## 1 Introduction  
Crack and hole are two common kinds of defects existing in natural rock mass. At present, it is generally known that the occurrence of the defects worsens the internal structure of rock mass, and the concentrated stress that distributes at the periphery of the defects makes crack initiation tend to emerge at their tips or corners, resulting in a significant weakening of the mechanical performance and complex deformation and instability behaviors of rock mass. In rock engineering, the common types of crack-like flaws include micro-crack, weak planes, fissures, faults, joints, and beddings. Up to now, considerable theoretical, laboratory and numerical attempts have been made upon the mechanical responses of rock or rock-like media containing diverse crack flaws under different loading conditions, which greatly improves the understanding of rock mass failure characteristics and instability mechanisms [1; 2; 3]. In our previous studies, the crack initiation, development and penetration behaviors of jointed specimens were also systematically reviewed, which is found to be attributed to multiple factors, e.g., the size, inclination, number and configuration of crack flaws, material properties and loading conditions [4; 5]. Additionally, the failure is considered to be the course of crack initiation, development and intersection, and the instability mode and coalescence type are the results of competition between tensile cracks and shear cracks. Likewise, a variety of openings varying from tiny holes to large-scale cavities are widespread in rock masses, such as the pores in basalt, natural caves in mountain and Karst caves in underground carbonate strata (see Figure 1). In addition, the excavated tunnels in hard rock mines could also be regarded as holes in plates according to elastic mechanics theory. Obviously, the impact of holes on the quality and performance of rock mass is noticeable, raising the concerns of scholars in recent decades. Inspired by the V-shaped failure phenomenon of surrounding rock in deep-buried tunnels, [PERSON] [6] took the lead in conducting biaxial compression photo-elastic tests on prismatic resin glasses and granite samples with a circular cavity, and observed the existence of primary tensile cracks and remote cracks. This fracture phenomenon has also been found in uniaxial compression experiments of other rock materials with one single circular hole, and the two sorts of cracks were verified towards the direction of compression [7; 8]. In summary, there exist three types of cracks formed around a round hole in prismatic specimens under uniaxial and biaxial loads with low-confined pressure, namely the primary tensile cracks at the top and bottom of the opening, the spalling cracks at the hole sidewalls and the remote cracks at the hole corners. [PERSON] and [PERSON] [9] successfully measured the initiation stresses of the three categories of cracks through attaching substantial resistance strain gauges near the round hole, and revealed the relation between the fracture propagation speed and the cavity diameter. [PERSON] et al. [10] held that the primary tensile fractures are prone to initiate and propagate in small-width specimens with a large-diameter round hole. [PERSON] and [PERSON] [11] further proposed a functional equation of the primary crack length on fracture toughness, hole radius, sample strength and lateral pressure coefficient. Given that the holes in rock engineering are not generally circular, [PERSON] et al. [12] incorporated AE plus DIC measurements to reproduce the strain localization characteristics and fracturing process of samples with an elliptical hole of different geometries subjected to uniaxial compression. In addition, other scholars [13; 14] have further investigated the fracturing responses of samples with a hole of different shapes under axial and biaxial loading numerically and experimentally, and found the effect of hole shape upon the strength and fracturing law is remarkable. By PFC code, [PERSON] et al.