# 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
### Influence of the Notch Length on the Failure Mechanism
The  
Firstly, the influence of the confinement on the failure mechanism in the specimens with a circular hole (Figure 5a) is investigated. The failure pattern in the specimens subjected to different confining pressures is shown in Figure 15a. The figure shows the failure patterns at 80% post-peak stress level. In Figure 15a, when the confinement is zero, the fractures are accumulated at the wall of the hole (\(\theta=0^{\circ}\), \(180^{\circ}\)). For this case, a minor tensile fracture is formed at the bottom of the hole. The failure planes are extended to the external boundaries of the models which represent the rupture of the specimen. With the increase in the confinement, larger volumes of rock around the hole are fractured. Moreover, the width of the shear bands becomes wider. The influence of the confinement on the peak strength of the specimens is shown in Figure 16. This figure indicates that the strength of a specimen with a circular hole increases with the increase of the confinement. Next, the influence of the confinement on the failure mechanism in the specimens with a notched hole (Figure 5b) is studied. Two notches with the length of \(L=5\) mm (\(L\)/R ratio of 0.50) are created in the model. In Figure 15b, when the confinement is zero, the failures are nucleated from the notch tips. Some minor tensile fractures are formed at the bottom of the hole (\(\theta=270^{\circ}\)), where the tensile stress is maximum. At higher confements, this tensile cracking does not appear. When the confining pressure is increased to 2 MPa, a few cracks turned back toward the surface of the hole (\(\theta=135^{\circ}\) and \(315^{\circ}\)). However, a larger volume of the rock at the sides of the notches remained unfratured. In the models with higher confements, the damage to the rock at the wall of the hole increased. Figure 15 shows that, at higher confements, the number of tensile and shear cracks is significantly increased, and the failures bands are wider. In Figure 15b, when the confinement is 6 MPa, cracks coalesced and created crushed zones around the hole, and the notches do not prevent failures at the surface of the hole. The peak strength of the specimens at different confining pressures is illustrated in Figure 16. The figure indicates an upward trend in the strength as the confining stress increases. In this figure, the strength of the specimens in the notched hole models is slightly smaller than that in the circular hole model. In the unconfined  
Figure 14: The failure patterns in the models with the width of 200 mm and different notch lengths (80% post-peak stress). case, the difference between the strengths is 1.4 MPa. By increasing the confinement, the difference between the two aforementioned strengths decreases and becomes negligible at the confinement of 6 MPa (0.4 MPa). Figures 15b and 16 show that in the simulated notched hole (\(L\) =5 mm; \(L\)/\(R\) ratio of 0.50), the notches have a meaningful effect on the failure mechanism at confinements up to 4 MPa. However, at higher confining pressures, the influence of the notches on fracturing mechanism becomes negligible. Figure 16: The peak strength at different confining pressures in the two models. Figure 15: Failure patterns in the (**a**) circular hole and (**b**) notched hole models at 80% post-peak stress level for different confining pressures. Numerical simulations are only approximate imitations of real-world systems. Therefore, the accuracy and reliability of the model outputs should be examined. There are different approaches with which to validate a computer model. One approach which is commonly used is to compare the simulation results with real-world observations. However, sometimes it is difficult, expensive, or even impossible to conduct physical experiments. Moreover, in concept studies, the physical tests can be conducted only after a general picture of the mechanisms is drawn through numerical simulations. In these conditions, the numerical results are verified by examining the model output rationality [42].