*4.1. Distribution Characteristics of Cracks in the Surrounding Rocks under the Combined Support of Short Bolts and Long Anchor Cables*

The simulated roadway is controlled according to the original combined support of the mine in Figure 2 with the combination of 14 short bolts, with a length of 2.2 m, and 5 long anchor cables, with a length of 7.0 m. With the gradual release of the surface stress of the roadway in stages, the evolution characteristics of cracks in the surrounding rocks with the number of operation steps are shown in Figure 11. When the number of operation steps reaches 2.5 × 104, that is, R = 0.7, the number of cracks in the surrounding rocks in Zone A of the roadway is 257, while the number of cracks in the surrounding rocks in Zone B is only 43, indicating that the surface stress has not been completely released, such that the damage degree of the rock mass shows a great difference. It can be further seen from the crack distribution diagram that the maximum depth of crack evolution in Zone A is still in the bolt anchorage area, while the cracks in Zone B are only distributed on the shallow surface of the roadway. When the number of operation steps reaches 10 × 104, that is, R = 1.0, the number of cracks in the surrounding rocks in Zone A and Zone B is 794 and 117, respectively, and the cracks in different positions of the roadway increase to different extents. As shown in the lower-right figure, the cracks in Zone A expand significantly, and the evolution depth exceeds the bolt anchorage area, with the maximum crack depth reaching 3.5 m. At this time, the rock mass in the whole bolt anchorage area is seriously cracked, with the risk of overall collapse and instability.

**Figure 11.** Evolution characteristics of cracks in the surrounding rocks under the primary support.

*4.2. Thick-Layer Anchorage Principle and Differential Equivalent Reinforcement Technology*

The number of cracks in the surrounding rocks in Zone A and Zone B of the roadway under the primary support of the mine is greatly reduced by 775 and 31, respectively, compared with that when there is no support, with a reduction rate of 49.4% and 20.9%, respectively. Although the primary support has a certain effect on restraining the development of cracks, it does not change the damage status of the seriously deteriorated zone of the roadway (Zone A). The anchor point in the bolt on this side is still located in the crack circle, and the bolt anchorage zone shows an overall movement trend; however, since the anchor cable is too long it has a limited reinforcement effect on the rock mass in this range, and the anchor cable is easy to break. Therefore, the bolt and anchor cable combined technology needs to be changed urgently.

It is assumed that the anchored rock beam of the foundation of the roadway roof is simplified as a simply supported beam, as shown in Figure 12. When the rock beam experiences pure bending deformation, according to the maximum tensile stress theory (the first strength theory), the maximum dangerous point of the roof is at the center of the anchored rock beam surface (i.e., Point C). At this time, the maximum tensile stress of the rock beam (see Equation (8)) is as follows:

$$
\sigma\_{\text{max}} = \frac{\mathbf{M}\_{\text{max}} y\_{\text{max}}}{I\_Z},
\tag{8}
$$

where Mmax <sup>=</sup> qL2 <sup>8</sup> , *<sup>y</sup>*max <sup>=</sup> *<sup>h</sup>* <sup>2</sup> , and *IZ* <sup>=</sup> <sup>b</sup>*h*<sup>3</sup> <sup>12</sup> . The relationship (see Equation (9); *k* stands for constant) between the maximum tensile stress and the thickness of the rock beam is further obtained as follows:

$$
\sigma\_{\text{max}} = \frac{3\mathbf{q}\mathbf{L}^2}{4\mathbf{b}h^2} \Rightarrow k\frac{1}{h^2} \propto \frac{1}{h^2} \,\tag{9}
$$

**Figure 12.** Mechanical model of a simply supported beam for an anchored rock beam.

It can be concluded from Equation (9) that the maximum tensile stress of an anchored rock beam is inversely proportional to the square of its thickness, indicating that the greater the thickness of an anchored rock beam the smaller the tensile stress value and the more stable the roof rock stratum. Therefore, in order to realize the long-term stable control of the roadway, the foundation anchorage thickness in the support system shall meet the cross-boundary requirements of the thick layer [27,28]; that is, the foundation bolt support shall span the surrounding rock crack circle as well as plastic circle, and the inner anchorage point shall be anchored into the elastic circle to form a thick reinforcement circle that is closely connected with the stable rock mass in the deep part. In order to improve the strength and stiffness of the anchorage bearing layer and resist the disturbance of mining stress as well as the long-term creep effect of soft rock, the bidirectional linkage control of the deep and shallow displacement is realized by increasing the thickness of the foundation anchorage layer and restricting the large displacement in the shallow part with the small displacement in the deep part, which is suitable for a roadway under any surrounding rock inclination angle.

According to the peep images and numerical simulation results of the surrounding rocks of the roadway, the initial cracks in the surrounding rocks of the roadway in the steeply inclined coal seam after excavation are characterized by an obvious asymmetric distribution. The crack depth in Zone A is generally greater than 1.5 m, while the crack depth in Zone B is generally less than 0.5 m, as shown in Figure 13a; however, the equallength and equal-strength combined support form of the primary support is no longer suitable, and the key positions are not reinforced by deep anchorage, so the maintenance and control effects of the roadway are extremely poor. According to the cross-boundary anchorage principle, the bolt–anchorage thickness of the severely deteriorated Zone A shall be significantly greater than that of the slightly damaged Zone B. At the same time, due to the repeated staggered distribution of the steeply inclined coal–rock seams in Zone A, in order to ensure the long-term bearing of the anchored rock mass, the grouting method shall be adopted to modify the lithology of the surrounding rocks, especially the grouting reconstruction of the rock mass in the floor corner. Unequal-length differential anchorgrouting support technology is used to construct the overall thick-layer bearing structure of the full-section surrounding rocks of the roadway, that is, the equivalent reinforcement layer, to adapt to the long-term creep effect of the weak surrounding rocks, and then realize the long-term stable bearing of the roadway in the steeply inclined coal seam, as shown in Figure 13b.

**Figure 13.** Asymmetric deterioration characteristics and equivalent reinforcement principle of the roadway in the steeply inclined coal seam. (**a**) Sketch of the asymmetric distribution of cracks; (**b**) equivalent reinforcement effect.

In view of different coal–rock properties, crack characteristics, and crack depths in each part of the roadway in the steeply sloping coal seam, two support forms, namely hollow grouting cables and flexible bolts, are used in Zone A and Zone B, respectively, to construct an equivalent reinforcement layer with a thickness of 2.5–3.0 m for the roadway in the steeply inclined coal seam. For the surrounding rocks in Zone A the anchor-grouting combined reinforcement method shall be adopted, and the foundation anchorage thickness shall exceed 4.0 m. For Zone B only the end anchorage is required, and the foundation anchorage thickness can be less than 3.5 m.
