<p>Natural rock contains cracks, joints and other defects, which have significantly influence on the failure of rock. To simulate the cracking process of rock with preset cracks, a self-developed continuum-discontinuum method combining the Lagrangian element method and discrete element method was adopted, and the internal cracking of elements was considered. This method has the capacity for simulating the propagation of cracks, contact and motion of blocks. Cracking processes of discs and uniaxial compressive rock specimens with preset cracks were simulated, the influence of hydrostatic pressure and support on the propagation of cracks in surrounding rock with a circular cavern was investigated, and the rockburst at Jinping II hydropower station is simulated. It is found that for disc rock specimens, firstly, tensile cracks generate at tips of preset cracks; then, the preset cracks are connected; finally, tensile cracks run through the disc. The direction of the tensile crack through the disc leans to the direction of preset cracks. The rapid decrease of load is correlates to the rapid propagation of tensile cracks. For uniaxial compressive rock specimens, the direction of the main crack leans to the direction of preset cracks. The bearing capacity does not decrease during tensile cracks slowly propagate, but it decreases rapidly when the tensile and shear cracks propagate rapidly. After excavation, there are shear cracks propagating counterclockwise and clockwise near the surface of the cavern, constituting V-shaped or petal-shaped cracks. The propagation of shear cracks is hindered when they intersect with preset cracks, leading to the formation of shear cracks at the tips of the preset cracks. The higher the hydrostatic pressure, the denser the shear cracks near the cavern, the larger the range of cracks, the more symmetrical the distribution of cracks, and the easier the petal-shaped cracks appear. Support has little effect on the morphology of cracks, but it reduces the propagation speed of cracks. After supporting, the trend of the number of shear cracks is similar to that without supporting, but the number of cracks decreases. For the engineering model, the pattern of cracking zone obtained by the numerical simulation is consistent with the failure profile in practical engineering.</p>