Mechanical characteristics and constitutive modeling of unloading-damaged sandstone under coupled pore water-confining pressure effects

Abstract The surrounding rock of hydraulic tunnels, which has experienced unloading-induced damage, is highly prone to engineering failures such as large tunnel deformation and sudden water inrush under high pore water pressure. Using a triaxial rheological testing system, triaxial reloading tests were conducted on damaged sandstone under three confining pressures and four pore water pressures to acquire complete stress–strain curves and mechanical parameters. With particular attention to the compaction stage, a piecewise statistical damage constitutive model was established based on the Weibull distribution and the Drucker-Prager criterion, considering the coupled effects of pore water pressure and confining pressure. The results indicate that: (1) Under varying conditions, the stress at the end of the compaction stage of unloading-damaged sandstone generally remains around 30 MPa, whereas the corresponding axial strain increases with pore water pressure but decreases with confining pressure. (2) The peak strength of unloading-damaged sandstone decreases exponentially with increasing pore water pressure, and the elastic modulus exhibits a sensitivity to pore water pressure that is 1.63 times greater than that to confining pressure. Pore water pressure has a significantly greater detrimental impact on the mechanical properties. (3) The constructed segmented statistical damage constitutive model effectively captures the nonlinear mechanical response characteristics of sandstone under unloading damage conditions, influenced by the coupled effects of pore water pressure and confining pressure. The theoretical curve shows excellent agreement with the experimental results, thereby validating the accuracy and rationality of the proposed model. (4) The sensitivity of the Weibull distribution parameters m 2 and F 02 of the non-compacted section to pore water pressure is 1.75 and 1.49 times greater, respectively, than that to confining pressure. The results indicate that pore water pressure is the primary factor influencing the strength of micro-elements and triggering the transition of rock samples towards brittle failure modes. The research findings can serve as a valuable reference for the stability analysis and prediction of damage evolution in hydraulic tunnels subjected to excavation disturbance and pore water pressure effects.