Keywords: diffusion model, damage, cementitious media.

Moisture diffusivity is the key physical parameter that is required for computation of moisture transport in cementitious materials. The transport coefficient is largely material specific, i.e. depends exclusively on material porosity, pore structure and moisture content. It is known that in the diffusion of gas through a catalyst, the diffusion paths are tortuous, irregularly shaped channels; accordingly, the flux becomes less than it would be in a uniform pore of the same length and mean radius. The effective coefficient of diffusivity in linear diffusion problems can be expressed in terms of a tortuosity parameter, , a factor that describes the relationship between the actual path-length relative to the nominal length of the porous media. In lieu of measuring the tortuosity, diffusivity may be established as a regressed function of the water-cement ratio for cementitious materials. However, inasmuch as the diffusion of moisture through concrete is now known to be a non-linear problem, the influence of moisture concentration level on the diffusivity has also to be considered. External influences like ambient temperature, humidity and wind speed are also believed to have an influence on the diffusivity coefficient and the convective surface transfer coefficient. Water transport processes are often accompanied by temperature variation. From the thermodynamic theory, it should be expected that the transport properties increase with the temperature. It is known that the modeling of stresses and damage associated with the restrained shrinkage of concrete cannot be established using constant values for the coefficient of diffusivity. The simulation of this problem can only be achieved by treating moisture diffusivity as a function of moisture concentration, which renders the boundary value problem non-linear. One feasible approach for this is to calibrate an assumed form for the coefficient of diffusivity in terms of unknown parameters of known functions of moisture concentration level, water-cement ratio and concrete temperature, using data from experiments and numerical results from a finite element driven program [1].

An user friendly model has been derived that can be used to design a concrete mix in terms of the water-cement ratio w/c for hot-weather conditions. Detailed equations for the model are presented using a 45-day threshold free shrinkage strain criterion s. The distinction between simulation of moisture diffusivity for unstressed material and that of structural in the latter case the diffusivity parameter has to be modified to include the accompanied damage. One form of diffusivity has been suggested yet it remains to ascertain the proposed functional form by calibrated with experimental results. Other forms of diffusivity-based damage could then be proposed.

1

Rahman, M.K., "Simulation and assessment of concrete repair system", PhD dissertation, King Fahd Univ. of Petroleum & Minerals, Dhahran, Saudi Arabia, 1999.

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