The pressure relief protection effect of different strip widths, dip angles and pillar widths of an underside protective seam

To design underside protective seam strip layout. Similarity model experiments, numerical simulations and theoretical calculations are used to quantitatively study the pressure relief protection effect of different strip widths, dip angles and coal pillar widths of a thin underside protective seam under deeply buried conditions. The optimal strip width range is obtained according to the change law of strain during the mining process of the underside protective seam in a similar model experiment. The change law of the expansion of the protected coal seam is obtained and the fitting surfaces among the dip angle and strip width of the coal seam with the protection distance and pressure relief angle along the strike and dip of the protected coal seam are established according to the numerical simulation results of underside protective seam mining. It is concluded that the best pressure relief effect can be achieved when the dip angle is 16.7° and the strip width is 70 m. According to the stability threshold of coal pillars considered in strip mining theory, the coal pillar width is calculated to be 50 m. Similarity model experiments and numerical simulations of protected coal seam mining verify the pressure relief effect of the designed protective seam strip width and pillar width. A calculation method of the protective seam strip width, position and pillar width required by the specific width of the protected seam is proposed.


Introduction
The mine studied here is a coal and gas outburst mine, with a thin, deeply buried #4 coal seam, a complex geological structure including many faults, and poor economic benefits. Therefore, strip mining of the #4 coal seam as an underside protective layer not only solves the problem of the difficult mining of the #4 coal seam but also protects the #2 coal seam to a certain.
According to the theory of mine pressure control [53][54][55], the maximum heights of the caving zone and the fractured zone are calculated by Eq (1) and Eq (2) when the overburden is hard [56,57].
where H c is the height of the caving zone, m; M is the mining height of the coal seam, 5 m, and H f is the height of the fractured zone, m. The coal seam #2 overburden is mainly composed of hard rock, therefore, the height of the caving zone and the fractured zones are 16.37~21.37 m and 53.6~71.4 m, respectively. The calculation here does not consider protective seam mining.

Model establishment
The similarity model experiment is based on the two-dimensional test bed of the laboratory of China University of Mining and Technology (Beijing). The length, width and height of the test bed are 1800 mm, 160 mm and 1200 mm, respectively. According to the similarity principle [58], the geometric similarity ratio between the entity and the model is set as 100, the time similarity ratio is set as 10, the gravity similarity ratio is set as 1.6, and the stress similarity ratio is set as 160. The compressive strength of each layer is shown in Table 1. The No. ratio of similar materials corresponding to the compressive strength of rocks can be obtained according to the similarity ratio [59], as shown in Table 1.
The similar materials were sand, lime, gypsum, and water, and the model materials were proportioned according to the similarity ratio. Mica slices were placed between adjacent layers to simulate stratification. The physical model was constructed layer by layer with a thickness of approximately 10 mm and a total thickness of 1.2 m. The remainder of the height is only simulated to the surface with a counterweight. The completed physical model was allowed to dry naturally. The physical model after removing the mold is shown in Fig 1. In the model, the resistance strain gauges were arranged 10 cm above the #2 and #4 coal seam roofs, and a total of 34 strain observation points were arranged at a horizontal interval of 10 cm. The resistance strain gauges buried in the experimental model were connected to a laptop through a DH3816 static strain test system, and the strain results were displayed on the laptop through supporting software.

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The pressure relief protection effect of an underside protective seam

#4 coal mining
In the model, the displacement, strain, fracture angle, interval of roof collapse, and height of roof collapse development were recorded for each 5 cm of mining. The distance between both ends of coal seam #4 and the boundary is 25 cm. The overburden status at the coal mining depth of 130 cm corresponding to coal seam #4 is shown in Fig 2. Because coal seam #4 is relatively thin, roof fracture of the coal seam is not obvious during mining. With the mining of coal seam #4, the caving zone supports the overlying rock mass, the coal roof collapses periodically, and the fracture angle of the overburden at the mining side changes periodically. The mean fracture angle at the mining side is less than that of the open-off cut side, and the fracture angle at the side of the open-off cut is approximately 60˚. When the coal seam #4 is mined to a depth of 75 cm, the coal seam #2 exhibits obvious separation cracks, and when the coal seam #4 is mined to a depth of 130 cm, the coal seam #2 curve subsides, indicating that the coal seam #4 has a depressurization effect on the coal seam #2.

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The pressure relief protection effect of an underside protective seam Every 5 cm of mining, before continuing, the value at every strain point was measured and recorded. The change in strain value at each point with mining distance and the strain distribution at each point at different mining distances are shown in Fig 3. After mining, the strain at each strain monitoring point increased slightly, then increased rapidly, and finally tended to be stable. Due to the periodic fall of the roof of the coal seam #4, there is a small periodic fluctuation in the strain above the coal seam #4. The strain value above the coal seam #2 is less affected by periodic collapse.
When the coal seam #4 is at a mining depth of 30 cm, the strain at 10 cm above the coal seam #4 begins to change significantly; when the mining depth ranges from 30 cm to 45 cm, the maximum strain change is observed; when the mining depth is greater than 55 cm, the rate of increase in the strain is very low. It can be concluded that when the shortest strip width of the coal seam #4 is greater than 55 cm, the pressure relief effect of the coal seam #4 can be achieved.
When the coal seam #4 is at a mining depth of 70 cm, the most obvious change in strain occurs at 10 cm above the coal seam #2; when the mining depth range from 70 cm to 90 cm, the strain change is the largest; when the mining depth is greater than 90 cm, the rate of increase in the strain is very low. The shortest strip width of the coal seam #4 that relieves the pressure of the coal seam #2 is less than 90 cm.
The similarity model experiment of coal seam #4 mining shows that the optimal range of the strip width of the coal seam #4 is 55~90 m due to the model similarity ratio of 100.

Coal seam #2 mining
The distances between the open-off cut side and the mining side of coal seam #2 and the boundary are 40 cm and 30 cm, respectively. The overburden status of the coal seam #2 at a mining distance of 110 cm is shown in Fig 4. After the coal seam #4 is mined, during the coal seam #2 mining, the interval of roof breaking is small, and the cracks in the overlying strata are fully developed. The height of the caving zone of the coal seam #2 is approximately 30 m due to the model similarity ratio of 100, which is greater than the theoretical calculation value. It is concluded that the coal seam #4 protective layer provides a pressure relief effect.

Numerical model
Based on FLAC3D numerical simulation software, a mechanical model of the coal mining face is established. The model mainly studies the pressure relief protection effect during strip protective seam mining, and the Mohr Coulomb constitutive model is used to establish this mechanical model. According to the geological conditions of the working face, the dip (y-axis direction), strike (x-axis direction) and height (z-axis direction) of the model are 200 m, 500 m and 250 m, respectively. According to the burial depth of the coal seam and the gravity of the overburden, the vertical stress is 15 MPa and the horizontal stress is 12 MPa. The monitoring points are set to monitor the changes in the stress and displacement of the overlying strata during mining. The physical and mechanical parameters of the strata in the model are shown in Table 2.
A preliminary grid model is established and can be solved to generate the initial ground stress field. After the superimposed force is applied to the model, the use of empty cell excavation is used to simulate the coal seam mining face. The model is divided into 26 adjacent layers with different lithologies. The strike of the strip is mined from x = 100 m to x = 400 m. Each time the model unit is mined 20 m, the unbalanced force ratio is set to 1e-5, and 15 excavation steps are used.

The dip protection effect produced by the dip angle and strip width
When studying the pressure relief protection effect of the underlying coal seam mining on the overlying coal seam, the expansion rate of the protected seam is an important index for evaluating the protection effect. The increase in the expansion rate has a great impact on enhancing the permeability of the overlying coal and rock seam. According to the "Detailed rules for

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The pressure relief protection effect of an underside protective seam prevention of coal and gas outburst", the maximum expansion rate of the protected layer is 3‰ and serves as a critical index at which to measure the protective effect of the protective layer. The average thickness of the coal seam #2 is 5 m, and the swelling capacity of 3‰ is 0.015 m. To quantitatively analyze the pressure relief effect of coal seam #4 mining on the coal seam #2, 71 displacement monitoring points are arranged at equal intervals on the #2 coal roof and floor along the dip. Based on the displacement of coal seam #2, when the dip angles are 30˚, 20˚, 10˚, and 0˚, the swelling capacity distributions of coal seam #2 in the dip are shown in Fig 6 for different strip widths.
When the dip angle is the same, the swelling capacity of the coal seam #2 increases with increasing strip width, and the rate of increase in the speed decreases; in the dip direction, both ends of the coal seam #2 are in a compressed state, and the lower part of the coal seam #2 undergoes a larger compression. It could be concluded that the larger the strip width is, the better the pressure relief effect.
According to the distribution of the swelling capacity of coal seam #2 in the dip direction, the pressure relief protection parameters under the 24 sets of model test conditions can be obtained (as shown by the red balls in Fig 8). When the dip angle is 30˚and the horizontal strip width is 30 m, a schematic diagram of the pressure relief protection effect is shown in Fig 7. θ and y are independent variables, and Z, Γ 1 and Γ 2 are the dependent variables. Using Origin, the Parabola2D fit is selected for the fitting process; the fitting equations are shown in Eqs (3), (4) and (5), respectively, and the fitting diagrams are shown in Fig 8. Z ¼ À 21:6191 þ 0:5116y þ 1:0464y À 0:0153y 2 À 0:0003y 2 R 2 ¼ 0:9990 ð3Þ G 1 ¼ 74:4003 þ 0:9178y À 0:0222y À 0:0120y 2 À 0:0003y 2 R 2 ¼ 0:9939 ð4Þ G 2 ¼ 71:4673 À 0:0616y À 0:0833y À 0:0148y 2 À 0:0006y 2 In Eqs (3), (4) and (5), θ ranges from 0~30, y is ranges from 30~90, and the correlation coefficient (R 2 ) is greater than 0.98. Z is affected more by y than by θ, and Z has an approximately linear relationship with y. Z is less affected by θ, and Z reaches its maximum value at θ = 16.7˚; Z has a parabolic function relationship with the θ. Γ 1 is mainly affected by θ, Γ 1 increases with increasing θ, and the rate of increase gradually decreases. The change in Γ 2 is relatively small and is mainly affected by θ. Γ 2 decreases with increasing θ, and the rate of decrease gradually increases. It is concluded that the dip angle of the coal seam with the best pressure relief effect is 16.7˚.
Under the condition of a known coal seam dip, according to fitting Eq (3), the strip width required by the seam pressure relief protection in the dip direction can be obtained. From the obtained strip width, the pressure relief angle can be obtained according to fitting Eqs (4) and

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The pressure relief protection effect of an underside protective seam

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The pressure relief protection effect of an underside protective seam (5), that is, the strip position corresponding to the protected seam can be inverted in the dip direction.

The strike protection effect produced by the dip angle and strip width
Seventy-two displacement monitoring points are arranged equidistantly on the #2 coal roof and floor in the strike direction. Based on the displacement of coal seam #2, when the dip angles are 30, 20˚, 10˚, and 0˚, the swelling capacity distributions for the different strip widths of coal seam #2 in the strike direction are shown in Fig 9. When the dip angle is the same, the swelling capacity of coal seam #2 increases with increasing strip width, and the rate of increase in the speed decreases; in the strike direction, the expansion of coal seam #2 at the open-off cut side is greater than that at the mining side.
According to the distribution of the swelling capacity of coal seam #2 in the strike direction, the pressure relief protection parameters under the 24 conditions of the model can be obtained (as shown by the red balls in Fig 10), where L is the pressure relief protection length in the strike, m; F 1 is the pressure relief angle at the open-off cut side,˚; and F 2 is the pressure relief angle at the mining side,˚.

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The pressure relief protection effect of an underside protective seam Under the condition of a known coal seam dip, according to fitting Eq (6), the strip width required by the seam pressure relief protection in the strike direction can be obtained. From the obtained strip width, the pressure relief angle can be obtained according to fitting Eqs (7) and (8), that is, the strip position corresponding to the protected seam can be inverted in the strike direction.
The optimal strip width obtained by the numerical simulations is within the range of similarity model experiment results. The law that the pressure relief angle at the open-off cut side is greater than the pressure relief angle at the mining side obtained by the numerical simulations is consistent with the law of the breaking angle at both sides obtained by the similarity model experiment. The pressure relief angle at the open-off cut side obtained by the numerical simulation is 70˚, which is greater than the break angle at the open-off cut side obtained by the similarity model experiment, which is 60˚. This is because the pressure relief range is greater than the breaking range, and the numerical model is established under ideal conditions. The results of the similarity model experiment verify the results of the numerical simulations.

Coal seam #2 mining after the double strip mining in the underside protective seam
The stability of coal pillar during strip mining Scholars have previously evaluated the stability of coal pillars in strip mining [60][61][62][63][64]. The calculation of the width of the yield zone of the coal pillar is an important part of the stability analysis of the coal pillar. The corresponding empirical formula is as follows [65,66]: where W is the width of the yield zone, m, m is the mining height, m, and H is the burial depth, m.
To ensure the long-term stability of a coal pillar, if the coal seam is weak, the ratio should be larger than 0.65 [67,68]. If the safety factor is larger than 1.6, it can ensure the long-term stability of the coal pillars [69,70]. The calculation methods of the ratio and the safety factor are shown in Eq (10) and Eq (11) respectively [71,72].
where r is the ratio; (P-2W) is the pillar core width; P is the pillar width, m; F is the safety factor; P u is the ultimate coal pillar load; and P a is the actual coal pillar load. The expressions of P u and P a are shown in Eq (12) and Eq (13) [66].
where γ is the average volume weight of the overlying strata, kN/m 3 , and Y is the mining strip width, m.
To ensure the safety of the coal pillar, the maximum burial depth (600 m) and mining height (1.3 m) are used to calculate the yield zone width according to Eq (9). The yield zone width is approximately 3.84 m. The strength of the coal seam #4 is weak; thus, the ratio (r) should be larger than 0.65, according to Eq (10), and the coal pillar width should be larger than 21.94 m.
When the strip width (Y) is 70 m, to maintain a safety factor (F) greater than 1.6, according to Eq (11), the pillar width (P) needs to be greater than 48.53 m; thus, Y = 70 m, and P = 50 m. According to Eq (10) and Eq (11), r = 0.85 and F = 1.63, which can ensure the long-term stability of a coal pillar. A method for calculating the coal pillar width based on the strip width is proposed.

The double-strip numerical model
The dip (y-axis direction), strike (x-axis direction), height (z-axis direction) and dip angle of the model are 200 m, 500 m, 250 m, and 0˚, respectively. The remaining parameters of the After the coal seam #2 is mined, the vertical stress in the goaf is reduced to a pressure relief zone, the minimum stress is reduced to 0 MPa, and the coal walls at both sides show stress concentration. Affected by the strip mining of the coal seam#4, the stress concentration on the left side is greater than that on the right side after coal seam mining #2. This is because the coal seam #4 corresponding to the left side of the underside protective layer is the first mining strip, and the pressure relief is greater there.
Along the height of the roof of the coal seam #2, the vertical stress at the center of the goaf begins to increase when the distance from the roof is 25 m, and the maximum vertical stress difference at the center of the goaf is 60 m from the roof. It can be inferred that the heights of the caving zone and the fractured zone are 25 m and 60 m, respectively.
The vertical displacement distribution of the overburden of the coal seam #2 in the dip direction and the vertical displacement distribution at the center point in the vertical direction are shown in Fig 12. The vertical displacement change law is the same as the vertical stress change law. Along with the height of the roof of coal seam #2, when the distance from the roof is 20~25 m, the vertical displacement gradient of the goaf center point is the largest, and when the distance from the roof is 60 m, the rate of increase in the vertical displacement of the goaf center point decreases. It can be inferred that the heights of the caving zone and the fractured zone are 25 m and 60 m, respectively.
The height of the caving zone obtained by numerical simulation of the coal seam #2 overlying strata is greater than that of the theoretical calculation. The height of the fracture zone obtained by numerical simulation is consistent with that of the theoretical calculation. The underside protective seam mining increased the development height of the caving zone of the protected seam, indicating that the double-strip mining of coal seam #4 had a pressure relief protection effect on coal seam #2. The rationality of the designed protective seam strip width and coal pillar width is verified.

Conclusions
1) Through the changes in strain during underside protective coal seam #4 mining at a similarity model experiment, it was concluded that the optimal range of the strip width of the coal seam #4 is 55~90 m. The coal seam #2 mining verified the pressure relief protection effect.
2) Through the numerical simulation of protective seam mining under different dip angles and strip widths, it is concluded that Z is greatly affected by y, Z has an approximately linear relationship with y, and Z reaches its maximum value at θ = 16.7˚; Γ 1 and Γ 2 are mainly affected by θ. L, F 1 and F 2 are mainly affected by y, they increase with increasing y, and the rate of increase speed gradually decreases. The dip angle of the coal seam for the best pressure relief effect is 16.7˚, and the corresponding strip width is 70 m. According to the fitting equation, the strip width and the strip position corresponding to the protected seam required for the protected seam width in the dip and strike can be obtained by inversion.
3) The results of the similarity model experiment verify the results of numerical simulations. The optimal strip width obtained by the numerical simulations is within the range of similarity model experiment results. The results of the numerical simulations suggest that the pressure relief angle at the open-off cut side is greater than the pressure relief angle at the mining side, consistent with the law of the breaking angle at both sides obtained by the similarity model experiment.
4) A method for calculating the coal pillar width based on the strip width is proposed. According to the related theory of the stability of coal pillars in strip mining, a strip width of 70 m and pillar width of 50 m can ensure the long-term stability of a coal pillar. 5) According to the laws of the vertical stress and vertical displacement of the overlying strata based on double-strip numerical simulation, it is concluded that the height of the caving zone is 25 m greater than that of the theoretical calculation and that the height of the fracture zone is 60 m, consistent with the results of the theoretical calculation. The underside protective seam mining increased the development height of the caving zone of the protected seam and verified the pressure relief protection effect of the designed protective seam strip width and pillar width.