Energy characteristics of progressive damage of Jinping marble under cyclic loading and unloading

In order to investigate the energy characteristics of Jinping marble during progressive damage, triaxial cyclic loading and unloading tests on marble samples under five different confining pressures were carried out. The evolution of elastic modulus, the rule of energy evolution and distribution, the effect of confining pressure on energy evolution, and the characteristics of progressive damage evolution of marble under cyclic loading and unloading were analyzed. Furthermore, the energy failure criteria of rock strength based on energy consumption ratio and energy consumption difference were systematically discussed. The results show that both the loading and unloading elastic moduli of the marble are monotonically degraded during the whole deformation and failure process from the initial yielding to the residual stage. The deviation of elastic strain energy calculation with the assumption of constant modulus of elasticity should be avoided. The increase of confining pressure can not only effectively enhance marble's energy absorption and storage efficiency, but also strengthen marble's energy absorption and storage limit. It can also restrain marble's energy dissipation efficiency and the increase amplitude of dissipation energy. The ratio of elastic energy decreases and the ratio of dissipative energy increases from pre-peak to post-peak, and the ratio of residual energy tends to be stable. The residual elastic energy and the residual dissipated energy increase approximately linearly with the increase of confining pressure, while the maximum elastic energy and the maximum dissipated energy increase nonlinearly with the increase of confining pressure. The modified damage evolution equation considering initial damage and residual bearing capacity can well capture the variation characteristics of damage variable based on dissipative energy under different confining pressures. The criterion of energy consumption ratio based on the definition of energy relative proportion can be regarded as the criterion of failure of marble material. While the criterion of energy consumption difference based on the definition of absolute difference of energy can be regarded as the criterion of failure of marble structure.