Abstract：The applicability of a failure criterion for the strain energy density of rock under static-dynamic loading is proposed. According to the analysis，critical value of strain energy density of rock is mainly determined by preceding irreversible deformation process and current environmental state；and the irreversible deformation is mainly caused by nonelastic deformation，damage and other possible intrinsic dissipative mechanisms of rock in a mechanical system；and volume deformation energy associated with hydrostatic stress effects can not be neglected on some stress states. Using mechanical model to represent the reduction of elasticity，occurrence of inelasticity deformation and effect of loading rate are proposed. On the basis of mechanical model，the critical value of strain energy density of rock under static-dynamic loading is derived. According to the catastrophe model for impact buckling of static-loading structures，a new catastrophe model for impact disturbance fragmentation of a rock system under static loading is established to analyze the rock failure under static-dynamic coupling loading ulteriorly. Finally，by using of the Instron electro-hydraulic and servo-controlled material testing machine and adopting low-cycle-index fatigue loading method，the test of red sandstone failure with medium strain rate under dynamic loading is carried out to verify the strain energy density criterion and catastrophe theory model. There is a good agreement between theoretic and experimental results.
