Comparative study on three-dimensional conventional and modified statistical damage constitutive models

Abstract

Considering the random distribution of the microscopic unit strength of rock, lognormal distribution in the past was widely used as the distribution function of the strength of the rock. Based on rock damage theory and statistical strength theory, a traditional damage constitutive model and a modified damage constitutive model in this paper are established. Then, we carry out traditional triaxial compression experiment to validate and compare these two damage constitutive models. These results show that: (1) in the elastic stage of rock deformation, these two theoretical damage constitutive model curves are in good agreement with their experimental curves; (2) in the plastic stage of rock deformation (yield and strain softening), the fitting effect of damage constitutive model with residual strength is better than that of traditional damage constitutive model. Moreover, compared with the traditional damage constitutive model, the modified damage constitutive model can better describe the transition process from brittleness to ductility with the increasing confining pressure. Finally, by comparing the damage variable D of the two damage constitutive models, we can find that the damage variable D of the modified model is closer to actual damage degree of rock, which can better reflect the damage condition of rock during loading. Therefore, the modified damage constitutive model can better describe the deformation of rock under loading and has better rationality.