Statistical damage constitutive model considering water-weakening effect based on the Hoek-Brown criterion

The water-weakening effect is a significant cause of large deformations and damage in rock engineering. In order to accurately describe the stress-strain relationship during the rock damage process, a constitutive model based on statistical distribution has proven to be effective. However, most rock microelements strength is characterized by the Drucker-Prager or Mohr-Coulomb criterion, which fails to account for the influence of the damage threshold on the rock damage metric and presents inconsistencies in the linear stress-strain relationship at low stresses. To address these shortcomings, this study proposes a new statistical damage constitutive model based on the Hoek-Brown criterion that considers the water-weakening effect. The proposed model divides the rock damage process into two stages: water-weakening and stress loading. The rock damage is represented by infinite microelements, with the elastic part following Hooke's law and the damaged part retaining the remaining strength. The strength of the rock microelements follows the Hoek-Brown criterion, and the relationship between rock microelement strength and damage variables is derived using the strain equivalence hypothesis. The proposed model is validated using triaxial test data from representative rock samples subjected to the water-weakening effect and triaxial stress loading under different confining stresses and water absorption rate degrees. Results indicate that the proposed model can accurately express the entire stress-strain curve of rock without exceeding the experimental accuracy, particularly at low confining pressure. Overall, this study demonstrates that the new statistical damage constitutive model has significant potential in accurately describing the stress-strain relationship during the rock damage process, particularly for the presence of the water-weakening effect.