*2.3. Methods*

A geometric model was established based on the 30503 return roadway, as shown in Figure 4, and the perspective view is shown in Figure 5. In order to reduce the influence of other factors on the model, the model was constructed with 3–5 coal as the vertical center and based on the coal seam histogram. Nine layers of rock were constructed upward and downward, and the length and width of the model were set to 100 times the width of the roadway and rounded to 500 m; in other words, the model's size was 500 m × 500 m × 156 m. Moreover, since the burial depth of the top of the model was 348 m, according to the traditional ground stress calculation method, the top of the model was subjected to a vertical stress of 8.7 MPa. The vertical stress of 8.7 MPa was applied to the top of the model, and the numerical simulation was carried out by FLAC3D finite element difference software. Due to the large size of the model, the influence of the roadway and residual coal pillars is negligible, so the front, back, left, and right sides of the model as well as the bottom are fixed with fixed displacement and fixed boundaries, and the Mohr–Coulomb principal structure model is used. In order to improve the accuracy of the calculation, the encryption around 30 m of the roadway is 1 m per frame; at around 15 m, it is 0.5 m per frame, and around 15 m of the coal pillar, it is 1 m per frame. The demonstrated basic mechanical parameters involved in the numerical simulation are shown in Table 1. These data were obtained from the paper "Research on the mining method of close extra-thick coal seam in Datong Tashan coal mine of China National Investment Corporation" [36].

**Figure 4.** A figure of the numerical model.

**Figure 5.** Numerical model perspective view.



#### **3. Results**

*3.1. Plastic Zone Morphology and Distribution*

3.1.1. Roadways with Vertical Layer Differences

(1) Roadway excavation along the roof

The horizontal distance between the roadway dug along the top and the residual coal column of the overlying coal seam is 15.2 m, and the vertical distance is about 4.4 m. From the stress cloud diagram (Figure 6), the maximum and minimum principal stresses appear at the residual coal pillar, and the maximum principal stress (σ1) near the coal pillar is about 70–120 MPa; the minimum principal stress (σ3) is about 26–50 MPa. σ<sup>1</sup> around the roadway is about 6–20 MPa, and σ<sup>3</sup> is about 3–10 MPa.

**Figure 6.** Principal stress distribution contour of the roadway's surrounding rock when the roadway excavation along the roof. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

To further analyze changes in the surrounding rock stress in the vertical direction and horizontal direction of the roadway when digging along the top, the measurement lines were arranged in the vertical direction and horizontal direction of the roadway center, respectively, and the main stress change curve was obtained (Figure 7). In the horizontal direction, σ<sup>1</sup> and σ<sup>3</sup> in the surrounding rock gradually decrease from the positive gang to the negative gang of the roadway. At approximately −30 m away from the positive gang of the roadway, σ<sup>1</sup> and σ<sup>3</sup> in the surrounding rocks reach the peak values of 67 MPa and 15 MPa, respectively, and the site is located below the residual coal pillar. Meanwhile, the ratio of σ<sup>1</sup> and σ<sup>3</sup> in the surrounding rocks can be found from in positive gang to the negative gang of the roadway. The ratios of σ<sup>1</sup> and σ<sup>3</sup> in the surrounding rocks gradually decrease from the positive to the negative gang of the roadway. From the vertical direction, σ<sup>1</sup> and σ<sup>3</sup> at the location of the roadway are small, while the principal stresses below the roadway are large, and the principal stresses at the location of the coal seam floor reach the peak; the ratio between σ<sup>1</sup> and σ<sup>3</sup> reaches the maximum at this moment. σ<sup>1</sup> and σ<sup>3</sup> at the roadway are about 9.5 MPa and 4.5 MPa, respectively.

**Figure 7.** Changes in the principal stresses of the roadway's surrounding rock when the roadway excavation along the roof. (**a**) Horizontal direction. (**b**) Variation direction.

Figure 8 shows the cloud map of the plastic zone. In the figure, the range of different color areas represents the range of the plastic zone. Each color distribution indicates the damage form at the location, including shear damage, tension damage, and volume damage. "n" in the figure represents the current state, and "p" represents the previously existing state. As observed in the figure, the plastic zone of the roadway presents an asymmetric distribution pattern, and the plastic zone of the positive gang of the roadway is larger in scope due to the superposition and concentration of stress at the residual coal pillar, which is connected with the plastic zone of the residual coal pillar. As the roadway is excavated

along the top, the top plate of the roadway comprises rock, and the strength of the coal seam is smaller than the strength of rock, so the range of plastic zone of the top plate of the roadway is smaller than the two gangs and the bottom plate.

**Figure 8.** Plastic zone distribution cloud map when the roadway excavation along the roof.

(2) Roadway excavation leaves top coal bottom coal

The horizontal distance between the roadway dug by the retained top coal and bottom coal and the residual coal column of the overlying coal seam is 15.2 m, and the vertical distance is about 15.4 m. According to the stress cloud diagram (Figure 9), σ<sup>1</sup> and σ<sup>3</sup> appear in the residual coal column of the overlying coal seam, σ<sup>1</sup> near the residual coal column of the overlying coal seam is about 60–110 MPa, and σ<sup>3</sup> is about 25–58 MPa. σ<sup>1</sup> around the roadway is about 8–16 MPa, and σ<sup>3</sup> is about 0.3–5 MPa.

**Figure 9.** Principal stress distribution contour of the roadway's surrounding rock when the roadway excavation leaves top coal bottom coal. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

As observed in the main stress change curve (Figure 10), in the horizontal direction, the maximum main stress and the minimum main stress increase and then decrease from the residual coal pillar relative to the direction of the roadway. The peak stress appears at the residual coal pillar; the further the location from the residual coal pillar, the smaller the stress value and the smaller the stress ratio. From the upper and lower levels, the further away from the bottom plate, the smaller σ<sup>1</sup> and σ<sup>3</sup> are, and the stress ratio also decreases. Due to the influence of the residual coal pillar, the σ<sup>1</sup> value decreases at the

location of where the roadway's layout increases, and σ<sup>1</sup> at the location of the roadway roof reaches the lowest point of the stage, and then, the maximum principal stress continues the decreasing trend after a slight increase is inflicted by the influence of the residual coal column of the upper coal seam. The maximum principal stress and the minimum principal stress at the center position of the roadway are about 16.2 MPa and 6.2 MPa, respectively.

**Figure 10.** Changes in the principal stresses of the roadway's surrounding rock when the roadway excavation leaves top coal bottom coal. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone distribution cloud map (Figure 11), the plastic zone of the roadway is still asymmetrically distributed. The range is slightly smaller than the range of the roadway when dug along the top, and the plastic zone of the roadway is connected with the plastic zone of the residual coal column. The plastic zone mainly appears at the top and negative gang of the roadway, while the plastic zone at the positive gang and bottom of the roadway is smaller.

**Figure 11.** Plastic zone distribution cloud map when the roadway excavation leaves top coal bottom coal.

(3) Roadway excavation along the floor

The horizontal distance between the roadway dug along the bottom and the residual coal column of the overlying coal seam is 15.2 m, and the vertical distance is about

20.4 m. According to the stress cloud diagram (Figure 12), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal column of the overlying coal seam, and σ<sup>1</sup> near the residual coal column is about 70–110 MPa; σ<sup>3</sup> is about 25–58 MPa. σ<sup>1</sup> around the roadway is about 5–13 MPa, and σ<sup>3</sup> is about 0.8–2 MPa.

**Figure 12.** Principal stress distribution contour of the roadway's surrounding rock when the roadway excavation along the floor. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

This can be seen in the main stress variation curve (Figure 13). In the horizontal direction, σ<sup>1</sup> and σ<sup>3</sup> increase and then decrease from the residual coal pillar to the direction of the roadway, and the peak stress appears at the residual coal pillar. At the location away from residual coal pillars, the smaller the stress value, the smaller the stress ratio. From the vertical direction, at distances further from the bottom plate, σ<sup>1</sup> and σ<sup>3</sup> experience smaller decreases, and the stress ratio also decreases. σ<sup>1</sup> at the roadway is about 18.5 MPa, and σ<sup>3</sup> is about 6.5 MPa.

**Figure 13.** Changes in the principal stresses of the roadway's surrounding rock when the roadway excavation along the floor. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone's distribution cloud map (Figure 14), the plastic zone of the roadway is not connected with the plastic zone at the residual coal pillar, and the range of the plastic zone of the roadway obviously reduced the plastic zone. The maximum damage depth is 6 m, and the plastic zone mainly appears at the top plate and positive gang of the roadway.

**Figure 14.** Plastic zone distribution cloud map when the roadway excavation along the floor.

3.1.2. Roadways with Horizontal Layer Differences

(1) The coal column is 4 m

When the coal pillar is 4 m, the horizontal distance between the roadway and the residual coal pillar is 31.85 m, and the vertical distance is about 18.5 m. According to the stress cloud diagram (Figure 15), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal column of the overlying coal seam, and σ<sup>1</sup> near the residual coal column is about 60–115 MPa. σ<sup>3</sup> is about 22–60 MPa. σ<sup>1</sup> around the roadway is about 5–18 MPa, and σ<sup>3</sup> is about 0.4–1 MPa.

**Figure 15.** Principal stress distribution contour of the roadway's surrounding rock when the coal column is 4 m. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

This can be seen in the main stress variation curve (Figure 16). In the horizontal direction, σ<sup>1</sup> and σ<sup>3</sup> increase and then decrease from the residual coal pillar to the direction of the roadway, and the peak stress appears at the residual coal pillar. At a location away from residual coal pillars, the smaller the stress value, the smaller the stress ratio. From the vertical direction, σ<sup>1</sup> increases and then decreases as it moves away from the center of the roadway, while σ<sup>3</sup> gradually decreases. σ<sup>1</sup> at the center of the roadway is about 13.5 MPa, and σ<sup>3</sup> is about 6 MPa.

According to the plastic zone distribution cloud map (Figure 17), the maximum damage depth of the roadway plastic zone is 3 m. The range is small and is mainly distributed in the top plate and two gang positions. The bottom side has almost no plastic zone distributions, the roadway plastic zone in an independent state.

**Figure 17.** Plastic zone distribution cloud map when the coal column is 4 m.

(2) The coal column is 8 m

When the coal column is 8 m, the horizontal distance from the residual coal column is 27.85 m and the vertical distance is about 18.5 m. According to the stress cloud diagram (Figure 18), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal column of the overlying coal seam, and σ<sup>1</sup> near the residual coal column is about 54–115 MPa; σ<sup>3</sup> is about 25–59 MPa. σ<sup>1</sup> around the roadway is about 6–18 MPa, and σ<sup>3</sup> is about 0.2–4 MPa.

**Figure 18.** Principal stress distribution contour of the roadway's surrounding rock when the coal column is 8 m. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

The stress change curve shows (Figure 19) that, along the horizontal direction, the stress peak directly below the residual coal pillar is reached, and after moving away from the residual coal pillar, σ<sup>1</sup> and σ<sup>3</sup> gradually decrease, and σ1/σ<sup>3</sup> gradually decrease. Along the vertical direction, σ<sup>1</sup> first increases and then decreases as it moves away from the center of the roadway, while σ<sup>3</sup> gradually decreases. σ<sup>1</sup> at the center of the roadway is about 14 MPa, and σ<sup>3</sup> is about 6 MPa.

**Figure 19.** Changes in the principal stresses of the roadway's surrounding rock when the coal column is 8 m. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone's distribution cloud map (Figure 20), the maximum damage depth of the plastic zone of the roadway is 3.5 m, the range is slightly increased than that of the 4 m coal pillar, and the distribution pattern is similar to that of the 4 m coal pillar.

(3) The coal column is 15 m

When the coal column is 15 m, the horizontal distance from the residual coal column is 20.85 m, and the vertical distance is about 18.5 m. According to the stress cloud diagram (Figure 21), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal column of the overlying coal seam, and σ<sup>1</sup> near the residual coal column is about 67–113 MPa; σ<sup>3</sup> is about 26–59 MPa. σ<sup>1</sup> around the roadway is about 5–26 MPa, and σ<sup>3</sup> is about 0.6–5 MPa.

The stress change curve shows (Figure 22) that along the horizontal direction, the stress peak directly below the residual coal pillar is reached, and after moving away from the residual coal pillar, σ<sup>1</sup> and σ<sup>3</sup> gradually decrease, and σ1/σ<sup>3</sup> gradually decrease. Along the vertical direction, σ<sup>1</sup> first increases and then decreases as it moves away from the center of the roadway, while σ<sup>3</sup> gradually decreases. σ<sup>1</sup> at the center of the roadway is about 15.6 MPa, and σ<sup>3</sup> is about 6 MPa.

**Figure 20.** Plastic zone distribution cloud map when the coal column is 8 m.

**Figure 21.** Principal stress distribution contour of the roadway's surrounding rock when the coal column is 15 m. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

**Figure 22.** Changes in the principal stresses of the roadway's surrounding rock when the coal column is 15 m. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone distribution cloud map (Figure 23), the maximum damage depth of the plastic zone of the roadway is 5.5 m, and the range further increases. The distribution pattern is similar to those above the 4 m and 8 m coal pillars. When the coal pillar's size is 20 m, this condition is consistent with the situation of the roadway dug along the bottom in the previous subsection, and it will not be repeated here. The maximum depth of damage in the plastic zone of the roadway is 6 m, and the extent of the plastic zone continues to grow.

**Figure 23.** Plastic zone distribution cloud map when the coal column is 15 m.

(4) The coal column is 25 m

When the coal column is 25 m, the horizontal distance from the residual coal column is 10.85 m, and the vertical distance is about 18.5 m. According to the stress cloud diagram (Figure 24), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal column of the overlying coal seam, and σ<sup>1</sup> near the residual coal column is about 65–110 MPa; σ<sup>3</sup> is about 25–58 MPa. σ<sup>1</sup> around the roadway is about 4–25 MPa, and σ<sup>3</sup> is about 0.4–6 MPa.

The stress change curve shows (Figure 25) that along the horizontal direction, the stress peak is reached directly below the residual coal pillar, and after moving away from the residual coal pillar, σ<sup>1</sup> and σ<sup>3</sup> gradually decrease, and σ1/σ<sup>3</sup> gradually decreases. Along the vertical direction, σ<sup>1</sup> first increases and then decreases as it moves away from the center of the roadway, while σ<sup>3</sup> gradually decreases. σ<sup>1</sup> at the center of the roadway is about 21 MPa, and σ<sup>3</sup> is about 7.5 MPa. σ<sup>1</sup> and σ<sup>3</sup> are in a constant state of growth.

**Figure 25.** Changes in the principal stresses of the roadway's surrounding rock when the coal column is 25 m. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone distribution cloud map (Figure 26), the maximum damage depth of the plastic zone of the roadway is 7.5 m, the plastic zone appears with an obvious butterfly shape, and the upper butterfly lobe's development is obvious and is mainly distributed at the top of the roadway and the positive gang. The lower butterfly lobe's development is smaller. The upper butterfly lobe points to the direction of the residual coal pillar. The plastic zone of the roadway's surrounding rock and the plastic zone at the residual coal pillar are not yet connected.

**Figure 26.** Plastic zone distribution cloud map when the coal column is 25 m.

(5) Roadway dug directly below the residual coal pillar

When the roadway is located directly below the residual coal pillar, the vertical distance from the residual coal pillar of the overlying coal seam is about 18.5 m. According to the stress cloud diagram (Figure 27), σ<sup>1</sup> and σ<sup>3</sup> appear at the residual coal pillar of the overlying coal seam, and σ<sup>1</sup> near the overlying residual coal pillar is about 61–104 MPa, and σ<sup>3</sup> is about 22–50 MPa. σ<sup>1</sup> around the roadway is about 5–24 MPa, and σ<sup>3</sup> is about 0.4–7 MPa.

**Figure 27.** Principal stress distribution contour of the roadway's surrounding rock when the roadway dug directly below the residual coal pillar. (**a**) σ<sup>1</sup> cloud. (**b**) σ<sup>3</sup> cloud.

The stress change curve shows (Figure 28) that along the horizontal direction, the stress peak is reached directly below the residual coal pillar, and after moving away from the residual coal pillar, σ<sup>1</sup> and σ<sup>3</sup> gradually decrease, and σ1/σ<sup>3</sup> gradually decreases. Along the vertical direction, as the distance from the center of the roadway increases, σ<sup>1</sup> gradually increases, while σ<sup>3</sup> gradually decreases. σ<sup>1</sup> at the center of the roadway is about 41 MPa, and σ<sup>3</sup> is about 20 MPa, at which time both σ<sup>1</sup> and σ<sup>3</sup> reach their maximum values.

**Figure 28.** Changes in the principal stresses of the roadway's surrounding rock when the roadway dug directly below the residual coal pillar. (**a**) Horizontal direction. (**b**) Variation direction.

According to the plastic zone's distribution cloud map (Figure 29), the plastic zone of the roadway is connected with the plastic zone at the residual coal pillar. The plastic zone appears with an obvious butterfly shape, and the butterfly's lobe development is obvious. the top plate of the roadway and the top angle position of the two helpers have a large ranged plastic zone.

**Figure 29.** Plastic zone distribution cloud map when the roadway dug directly below the residual coal pillar.
