A progressive fracture process in rocks subject to uniaxial compression is the focus of the current research [1]. The effect of pre-existing open faults with varied orientations on the emergence and coalescence of fractures in marble specimens at the meso-level was thoroughly investigated. Marble was described as a cohesive/bonded granular material in which constituent particles exerted mutual forces on one another through their contacts. A 3D particle DEM model, which has been demonstrated in the literature to be particularly effective in simulating the progressive failure of rocks, was used to replicate the behaviour of cracked rock specimens. In order to determine whether DEM could accurately simulate wing and secondary cracks developing at the tips of pre-existing flaws and to gain meso-mechanical insights into the damage mechanisms associated with those cracks, a series of numerical tests were conducted in the current paper on intact and pre-cracked/notched marble specimens under uniaxial compression. Here, particular attention was paid to how the inclination of pre-existing faults affected the specimens' fracture pattern and compressive strength. For comparison, either a packing of bound spherical elements or clumped discrete elements were used to represent the fracture in marble specimens. The numerical simulations were compared directly to the experimental findings by Yang et al. [2].