Effect of intermediate principal stress and minimum principal stress unloading stress path and rate on energy evolution of sandstone under true triaxial compression

In the process of deep coal mining, the unloading stress path and unloading rate of deep rock are complicated and changeable due to the influence of excavation and unloading. Different stress paths and rates may lead to different deformation and failure characteristics of rocks. To understand the influence of stress changes, energy evolution, and damage in deep rock under true triaxial unloading in complex stress environments, a designed true triaxial stress balance unloading test was employed to analyze the energy and damage in true triaxial unloading principal stress tests. First, true triaxial unloading principal stress tests on sandstone were conducted under different unloading stress paths and rates (σ_x-σ_y-σ_z test and σ_y-σ_x-σ_z test). Then, a damage-free true triaxial stress balance unloading test was designed, and acoustic emission technology was used to verify the damage-free characteristics during the unloading process. Based on this test, an energy analysis method for true triaxial unloading principal stress tests was proposed. Finally, by analyzing the degree of crack opening on the outer surface of the specimen after unloading and its connection with energy dissipation, the impact of unloading stress paths and rates on rock damage was elucidated. The research results indicate that during the unloading process in one principal stress direction, the input strain energy density, elastic strain energy density, and dissipated strain energy density in the other principal stress directions increase, and these densities also increase with the unloading rate. Additionally, the released rock strain energy in the unloading principal stress direction increases with the unloading rate, and the released strain energy along the unloading direction is significantly lower than the stored energy in that direction. By comparing the test results of the σ_x-σ_y-σ_z test and the σ_y-σ_x-σ_z test, it was found that the dissipated strain energy density is positively correlated with the degree of sandstone damage, meaning that the greater the dissipated strain energy density generated by the unloading principal stress, the higher the degree of rock damage, and the unloading stress path of the σ_y-σ_x-σ_z test is more likely to induce rock mass damage.