Experimental and Theoretical Research on the Anisotropic Deformation and Energy Evolution Characteristics of Shale under Uniaxial Cyclic Loading and Unloading

Shale is often encountered during rock engineering. The inherent anisotropy of shale and the loading and unloading path affect the failure characteristics of this material. In this study, shale specimens with seven different bedding orientations were used to carry out cyclic loading and unloading experiments to explore the anisotropy of the mechanical properties of shale and the energy evolution of its failure. The experimental results indicate that with an increasing number of cycles, the secant modulus of shale with bedding orientations of 0°, 15°, 45°, and 90° decreases; however, for bedding orientations of 0°, 30°, and 75°, the secant modulus increases or becomes constant. During cyclic loading, hysteresis and irrecoverable strain are clearly observed. The irrecoverable deformation with a bedding orientation of 45° is the largest. The energy evolution during cyclic loading clearly presents anisotropic characteristics. Under the same axial stress, the elastic energy storage capacity, which nonlinearly increases with the axial stress, is the largest for the bedding orientation of 15° and the smallest for the bedding orientations of 60° and 90°. The dissipated energy is much larger for bedding orientations of 45° and 75° than for other bedding orientations. A comparison of the damage evolutions defined by the damage energy release rate suggests that the damage evolution trends are the same for all bedding orientations, but damage is more easily generated with bedding orientations of 60° and 75°. To theoretically describe the energy evolution, an elastic energy evolution model that considers the external incentive effect, self-promotion effect, and self-inhibition effect of energy was established. An energy release dispersion coefficient and fabric tensor were defined to consider the effect of confining pressure and inherent anisotropy. Then, a modified energy-based strength criterion for anisotropic sedimentary rocks was proposed. The results show that both the energy evolution model and the strength criterion have good correlations with experimental data.