6 AN ORIGINAL METHOD TO DETERMINE THE NON LINEAR CHLORIDE BINDING ISOTHERM FROM BULK SPECIMENS OF MORTAR

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1 6 AN ORIGINAL METHOD TO DETERMINE THE NON LINEAR CHLORIDE BINDING ISOTHERM FROM BULK SPECIMENS OF MORTAR J.P. BIGAS1, F. LAMBERT2, J.P. OLLIVIER3 ' LMSC, Cergy Pontoise, France DESD SCCD, CEA, Cadarache, St Paul lez Durance, France LMDC, INSA-UPS GCnie Civil, Toulouse, France Abstract The calculation of chloride transport coefficient of a concrete structure can be carried out from the measurement of the effective diffusion coefficient and from the determination of the non linear binding isotherm between chloride and concrete. We propose a new approach of modeling the binding process as a Freundlich isotherm, by the calculation of its equation from several traditionnal diffusion tests in steady state conditions. The advantage of our method, contrary to classical experimental techniques in which the binding isotherms are obtained from crushed specimens, is the access to the non linear binding isotherm equation for the real microstructure of concrete in service. Then, it could be possible to study the influence of the microstructure on the binding of chloride ions. Keywords : Chloride diffusion, Binding isotherms, Modelling. l - Introduction To evaluate the service life of concrete structure exposed to marine environnment, it will be important to predict the penetration of chloride ions into concrete. The Fick's second law gives the chloride concentration C as a function of the distance X from the exposed surface and as a function of the time t, assuming a constant D, intrinsic chloride diffusion coefficient in a semi infinite porous medium : 43

2 Equation (1) is valid only if there is no interaction between chloride and solid phases. In fact, when binding process (chemical and physical) occurs, the chloride penetration is slower. Then, the determination of D should be reduced to : 1. the measurement of the effective diffusion coefficient De, 2. the quantification of the binding process. The differential equation describing the migration of chloride into concrete [l] should be written as (2) : Dz De with D, = a = - defined as the apparent diffusion coefficient, taking into account the a binding phenomenon between the liquid phase and the solid phase [2][3]. The capacity factor a is expressed as a = z + (1-7) p, Kd. Assuming an instantaneous exchange driven by a linear binding isotherm, Kd is the binding capacity as C, = K, C with C, as bound chloride, z as concrete porosity and p, its density. In fact, the apparent diffusion coefficient D, which takes into account chloride binding, is not a constant because the binding isotherm is non linear. Classical determinations [4] of binding isotherm are done on crushed materials, neglecting the real microstructure of the concrete, particularly the microcracks: Our original approach [6][7], which takes into account the bulk microstructure of the material, is based on the data obtained with classical diffusion tests. 2 - Materials and methods These tests were realized on mortar samples (Table 1). The 28 day characteritics for the mortar cured in water at 20 C are : compressive strength = 40 MPa, density p,= kglm, water porosity z, = 0.16 and mercury porosity z = Table 1. Mix proportions. materials CPA CEM I 519 kg/m3 Siliceous sand ( mm) 1067 kg/m3 Siliceous sand ( mm) 457 kg/m3 Water 255 l/m3 After curing, slices were removed from 11*22 cm cylinders and placed in diffusion cells. The diffusion area is m2, and the volume of both compartment of these cells is m3. Each cell was filled with an alcaline solution of KOH (4.65 kg/m3) + NaOH ( l kg/m3) at ph

3 Different concentration gradients (Table 2) are obtained using different initial concentrations CO of chloride and using different thicknesses of slices. Table 2. Experimental program. The X sign indicates the tested variables. The downstream solution was removed at regular term (twice a month) to maintain the C = 0 condition at X = L. At each term the chloride content was determined by potentiometric method. 3 Modelling For linear binding, the resolution of Fick's second law, shows an asymptotic increase of the quantities of diffused chloride with time when steady state dccurs (Fig 1). The time al2 lag ti, is defined as the abscissa of the intercept of the asymptot [I] : ti = e D,, is assumed to be independant of CO, and calculated from the slope of the asymptot. Without binding, the capacity factor a is represented by the porosity and the time lag is: L216D ti Time Fig 1 : diffusion curves : WB diffusion without binding, LB diffusion with linear binding, NLB diffusion with non linear binding 45

4 The steady state regime, characterized by a linear concentration profile in the liquid phase between the upstream and the downsteam cells, is independant of the non linearity or linearity of the isotherm. In case of non linear binding, we can write : where aeq is the equivalent capacity factor of the diffusion with linear binding which has the same asvmptotic flow as the diffusion with non linear binding. The abscissa of the intercept of the asymptot is : where Kdeq is the equivalent binding capacity of the equivalent linear isotherm. Definition of an equivalent linear isotherm and an equivalent cauacitv factor Let us assume that the non linear binding is described by a Freundlich isotherm CS = a CY with 0 5 y I 1. The basis of our modelling is to make the non linear Freundlich binding isotherm similar to an equivalent linear isotherm. The equivalent linear isotherm, associated to aeq, is defined as the one, which gives at CJ2, the same bound chloride concentration as the non linear isotherm (fig 2). Fig.2 : Chloride binding isotherms : Curve 1 is the equivalent linear isotherm and curve 2 is the Freunlich isotherm. 46

5 4 Experimental results For each diffusion test drived for a given concentration or a given thickness, we obtain the data for ti, D, and aeq (Table 3) by a graphic determination from the diffusion curves. Table 3. Experimental data for ti, D, and aeq CO L ti (d) De aeq (kg/m3) m2) experimental experimental (10-12 m2/s) l On the basis of these experimental results, we make a numerical simulation [7] resolving the Fick's second law in the case of binding drived by an equivalent linear isotherm (in this case y = l). Then we obtain the corrected values of D, and aeq Also the decrease in the concentration in the upstream cells can be calculated for a given term (Table 4). Table 4. Adjusted data obtained by numerical simulation with the equivalent linear isotherm. L De : (10-2 m) corected values ( m2/s> a equivalent: corrected values Two main observations should be made : Firstly. the effective diffusion coefficient is a function of the chloride concentration and secondly. the equivalent capacity factor is a function of the chloride concentration. 47

6 5- Determination of The Freundlich isotherm parameters The definition of the equivalent linear isotherm specify that the retention rates are the same for Cd2 considering linear or Freundlich isotherm. So we can write : CO c, y Kdeq (g = a (5-1 then and : 1st RILEM workshop on Chloride Penetration into Concrete CO y-l aeq=z+(1-z) PS a (y) Based on experiments, each diffusion test give us several couples of data (Co; aeq) and from the equation (7) the equivalent capacity factor % can be considered as a CO y-l linear function of (T). A linear regression procedure is then carried out to determine the Freundlich parameters y and a. In this procedure y is considered as a parameter varying from 0 to 1. Fig 3: Standard deviation on Cteq VS Y. c, Y-l Fig 4: aeq VS (y) for y = CO y-l Experimentals data of aeq are plotted (fig 4) as a function of (y) and for each value of y, we determine the regression straight line and the standard deviation. The value of y chosen is the one which gives us the minimum standard deviation (fig 3) associated to a realistic value of the porosity. Next it is then possible to determine the porosity z and the coefficient << a >> of the Freundlich equation calculated from the slope [(l - z) p, a] of the regression straight line. From our experimental studies, we obtain a minimum standard deviation and a porosity value of 0,14 for y = The straight line equation is : 48

7 So, we get a = For our mortar, the non linear isotherm equation expressed as a Freunlich isotherm is : 6 Conclusion Seven classical chloride diffusion tests on mortar made with CPA-CEM have shown the dependance between the chloride concentration C, in the upstream cell and the quantity of chloride bound by the solid phase. The non linearity of chloride binding for the bulk material could be expressed by a Freundlich isotherm. A method based on equivalent linear isotherms has been presented. 7 References 1. Cranck, J. "The Mathematics of diffusion", 2nd edition (Clarendon Oxford, 1975). 2. Massat, M., Nilsson, L.O. and Ollivier, J.P., " A clarification of the fundarnmental relationships concerning ion diffusion in porous materials " 3rd MRS Colloquium (1992) 3. Atkinson, A. and Nickerson, A.K., "The diffusion of ions through water-saturated cement " Journal of Materials Science 18 (1984) Tang, L. and Nilsson, L.O., "Chloride binding capacity and binding isotherms of OPC pastes and mortars" Cement and Concerte Research 23 (1993) Bigas, J.P, " La diffusion des ions chlore dans les mortiers" PhD thesis, Toulouse (1994). 6. Bigas, J.P, Lambert, F. and Ollivier, J.P, " ModClisation globale des interactions physicochimiques rcgies par des isothermes non 1inCaires entre ions chlore et mortier de ciment Portland " Materials and structure (to be published). 7. Lambert, F., PhD thesis, USTL Montpellier (1977). 49

CONCEPTS ON THE CHLORIDE DIFFUSION COEFFICIENT

CONCEPTS ON THE CHLORIDE DIFFUSION COEFFICIENT C. Andrade Institute of Construction Science Eduardo Torroja, CSIC, Madrid, Spain Abstract Diffusion coefficient D, is considered the rate determining parameter