1) Strain-softening model for coal and rock simulation

After the stress peaks, the strength of the rock drops rapidly to a lower level as the deformation continues to increase, a phenomenon known as “strain softening”. The strain-softening model believes that the properties of rock materials change with the plasticity. After plastic yielding begins, the cohesion, internal friction angle, and dilatancy angle of the rock will all attenuate with the plastic strain constantly. In the numerical simulation calculation, the strain-softening model can truly reflect the failure of the surrounding rock. Thus, this model is extensively applied in the fields of rock mechanics, geotechnical, and mining engineering. The softening parameters are shown in Table 2, and the internal friction angle and the cohesion of the coal and rock change with shear strain.

2) Double-yield model for goaf simulation

The gangue collapsed in the goaf is in a loose state at first and is gradually compacted under the action of its own gravity and overlying rock pressure as the working face advances. The strength and modulus of the rock mass in the caving zone increase gradually during the gradual compaction process, but it is impossible to reach its original state. This progressively compacted property can be simulated using the double-yield model in FLAC3D. The double-yield constitutive model proposed by Salamon (Salamon 1990) is widely used to analyze the mechanical properties of goaf materials. The formulae are shown below: σ = E 0 ε 1 − ε / ε m , (1) ε m = b − 1 b , (2) b = h c a v + h m h c a v , (3) E 0 = 10.39 σ c 1.042 b 7.7 . (4)

In the equations, ε m is the maximum strain, E₀ is the initial modulus, b is the bulking factor, hm is the height of the caving zone, h_cav is the mining height, and σ_c is the virgin vertical stress. According to the field data of the working face with a mining height of 15.3 m collected by the EH4 magnetotelluric imaging system, it is estimated that the caving height of the goaf is 80 m (Wu et al. 2019). Therefore, the maximum strain and bulking factor of the collapsed rock are calculated to be 0.15 and 1.16 by Eqs 2, 3, respectively. Eq. 1 is utilized to quantify the goaf displacement for making a comparison with the simulation results. Table 3 tabulates the stress and strain of goaf materials calculated by Salamon’s equations.

In order to obtain the relevant parameters of the double-yield model of the goaf in the Tongxin coal mine, a single cubic model of 1 × 1 m×1 m is established. The parameters of the model are assigned by trial and error until the stress–strain curves match each other, as shown in Figure 3. The two curves are in good agreement, confirming the applicability of the double-yield constitutive model in FLAC3D for goaf simulation. The mechanical parameters of the double-yield model determined that the bulk modulus was 8.6 GPa, shear modulus was 6.3 GPa, density was 2000 kg/m³, cohesion was 0.1 MPa, internal friction angle was 5°, and dilation angle was 6°.

By taking the 8,104 and 8,105 working faces in the Tongxin coal mine as the engineering background, numerical simulation software FLAC^3D is used to establish a model with a size of 400 × 645 × 324.3 m (length × width × height), and the number of the model elements is 758,400 (Figure 4). Physical and mechanical parameters are described in Table 4. The four sides and the bottom of the model are constrained by displacement. A gradient stress of 15–24.73 MPa is applied in the advancing direction of the working face, and a gradient stress of 12.5–20.6 MPa is applied in the vertical direction of the model.

To accurately investigate the stress distribution in the coal pillar, a 65 × 65 × 65 m grid densification area is established in the middle of the model. Based on the research of Galvin (Galvin 2016), the caving angle of the hard and soft roof is set at 50° and 80°, respectively. In the numerical model of the weak roof, the strength is reduced to 25% of the hard roof. The 8,105 working face is first excavated. After it is completed, mining the 8,104 working face begins. According to the onsite situations in the mine, the 8,104 and 8,105 working faces advance 20 m every step in the numerical model.

1) Mining stress distribution at the working face during the first face advance.

The overhanging state of the roof above the working face varies with different overlying rock strengths. In hard roof conditions, as the working face proceeds, the overhanging area of the roof increases. The working face will bear more abutment pressure, and the roof is not easy to collapse, resulting in strong mining stress. In view of this, the mining stress distribution at the working face is analyzed based on numerical simulation and comparison with the mining process with soft roofs.

Figure 5 shows the mining stress distributions during mining the 8,105 working face in hard and soft roof conditions, respectively. The stress concentration area in front of the working face presents a symmetrical stripe-shape distribution. In hard roof conditions, the influence zone of the front abutment pressure is up to 80 m, the peak stress reaches 26.4 MPa, and the stress concentration factor is 1.84. In soft roof conditions, the influence zone of front abutment pressure is 74 m, the peak stress is 22 MPa, and the stress concentration factor is 1.53.

It can be seen that the roof strength has an obvious influence on the stress concentration area and stress peak value at the mining face. The influence zone of the front abutment pressure is 6 m wider, and the stress peak value is 4.4 MPa higher in hard roof conditions than that in soft roof conditions. The hard overlying strata are more difficult to collapse in the mining process than soft ones and can generate a larger area affected by the higher abutment pressure. Hence, more intense mining stress is produced at the working face during mining the coal seam with a hard roof.

2) Mining stress distribution at the working face during the second face advance.

The stress distributions during mining the 8,104 working face with different roof strengths are compared. In the second mining process, the zone ahead of the working face is affected by two driving disturbances, that is, the influences of the lateral abutment pressure of the adjacent goaf and the front abutment pressure of the working face. The stress will be concentrated in the area close to the goaf, forming a triangular stress concentration zone.

Figure 6 shows the stress distributions in the second excavation under different roof conditions. For hard roof circumstances, the influence range of front abutment stress reaches 97 m, the peak stress increases to 55.4 MPa, and the stress concentration factor gets to 3.85. In the other condition, the influence range of front abutment stress is 91 m, the peak stress is 45 MPa, and the stress concentration factor is 3.13.

It can be seen that the roof strength has a significant impact on the stress concentration zone and stress peak value at the working face. The influence zone of the front abutment pressure is 6 m wider, and the stress peak value is 10.4 MPa higher than a soft overburden. The data indicate that there is greater abutment pressure in front of the working face because the overhanging length of the roof is larger under hard roof conditions. In terms of mining stress, the mining stress at the working face is higher under the condition of a hard overburden, which is more harmful to the safety of the working face.

1) Influence of the roof strength on coal pillar stability in the first face advance

Figure 7 shows the coal pillar after one mining under different roof strengths. It can be seen that the 45-m-wide coal pillar is not completely yielded after the first panel extracted despite different roof conditions. The stability of the coal pillar with different roof strengths has little difference at this time. The width of the plastic zone in the coal pillar under hard roof conditions is the same as that under soft roof conditions. The elastic zone width (14 m) occupies 31.1% of the pillar width (45 m). Due to the influence of the mined-out space, the area of the coal pillar approaching the goaf is destroyed, but the yield zone fails to penetrate through the pillar which is still in a stable state.

The peak stress in the coal pillar with a hard roof is 30.83 MPa which is 4.92 MPa higher than that with a soft roof (25.91 MPa). It is clearly seen from Figure 8 that the stress exhibits a unimodal-shape distribution due to the effect of the lateral abutment pressure in the goaf. The stress is concentrated in the area close to the solid coal. The lower stress area nearby the goaf indicates that the coal pillar at this region has yielded. The positions bearing the largest stress are basically the same under different roof strengths, but the peak stressed place is much closer to the solid coal under hard roof conditions, and the stress in the coal pillar is also greater.

2) Influence of the roof strength on coal pillar stability in the second face advance

Figure 9 shows the coal pillar after secondary mining under different roof strengths. The plastic zone in the coal pillar is enlarged due to the effects of the two goafs. It can be seen that

Elastoplastic Regional Correlation of the Coal Pillar:

① At 80 m behind the working face, despite different roof strengths, the 45-m-wide coal pillar is yielded in the whole width, and the coal pillar is completely destabilized owing to the influence of the two goafs.

② At the working face, the elastic zone in the pillar is 5 m, accounting for 11.1% of the total pillar width in hard roof circumstances, while the elastic zone width is 16 m, which is 35.5% of the pillar width in soft roof circumstances. Thereby, hard overlying rocks are unfavorable to the stability of working faces and mining roadways.

③ At 25 m ahead of the working face, the elastic zone width is 11 m, accounting for 24.4% of the pillar width. Regarding the soft roof, the elastic zone is 15 m, that is, 33.3% of the pillar width. The failure zone under hard roof conditions is 4 m wider than that under soft roof conditions. By comparison, the plastic failure zone in the hard roof coal pillar is bigger; the coal pillar is easier to lose stability, the roof is more prone to collapse, and the roadway is easily deformed.

④ At 80 m in front of the working face, for mining with a hard roof structure, the elastic zone width (12 m) is 26.6% of the pillar width. Considering mining the coal seam beneath the soft rock strata, the elastic zone width is 15 m and accounts for 33.3% of the pillar width. The plastic zone width in the first mining situation is 3 m larger than that in the second situation. The comparison shows that the stability of the coal pillar with a hard roof is worse than that with a soft roof, and the roadway is easier to fail.

Comparison of the Stress Distribution Diagram of the Coal Pillar (Figures 9, 10):

① In spite of different roof conditions, the stress has little difference at two monitoring points, namely, 80 m behind the working face and the working face position. The peak stress in the coal pillar under hard roof conditions is 21.9 MPa and that under the other situation is 21.67 MPa. The stress values are quite similar and relatively small, implying that the coal pillar is in a complete yield state.

② At the face position, the peak stress in the coal pillar with hard overlying strata is 35.27 MPa, which is 5.13 MPa higher than that with soft overlying strata (30.14 MPa). This suggests that the coal pillar is in a relatively low stress state but still in a yield condition, and the coal pillar has a poor load-bearing capacity. The overburden load will impose on the face supports. As a result, the face supports bear more loads, and the working face encounters more mining stress when extracting a coal seam with a hard roof, leading to face support damage and further influencing the stability and safety of the mining roadway and working face.

③ At 25 m in front of the working face, the maximum stress is loaded on the coal pillar. At this position, the difference in peak stress in the coal pillar under different roof strengths is the largest. The peak stress under hard roof conditions (55.76 MPa) is 24.84 MPa higher than that under soft roof circumstances (30.92 MPa). The stress state here manifests that in hard-rock coal mining, the peak stress in front of the working face acts upon the coal pillar, leading to the pillar bearing a greater stress. Hence, the coal pillar is more prone to lose stability, making the working face bear more front abutment pressure.

④ At 80 m ahead of the working face, the peak stress in the coal pillar having a hard roof is 41.77 MPa. It is 13.19 MPa higher than the peak stress in the coal pillar having a soft roof (i.e., 28.58 MPa). This shows that under hard roof conditions, the loads in the coal pillar are larger, and the pillar is easier to fail, and the roadway is more likely to deform.

3) The action mechanism of the hard roof on the working face and pillar system

With the mining of the working face, the roof strata gradually collapsed, and the pressure of the overlying strata was transferred to the coal pillars and the coal body at the goaf boundary. For the mining of extra-thick coal seams, the cantilever beam structure with a height of 80 m is formed because the range of the caving zone is as high as 80 m. For the hard roof, because it is not easy to collapse, the gangue in the goaf cannot support the cantilever beam structure. Moreover, the high-strength roof creates a larger cantilever structure on the horizontal scale. Therefore, most of the overburden pressure acts on the coal walls around the working face and pillars. If the coal pillar does not have sufficient strength, the damage of the cantilever beam structure will occur on the coal body or the coal pillar, further increasing the deformation and damage of the coal pillar. If the coal pillar has high strength, the damage of the cantilever beam structure will occur at the edge of the gob and will not increase the stress of the coal pillar.