## 3 Test Results and Discussion
### Crack Stress Thresholds  
According to the method proposed in Section 3.4, several stress thresholds corresponding to the fracture process of intact specimens and pre-holed specimens were calculated, as listed in Table 4. The effect of filling mode and hole angle on the crack closure stress \(\sigma_{\text{cc}}\), initiation stress \(\sigma_{\text{ci}}\) and damage stress \(\sigma_{\text{cd}}\) of each group of specimens and their corresponding stress levels are shown in Figure 14. It can be seen from Figure 14a that the \(\sigma_{\text{cc}}\) of the pre-holed specimens with \(\alpha=0^{\circ}\) and \(45^{\circ}\) are 12.14 MPa and 12.15 MPa, which are 39.30% and 39.25% lower than that of intact specimens, respectively. After filling, with the increase of the mechanical properties of the filling material, the \(\sigma_{\text{cc}}\) of the pre-holed specimens increases, but it is still smaller than that of the intact specimen. Among them, the increase rates of \(\sigma_{\text{cc}}\) of specimens with \(\alpha=0^{\circ}\) and \(45^{\circ}\) are 13.10% and 6.01% in filling mode B, and 24.88% and 22.88% in Filling Mode C, respectively. The above results show that the crack closure stress of rock can be significantly reduced by the existence of holes and improved by the filling treatment, but it seems to be less affected by the hole angle. In addition, the crack closure stress levels \(\sigma_{\text{cc}}/\sigma_{\text{c}}\) of the pre-holed specimens also increase with the change of Filling Mode from A to C, but the increase rate is very small. The stress levels of specimens with \(\alpha=0^{\circ}\) are 0.23-0.25, and that of specimens with \(\alpha=45^{\circ}\) are 0.26-0.28. However, the stress levels of specimens with \(\alpha=45^{\circ}\) are generally higher than that of specimens with \(\alpha=0^{\circ}\), especially in Filling Mode C, the stress level of the specimen with \(\alpha=45^{\circ}\) is even greater than that of intact specimen. This indicates that the effect of hole angle on the crack closure stress levels of the pre-holed specimens is more significant than that of the filling effect. Figure 14: _Cont._The crack initiation stress and corresponding stress levels of each group of specimens are shown in Figure 14b. It can be seen that the crack initiation stresses of pre-holed specimens with \(\alpha=0^{\circ}\) and \(45^{\circ}\) are 19.62 MPa and 20.00 MPa, which are 46.19% and 45.15% lower than that of intact specimens, respectively. After filling, it is interesting to note that for the specimens with inclusions, i.e., under Filling Mode B and C, there are two crack initiation stress values, \(\sigma^{\prime}_{\text{ci}}\) and \(\sigma_{\text{ci}}\), which are the crack initiation stress of inclusions and rock matrix, respectively, as mentioned in Section 3.4. Due to the weak mechanical properties of Type I inclusion and strong mechanical properties of Type II inclusion, the \(\sigma^{\prime}_{\text{ci}}\) of the pre-holed specimens first decreases and then increases with the change of filling mode from A to C, but the difference of \(\sigma^{\prime}_{\text{ci}}\) between \(0^{\circ}\) and \(45^{\circ}\) specimens is very small. However, the crack initiation stress levels \(\sigma^{\prime}_{\text{ci}}\)/\(\sigma_{\text{c}}\) of \(0^{\circ}\) specimens in Filling Modes B and C are 0.29 and 0.39, while those of \(45^{\circ}\) specimens are 0.36 and 0.43, respectively. The above results show that the hole angle has little effect on the \(\sigma^{\prime}_{\text{ci}}\) of inclusions, but has a significant enhancing effect on the corresponding stress levels, and the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen No.