# Failure Mechanism of Rock Specimens with a Notched Hole under Compression--A Numerical Study
## 1 Introduction  
Discontinuity is an inherent characteristic of rocks and rock-like materials. Generally, rocks include defects and discontinuities at various scales. Different types of defects exist in rocks such as faults, bedding planes, pores, grain boundaries, joints, holes, cracks, and notches. These natural defects originate from the various geological processes acting on the rocks. Moreover, defects in rocks may be created artificially for some engineering purposes. Whether the defects are formed naturally or created artificially, they affect the load-bearing capacity of the rock [1; 2; 3; 4]. Defects in rock masses are stress-raisers and play a key role in the rock fracturing processes. Therefore, understanding the role of different types of defects on the mechanical behavior of rocks under various loading conditions is an essential task for any rock engineering design. Cracks and notches are two types of planar defects that may exist naturally in rock masses or may be created artificially in different structures, such as dams, tunnels, and wells. The definition of a \"crack\" refers to a defect that is generated during the loading process, and a \"notch\" or a \"flaw\" refers to a preabricated defect in the solids. In this article, the word \"notch\" refers to a cut at the surface of the specimens. Cracks and notches show a similar behavior under tensile loads. However, their behavior under compressive and shear stresses are different. When a crack is subjected to pure compression, the two faces of the crack are pushed together and the free space between them closes due to the penetration of the molecules on each face moving into another face. In this condition, the presence of the crack has little or no effect on the strength of the solid. Thus, the crack behavior under pure compression (negative Mode-I) is not crucial to the stability of a structure. In contrast, a notch under compression can affect the stability of a solid depending on the distance between the two faces of the notch and its geometry. In rock structures, rocks are subjected to different loading conditions. Damage initiation and propagation from a pre-existing defect in a rock depends on the loading condition. In theory, three basic modes of crack extension are postulated: Opening mode (Mode-I), shearing mode (Mode-II), and tearing mode (Mode-III). Basic modes of crack extension are sketched in Figure 1. In the rock mechanics and the fracture mechanics literature, a large number of studies have been devoted to the study of initiation, propagation, and the coalescence of cracks in rocks and brittle materials under different loading conditions [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. These studies have revealed many fracturing characteristics of rocks and have led to the improvement of safety in rock structures. In the studies related to failure mechanism, defects are usually in either the form of holes with different geometries (e.g., circular, rectangular, and triangular) or planar defects, such as cracks, flaws and notches. A large number of research studies have investigated the failure mechanisms in rock specimens containing holes under different loading modes [19; 20; 21; 22]. However, in the study of defected rocks, the inclusion of planar defects, tensile, and shear loads are usually more applied, while the pure compression is neglected [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. For example, [PERSON] and [PERSON] studied the failure mechanisms of pre-flawed specimens under mixed mode I/II loads. They observed three different types of cracks including wing cracks, coplanar shear, and oblique shear cracks [12]. In rock structures such as mine pillars, tunnel walls, and slopes, the existing defects at the surface of the excavations can be subjected to pure compression. Hence, the influence of the presence of a defect on the failure evolution of rocks under compression is important. The fracturing behavior of defects under pure compression has been studied in a limited number of investigations [23; 24; 25].