Energy evolution and damage characteristics of coal rock under graded cyclic loading and unloading with confining pressure

This work conducts staged confining pressure cyclic loading and unloading (SCPLU) tests on coal rock to explore its energy evolution and damage features under complex stress states. A novel damage variable based on dissipated energy and enhanced modulus of elasticity is proposed. Results show that under low confining pressure, coal rock failure is minimally affected by cyclic unloading, with few micro-cracks. However, under high confining pressure, micro-cracks increase with rising confining pressure and unloading cycles. After each stage of loading and unloading, stress redistribution in coal rock causes micro-crack propagation, more dissipated energy, increased irreversible plastic deformation, and worsened damage. The damage variable based on dissipated energy and the improved modulus of elasticity has a high fitting degree of 0.998 with the damage evolution equation based on the Weibull distribution, which is superior to the improved modulus of elasticity method alone. The failure process of coal rock can be divided into five stages: compaction segment, elastic segment, crack instability development segment, crack instability propagation segment, and residual strength segment. This classification effectively characterizes the failure process of coal rock and provides a reference for further revealing the damage evolution mechanism of coal rock under complex stress paths.