Statistical modelling of compressive strength controlled by porosity and pore size distribution for cementitious materials

The compressive strength of cementitious materials is significantly affected by its pore system inherent in the matrix of cement paste, not only porosity but also pore size distribution. In present work, by deconvolution analysis, the total pore size distribution of cement paste is represented by a multiple distribution consisting of two single distributions for the capillary pores and the macro pores respectively. In this way, the widely accepted Raleigh-Ritz (R-R) function is challenged and the lognormal distribution is found to be best to approximate the pore size distribution for cementitious materials. With pore size distributions, a statistical model based on probability principle and fracture criterion is proposed to reveal the physical mechanism of reduction in compressive strength induced by porous structures. Parameters in the model, e.g. fracture toughness of cement paste matrix, fracture mode, volume of specimen, porosity and pore size distributions, are further discussed and examined quantitatively.