*2.1. Analysis of the Influence of Lithology on the Borehole Stability* 2.1.1. Model Building

Given that the roof-directed long borehole has a large span in the roof, the horizon and rock lithology through which the hole passes is complex. The borehole stability of coal, mudstone, fine-grained sandstone, and coarse-grained sandstone in the working face rock mass was investigated using the Universal Distinct Element Code (UDEC). The model is 300 m long and 180 m high as shown in Figure 1a. According to the histogram distribution of rock layers, joints are set and grids are divided, and the number of grids is 2,976,224. At the upper boundary of the model, the self-weight stress of the overlying strata is imposed, and the simulated mining depth is 430 m. According to the actual situation, it is assumed that the left and right sides are mined together, and the distance between the mining boundary and the left and right boundaries of the model is 60 m, each mining is 10 m, and the mining length is 180 m. To facilitate simulation and calculation, the model is partially simplified: The change in coal seam dip angle and thickness is ignored, and the calculation is based on the average coal seam thickness. Considering the large span of high-level directional drilling in horizontal and vertical directions, the strata and rock lithology through which the drilling passes are also complicated. Therefore, these study models and analyzes the stability of high-level directional drilling under different lithologies based on mining disturbance. Considering the different lithologic horizons that are encountered in drilling practice, four main rock layers are selected for study in the model, namely coal rock, mudstone, fine-grained sandstone, and coarse-grained sandstone. Given that the roof-directed long borehole has a large span in the roof, the horizon and rock lithology through which the hole passes is complex. The borehole stability of coal, mudstone, fine-grained sandstone, and coarse-grained sandstone in the working face rock mass was investigated using the UDEC. A 1 m × 1 m rock mass model with a 130 mm aperture is created as shown in Figure 1b,c. In this model, Voronoi is used to generate joints, and the blocks are distributed in triangular mesh elements. The upper boundary is set as the vertical downward self-weight stress boundary, the lower boundary is fixed as a constraint, and the left and right boundaries are restricted horizontal displacements, as shown in Figure 2. When the calculation model is set, the model should be assigned according to the constitutive model. The Coulomb slip model is selected for numerical simulation, and the rock mechanics parameters of 208 working faces in the Tingnan Coal Mine are shown in Table 2.


**Table 2.** The rock mechanics parameters.

(**a**) Coal seam mining model of directional drilling structure

**Figure 1.** The Numerical computation models. (**a**) The model of the coal seam mining model of directional drilling structure; (**b**) the joint distribution of the model; (**c**) the grid division of the model.

**Figure 2.** Schematic diagram of boundary constraints.


The stress variation range of the surrounding rock is shown in Figure 3. The stress around the borehole in coal and rock ranges from 1.92 MPa to 35.57 MPa, that which around the borehole in mudstone ranges from 1.77 MPa to 29.84 MPa, that which around the borehole in fine-grained sandstone ranges from 1.49 MPa to 27.58 MPa, and that which is around the borehole in coarse-grained sandstone ranges from 1.71 MPa to 27.20 MPa. From the stress range, it can be seen that coal and mudstone have large stress peaks and stress fluctuations, while the stress ranges of fine-grained sandstone and coarse-grained sandstone are relatively small and proximate to each other.

The maximum principal stress contour of the borehole is shown in Figure 4. The peak value of the maximum principal stress is mainly distributed in some borehole walls near the left and right sides of the borehole, while the rest of the rock mass is evenly distributed with lower stress. The maximum principal stress results of different lithologies show that the stress concentration of coal and mudstone is higher, the high-stress area of rock mass around the borehole is larger, and the stress distribution of fine-grained sandstone and coarse-grained sandstone is relatively more uniform. It indicates that the stress state of coal and mudstone is unstable.

#### (2) Variation of the borehole displacement

The displacement contour of the boreholes with different lithologies is shown in Figure 5. As can be seen from Figure 5, the overall displacement trend of the borehole under the four lithologies is similar, and the displacement is all in the direction of the borehole center. The displacement of the rock mass around the borehole is small, and the displacement of the rock mass on the upper and lower sides of the borehole is larger than that on the left and right sides. However, there are still some differences in the borehole displacement of different lithologies. The borehole displacement of coal and mudstone is obviously larger than that of fine-grained sandstone and coarse-grained sandstone, especially on the upper and lower sides of the borehole. The block with the largest displacement is coal, followed by mudstone. The four lithologies are similar on the left and right sides.

**Figure 4.** Maximum principal stress contours. (**a**) The maximum principal stress contour of the coal; (**b**) the maximum principal stress contour of the mudstone; (**c**) the maximum principal stress contour of the fine-grained sandstone; (**d**) the maximum principal stress contour of the coarse-grained sandstone.

**Figure 5.** Displacement cloud map in Y direction. (**a**) The displacement cloud map in Y direction of the coal; (**b**) the displacement cloud map in Y direction of the mudstone; (**c**) the displacement cloud map in Y direction of the fine-grained sandstone; (**d**) the displacement cloud map in Y direction of the coarse-grained sandstone.

During the simulation, four measuring points A, B, C, and D were set at the top, bottom, left, and right sides of the borehole. The displacement change of the measuring point is shown in Figure 6. The displacement of each monitoring point first increases and then tends to be stable within the hole. The maximum displacement of the four points is 3.15 mm of the coal at point D, and the minimum is 0.49 mm of the fine-grained sandstone at point A, which shows that the rock mass around the borehole of each lithology is only slightly displaced and remains unchanged. The results of the four measuring points show that the displacement of the coal rock is significantly larger than that of the other three lithologies, and the displacement of the mudstone is also larger than that of the other two lithologies. The displacement changes of fine-grained sandstone and coarse-grained sandstone are similar, and that of coarse-grained sandstone is slightly larger than that of fine-grained sandstone. The results show that there are differences in rock mass displacement around the borehole under different lithologies, which are caused by different rock mechanical parameters. The density, bulk modulus, shear modulus, and tensile strength of coal and mudstone are all low, which leads to cracking or even fracturing of the surrounding rock mass after the borehole is drilled, and then the displacement changes.

**Figure 6.** Displacement variation under different lithologies. (**a**) The displacement variation in the A (0.40, 0.50); (**b**) the displacement variation in the A (0.60, 0.50); (**c**) the displacement variation in the A (0.50, 0.40); (**d**) the displacement variation in the D (0.50, 0.60).

In summary, the stress and displacement changes of the rock mass around the borehole are obviously larger in the coal and mudstone than in the fine-grained sandstone and coarsegrained sandstone, and the stress and displacement of the rock mass after the borehole is

drilled are strongly influenced by the lithology, which also shows that the borehole stability is high in the fine-grained sandstone and coarse-grained sandstone, while that in the coal and mudstone is poor.
