Effect of crack angles on energy characteristics of sandstones under a complex stress path

In order to obtain influence laws of crack angles on energy characteristics of sandstones in complex stress environment, this study performed a cyclic loading and unloading test under stress gradients with a constant lower limit of stress on sandstone samples with cracks at different angles. By utilizing the integral method for area, total energy density, elastic energy density and dissipated energy density of the sandstone samples with cracks at different angles were derived. Moreover, this study explored the increase laws of the three energy densities with the number of cyclic loading and the upper limit of stress in each cyclic loading. The results demonstrate that during the whole cyclic loading process, the three energy densities increase with the increase of the number of cyclic loads, and the growth rate of elastic energy density is obviously larger than that of dissipated energy density. In addition, In the whole cyclic loading and unloading process, the energy densities of the sandstones with cracks at different angles show obvious growth relationships in the form of a quadratic function with upper limit of stress in single cyclic loading and unloading. The index that characterizes the storage energy capability and dissipated energy capability of the rock, namely the energy storage coefficient and the energy dissipation coefficient, is defined. By analyzing the relationships of energy storage coefficient and energy dissipation coefficient of rocks with crack angles in rocks, it is found that the larger the crack angle, the larger the energy storage coefficient of rocks while the smaller the energy dissipation coefficient. This explains the phenomenon that the larger the crack angle, the stronger the bearing capacity of rocks from the perspective of energy.