Analytic modelling and experimental study of the porosity and permeability of a porous medium—application to cement mortars and granitic rock

In this work an analytic relationship between the permeability and porosity of a porous material is developed. This modelling is based on the use of a statistical pore size distribution, which is first used to establish an analytic expression for the porosity in relation to an average pore radius and a location parameter. Two types of measurement were performed on three cement mortars and a granitic rock: mercury intrusion porosimetry measurements so as to adjust parameters of the distribution law and deduce the ‘theoretical’ permeability from the model, and direct water permeability measurements by the application of the Darcy law so as to validate the analytic model. Globally, the ‘experimental’ permeabilities obtained were inferior to those calculated. The main explanation for these differences may be in the fact that in the calculation of the permeability, all types of pores are taken into account, and not only ‘open’ pores which are the only ones responsible for the flow in porous materials.