Based on the Mohr-Coulomb failure criterion and the hypothesis of the rock micro-unit strength subject to Weibull random distribution, a new statistical damage constitutive model is established by introducing the pore water pressure by means of the effective stress theory. The new model can consider the influences of both pore volume change and damage threshold. In addition, a novel micro-unit strength calculation method for the rock is proposed. In order to make the model parameters have definite physical meaning, the model parameters m and F₀ are determined by using the peak point strength in the stress strain curve. In this study, the conventional triaxial compression tests for sandstone are conducted to verify the rationality of the model, by which the damage evolution and porosity variation of the rock under different confining pressures are analyzed, and the effects of confining pressures on the model parameters are explored. The findings show that the model can well reflect the relationship between triaxial stress and strain of the rock.