Determination of the key parameters of high‐position hard roofs for vertical‐well stratified fracturing to release strong ground pressure behavior in extra‐thick coal seam mining

Traditional methods of controlling hard roofs have a limited scope of action and cannot effectively release the strong ground pressure behavior (SGPB) induced by high‐position hard roofs (HHRs) in extra‐thick coal seam mining (ETCSM). Thus, an innovative control technology of fracturing HHRs by vertical‐well stratified fracturing (VWSF) has been proposed. However, the key parameters of VWSF, namely fracturing horizon and fracturing thickness of HHRs, which have a significant influence on stope stability, remain uncertain. In this study, a mechanical model of the “coal wall–hydraulic support–gangue” support system is established by considering the effective loading acting on HHRs, through which modified expressions for the periodic breaking span and impact kinetic energy of the stope are deduced. Based on the self‐bearing of bulking rocks, the stability principle of the surrounding rock, and energy dissipation theories, the criteria for determining the fracturing horizon and thickness of the HHR are obtained. Next, a numerical model of ETCSM, which accounts for the supporting effect of gangue, is constructed in FLAC3D. The support load and energy released by stratum breakage are determined through modeling under various hard roof parameters, thus verifying the correctness of the determination criteria. The results show that the energy released by a hard roof, average support load, and critical support load are positively correlated with thickness, and first increase before declining with respect to an increase in the fracturing horizon. The key parameters for a real coal mine are obtained by theoretical calculations and numerical simulations. A field application demonstrates that the support load and advance roadway deformation can be decreased using the proposed parameterization. This provides theoretical support for determining the key parameters of HHRs for VWSF and facilitates the widespread application of VWSF technology in HHR control.


| INTRODUCTION
The caving span of a hard roof is large, resulting in strong ground pressure (SGP) on the working face in extra-thick coal seam mining (ETCSM). Thus, the control of hard roofs is a challenging aspect of achieving safe and efficient coal mining. When the overburden contains hard roofs in ETCSM, breakages and instabilities in the multi-layer structures result in ground pressures of varying degrees. 1,2 In particular, breakages and instabilities in high-position hard roofs (HHRs) result in strong ground pressure behavior (SGPB) and support failures in the working face and entry owing to their large caving span and hanging area ( Figure 1). [3][4][5] These hazards represent a severe danger to safe production and pose a new challenge to achieving hard roof control in ETCSM. [6][7][8][9] According to incomplete statistics, up to 132 SGP activities (the shrinkage of the support pillar exceeding 600 mm) have been recorded in Tashan and Tongxin coal mines since the ETCSM in 2008, of which approximately 21 frame-pressing accidents occurred in stopes. These problems are not unique in China, and have been reported in India and the USA. Indeed, in the Chirimiri colliery and the Drift mine in Eastern Kentucky, the frequent occurrence of SGP led to cable bolt cutting, resulting in roof falls and at least four fatal accidents and two serious injuries during ETCSM. 10,11 The high-position strata in large spaces have a complex structure and a wide range of ground pressure behavior in the presence of overlying hard roofs. 12 The fracture and rotation of the high-position structure produces radial compression on the adjacent roadway, resulting in coal pillar stress of up to [3][4] times that of the original rock stress. 5,13 Controlling HHRs and eliminating SGPB in ETCSM is a major problem that urgently requires a solution.
The problem of hard roof control has been hotly debated in research on mine disaster prevention. [14][15][16] As hard roofs are notoriously difficult to collapse, control technologies have been studied since 1951, and a series of hard roof control theories and technological methods have been developed. [17][18][19] At present, the most commonly used technologies are coal pillar supports, gob-side entry retention, goaf filling, a spatiotemporal coupling fracturing method using a nonexplosive expansion material, water injection to weaken the roof, presplitting blasting, deep hole blasting, energy-cavity blasting, and hydraulic slitting. 2,14,15,[20][21][22][23][24][25][26][27][28] The main ideas can be summarized as follows: (a) maintain the stability of the hard roof and support the stope space; (b) weaken the hard roof and reduce its rock mass strength; and (iii) transfer the stress or release the strain energy to eliminate the source of SGP.
To some extent, the existing hard roof control technologies inhibit the occurrence of SGP induced by hard roofs. However, there are obvious deficiencies in the prevention and control of SGP induced by HHRs, which are mainly reflected in the following aspects: (a) The locality of traditional methods cannot solve the problem of SGP induced by HHRs. 1 Existing technologies are limited by the small underground working spaces and cannot apply high-performance equipment. Field construction is difficult, and the effect range is limited (mainly confined to strata in the range of 30-50 m from the coal seam). (b) The passivity of disaster prevention methods. Traditional methods are implemented after the formation of the working face system or roadway cross-section, lagging behind SGP. (c) The risks of the implementation process. Traditional methods are implemented in disaster risk areas, and SGP may appear in the process of implementation. (d) The timeliness of disaster prevention and control is poor. The functions of traditional methods have two aspects: Although they can inhibit the occurrence of SGP, they may also induce it. The timeliness of prevention and control cannot be guaranteed over a long period. (e) Contradiction with production. The construction and production of traditional methods cannot work in parallel, resulting in a contradiction between the implementation of suitable and the production process. (f) Labor-intensive nature of the work. Traditional methods are point-by-point construction techniques, which require considerable drilling, resulting in a large engineering effort.
In view of the problems faced by current hard roof control methods and the advantages of vertical-well stratified fracturing (VWSF), an innovative method of weakening HHRs for VWSF is proposed to reform roof structure integrity. For VWSF technology, there has been significant research in the fields of petroleum and shale gas, and the design of hydraulic fracturing parameters for vertical wells has matured. [29][30][31][32][33] The application of VWSF for petroleum and shale gas is different from that in the presence of HHRs. The main purpose of VWSF for HHRs in coal mines is to control the SGPB in the stopes. The weakening effect of VWSF on SGPB induced by HHRs is closely related to the fracturing horizon, fracturing thickness, fracturing technology parameters, drilling technology parameters, and hydraulic support parameters. Fortunately, the design of the fracturing process parameters, vertical well parameters, and hydraulic support parameters is relatively mature. Therefore, the design of fracturing horizons and fracturing thickness for VWSF is one of the core issues of this technology, having an important impact on HHR control, SGP weakening, and the surrounding rock stability in stopes. VWSF is a new technology for HHR control, and there has been little research on its key parameters, especially the fracturing horizon and fracturing thickness of HHRs. This study takes a fully mechanized top-coal caving face in an extra-thick coal seam in the Tashan coal mine, Shanxi Province, China, as the engineering background. The key parameters of HHR for VWSF are systematically studied by combining theoretical analysis, numerical simulations, and field tests.

VWSF TO RELEASE SGPB IN THE STOPE
The excavation of a fully mechanized top-coal caving face in an extra-thick coal seam redistributes the stress around the stope, and the overlying strata movement will form large and small structures above the stope ( Figure 2). 34,35 After the HHRs in the large structure break, their weight and the follow-up rock load (q) are transmitted to the coal wall and the hydraulic support through the lower roof. The hydraulic support and the coal wall share the roof rock mass and transfer load (F L ) in the small structure of the stope. When the high stratum is an HHR, a large lateral cantilever (key block B) is formed. 25 The movement process of key block B determines the stability of the small structure. The high-position structural instability causes the near-field roofs to break. The linkage instability effect is the essential reason for the SGPB of a fully mechanized top-coal caving face in ETCSM. 36 The hanging length and thickness of key block B and the support strength of the hydraulic support affect the breakage and instability state of the hard roof. However, the control effect of hydraulic supports is limited because of HHRs.
Reducing the thickness or hanging length of key block B is a significant means of improving the HHR control effect.
Therefore, in view of the shortcomings of traditional control methods, this paper proposes an innovative method of weakening HHRs by VWSF based on petroleum fracturing technology (Figure 3). A fracturing fluid is injected into the HHRs. Large artificial cracks are formed in the target horizons, reducing the integrity and strength of the rock. Additionally, the overlying roofs may collapse, reducing the weighting strength of the roof. Moreover, this prevents the concentrated stress release from the sudden and large-scale collapse of the roofs. In general, the vertical stress of HHRs is lower than their horizontal stress. The hydraulic fracturing cracks in HHRs extend along the horizontal direction.
The effect of fracturing HHRs by VWSF is to generate hydraulic fractures over a wide range, weakening the integrity of HHR, and produce a layered structure. The weakened part of the HHR will collapse with the mining, releasing the weight and energy through HHR breakage. The gangue of the bulking rock can support the overlying roof, further reducing the effective stress transferred to the small structure ( Figure 4).

| Mechanical model of "coal wall-
hydraulic support-gangue" support system for HHRs 3.1.1 | Construction of mechanical model of the "coal wall-hydraulic supportgangue" support system for HHR According to the above analysis, a mechanical model of the "coal wall-hydraulic support-gangue" support system of HHR is constructed, as shown in Figure 5.
In Figure 5, h c is the residual thickness of HHR, M is the coal seam thickness, H is the mining depth, h 0 is the height of HHR from the surface, H L is the height of HHR from the coal seam, and q is the uniform load acting on the key block B F L is the load transferred from the overlying roofs to the coal wall and hydraulic support. T E is the extrusion pressure between key blocks A and B, T H is the extrusion pressure between key blocks B and C, Q E is the friction force between A and B, Q H is the friction pressure between B and C, P b is the support strength of coal wall, P z is the support load, P g is the pressure of gangue on key block B, and F 1 is the force exerted by the lower roofs on key block B.

| Effective load acting on the HHR
The subsidence of key block B s x = S 0 + x sin . The compression amount of gangue s y is.
where δ is the recovery rate of working face; K M and K L are the crushing expansion coefficients of coal and rock, respectively; θ is the rotation angle of key block B; and S 0 is the subsidence of key block B at the fracture. S 0 is small before the lower strata is fractured, while S 0 is large after the lower strata is fractured.
The supporting force produced by gangue per unit area is.
where K G is the supporting coefficient of gangue. When the gangue is touched at first, the rotation angle of the key block B is.
If θ ≤ θ 0 , key block B has no contact with gangue, and P g = 0; if θ > θ 0 , key block B has touched the gangue. If s y = 0, let s y = 0, and then the abscissa of key block B just touches the point.
Therefore, the supporting stress of gangue is.
According to key strata theory, 37 after fracturing, the load on HHR becomes, where h 1 , h 2 , ⋯, h n are the thickness of the overburden strata over the HHR, respectively, E 1 , E 2 , ⋯, E n are elastic modulus for the overburden strata, respectively, and γ 1 , γ 2 , ⋯, γ n are unit weight of the overburden strata.
After separated fracturing, the effective loading acting on HHR becomes.
where L is the periodic weighting interval of HHR before fracturing and L 1 is the periodic weighting interval of HHR after fracturing.
The supporting stress of the gangue formed by fracturing is the direct reason for the reduction in the roof pressure of the working face, as shown in equation (7). The supporting effect of the gangue from the bulking rock on the roof decreases with distance from the hydraulic fractures. Therefore, the influence of hydraulic fractures has a certain range, and this influence is more obvious closer to the hydraulic fractures.

| Periodic fracture span of HHR
The HHR satisfies the thin-plate theory requirement, and the roof breakage problem can be studied according to Kirchhoff's hypothesis. 38 Based on the theory of plates and shells, 14 the HHR for a continuous mining face can be approximately regarded as an elastic rectangular thin plate with two clamped edges and two simply supported edges, as shown in Figure 6.
In Figure 6, the inclined overhang length is L 2 . The perturbation expression of HHR with two clamped edges and two simply supported edges 39 is. (1) where D is the flexural rigidity of the hard roof. As the HHR is far away from the coal seam, a fracture form of transverse "OX" type will be produced, and the upper surface of the solid supporting edge will reach the tensile limit t during the bending sinking process. 40,41 The calculation formula for the broken span of the HHR 38 is. where.

| Impact kinetic energy of the stope
As the separation space at the bottom of the HHR is gradually increased, internal bending moments and torques act on the HHR and are stored in the rock strata in the form of bending deformation energy. As torque does not affect the bending moment, the sum of the two is the bending deformation energy W b , 42 that is.
Therefore, According to the principle of conservation of energy, the energy transformed during the HHR breakage is as follows: where E k is the impact kinetic energy; n is the thickness of overlying strata falling with HHR; and H i is the height of overburden strata, Only 1/100-1/10 of the impact kinetic energy is converted into a shock wave after the HHR is broken. 43 The energy after the vibration wave propagates a certain distance 20 can be expressed as: where l is the distance travelled by the shock wave, and l = H L sin ; ψ is the energy attenuation coefficient, ψ > 1. From formulae (11), (12), and (13), the following formula can be obtained:

| Control principle of the key parameters of HHR for VWSF
The weakening effect of VWSF on SGPB induced by HHRs is closely related to the fracturing horizon, fracturing thickness, fracturing technology parameters, drilling technology parameters, and hydraulic support parameters. Fortunately, the design of the fracturing process parameters, vertical well parameters, and hydraulic support parameters is relatively mature. Therefore, based on previous theoretical research, this paper only analyzes the design principles of the fracturing horizon and fracturing thickness.

| Determination principle for the fracturing horizon of HHR
A reasonable fracturing horizon allows the rock strata in the fracturing range to fully collapse and fill the whole goaf, providing a better supporting role for the upper strata. Moreover, the impact load of HHR breakage and the disturbance of HHR rotary subsidence on the working face are reduced by VWSF. Furthermore, the SGPB in the stope is effectively weakened.

Criterion for the HHR supported by caved rocks
Before fracturing, the criterion for the HHR supported by caved rocks is as follows: where Δ is the free space height 44 ; K L is the average residual fragmentation coefficients of strata, which is usually 1.06-1.15; when Δ reaches the critical value, the HHR will be supported by caved rocks.
Therefore, the highest level of fracturing horizon is.

Criterion for critical support force
The hydraulic supports are located under key block B. The longer cantilever causes the hydraulic supports to bear excessive additional load and damage, thus affecting the deformation and instability of the surrounding rock structure of the stope. Key block B is very important for the stability of the stope. Stress analysis of key block B is illustrated in Figure 7. By ∑ M EF = 0, we obtain the following: where x 1 is the moment of F 1 ,x 1 = s+d 2 ; x 2 is the moment of P g ,x 2 = s + d + tan H L ; s is the limit equilibrium zone size on one side of the coal wall in the mining space; d is the roof control distance;L H is the moment of . According to the theory of stress balance in a loose medium, 45 the following is obtained, where ψ is the lateral pressure coefficient, = 1− , μ is poison's ratio; θ 0 is the internal friction angle of the coal seam, c 0 is cohesive strength; P x is the supporting strength of the solid coal side; k is the maximum stress concentration coefficient; and 2-3.5 is selected according to the following experience.
According to formula (1), the friction force between B and C is.
The thrust of key block C to key block B can be calculated according to formula (3) 46 : The increase in thickness of one-time mining coal seams in the fully mechanized caving faces of extra-thick coal seams produces an increase in the mining disturbance range. Additionally, the surrounding rock of the working face changes from "rotary instability" to "sliding instability". 47 According to the "S-R" stability theory of voussoir beam structures, the stability of key block B is affected by key block A. 48 To prevent key block B from sliding and losing stability along the fracture position, the following condition must be satisfied: where φ is the friction angle, and β is the breaking angle.
According to formulas (21), (22), and (23), the available supporting force (F 1 ) needs to meet the formula (24) so that key block B can keep its balance.
According to the condition of mechanical equilibrium, P z is as follows: The formula for calculating the minimum support load when the key block B does not slide and lose stability can be obtained as follows: where K g is the load transfer coefficient. According to the stress equilibrium theory of loosened material, 49 the width s of the stress limit equilibrium zone and seam interface stress σ y are, 14 respectively.
where φ 0 is the internal friction angle of the interface between the coal seam and the roof; λ is the lateral pressure coefficient, = 1− ; μ is the Poisson's ratio; k is the stress concentration factor; and c 0 is the cohesion of the interface between the coal seam and the roof.
The load transferred to coal and rock 48 is as follows: where F gj is the load of the jth key strata block transferred onto the coal seam on one side, j = 1-m-1, m is the number of key strata above the coal seam; K gj is the load transfer coefficient of the jth key strata; h j and h gj are the average thickness of the jth key strata and its controlled strata, respectively; l j is the length of the jth key strata block; γ is the average volume weight of strata.
Therefore, the critical support stress of hydraulic supports for key block B to remain stable is.
The design support strength of the hydraulic support is [P]. If P z is greater than [P] (satisfying equation (31)), the hydraulic support column will shrink too much during the SGPB, and key block B will slide and lose stability. In this scenario, stratified fracturing measures must be taken.

Criterion for the impact kinetic energy of the working face
Too much energy in the HHR breakage will lead to rock burst in the working face. If equation (32) is satisfied, the HHR should be fractured by VWSF.
In summary, considering the construction efficiency, engineering effort, and cost input, it is not necessary to fracture all HHRs in practice. Once suitable parameters have been determined, the highest fracturing horizon of HHR is given by equation (16). The hard roofs near the highest horizon are then determined. And the relevant parameters are substituted into equations (31 and 32). As long as one of these expressions is satisfied, the HHRs should be fractured by VWSF.

Criterion for HHRs supported by caved rocks
We make full use of the characteristics of rock bulking, so that the strata in the fracturing fully collapse and fill the whole goaf, providing a better supporting role for the upper strata. Moreover, the impact load of HHR breakage and the disturbance of HHR rotary subsidence on the working face are reduced by VWSF. After fracturing, the criterion for the HHR supported by caved rocks is as follows: When Δ reaches a critical value, the HHR will be supported by caved rocks. Therefore, the minimum fracturing thickness of the HHR is.

Criterion for critical support force
The purpose of fracturing the HHR is to ensure that the critical support force of the hydraulic supports (P ′ z ) after fracturing is not greater than [P], that is.

Criterion for the impact kinetic energy of the working face
To prevent SGP from occurring following a mine earthquake caused by HHR breakage, U r should be less than 10 5 J. 48 Thus, Theoretically, smaller values of h c are preferable. However, considering the construction efficiency, engineering effort, and cost input, the reasonable HHR fracturing thickness can be obtained by simultaneous consideration of equations (34)(35)(36) once the relevant parameters have been determined.

| Numerical simulation for ETCSM
To verify the theoretical analysis and obtain the optimal HHR parameters for VWSF, according to the on-site geological conditions of working face 8101 at Tashan coal mine ( Figure 19C), a ETCSM numerical simulation method is used to establish a numerical calculation model by means of FLAC3D (Figure 8). This allows the key parameters of HHR for VWSF to be analyzed.
In the mechanical calculation, the rock strata was described by the continuum damage model. For the cave-in zone, a new consolidation model was developed based on a confined compression test on loose ceramic sand. 50 The rock damage was used to determine the roof caving, meanwhile a local contact criterion was introduced to confirm the roof contact with the cave-in zone. The cave-in zone height is calculated as the product of the caved roof thickness and the bulk factor. 6 In order to calculate the hydraulic support load numerically, a support element at the bottom corner of the working face is generated to approximately model the mechanical behavior of the hydraulic power support. 51 According to the elasto-plasticity theory, a special module was developed to calculate the released energy. 6 This model is 1,600 m long and 540 meters high, and it consists of units 52 890. On the upper part of the model, the free boundary is adopted, and the lower part of fixed boundary controlled in horizontal displacement. In order to eliminate the boundary effect, 200 m is reserved on each side of the model. 3 m of mining is simulated each time, and the mining range from cutting to 1200 m is simulated. The ground stress field is inverted according to the on-site measured geo-stress data. The rock mechanics parameters of the model are presented in Table 1.
The simulation results are shown in Figures 9 and 10. At the initial stage of mining ( Figure 9A and 9), the low-position roof strata mainly suffer from shear failure. After the working face is advanced to 960 m, the high-position roof strata mainly suffer from tensile failure (the black rectangular range of Figure 9E Figure 9A, 9, 9, and 9 indicate that shear sliding occurs on the roof directly above the working face, whereas the HHRs are mainly cracked through tensile failure in the nearly vertical direction. Figure 9B, 9, and 9 shows that stress-concentrated areas gradually appear in the surrounding rocks on both sides of the goaf. After the working face is advanced to 960 m, a stress-concentrated area forms in the HHR (layers #21 and #27; white rectangular range of Figure 9F and 9). As shown in Figure 9F and 9, the loose gangue densifies and begins to withstand the strata pressure from the HHRs. This is the result of the full collapse of the roof and the filling of the goaf, which transfers stress to the working face.

10). The results in
In the numerical modeling, the support load is also registered and compared with the measured results in Figure 11. The comparison reveals a similar tendency of the support load which is significantly violent with high peak load over 36.86 MPa (Figure 11).
Strata breakage is an energy release process. Figure 12 shows that the energy released by strata breakage declines with distance from the roof. The energy released by hard roofs is remarkably larger than that of the neighboring strata. The energy released from the HHRs (layers #21, #27, and #38) is similar to that released by the near-field hard roofs (layers #7 and #12), revealing that lithology has a significant impact on energy release. Moreover, far away from the coal seam, the large thickness of layer #33 leads to a big energy release, which means that thickness also plays an important role in the energy release of rock strata.
In short, strata with characteristics of being close to the working face, strong rigidity, and large thickness produce an intense energy release. When any two of these characteristics are combined, the intense energy release will be followed by a shock, which will cause SGP to occur in stopes. Therefore, when fracturing HHRs, those with large energy releases should be prioritized. In working face 8101, all the HHRs with such characteristics are in layers #21, #27, and #38. adopted in the simulations. The thickness of the hard roof was set to 15 m. The numerical simulation results are shown in Figures 13 and 14.

| Numerical simulation of hard roof horizon
Other conditions being the same, the energy released by hard roof breakage first increases and then decreases with distance from the working face, as shown in Figure 13. The energy released by the hard roof breakage at 110 m and 145 m horizons is much greater than that of the other hard roof horizons. As can be seen from Figure 13, the theoretical calculated energy is slightly larger than that given by numerical simulations, but the overall trend is similar. The impact kinetic energy of the working face caused by the breakage of the hard roof horizons from 56 to 220 m is greater than 10 5 J, which indicates that measures should be taken in KS1-KS4.
Working face 8101 uses a ZF15000/27.5/42 hydraulic support. The rated support force is 15 000 kN, corresponding to the rated support load of 36.86 MPa. As shown in Figure 14A, the support load is less than 36.86 MPa and greater than 26.67 MPa, accounting for 0.82% of the breakage and instability of the hard roof at the 56 m horizon. Figure 14B shows that the support load is greater than 36.86 MPa (accounting for 2.41%) and greater than 37.73 MPa (accounting for 0.83%) of the breakage and instability of the hard roof at the 110 m horizon. Figure 14C shows that the support load is greater than 36.86 MPa (accounting for 8.84%) and greater than 40.69 MPa (accounting for 0.41%) of the breakage and instability of the hard roof at the 145 m horizon. Figure 14D shows that the support load is greater than 36.86 MPa (accounting for 2.81%) and greater than 37.81 MPa (accounting for 1.61%) of the breakage and instability of the hard roof at the 220 m horizon. As shown in Figure 14E, the support load is less than 36.86 MPa and greater than 35.81 MPa (accounting for about 5.22%) of the breakage and instability of the hard roof at the 270 m horizon. These results indicate that the theoretical analysis is consistent with the numerical simulations.
The critical support load of the hydraulic support given by the theoretical calculations basically satisfies the requirements. Figure 15 shows that the average support load and the critical support load first increase rapidly and then decrease slowly with distance from the working face. The critical support load at horizons of 110-220 m is greater than that for other horizons and is greater than the rated support load, which could easily result in overloading and SGPB in stopes.
The results show that the energy release of the hard roof horizons at 110 m, 145 m, and 220 m has a greater impact on the support loads than in the 55 m and 270 m cases. The main strata horizons influencing the SGPB of working face 8101 are the hard roofs located at 110-220 m, which is consistent with the position of the main control rock strata for microseismic monitoring in Tashan coal mine. 38

| Numerical simulation of HHR thickness
Using the 2-D numerical model, five hard roof thicknesses (5,10,15,20, and 25 m) were considered with a horizon of 145 m. The numerical simulation results are shown in Figures 16-18.
The results show that the hard roof thickness has a significant impact on the energy release. Other conditions being the same, the energy released by hard roof breakage first increases and then decreases as the hard roof thickness rises ( Figure 16). As can be seen from Figure 16, the theoretical energy is slightly larger than the value given by numerical simulations, but the overall trend is similar. The impact kinetic energy of the working face caused by the breakage of hard roofs with thicknesses of 10-25 m is greater than 10 5 J, which indicates that measures are required for hard roof thicknesses greater than 10 m. Figure 17A shows that the support load is less than 36.86 MPa, and that pressures greater than 34.98 MPa (accounting for about 2.41%) of the breakage and instability of hard roof with a thickness of 5 m. Figure 17B shows that the support load is greater than 36.86 MPa (accounting for about 2.41%) and greater than 38.93 MPa (accounting for about 0.41%) of the breakage and instability of hard roof with a thickness of 10 m. Figure 17C shows that the support load is greater than 36.86 MPa (accounting for 8.84%) and greater than 40.69 MPa (accounting for 0.41%) of the breakage and instability of hard roof with a thickness of 15 m. Figure 17D shows that the support load is greater than 36.86 MPa (accounting for about 11.25%) and greater than 43.58 MPa (accounting for about 0.82%) of the breakage and instability of hard roof with a thickness of 20 m. Figure 17E shows that the support load is greater than 36.86 MPa (accounting for about 13.25%) and greater than 44.13 MPa (accounting for about 0.41%) of the breakage and instability of hard roof with a thickness of 25 m. The results show that the strength of the ground pressure behavior in stopes is directly proportional F I G U R E 1 3 Energy released from the hard roof breakage under different horizons to the HHR thickness and that the critical support load obtained by theoretical analysis is consistent with the simulation analysis. Figure 18 shows that the average support load and the critical support load are positively correlated with the hard roof thickness. The critical support load when the thickness is above 5 m is greater than the rated support load, which may result in overloading and SGPB in stopes. The results show that lower values of the hard roof thickness lead to smaller energy release by strata breakage, thus reducing the influence on the working face.
In summary, the hard roof horizon and thickness have a significant impact on the energy release and support load. When the hard roof thickness is less than 5 m and the horizon is 150 m, the energy released by hard roof breakage is less than 10 5 J, satisfying the criterion for the impact kinetic energy of the working face. At the same time, the stress field of the surrounding rock is optimized.

| Engineering background
The site of the field test was selected as the 8101 working face in Tashan

Determination of fracturing horizon for HHRs
According to the on-site engineering geological conditions of working face 8101 in Tashan coal mine, M = 16.8 m and K p = 1.1 according to equation (16).
The higher level of the fracturing horizon is layer #27, and so KS3 and KS4 are the fracturing ranges to be considered. Substituting the relevant parameters of KS3 and KS4 into equations (31 and 32), the calculation results show that P z = 16 558 kN > [P], U r > 1.20 × 10 5 J, satisfying the relevant conditions. Therefore, KS3 and KS4 need to be fractured by VWSF. At the same time, the numerical simulations verify the correctness of the theoretical results.

Determination of fracturing thickness of HHR
The minimum fracturing thickness of KS3 is.
Obviously, KS3 requires fracturing of the entire horizon, h l =10.7 m.
The minimum fracturing thickness of KS4 is. According to the above results, when the fracturing thicknesses of KS3 and KS4 are 10.7 m and 4.9 m, respectively, the rock strata within the fracturing range can collapse in time and fill the whole goaf, providing better support for the upper strata. Moreover, the impact load of HHR breakage and the disturbance of HHR rotary subsidence on the working face are reduced by VWSF. Therefore, the fracturing thicknesses of KS3 and KS4 are determined to be 10.7 m and 4.9 m, respectively.

| Fracturing technology
The overall structure of the fracturing borehole requires three drilling operations. One of these is into the stable bedrock, the second goes to 120 m, and the third reaches to the No. 3-5 coal seam. The design data of the well bore structure are presented in Table 2, and the structure of the fracturing well is shown in Figure 20. The site construction area is shown in Figure 21.
Fracturing was performed twice, the fracturing of the first horizon lasted 140 min, and the initiation pressure was 24.48 MPa. During the crack stability expansion stage, the tubing pressure was 7.08-9.47 MPa, and the casing pressure

| Microseismic monitoring of the fracturing effect
The ground microseismic monitoring technology was used to monitor the expansion direction of the crack formed by hydraulic pressure. This technology used a geophone to monitor the microseismic wave elicited by the hydraulic fractured well to describe the geometrical shape and space distribution of the crack extension. The energy diagrams of microseismic events were shown in Figure 23A and 23, and the orientation of hydraulic fracture was shown in Figure 23B Table 3. • Figure 23B and 23 showed that the hydraulic fracture of the first horizon extended along the NE65° direction. The hydraulic fracture of the second horizon extended along the NW68° direction. The two hydraulic fractures were distributed in strike on the east and west wings with the vertical well as the center. The hydraulic fractures in the two wings were spread evenly and are basically distributed symmetrically. • The direction of the 8101 working face was NE22°, and the positional relationship between the 8101 working face and the two horizons of hydraulic fracture was shown in Figure  23C. It showed that the hydraulic fracture of the first horizon had the largest coverage area of the working surface. The hydraulic fracture of the second horizon was located in the coverage area of the hydraulic fracture of the first horizon. The hydraulic fracture area of the working face is 245 m along the working surface, and the boundary of the affected area is 301 m away from the working face (Table 3).   Figure 25.
According to the statistics of the support load, the ground pressure strength and the span distance, the following rules were obtained: • Hydraulic fracturing could reduce the ground pressure strength in the hydraulic fracture area. The maximum support load before the cutting seam was 41.3 MPa, and the maximum support load after the cutting seam was reduced to 35.5 MPa. The average support load decreased from 30.1 MPa to 24.5 MPa, which was reduced by approximately 18.6%. • The hydraulic fracture increased the periodic roof weighting interval. After hydraulic fracturing, the maximum roof weighting interval and the periodic roof weighting interval increased. The periodic roof weighting interval increased by 32% at approximately 3.5 m.  was serious in the working face. After fracturing, the ground pressure strength of the roadway was obviously reduced in the area affected by the hydraulic fracture. The SGP did not appear in the working face, and the opening rate of the hydraulic support safety valve was reduced by 37%.

| Influence of the fracturing HHRs on
advance roadway deformation Figure 26 shows that the deformation of the advance roadway is obviously improved in the hydraulic fracture area. The height deformation of the roadway was reduced from an average of 990 mm to 486 mm. The deformation of the roadway width was determined by an average of 446 mm and was reduced to 213 mm. The single pillars in the roadway were not damaged, and the advanced support section of the mining roadway was highly controlled. The VWSF solved the problem that traditional underground measures cannot fracture HHR. This dynamic was highly important for controlling similar SGPB disasters caused by the instability of HHRs.

| SUMMARY
• A mechanical model of a "coal wall-hydraulic supportgangue" support system for HHRs has been established. The effective load acting on the HHR was introduced, and F I G U R E 2 4 Monitoring arrangement for roof pressures and displacement at the active mining panel F I G U R E 2 5 Variation law of support load of the No. 76 hydraulic support modified expressions for the periodic breaking span (L) and impact kinetic energy (U r ) of the stope were deduced. The supporting effect of the gangue caused by fracturing is the direct reason for the reduction in the hydraulic support pressure. The reduction of the effective load on the HHR is the fundamental reason for the increase in L and decrease in U r • Based on the self-bearing of bulking rocks, the stability principle of the surrounding rock, and energy dissipation theories, the criteria for determining the fracturing horizon, and thickness of HHRs were obtained. These provide a theoretical basis for the selection of key parameters. • A numerical model of ETCSM, which accounts for the supporting effect of gangue, was constructed using FLAC3D. This numerical model was used to perform numerical simulations of different hard roof horizons and thicknesses. The support load and energy released by strata breakage were determined, verifying the correctness of the determination criteria. The results show that the horizon and thickness of the hard roof have a significant impact on the energy release and support load. The results indicate that the main strata affecting the SGPB of working face 8101 are the HHRs located between 110 m and 220 m. Therefore, with regard to the working face 8101, the best fracturing horizons are KS3 and KS4. The optimal fracturing thickness of KS3 is 10.7 m, and that of KS4 is 4.9 m. • The research results were applied to working face 8101 of Tashan coal mine. Microseismic monitoring showed that the KS3 hydraulic fracture extends 250 m with an azimuth of NE65° and that the KS4 hydraulic fracture extends 218 m with an azimuth of NW68°. The support load of typical measuring points in the hydraulic fracture zone was reduced by 18.6%, and the periodic roof weighting interval was increased by 32%. The average height deformation of the advance roadway in working face 8101 was only 0.53 m, and the average width deformation of the advance roadway was only 0.23 m. There was no SGP during the mining process. This provides a support for determining the key parameters of HHR for VWSF and facilitates the widespread application of VWSF technology in HHR control.