A Statistical Damage Model for Rocks Considering Nonlinear Strength Characteristics

To investigate the mechanical behavior and damage evolution of rock masses under high stress in deep environments,triaxial compression tests were conducted on sandstone under varying confining pressures to study its deformation strength characteristics and macro-micro failure modes.The results indicate that under triaxial compression conditions,stress-strain curves of sandstone exhibit initial hardening followed by softening.As the confining pressure increases,the post-peak strain softening of sandstone gradually weakens,and the failure mode changes from brittle single shear failure to ductile plastic deformation,demonstrating distinct brittle-ductile transition characteristics.To address the limitation of the linear Mohr-Coulomb criterion,which significantly overestimates rock strength under high stress condition,a modified strength criterion was established by introducing a stress error term,accurately reflecting the nonlinear growth patterns of peak and residual strength with confining pressure.Combining statistical damage mechanics,a statistical damage model based on the nonlinear strength criterion was developed.The model’s prediction curve aligns with experimental data,demonstrating its ability to accurately describe the nonlinear damage evolution process of rocks under deep high-stress conditions,providing theoretical support for the stability analysis of deep underground engineering.