## 1 Introduction  
Many macro and micro-cracks, holes, and other defects are included in rock masses as a natural, heterogeneous, engineering geological material [1]. The rock mass defects that affect the mechanical properties of rock masses mainly include the shape, size, and geometric distribution. The crack initiation, propagation, and coalescence are greatly affected by defects in the rock masses. Therefore, deeply researching the effects of these defects on rock crack mechanisms and evolution laws has always been one of the focuses of rock mechanics. In researching the mechanical properties of cracked rocks, people study the strength, deformation characteristics, and the cracking evolution law of rocks with defects, by laboratory tests. Fractured rock materials mainly contain the following two defects: cracks and holes [2]. Rock-like materials or real rocks, which include crack defects, have been extensively studied by many people [3, 4, 5, 6, 7, 8, 9, 10, 11], who have usually focused on the mechanical behavior and cracking mechanisms. In terms of the mechanical properties of rock masses with holes, the crack propagation mechanism of the block with prefabricated holes, under uniaxial compression was observed by [PERSON] et al. [12] and [PERSON] et al. [13]. They studied the mechanical properties of sandstone specimens with two holes, under uniaxial compression. [PERSON] et al. [14] conducted a series of physical and numerical experiments on a heterogeneous solid, containing a single hole and proposed the crack coalescence mechanism of heterogeneous solids with a single hole, under uniaxial compression. [PERSON] et al. [15]improved the cracks of brittle rocks, containing pre-existing cylindrical cavities by a granite model and AE (acoustic emission) technology and showed that the effects of tensile stress and compressive stress on the fracture evolution around the cavity in brittle rocks are relatively significant. [PERSON] et al. [16] investigated sandstone specimens' mechanical properties, damage modes, and cracking characteristics with a single hole, under high-temperature conditions. The crack propagation mechanism inside the rock masses plays a crucial role in the rock mass failure, so studying the change of the stress-strain field in the rock masses from the crack generation to the propagation of the rock mass is important. However, it cannot be performed clearly by experimental observation alone. Moreover, the influence of these mineral contents and the spatial distribution produced by the geophysical process in crust formation was inevitable during the experiment. Furthermore, any small change during the experiment, including the placement of the specimen, the contact condition between the sample and loading platens, and the application of the load, may lead to differences in the test results. In such circumstances, compared with the laboratory test, the numerical model can maintain the same loading conditions and has great advantages in eliminating the individual differences of specimens and human operation errors. Thus, numerical methods, including the discrete element method (DEM) [17; 18], the boundary element method (BEM) [19; 20], the extended finite element method (XFEM) [21; 22], and the finite element method (FEM), have been widely used to replicate the rock-breaking process. It indicated that FEM is, perhaps, the most diffusely applied numerical method in conducted rock mechanics problems. Furthermore, the finite element method is more advantageous for heterogeneous materials and nonlinearity applications. However, in the numerical simulation studies of rock masses with holes, not many studies have been conducted on the fracture mechanism of shearing. Most of the previous numerical studies focused on uniaxial compression, biaxial compression, or triaxial compression; however, high-rock-slope engineering disasters are often induced by shear failure (Figure 1).