Energy characteristics of sandstones with different crack angles under true triaxial cyclic loading and unloading

The effect of crack angle on energy evolution during sandstone failure subjected to true triaxial cyclic loading and unloading is of great concern. However, the energy consumed in the crack initiation and compaction process is generally referred to the dissipated energy, which is inaccurate. To reveal the energy law in the breaking process of sandstone, a complex cyclic loading and unloading test is carried out on precast angled sandstone samples by employing the triaxial test system. The area integral methodology is exploited to evaluate the evolution of total energy density, elastic energy density, dissipated energy density, and plastic energy density of the rock samples of different crack angles. The variations of these four energy density levels in terms of the number of loading and unloading cycles and the upper limit of stress are explained and discussed. The obtained results reveal that during the entire cycle of loading and unloading, the variations of the above-mentioned factors of the rock sample fairly do not rely on the crack angle. The energy density increases with the number of cycles, and the total energy density and elastic energy density significantly increase faster than the consumption mode. The growth rate of the dissipative energy density is greater than that of the plastic energy density. Additionally, the aforementioned four energy quantities grow in a quadratic manner as a function of the upper limit of the loading stress. The releasable elastic energy gradually magnifies by increasing the upper limit of the loading stress. The plasticity density first decreases and then increases, reflecting the change law of the irreversible plastic deformation caused by newly developed cracks in the rock sample. The elastic energy density, the fitting coefficient of the dissipated energy density, and the total energy density are employed to define the characteristic coefficients of the rock energy storage and energy dissipation. The results indicate that the larger the rock crack angle, the stronger the energy storage energy and the weaker the energy dissipation capacity. It also explains that how the strength of the rock sample becomes higher as the crack angle increases.