# Failure Mechanism of Rock Specimens with a Notched Hole under Compression--A Numerical Study
## 4 Conclusions  
Discontinuity is an intrinsic characteristic of rocks which may exist in rocks in different shapes and sizes. The failure behavior of defects such as cracks and notches in rocks and brittle materials under different loading conditions has been studied in previous rock mechanics and fracture mechanics studies. However, the failure behavior of defects under pure compression (negative Mode-I) has been neglected in the previous studies. In this research, a numerical study was conducted to understand how the failure mechanism of specimens containing a circular hole would change in the presence of notches at the surface of the hole. Firstly, the uniaxial compressive test on a rock specimen with a circular hole was modeled and the failure evolution in the specimen was simulated. The results showed that the uniaxial strength of this specimen was 17.4% less than that in the intact specimen. The major failure zones in the specimen with a circular hole formed at the two sides of the hole (\(\theta\) = 0\({}^{\circ}\) and 180\({}^{\circ}\)). In a separate model, two notches were created at the surface of the hole. The uniaxial strength of the specimen with the notched hole was 23.3% and 7.1% less than that in the intact specimen and the specimen with the circular hole, respectively. The results showed that, when the notches were created in the model, failure zones around the hole were transferred to the tips of the notches, and the rock at the sides of the notches remained unfratured. Next, a parametric study was carried out to investigate the influence of the notch length on the fracturing behavior of the specimen by varying the notch length at \(L\) = 2.5, 5, 7.5, and 10 mm. It was found that the influence of the notches on the fracturing mechanism around a hole is a function of the notch dimensions. By increasing the notch length, the major failure zones were transferred to a farther distance away from the hole surface. Moreover, it was shown that the maximum strength of the specimens decreased as the notch length increased. Wider specimens with a width of 200 mm, which results in the ratio of 10 for the model width to the hole diameter, were modeled. The results confirmed that the modeling results were not affected by the boundary effect. Then, the influence of the confinement on the failure mechanism in the specimens with a circular hole was investigated. The results showed an upward trend in the peak strength of the specimens as the confining pressure increased, in which the strength of the specimens in the notched hole models was slightly less than that in the circular hole model. This difference became negligible at the confinement of 6 MPa (0.4 MPa). The results showed that the presence of notches resulted in the transfer of failure zones at confinements of up to 4 MPa. However,under the higher confining pressures, the notches do not play any meaningful role in the fracturing mechanism. The numerical modeling results presented in this study showed that the presence of defects (notches in this study) at the surface of a hole can affect the fracturing mechanism of the rock around that hole. In some cases, the failure at the boundary of the hole was prevented when the notches above \(L/R\) ratio of 0.5 were created in the model. It implies that the notches might be useful for controlling the failures at the underground excavation boundaries. It is important to point out that the minimum \(L/R\) ratio required to prevent failure at the boundary of the hole depends on the in-situ stresses, material properties, as well as on the boundary and loading conditions. Therefore, numerical modeling should be performed, incorporating the site-specific data to obtain the minimum \(L/R\) ratio. In addition, the validity of the numerical results should be examined in practice through physical modeling. In future, it is planned to conduct some laboratory experiments to verify the validity of the numerical results. Conceptualization, A.M. and P.H.S.W.K. ; methodology, A.M.; software, A.M.; validation, A.M. and P.H.S.W.K.