*2.2. Analysis of the Influence of Borehole Diameter on Borehole Stability*

A three-dimensional borehole model is created based on FLAC 3D and the borehole stability of four diameters, namely 100 mm, 130 mm, 160 mm, and 200 mm, is investigated. The borehole model is shown in Figure 7. The Moore-Coulomb constitutive model is selected for the simulation, which is suitable for solving rock mechanics and excavation problems. The initial stress is Sxx <sup>=</sup> −1.1985 × <sup>10</sup><sup>7</sup> Pa, Syy <sup>=</sup> −1.1985 × 107 Pa, Szz <sup>=</sup> −1.1985 × <sup>10</sup><sup>7</sup> Pa, and the lateral pressure coefficient is 1.0. The velocity of the left and right boundaries in the X direction is set to 0; the velocity of the bottom boundary in the Y direction is set to 0; and the top boundary is set to the gravity of the overlying strata. Then the excavation simulation was started after reaching the equilibrium level.

**Figure 7.** The borehole model.

#### 2.2.1. Analysis of the Stress and Displacement

The maximum principal stress contour of boreholes of different diameters is shown in Figure 8. The maximum principal stress nephogram at 100 mm and 130 mm is distributed in a regular and uniform circle around the borehole, and it begins to deform into an ellipse at 160 mm, while the contour is completely deformed at 200 mm, and the stress expands to the boundary region, resulting in stress equilibrium and instability of the surrounding rock. Thus, the results indicate that when the borehole diameter exceeds 160 mm, the maximum principal stress distribution of the borehole begins to deform, the stress balance tends to be destroyed, and the stress concentration area is proportional to the borehole diameter.

The displacement monitoring of the rock mass around the borehole is shown in Figure 9. According to the curve, the displacement range of the left side of the borehole is 0~3.5 mm, and the displacement ranges of the upper and lower sides are 0~12 mm and 0~25 mm, respectively. The displacement of the left side of the borehole is the smallest, and the displacement of the upper and lower sides of the borehole is much larger than that of the left side, indicating that the borehole damage is mainly caused by the large deformation of the upper and lower sides. The displacement of each monitoring point increases with the hole diameter, and the displacement of the rock mass around the hole changes more. Boreholes with different diameters produce displacements at almost the same time after drilling and then gradually stabilize.

**Figure 8.** Maximum principal stress contours. (**a**) The maximum principal stress contour of the borehole of diameter of 100 mm; (**b**) the maximum principal stress contour of the borehole of diameter of 130 mm; (**c**) the maximum principal stress contour of the borehole of diameter of 160 mm; (**d**) the maximum principal stress contour of the borehole of diameter of 200 mm.

(**a**) Borehole left surrounding rock

(**b**) Borehole upper surrounding rock

**Figure 9.** *Cont*.

**Figure 9.** The variation curve of surrounding rock displacement with different diameters. (**a**) The variation curve of borehole left rock displacement with different diameters; (**b**) the variation curve of borehole upper rock displacement with different diameters; (**c**) the variation curve of borehole under rock displacement with different diameters.

#### 2.2.2. Analysis of the Plastic Failure

The S-distribution and volume of plastic failure of the surrounding rock mass of boreholes are shown in Figures 10 and 11. The distribution of plastic failure zones is similar to that of the vertical stress and is symmetrical, extending around the hole wall. The volumes of plastic failure zones with four diameters of 100 mm, 130 mm, 160 mm, and 200 mm are 0.007 m3, 0.012 m3, 0.018 m3, and 0.03 m3 respectively. As the borehole diameter increases, so does the extent and volume of the plastic failure zone. The volume of the plastic failure zone can be divided into shear failure and tensile failure. The volume of tensile failure changes very little with the increase in pore diameter as can be seen from Figure 11. On the contrary, the volume of shear failure increases linearly with the increase in pore diameter and is much larger than that of tensile failure in all four-borehole diameters. Therefore, it can be concluded that the failure mode of the boreholes is mainly shear failure.

**Figure 10.** Distribution of plastic failure of boreholes with different diameters. (**a**) The distribution plastic failure of the borehole of diameter of 100 mm; (**b**) the distribution plastic failure of the borehole of diameter of 130 mm; (**c**) the distribution plastic failure of the borehole of diameter of 160 mm; (**d**) the distribution plastic failure of the borehole of diameter of 200 mm.

**Figure 11.** The volume of plastic failure zone with different diameters.

In summary, the analysis of the stress state and displacement of the borehole with four diameters of 100 mm, 130 mm, 160 mm, and 200 mm showed that the larger the diameter, the more unstable they are, and the plastic failure volume is directly proportional to the borehole diameter. Therefore, it can be inferred from the comprehensive stress, displacement, and plastic zone that the stability of the borehole decreases as the borehole diameter increases, and the borehole tends to be unstable when the diameters are 160 mm and 200 mm.

#### *2.3. Analysis of Protection Effect of the Hole Protection Pipe*

The stability of boreholes is investigated by simulating the application of a borehole protection tube to analyze the protection effect. The modeling process of boreholes is the same as in Section 2.2. The mechanical parameters of the casing are shown in Table 3; the casing is simulated after the borehole is excavated. The model of the casing is shown in Figure 12.



**Figure 12.** Model of the borehole protection pipe.

#### 2.3.1. Analysis of the Stress and Displacement

The maximum principal stress contour of the borehole before and after protection is shown in Figure 13. It can be seen from the contour that the stress concentration at the 160 mm and 200 mm borehole walls is greatly reduced compared to the borehole without the casing. The distribution range of stress concentration is obviously reduced compared to that before protection, especially the stress range before and after borehole protection of 200 mm boreholes changes greatly. This indicates that the borehole protection tube can provide effective support and change the stress state around the borehole wall.

**Figure 13.** Maximum principal stress contours with and without protection.

The displacement monitoring curve of the rock mass around the borehole before and after protection is shown in Figure 14. The displacement changes in the left, upper, and lower protection holes of the 160 mm borehole are 0.2 mm, 3.1 mm, and 2.2 mm respectively. The displacement changes in the left, top, and bottom protection holes of the 200 mm hole are 0.3 mm, 5.4 mm, and 2.7 mm respectively. The results show that the displacement of each monitoring point has obviously changed before and after hole protection, especially the displacement of the upper side of the borehole has the biggest difference. It also shows that the borehole protection pipe can weaken the displacement and deformation caused by borehole excavation, and improve the support and stability of boreholes.

(**a**) Borehole left surrounding rock

(**b**) Borehole upper surrounding rock

**Figure 14.** *Cont*.
