A unified rock damage constitutive model under different confining pressures

This study investigates the damage evolution characteristics throughout the complete deformation process of rocks. The analysis reveals five distinct stages in the stress–strain curves of rocks: elastic recovery, damage retention, damage initiation, damage acceleration, and damage slowdown. To simulate the stress–strain relationship of rocks, a damage model based on logistic equation is proposed. The model is developed using the “elastic modulus method,” derived from the hypothesis of strain equivalence, and experimental data obtained from complete stress–strain curves of marble and quartzite under various confining pressures. The proposed model effectively captures the brittle fracture deformation of rocks under uniaxial compression, as well as the strain softening, brittle–ductile transformation, and strain hardening deformation behaviors of rocks under different confining pressures. It adopts a simple function form with distinct parameters derived from physical characteristics, enabling the description of both pre-peak and post-peak deformation characteristics of rocks. The theoretical results obtained from the model align well with existing experimental findings. The physical significance of the model parameters is discussed in relation to damage evolution and constitutive relations, affirming the rationality of the proposed model. Overall, the proposed model exhibits significant potential for broad application in rock engineering.