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Concrete In Australia : December 2014
60 Concrete in Australia Vol 40 No 4 FEATURE: DURABILITY providing another constant, kCO2, is considered for the atmospheric exposure. Relating rCO2 to the amount of alkaline material able to bind CO2, it can be written as: DCO2 = kCO2 / ρef . rCO2 (7) Other parameters that need to be incorporated in the model are: • The ageing factor q and • The environmental factor k, which will be described in the following sections. 6.2 Service life model based on concrete resistivity The model proposed (Andrade, 2004) is based on measuring electrical resistivity as the main parameter for determining both ti and tp periods. In order to predict the corrosion onset it is necessary to have an equation in which the resistivity could be the rate determining parameter as a function of time. Considering the depassivation instant as a limit state (ti), the simple equation “square root of time” is used for estimating the penetration of the contamination front and time xi = VCO2,Cl.√t. The factor relating V represents the ease or velocity of penetration, VCl,CO2, then, t i = x2/VCO2, Cl. For corrosion propagation time(tp), taking into account the loss in rebar diameter, or pit depth, (Px) as the limit for corrosion attack, the structure service life can be assessed by the expression: t1=t i +tp=x i 2/VCO2,Cl+Px/Vcorr (8) Calculation of the initiation period How to relate VCl,CO2 to the resistivity? This can be made through another of Einstein’s equations which explains the random walk of an ion in an electrolyte, x i = √(D.t) which indicates that VCl,CO2 = √D. Rearranging this expression it gives the initiation period i.e: ti=xi 2·ρ app/2·FCl,CO2= xi 2·ρ es · rCl,CO2 / 2 · FCl,CO2 (9) The reaction factor r The reaction factors rCl and rCO2 (Andrade et al, 2012) depend on the type and amount of cement and therefore on the reaction of the penetrating substance with the cement phases. They can be calculated either by direct measurement, or indirectly by measuring the relation between the effective and apparent diffusion coefficients, or by calculation based on the cement composition. Table 2 presents examples of rCl values that were calculated based on test results obtained with the multi-regime chloride test (Castellote et al., 2001). Table 2: Examples of values of the reaction factor of chlorides, rCl, for 3 types of cement. Cement rCP Standard Deviation CEM I t1.9 1.3 CEM I + silica fume 1.5 0.5 CEM IIA (with pozzolan and fly ash, in ≤ 20%) 3.0 2.1 The environmental factor k The environmental factors kCl and kCO2 depend on the exposure conditions. Table 3 presents values that were calculated by inverse analysis of test results obtained on real structures. Table 3: Values of environmental factors kCl and kCO2 for exposure classifications of EN206. Exposure class k(cm3Ω/year) X0 200 XC1 1000 XC3 3000 XS1 (d > 500 m distance to the coast line) 5000 XS1 (d < 500 m distance to the coast line) 10000 XS2 17000 XS3 25000 Ageing factor q The apparent resistivity evolves with time due to the progression of hydration, the combination of the cement phases with the chlorides or carbon dioxide which usually decreases the porosity and by the concrete drying out (depending on the environment). All of these aspects are accounted for by the introduction of an “ageing” factor q to give an increase in resistivity with time. If the inverse of resistivity is plotted as a function of time (figure 7), the apparent evolution of resistivity can be expressed by a function in which the power exponent q is the slope of the straight line. This may have different values for OPC and blended cements (Andrade et al., 2011): Figure 6: Relation between resistivity and diffusivity as calculated from Einstein law. 57-64 - Andrade.indd 60 57-64 - Andrade.indd 60 21/10/14 2:22 PM 21/10/14 2:22 PM