DIFFUSION OF CHLORIDE IONS IN CEMENT-BASED MATERIAL

Transcription

1 DIFFUSION OF CHORIDE IONS IN CEMENT-BASED MATERIA Toshiki Ayano (1), Kazuyoshi Hosotani (), Kentaro Yamamoto (3) and Kenji Sakata (4) (1) Graduate School of Environmental Science, Okayama University, Okayama, Japan () Technical Research Institute, AISAWA Construction, Okayama, Japan (3) The Graduate School of Environmental Science, Okayama University, Okayama, Japan (4) Graduate School of Environmental Science, Okayama University, Japan Abstract In this study, the method to experimentally obtain the diffusion coefficient of chloride ions is proposed. The study focuses on the surface chloride ions and the intruding chloride ions from external. The diffusion coefficient and the film coefficient are required in analyzing the diffusion equation by numerical analysis, such as FEM. The chloride ion distribution calculated by FEM with the diffusion coefficient obtained by the proposed method was compared with the experiment data. The verification of the proposed method was confirmed by the comparison. 1. INTRODUCTION In the prediction of deterioration of the concrete structures, chloride ion is one of the important factors. Therefore, in the design for new concrete structures and the maintenance for the existing structures, the various methods in order simply and accurately to calculate the chloride ion distribution were proposed. [1, ]. The chloride ion distribution can be calculated by the diffusion equation. The diffusion equation is applied to the broad fields. Not only chloride ions but also moisture, heat, and so on are simulated by the diffusion equation. [3, 4]. However, it may be difficult for all engineers to obtain the chloride ion content by using FEM. So, in some specifications or design code, the simplified method has been proposed. For example, in Japanese Standard (Standard Specifications for Concrete Structures), Fick s second low has been adopted. In either simplified method or numerical method such as FEM, accurate diffusion coefficient is required to obtain the results. In this study, the method to obtain the diffusion coefficient experimentally is proposed. In order to confirm the verification of the proposed method, the chloride ion distribution in concrete and mortar were obtained in several chloride ion concentration solutions. They were compared with the simulation results by FEM.

2 Table 1: Mixture proportions of concrete Max Unit weight per volume Slump W/C Air s/a size (kg/m 3 ) Admix1. Admix. (cm) (%) (%) (%) (C %) (C %) (mm) W C S G 1~ ± Admix1: High-range water reducing admixture,admix: Air-entraining admixture. OUTINE OF THE EXPERIMENT.1 Mixture proportions and specimens Table 1 shows the mixture proportions of concrete used in this study. Table shows the mixture proportions of mortar. Table 3 shows the properties of used materials. The specimens used in this study were cylinder of φ1 15 mm and thin specimen of mm. Cylinder specimen was used for obtaining the chloride ion distribution. Thin specimen was used for obtaining the saturated chloride ion content in the mortar or concrete. The cylinder of φ 1 mm specimens were cured in the molds for 4 hours. Then, the specimens were cured in steam (the speed of rising temperature: /hour, maximum temperature: 6, holding time of maximum temperature: 4 hour). After the mold was removed, the specimen was cut at 5 mm from both top and bottom surfaces. As chloride ion was penetrated from top surface, the side and bottom surfaces had been sealed by the epoxy resin as shown in Figure 1. After the epoxy resin hardened, the specimens were cured in water of 4 for 7 days.. Chloride concentration The specimens of mortar were soaked in 3.5 % and 1 % Cl - solution. The specimens of concrete were soaked in 1 % Cl - solution. The chloride ion content distribution of each specimen was obtained at the time of 7, 14, 8, 56, 7, and 91 days after the start of soaking. In this study, nitric acid-soluble Table : Mixture proportion of mortar W/C Unit weight per volume (kg/m 3 ) (%) W C S Table 3: Property of materials Material Portland cement Fine aggregate Coarse aggregate Property Density: 3.15g/cm 3 Specific surface area: 3,cm /g River sand,density:.59g/cm 3 Water absorption:.1%,f.m.:.41 Crushed stone,density:.74g/cm 3 Water absorption:.58%,f.m.: 6.71 HRWRA Polycarboxylate type F.M.: Fineness modulus HRWRA: High-range water reducing agent Figure 1: Condition of intrusion of chloride ion

3 chloride ion was obtained. Nitric acid-soluble chloride ion was obtained by the optical absorbance method defined by JIS A Saturated chloride ion content was obtained by using thin specimen whose dimension was mm. At the time of 3, 7, 1, 14, 1 and 8 days after the start of soaking, chloride ion content was obtained. By regression of the change of chloride ion content with time, the saturated chloride content that is chloride content at ultimate soaking time was obtained. 3. THE PROPOSED METHOD TO OBTAIN DIFFUSION COEFFICIENT 3.1 Introduction of algebraic equation Equation (1) is the diffusion equation in one dimension. C( C( = D (1) where, C( is the chloride ion content; D is the diffusion coefficient; and x and t are distance in the direction of specimen thickness and soaking time, respectively. Equation (1) must be satisfied everywhere in the specimen. Equation () holds with respect to an arbitrary function F(. C( C( F( D = dx () Where, is the distance between top surface and the bottom surface, that is, 15mm. By means of partial integration, the first term of equation () can be rewritten as follows: C( C( F( C( D F( dx = F x t D D dx x (, ) (3) Substituting equation (3) into equation () leads to equation (4): C( F( dx = F( D Ct ( ) F( D Ct ( ) dx (4) where, F( D Ct ( ) = F(, D C(, F(, D C(, (5) From the boundary conditions, equations (6) and (7) are derived. C,t q( = D (6) (, ( ) C = (7) where, q( is the chloride ion content which passes through unit soaking surface area per unit time. Taking the boundary conditions expressed by equations (6) and (7) into consideration, and choosing C( for the arbitrary function F(, equation (4) can be rewritten as equation (8):

4 ( ) ( ) C t D dx = C(, q( Ct ( ) Ct dx (8) D can be obtained by equation (9). ( ) C(, q( Ct ( ) Ct D = C( dx dx Equation (9) is the proposed equation by authors. When C(,, q(, C(, C( x / C( x /, and, are known, the diffusion coefficient D can be obtained algebraically. Where, C(, is the chloride ion content at the surface at time t. q( is the chloride ion content which passes through unit soaking surface area per unit time. C( is the chloride ion content at the position x at time t. C( / is the change of chloride ion content at the position x with time. C( / is the change of chloride 4. ion content at time t with the direction x. 3. Time differential of chloride ion content at arbitrary position and chloride ion content at the soaking surface Figure shows the chloride ion content of the mortar specimens soaked in 1 % Cl - solution. The dimension of the specimen is shown in Figure 1. Chloride ion content at arbitrary position ultimately reaches the saturated value. The change of chloride ion content at arbitrary position was calculated by equation (1). C a in equation (1) is the ultimate chloride ion content which was obtained by using the thin specimen of mm. a x is the coefficient to express the speed of increasing chloride content at the position x. Each coefficient a x was obtained by regression. The curves shown in Figure are the regression curves by equation (1). Ca t C( = (1) a + t x Mortar soaking in 1% Cl - solution 1.5mm Distance from surface :.5mm Dotted line : Calculated value at surface 18.5mm days Figure : Chloride ion distribution of mortar specimen Specimen size: 45x45x5mm : Mortar soaking in 1% Cl - solution 1. : Concrete soaking in 1% Cl - solution : Mortar soaking in 3.5% Cl - solution days Figure 3: Chloride ion in the thin specimen (9)

5 Equation (1) is used to obtain the change of 4. chloride ion content at the position x with time C( / in equation (9). 3. Figure 3 shows the change of chloride ion content in the thin specimens whose size is mm., and in this figure are the experimental data of mortar soaked in 1. 1 % Cl - solution, those of mortar in 3.5 % Cl - solution and those of concrete in 1 % Cl - solution, respectively. These curves are the regressed hyperbolic curves in Figure 3. Chloride ion content intruded in the specimen seems to reach ultimate value. Therefore, hyperbolic curve by equation (11) was chosen to express the change of chloride ion content with lapse of time. Ca t Cthin ( = α + t Mortar soaking in 1% Cl - solution : 7days : 14days : 8days : 73.5days : 91days Figure 4: Nitric acid-soluble chloride ion distribution of mortar in 1% Cl - solution where, C thin ( is chloride ion content (kg/m 3 ) contained in the thin specimen at soaking time t. C a is the ultimate chloride ion content in the specimen. It is used in equation (1). Using the ultimate chloride ion content obtained from the thin specimen C a, the change of chloride ion content with time was regressed at each position as shown in Figure. Function a(x) was determined by using the coefficients a x obtained at each position. From function a(x), the change of chloride ion content at the soaking surface C(, in equation (9) was obtained, that is, zero was input to x. The dotted curve in figure 4 shows the calculated chloride ion content at the surface. 3.3 Chloride ion distribution Figure 4 shows the chloride ion distribution of the mortar specimen soaked in 1 % Cl - solution. Chloride ion distribution was regressed by equation (1). C ( x = C(, { 1 erf ( β x) }, (1) where, C(, is the chloride ion content at the surface expressed by the dotted curve in figure. β is an undecided coefficient determined by regression. x is the distance from the surface. erf(s) is error function expressed by equation (13). erf (s) = s e η dη (13) π In order to obtain the diffusion coefficient D in equation (9), equation (1) was used to C t / that is the change of chloride ion content at time t with the direction x. obtain ( ) x 3.4 Chloride ion content passing through unit soaking surface area per unit time Figure 5 shows the relationship between soaking time and the total chloride ion Q( in the specimen., and in this figure are total chloride ion content of mortar specimen soaked in 1 % Cl - solution, that of mortar specimen in 3.5 % Cl - solution and that of concrete (11)

6 specimen in 1 % Cl - solution, respectively. Total chloride ion content Q( was regressed by equation (14). Q ( = α{ log( β + log( β )} (14) where, α and β are the coefficients determined by regression. The chloride ion content past through the unit surface per unit time equals to the time differentiation of the total chloride ion content Q(. α q( = (15) β + t Equation (15) is used for q( in equation (9). 3.4 Diffusion coefficient obtained by the proposed method and in Figure 6 is the denominator and the numerator of equation (9), respectively. In order to obtain these values, equation (1) was used to obtain C( /. Equation (1) was used to obtain C( /. Equation (15) is used for q(. The experimental data of chloride ion content at position x at time t is used for C( in equation (9). The change of each value has the same tendency. The ratio of the value shown by to that shown by is almost same at each soaking time. The diffusion coefficient was calculated from the ratio of the time integration of the numerator to that of the denominator of equation (16). The integral range of the analytical object is from 7 days to 91 days after the start of soaking. 91 C(, q( Ct ( ) Ct ( ) dx dt 7 D = 91 C( dxdt 7 (16) 4. FIM COEFFICIENT The film coefficient H F can be expressed by equation (17) if the relationship between Total chloride ion content - kg/m 3 mm : Mortar soaking in 1% Cl - solution : Concrete soaking in 1% Cl - solution 1 : Mortar soaking in 3.5% Cl - solution days Figure 5: Total chloride ion in concrete specimen The denominator and the numerator of equation (9) Mortar specimen soaking in 1% Cl - solution : the numerator : the denominator days Figure 6: Denominator and numerator of equation (9) Chloride ion content through unit area per unit time - kg/m 3 mm/day Mortar soaking in 1% Cl - solution Mortar soaking in 3.5% Cl - solution Concrete soaking in 1% Cl - solution Chloride ion differential between ultimate and arbitrary time - kg/m 3 Figure 7: Film coefficient for FEM analysis

7 Table 4: Parameters for analysis obtained by the proposed method Deterioration Diffusion coefficient Film coefficient (mm /day) (mm/day) Mortar soaking in 3.5% Cl - solution Mortar soaking in 1% Cl - solution Concrete soaking in 1% Cl - solution q( obtained from equation (15) and (C a -C(,) shown in section 3. is liner. Film coefficient is necessary for FEM analysis to express the boundary condition. q( H F = (17) C C ( a surface where, C a is saturated chloride ion content (kg/m 3 ). C(, is chloride ion content at surface (kg/m 3 ). Figure 7 shows the relationship between q( and C a -C(,. As is clear from this figure, The relationship between q( and C a - C(, is linear. Film coefficient is the slope. of this line. 5. VERIFICATION OF THE PROPOSED METHOD Table 4 shows the diffusion and the film coefficients obtained by the proposed method. Figure 8, Figure 9 and Figure 1 show the chloride ion distributions of the mortar specimen in 1% Cl - solution, those of the mortar specimen in 3.5% Cl - solution and those of the concrete specimen in 1 % Cl - solution, respectively. The curves in these figures are calculated data by FEM with the diffusion and film coefficients shown in Table 4. The calculated data fit with the experimental data well, and demonstrate the verification of the proposed method. The chloride ion distributions of the concrete specimens in 1% Cl - solution at 133 days and 414 days are shown in Figure 11. The diffusion coefficient was obtained from the test result by 91 days after the start of soaking. It is shown in table 4. As is clear from this figure, the calculated value at 133 and 414 days after the start of soaking fit with the experimental data well Mortar soaking in 3.5% Cl - solution : 7days : 14days : 8days : 56days : 7days : 91days Figure 8: Comparison between experimental data and calculated data Mortar soaking in 1% Cl - solution : 7days : 14days : 8days : 7days : 77days : 91days Figure 9: Comparison between experimental data and calculated data

8 6. CONCUSIONS In this study, an experimental approach is proposed to obtain the diffusion coefficient of chloride ion of cement-based material. The chloride ion distribution at an arbitrary time was calculated by FEM with the diffusion and the film coefficients obtain by the proposed method. It has been confirmed that the calculated chloride ion distribution at an arbitrary time fit with the experimental data well, which demonstrates the verification and the applicability of the proposed method Concrete soaking in 1% Cl - solution : 7days : 14days : 8days : 56days : 7days : 91days Figure 1: Comparison between experimental data and simulation REFERENCES [1] K. Wakatake, H. Hamada, T. Noguchi, T. Shimomura and A. Yamaguchi, A Study on Environmental Conditions Affecting ongterm Deterioration of Concrete Structure in Japan, JCI Proceedings 6 (1) 7-36 (4) (in Japanese) [] Y. Hosokawa, K. Kazuo, M. Takami, T. Sugiyama, Study on diffusion coefficient of chloride ions evaluated by migration and submergence in salt water, Japan Society of Civil Engineers 5 (1) (3) (in Japanese) [3] T. Ayano K. Sakata and F. H. Wittmann, Moisture distribution, Diffusion Coefficient : 414days : 133days : 91days Figure 11: Prediction of chloride ion distribution at the soaking time 414 days and Shrinkage of Cement-Based Materials, JSCE 45 (634) (1999) [4] O. Kuramoto, Study on calculation of crack due to drying shrinkage strain in high strength concrete, Okayama university doctoral thesis, 3 (in Japanese)