A New Rock Damage Constitutive Model Based on Usher Function and its Application to Brittleness Evaluation

The rock damage constitutive model and brittleness evaluation method are significant research topics in rock mechanics. To address the shortcomings of the existing rock damage evolution model based on the logistic function, a new, flexible, and more applicable S-shaped damage evolution model is developed from a phenomenological perspective using the Usher function. Considering the non-linear deformation characteristics of the initial compaction stage of rocks, a damage constitutive model that describes the complete process characteristics of rock compression deformation is established by combining damage mechanics theory and effective medium theory. Based on the damage model parameters, a new rock brittleness evaluation index, BIDE, is created. The uniaxial and conventional triaxial compression test results of granodiorite, glutenite, red sandstone, quartzite, and marble are utilized to verify the rationality of the proposed damage constitutive model and brittleness evaluation index. The research results indicate that the theoretical damage model constructed based on the Usher function accurately describes the complete damage evolution process characteristics of rock in a simple and unified expression. This model includes four stages: no damage maintenance, rapid damage development, constant damage development, and damage mitigation termination. Additionally, the damage constitutive model can accurately simulate the stress-strain process of different rock types under uniaxial and conventional triaxial compression. The parameters a, r, and c in the model have clear physical meanings, collectively determining the shape of the theoretical damage curve and constitutive relation curve. Comparisons with four existing damage models based on different statistical distribution functions reveal that the proposed damage model has the best simulation effect. Finally, the feasibility of the new brittleness evaluation index BIDE, which is established based on damage evolution characteristics, is verified. A new, flexible, and more applicable S-shaped damage evolution model is developed from a phenomenological perspective using the Usher function.A damage constitutive model capable of describing the entire process of rock pre-peak compaction and post-peak strain softening deformation is established and verified by a series of test results.A new brittleness index, , considering the entire process characteristics of rock damage evolution, is established based on the proposed damage model.