Damage constitutive model of rock and application based on strength theory

Abstract

Extending the one-dimensional damage constitutive model of rock materials to three dimensions using classical methods fails to capture the significant differences in tensile, compressive, and shear strengths exhibited by the rock materials. Consequently, it is necessary to revise the existing damage constitutive model to describe the damage evolution law and constitutive relationship of rock materials more accurately and provide a theoretical basis for the safety and stability analysis of underground engineering more scientifically, thus ensuring the sustainable development of underground engineering. By introducing the Weibull distribution function and building upon strength theory, a correction function was established. This correction function adjusted the equivalent strain, enabling the development of a three-dimensional damage constitutive model that accounted for the varying tensile, compressive, and shear strengths of rock materials. The impact of various parameters on the model's fitting effectiveness was evaluated, and a comparative analysis was conducted against pertinent experimental results. Using the theory of neutral axis deviation, the relationship between bending moment and damage variables in a purely bending rock beam was derived. The study revealed that all parameters of the damage constitutive model could be derived from the uniaxial stress-strain curve, and its theoretical findings exhibited strong agreement with experimental results obtained from rock and rock-like materials under uniaxial tension, compression, and triaxial compression. Based on the examined cases, it was concluded that, when considering both tensile and compressive damage, the ultimate bending moment of a rock beam was approximately one-third of its elastic limit bending moment in an undamaged state. The results have verified the feasibility of the damage constitutive model.