Based on the meso-scopic damage mechanics and the finite element method

a numerical code of rock fragmentation process analysis (RFPA) is used to simulate fragmentation process under three different loading conditions

i.e. single dynamic

combined dynamic and static loading

and the combined dynamic loading under the confining pressure. In the analysis model

the visco-elastic boundary is considered to eliminate the influence of the reflected stress waves from the boundary. Numerical simulation results show that the presence of static pressure has little effect on the value of the minimum principal stress within the rock mass

but significantly improve the level of the maximum principal stress; so the value of the shear stress is increased

as well as the possibility of the shear failure. While in the confining pressure condition

the tensile zone in the rock reduces and rock mass strength increases on the other hand. In according to the property of the rock which preformed strong in resist pressure but weak in the resist tensile

the capability of the rock increased within the certain range of the confining pressure. The cracks extend towards both side of the free surface and the failure in the rock becomes more complex under the influence of the confining pressure. The proportion of the pressure failure increases obviously while almost all the damage is tensile failure occurred in the single dynamic loading and combined dynamic and static loading model. The research results will be helpful for understanding the mechanism of rock failure under the dynamic-static loading and underground engineering construction.