Comparative Analysis of Rock Damage Models Based on Different Distribution Functions

The mechanical behaviors and constitutive relationships of rocks in failure process have always been the hot issues in the field of geotechnical engineering. According to the characteristics of random distribution of rock micro-element strength, based on Weibull distribution function, the improved Harris distribution function, power function and composite power function, the evolution equations of rock damage under different distribution functions were derived, and the statistical constitutive models of rock damage in the form of axial deviatoric stress–strain curve were established by combining rock damage theory and statistical strength theory. The validity comparison and analysis of these models were then implemented underpinned by traditional triaxial experimental data of sandstone in reported literature. Primarily, the theoretical curves of four damage models are all in good agreement with the experimental finding in the pre-peak stage. The curve originated from the power function model failed to describe the strain softening characteristic in the post-peak stage, and a sharp drop could be observed, while the others presented a better consistency with the data to a certain extent. Wherein, similar matching effect of curves to data based on the Weibull distribution function and the composite power function was discovered.