A novel statistical damage constitutive model of rock joints considering normal stress and joint roughness

Abstract

The shear constitutive model of rock joints is of great significance to the stability analysis in rock engineering, and it is closely related to the normal stress ( ${\sigma }_n$ ) and joint roughness coefficient (JRC). However, the existing investigations seldom consider the influences of ${\sigma }_n$ and JRC simultaneously. Therefore, a novel damage constitutive model considering the ${\sigma }_n$ and JRC is developed in this work. In the presented model, it is assumed that the rock materials are composed of damaged and undamaged microunits, and the damage evolution law of the microunits conforms to the Weibull distribution in the shear process. Based on the proposed assumption, the constitutive relationship between shear stress and shear displacement is deduced. The evolutions of the mechanical parameters and damage variable versus ${\sigma }_n$ and JRC are analyzed in detail. The proposed damage model that involves ${\sigma }_n$ and JRC is verified by comparing theoretical values with the laboratory results. The results show that the damage constitutive model is in good agreement with the test results. Additionally, the influences of ${\sigma }_n$ and JRC on the shear stress-displacement curves are studied. This work can provide a valuable theoretical method for analyzing the shear mechanical characteristics and damage evolution laws of rock joints.