*4.1. Construction of Numerical Model*

According to the specific engineering geological conditions of the 8102 and 9101 working faces of Xiashanmao coal mine, and combined with the existing underground pressure monitoring results, the finite difference software FLAC3D was used to establish a three-dimensional solid model. The distribution characteristics of mining stress in the mining process of the 9101 working face were studied. The numerical calculation model is shown in Figure 6. The calculation range was 330 m × 230 m × 100 m (length × width × height). The model simulated 12 layers of strata, including 8 # coal seam, 9 # coal seam and roof and floor strata, and truly reflected their occurrence conditions. Because the coal seam under actual working conditions could be regarded as a near-horizontal coal seam, the coal seam in the model was designed as a horizontal coal seam.

**Figure 6.** Three-dimensional numerical calculation model.

### *4.2. Determining Model Parameters*

For rock mass materials, the elastic modulus of rock mass greatly influences the accuracy of simulation results. Therefore, in the process of numerical simulation, the rock elastic modulus should be corrected and verified repeatedly to reduce the error with the actual value to ensure the reliability of simulation results. The physical and mechanical parameters of strata were obtained according to the test of rock core samples from geological drilling in the testing field, and the elastic modulus of rock was taken to be 1/10 of the elastic modulus of rock block by comparing with the physical parameters of rock strata in the adjacent working face. In this study, the mole-coulomb model was selected as the constitutive model, and the effective physical and mechanical parameters of rock mass were finally determined based on the physical and mechanical parameters of the rock mass involved, as shown in Table 2.


**Table 2.** The physical and mechanical parameters of rock.

### *4.3. Simulation Scheme*

According to the actual working conditions, the corresponding simulation scheme was formulated. The geometry and boundary conditions of the model are shown in Figures 7 and 8 respectively. The model was fixed around to limit the horizontal movement, and fixed at the bottom to limit the vertical movement, and 5 MPa uniform load was applied at the top to simulate the self-weight boundary of the overlying strata. The mining scheme of coal seam was as follows. For the large pillar mining, (a) the 8102 working face was firstly mined step by step, the excavation footage of each step was set as 10 m. After each step was balanced, the next step of excavation was calculated to balance, and the calculation was carried out step by step. (b) Three mining roadways of 9101 and 9102 working faces were excavated at one time, and a pillar with a width of 15 m was set, and the calculation was made to the model balance. (c) The 9101 working face was excavated step by step, and the excavation footage was set as 10 m. The mining direction was perpendicular to that of the 8102 working face. For the small pillar mining, (a) ditto; (b) three mining roadways of the 9101 and 9102 working faces were excavated at one time, a pillar with a width of 5 m was set, and the calculation was made to the model balance; (c) ditto. For the non-pillar mining, (a) ditto; (b) two mining roadways of the 9101 working face were excavated at one time, and the calculation was made to the model balance; (c) pre-cracking roof cutting was conducted firstly. Then the 9101 working face was excavated step by step, and the excavation footage was set to 10 m. The mining direction was perpendicular to that of the 8102 working face.



#### (**b**)

(**c**)

**Figure 7.** Geometry of the model. (**a**) Geometry of model of large pillar mining; (**b**) geometry of model of small pillar mining; (**c**) geometry of model of non-pillar mining.

**Figure 8.** Boundary conditions of the model.

#### **5. Distribution Law of Three-Dimensional Stress Field**

#### *5.1. Distribution Law of Vertical Stress*

In order to analyze the evolution law of stress distribution in the surrounding rock of stope, when the working face advances to 120 m, monitoring lines are arranged at different positions of the model, and vertical stress is monitored by monitoring lines. The location of monitoring lines is shown in Figure 9. Among them, one, two and three monitoring lines are located in the inner 10 m of the 9101 ventilation roadway, the middle of the 9101 working face, and the inner 10 m of the 9101 haulage roadway; four, five and six monitoring lines are located 5 m, 10 m and 20 m in front of the working face, respectively; seven, eight and nine monitoring lines are located on the left side of the working face, 5 m, 10 m and 15 m in front of the working face respectively; 10, 11, 12 and 13 monitoring lines are located on the left side of working the face, 5 m, 10 m, 30 m, and 80 m behind the working face, respectively.

(**a**)

**Figure 9.** *Cont.*

**Figure 9.** Location of monitoring lines. (**a**) Location of monitoring lines of large pillar mining; (**b**) Location of monitoring lines of small pillar mining; (**c**) Location of monitoring lines of non-pillar mining.

#### 5.1.1. Stress Distribution in Front of Working Face

#### (1) Stress distribution along working face strike

The vertical stress distribution nephograms and stress distribution curves at monitoring line 1 are shown in Figure 10. Figure 10 shows that the vertical stress distribution along the working face strike was similar under the three mining methods, and the advanced mining stress concentration area of the remaining pillars mining was larger than that of non-pillar mining, and the stress value was slightly higher. The peak of advanced mining stress was located 10 m in front of the working face, which was about 3.3 times that of the mining height of the working face. Among them, the peak stress of non-pillar mining was 14% lower than that of large pillar mining and 10% lower than that of small pillar mining. Within 3 m from the face, was the pressure-released zone of the stope; the vertical stress value was lower than the original rock stress, and the coal body mainly underwent

plastic deformation. Under the coupling effect of the overlying goaf and mining abutment pressure of this coal seam, a pressure boost belt was formed within the range of 3–33 m from the working face. The elastic deformation of coal body in this area caused the accumulation of elastic deformation energy, and the bearing capacity was higher. Within the range of 33–90 m from the working face, under the influence of pressure relief in the goaf of 8 # coal seam, the stress value was low. From 90–110 m away from working face, the residual pillar of 8 # coal seam formed a stress concentration zone here, and the stress value rose again. The stress distribution law at monitoring lines 2 and 3 was similar to that at monitoring line 1. The peak of advance mining stress was 10 m ahead of the working face. The peak stress of non-pillar mining was 23.88 MPa and 19.92 MPa respectively, which were 8%, 7% and −1%, 1% lower than that of traditional mining respectively (as shown in Table 3).

(**a**)

**Figure 10.** Vertical stress nephogram and stress distribution curve at the monitoring line 1 along the working face strike. (**a**) Vertical stress nephogram; (**b**) Stress distribution curve.


**Table 3.** Key parameters of the stress distribution characteristics along the working face strike.

Based on the above analysis, the key parameters of the stress distribution characteristics along the working face strike in the simulation results were summarized, and a matrix-type chart with resulting values and illustrations was made, so they can be visualized and compared in a single view (as shown in Table 3).

#### (2) Stress distribution along the inclination of working face

The vertical stress distribution nephograms and stress distribution curves at monitoring line 4 are shown in Figure 11. Figure 11 showed that, the distribution law of vertical stress along the inclination of the working face was similar under the three mining modes, that was, the stress data showed that the vertical stress increased first and then decreased. The stress curves of large and small pillars basically coincided, and the stress value was slightly higher than that of the non-pillar mining method. At the edge of the ventilation roadway, the three stresses were 10.8 MPa, 10.2 MPa and 7.6 MPa, respectively. The stress of non-pillar mining at the edge of the ventilation roadway was 30% and 25% lower than that of the large pillar and small pillar, respectively. At the distance of 10 m from the ventilation roadway, the three stresses reached 12.8 MPa, 12.3 MPa and 11.1 MPa. The stress of the non-coal pillar mining was 13% and 10% lower than that of the large pillar and small pillar mining, respectively. It could be seen that within the distance of 10 m from the ventilation roadway, the vertical stress increased greatly, while the non-coal pillar mining showed the characteristics of low stress compared with the traditional mining method. The main reason was that the roof rock beam was cut off by pre-cracking the roof cutting, which transformed it from a long-wall beam to short-wall beam and cut off the stress transfer between roofs, which improved the stress condition of surrounding rock obviously. The stress distribution law at monitoring lines 5 and 6 was similar to that at monitoring line 4. The stress increased rapidly within 10 m from the ventilation roadway and then slowed down. The stress distribution of traditional mining was axisymmetrical about the middle of the working face, while the stress of the side of the roof cutting of non-pillar mining was significantly lower than that of the non-roof cutting. Among them, the peak stress of non-pillar mining was 23.98 MPa and 19.41 MPa respectively, which were 7%, 7% and 10%, 8% lower than that of traditional mining respectively (as shown in Table 4).

(**a**)

**Figure 11.** Vertical stress nephogram and stress distribution curve at the monitoring line 4 along the inclination of the working face. (**a**) Vertical stress nephogram; (**b**) Vertical stress distribution curve.


**Table 4.** Key parameters of the stress distribution characteristics along the inclination of the working face.

Through the above analysis, the key parameters of the stress distribution characteristics along the inclination of the working face were summarized, and a matrix-type chart with resulting values and illustrations was made (as shown in Table 4).

5.1.2. Stress Distribution in Lateral Direction of Working Face

#### (1) Stress distribution in left front of working face

The vertical stress distribution curves at monitoring line 7 are shown in Figure 12. Figure 12 showed that there were two peaks along the working face inclination under the condition of large and small pillars mining. The locations of peak stress were 6 m, 23 m and 2 m, 15 m away from the edge of ventilation roadway respectively, with sizes of 17.7 MPa, 12.3 MPa and 10.8 MPa, 15.6 MPa. The stress concentration factors were 2.6, 1.8 and 1.6, 2.3. There was a wave peak along the inclination of the working face under non-pillar mining, which was located 5 m outside ventilation roadway, with a size of 14.8 MPa, and the stress concentration factor was 2.2. Compared with the peak stress, it could be seen that the non-pillar mining decreased by 16% and 5% for large and small pillar mining respectively, indicating that the non-pillar mining had less influence on the advanced mining stress of the roadway surrounding rock, that was, the technology of roof cutting and pressure relief cut off the stress transfer between the working face and roadway roof, and the stress control effect was better. By analyzing the location of peak stress, it could be seen that the peak stress of the retaining pillar mining mode was 6 m outside the roadway, while that of the non-pillar mining mode was 5 m outside the roadway, which indicated that the plastic zone of surrounding rock in the advanced position of a roadway under non-pillar mining mode was smaller. In addition, the advantages of this mining method on the stress control of surrounding rock were further reflected. The stress distribution law at monitoring lines 8 and 9 was similar to that at monitoring line 7. The advance abutment pressure in lateral direction of the working face was lower than that of monitoring line 7. The peak stress of traditional mining was 6 m outside the ventilation roadway, while the peak stress of non-pillar mining was 5 m from the ventilation roadway. The peak stresses of non-pillar mining were 13.5 MPa and 12.5 MPa respectively, which were 12%, 8% and 13%, 7% lower than that of traditional mining respectively (as shown in Table 5).

**Figure 12.** Vertical stress distribution curve at monitoring line 7 in lateral direction of the working face.


**Table 5.** Key parameters of the stress distribution characteristics in the left front of the working face.

Combined with the analysis results, the key parameters of the stress distribution characteristics in the left front of the working face in the simulation results were summarized, and a matrix-type chart with resulting values and illustrations was made (as shown in Table 5).

#### (2) Stress distribution in left rear of working face

The vertical stress distribution curves at monitoring line 10 are shown in Figure 13. Figure 13 showed that, there were obvious differences in the stress distribution characteristics along the inclination of the working face under the three mining methods, which were mainly reflected in the stress concentration area and the degree of stress concentration. Figure 13b intuitively showed that, in the lateral direction of the working face, the stress of the large pillar mining method was the largest, followed by the small pillar mining and the minimum of the non-pillar mining method. Under the traditional mining method, the vertical stress showed that the distribution characteristics were saddle-shaped, in which the large pillar mining first formed the stress concentration in the large pillar, that was, the first wave peak appeared. Then a small degree of concentration appeared at the roadway edge of the 9102 working face, forming a second wave peak, indicating that the stope underground pressure was mainly borne by the large pillar behind the working face. The small pillar mining was obviously different from large pillar mining. The larger stress concentration was located at the 9102 working face, and a smaller concentration occurred in the small pillar, indicating that the small pillar had a low bearing capacity behind the working face due to the limitation of coal pillar width, and the stress bearing area transferred to the deep part of the working face. Because of the elimination of pillars for the non-pillar mining method, the weight of overlying strata was borne by the solid coal on the working face, and a stress bearing area was formed in the 9102 working face. Therefore, the stress concentration position was transferred from the traditional pillar area to the deep part of the working face, and the peak of non-pillar mining was the smallest, which was 21% and 10% lower than the traditional mining method of large pillar and small pillar respectively. It could be seen that the technique of gob-side roof cutting effectively reduced the stress concentration in stope and optimized the stress distribution in the lateral direction of the working face. The stress distribution law at monitoring lines 11, 12, and 13 was similar to that at monitoring line 10. Traditional mining methods still showed the characteristics of double-stress wave peak distribution, in which the high stress concentration in large pillar, small pillar and no pillar mining methods occurred in the pillar, 9102 working face and deep part of the solid coal, respectively. The peak stresses were the smallest of non-pillar mining, which were 18%, 10%; 16%, 6% and 13%, 7% lower than that of traditional mining respectively (as shown in Table 6).


**Table 6.** Key parameters of the stress distribution characteristics in the left rear of the working face.

(**a**)

**Figure 13.** Vertical stress nephogram and stress distribution curve at monitoring line 10 in lateral direction of working face. (**a**) Vertical stress nephogram; (**b**) Vertical stress distribution curve.

With the help of the above analysis, the key parameters of the stress distribution characteristics in the left rear of the working face were summarized, and a matrix-type chart with resulting values and illustrations was made (as shown in Table 6).
