A three-dimensional statistical damage model for rock-like materials based on principal stress action

• A novel three-dimensional statistical damage constitutive model for rock-like materials is developed. • The proposed model effectively captures the behavior of rocks during both strain hardening and strain softening phases. • The proposed model can predict the peak and residual strengths at varying confining pressures through the deviatoric stress growth curve. • The parameter θ serves as an indicator of material brittleness or ductility, while parameter k reflects the strength characteristics of the material. Principal stress plays a critical role in the deformation and failure process of rock or rock-like materials. However, existing studies indicate that the construction of a damage model based on principal stresses for describing the entire process of three-dimensional rock fracturing is subject to certain limitations and inadequacies. In this study, an innovative three-dimensional statistical damage constitutive model is developed by integrating the principal stress effect with the Gamma distribution function. This model effectively captures the complete damage evolution process of rock materials with initial defects through the introduction of a compaction correction coefficient and a residual strength correction term. Notably, the simulation accuracy is significantly enhanced in both the initial compaction stage and the post-peak residual strength stage. The parameter θ serves as an indicator of the material brittle-to-ductile transition, whereas the parameter k reflects the material’s strength characteristics. The parameter calibration process consists of three steps: determining the θ value on the basis of the rock brittleness index, deriving the k parameter from the k value growth curve, and finally establishing the peak-residual strength prediction equation under given confining pressure conditions. Compared with the traditional statistical damage model based on the Weibull distribution, this model not only features clear physical significance and a simplified calculation procedure but also contributes to the advancement of the three-dimensional damage fracture theory system for rock mechanics. Moreover, it offers a robust framework for evaluating the mechanical response of rocks under varying confining pressures, which has significant implications for safe design and risk assessment in civil engineering or rock engineering.