8] Sakata Kenji A study on moisture diffusion in drying and drying shrinkage of concrete Cement Concr Res