# Failure Mechanism of Rock Specimens with a Notched Hole under Compression--A Numerical Study
## 3 Simulation of Failure in a Rock Specim with a Notched Hole
### Model Setup  
In this study, the bonded particle models are developed to simulate the fracturing process in rock specimens. In the bonded particle models, the cracking process is simply simulated by breakage of bonds between particles. This is a simple approach for the simulation of cracking in comparison to some other methods, in which the crack evolution is simulated by solving complex mathematical equations related to fracture mechanics. For the implementation of the bonded particle models, Particle Flow Code (PFC) [38] is utilized. Because the purpose of this study is to simulate the fracturing behavior of rectangular prismatic specimens, the problem can be simplified to a plane strain problem. Therefore, in this study, the two-dimensional version of the code (PFC\({}^{\text{2D}}\)) is used. In PFC modeling, it is not straightforward to assign the physical and mechanical properties of materials. The models need to be calibrated by changing several micro-parameter values to obtain macro-parameter values, such as for the elastic and the plastic properties of the material. For this purpose, usually the unconfined and confined compressive tests, as well as the Brazilian test, are simulated. In the calibration process, different micro-parameter values are varied to calibrate the model to get the desired macro-parameter values of the material. The procedures given by [PERSON] et al. [39] and [PERSON] [40] were used as guidance to perform the calibration process. The calibrated micro-parameter values and the used macro-parameter values for the simulated rock specimens in this study are listed in Tables 1 and 2, respectively. The macro-parameter values of the simulated rock are in the ranges of the mechanical properties of some soft rock types such as coal, chalk, soft shales and marl, and rock-like materials such as concrete. Figure 4: The tangential stress distribution around (**a**) a regular tunnel and (**b**) a notched tunnel [29]. In this study, a rectangular rock specimen with a width of 100 mm and a height of 200 mm, and including the mechanical properties listed in Table 1, was simulated. The geometry of the models is shown in Figure 5. The simulated specimen includes a rectangular assembly of 18,892 circular particles. The radius of the particles follows a Gaussian distribution function with a minimum and maximum radii of 0.4 mm and 0.66 mm, respectively. The particles are densely packed with a low locked-in isotropic stress of 0.15 MPa, which is less than 1% of the uniaxial compressive strength of the specimen. After reproduction of the rectangular assembly, the circular hole and notches are created by removing the particles at the appropriate locations. Deletion of the particles does not have a significant influence on the stress distribution in the assembly because the locked-in isotropic stress is set to a low value relative to the material strength. The circular hole with a radius of \(R=10\) mm is created at the center of the specimen (See Figure 5). The notches are created by removing the particles in a narrow strip with a width of 1.5 mm. This approach is appropriate for the simulation of open cracks. Simulation of closed and filled cracks can be done by assigning zero tensile strength to the bonds of neighbor particles in a straight line or by using smooth joint models [40]. The particle assembly of a notched hole with the length of \(L=10\) mm is illustrated in Figure 6. The pushing forces to the specimen's ends are applied by moving two parallel rigid walls toward each other in the direction of the loading. In this paper, the model containing a central circular hole is referenced as \"the circular hole\" (Figure 5a), and the model which includes notches at the surface of the hole is referenced as \"the notched hole\" (Figure 5b). It should be noted that in this study, one particle assembly is used in all models. In this way, only the influences of the geometry and the boundary condition changes are considered.