Roof Cutting Parameters Design for Gob-Side Entry in Deep Coal Mine: A Case Study

Roof cutting is an effective technique for controlling the deformation and failure of the surrounding rock in deep gob-side entry. The determination of the roof cutting parameters has become a popular research subject. Initially, two mechanical models are established for the non-roof-cutting and roof-cutting of gob-side entry in deep mining conditions. On this basis, the necessity and significance of roof cutting is revealed by analysing the stress and displacement of roadside prop. The Universal Distinct Element Code numerical simulation model is established to determine the key roof-cutting parameters (cutting angle and cutting height) according to the on-site situation of No. 2415 headentry of the Suncun coal mine, China. The numerical simulation results show that with the cutting angle and height increase, the vertical stress and horizontal displacement of the coal wall first increase and then decrease, as in the case of the vertical stress and displacement of roadside prop. Therefore, the optimum roof cutting parameters are determined as a cutting angle of 70◦ and cutting height of 8 m. Finally, a field application was performed at the No. 2415 headentry of the Suncun coal mine. In situ investigations show that after 10 m lagged the working face, the stress and displacement of roadside prop are obviously reduced with the hanging roof smoothly cut down, and they are stable at 19 MPa and 145 mm at 32 m behind the working face, respectively. This indicates that the stability of the surrounding rock was effectively controlled. This research demonstrates that the key parameters determined through a numerical simulation satisfactorily meet the production requirements and provide a reference for ensuring safe production in deep mining conditions.


Introduction
Gob-side entry retaining (GER) technology has been widely applied in Chinese coal mines. GER technology is a roadway layout method and surrounding rock control technology that retains the original entry along the gob side to serve the next working face [1][2][3][4]. It can make the requirement for a coal pillar redundant, realise continuous mining, alleviate the tension of mining replacement, and eliminate the stress concentration in the coal pillar. It is one of the most important development directions of coal resource mining in China [5][6][7][8][9]. However, the Chinese coal resources has gradually turned into deep coal mining the buried-depth of which has reached over 800 m in recent years. As compared with shallow and medium buried mining conditions, the buried-depth of which being Suncun coal mine is in Tai'an, Shandong province, China. The mine field is 9.1 km long, 3 km wide, and covers an area of 21.2 km 2 . The southern boundary of the minefield is a coal-seam outcrop. The northern boundary is a coal seam with a contour of −1050 m. The western boundary is the original position of fault F8. The eastern boundary is the boundary of the northern Jurassic scouring boundary between faults F6 and F10. The coal mine contains 19 coal seams, where No. 2,No. 4,and No. 11 are the main seams. The geological coal reserves are 96,634,900 t and the recoverable reserves are 49,958,400 t, of which the recoverable reserves below the −800 m level account for 64%, which has a very good development prospect. The layout of the mine location and 2415 working face are shown in Figure 1.   The No. 2415 headentry is a gob-side entry, and the roadway section is rectangular with a width of 4.0 m × height of 3.0 m. Owing to hard roof condition and some complex environmental factors (e.g., three highs and one disturbance) in deep mines, the roof of the No. 2415 headentry was seriously deformed, and the surrounding rock was extensively damaged, as shown in Figure 3.

Rock Mass Properties
Rock mechanical properties has an important influence on the roadway stability. To provide the guidance and reference for the numerical simulation, the mechanical properties of the surrounding rock at 2415 working face in Suncun coal mine were obtained by uniaxial compression test on in-site rock specimens.
The rock specimen properties were obtained through laboratory compression tests on small rock specimens as suggested by the International Society for Rock Mechanics [59]. As shown in Figure 4, the loading system comprises a Shimadzu AG-X250 electronic universal testing machine. The testing machine is driven by an AC motor servo, and the loading mode has a double screw structure. This equipment has good stability and high precision; it can be used to perform conventional mechanical tests such as compression and tension. The maximum test load can reach 250 kN. The displacement loading control was used during the test until the sample was destroyed, and the loading rate was set as 0.0005 mm/s.

Rock Mass Properties
Rock mechanical properties has an important influence on the roadway stability. To provide the guidance and reference for the numerical simulation, the mechanical properties of the surrounding rock at 2415 working face in Suncun coal mine were obtained by uniaxial compression test on in-site rock specimens.
The rock specimen properties were obtained through laboratory compression tests on small rock specimens as suggested by the International Society for Rock Mechanics [59]. As shown in Figure 4, the loading system comprises a Shimadzu AG-X250 electronic universal testing machine. The testing machine is driven by an AC motor servo, and the loading mode has a double screw structure. This equipment has good stability and high precision; it can be used to perform conventional mechanical tests such as compression and tension. The maximum test load can reach 250 kN. The displacement loading control was used during the test until the sample was destroyed, and the loading rate was set as 0.0005 mm/s. However, the discontinuity of the engineering rock mass resulted in a reduced macro-strength; hence, the rock mass strength was much smaller than that of specimens. We modify the mechanical properties of the rock mass appropriately to fit the numerical simulation. The mechanical properties used for the simulation are listed in Table 1. the loading system comprises a Shimadzu AG-X250 electronic universal testing machine. The testing machine is driven by an AC motor servo, and the loading mode has a double screw structure. This equipment has good stability and high precision; it can be used to perform conventional mechanical tests such as compression and tension. The maximum test load can reach 250 kN. The displacement loading control was used during the test until the sample was destroyed, and the loading rate was set as 0.0005 mm/s.

Mechanical Model
When GER technology is applied under a condition of deep hard roof mining, the lateral immediate roof collapses into the goaf, and the length of the hanging roof gradually increases. Furthermore, the main roof rotary subsides along the fracture line as the working face advanced [19][20][21][22][23]. Under these conditions, it becomes very difficult for the traditional roadway support to resist the large pressures caused by the surrounding rock deformation and lateral roof subsidence, which is destructive to the roadside supports and stability of the roadway. The roof cutting can cut off the hanging roof effectively and make the collapsed gangues act as a bearing body, which can fully exert its bearing characteristics to support the upper rock strata. In this manner, the stress of the roadside support body can be reduced, and the stress environment of the surrounding rock can be improved. To clarify the necessity and significance of roof cutting, simplified mechanical models are established for non-roof-cutting and roof-cutting conditions of GER, as shown in Figure 5.
The roadway roof is approximately regarded as an elastic beam supported by coal wall at one end, roadside prop in the middle, and gangues in goaf at the other end. In Figure 5, the mining height is h; the immediate roof thickness is m Z ; the main roof thickness is m E ; the distance from the fracturing line to the coal wall is L 0 ; the width of the roadway is L R ; the length of the hanging roof is L S ; the overlying strata load, q, is uniformly applied on the main roof; and the length of the rock beam B, is L E . The coal wall supporting resistance can be expressed by F M1 and F M2 , respectively, and the supporting resistance of roadside prop are P 1 and P 2 respectively. The supporting effect of gangues can be expressed by a trapezoidal distributed load, ranging 0_q 3 , and the bearing length is L G1 and L G2 respectively.

Roadside Prop Displacement
As shown in Figure 5a, in the process of rock beam B subsidence, the ultimate subsidence for non-roof-cutting 1 h Δ is determined as per the theory of elasticity [2,7].
where KA is the coefficient of dilatancy of the roof rock, which is related to the nature of the collapsed gangues. It generally ranges from 1.15-1.35. According to the movement feature of the overlying strata, the roadside prop displacement of non-roof-cutting SC1 can be obtained using the following equation.
where A = L0 + LR + LS. As shown in Figure 5b, the ultimate subsidence for roof-cutting 2 h Δ is determined as follows.

Roadside Prop Displacement
As shown in Figure 5a, in the process of rock beam B subsidence, the ultimate subsidence for non-roof-cutting ∆h 1 is determined as per the theory of elasticity [2,7].
where K A is the coefficient of dilatancy of the roof rock, which is related to the nature of the collapsed gangues. It generally ranges from 1.15-1.35. According to the movement feature of the overlying strata, the roadside prop displacement of non-roof-cutting S C1 can be obtained using the following equation.
where A = L 0 + L R + L S . As shown in Figure 5b, the ultimate subsidence for roof-cutting ∆h 2 is determined as follows.
At this time, the displacement of the roadside prop for roof-cutting S C2 can be obtained as follows.
where B = L 0 + L R . On using Equations (2)-(4), the following can be obtained: Therefore, from Equation (5), it can be observed that In addition, according to the roof movement law in the mining process, the lateral main roof rotation angle of non-roof-cutting θ 1 is as follows.
Similarly, the lateral main roof rotation angle of roof cutting θ 2 can be obtained.
Through the analysis of the above equations, the following can be derived.
From Equation (9), it can be observed that the lateral main roof rotation angle and the roadside prop displacement of the roof-cutting condition are smaller than those of the non-roof-cutting condition. Therefore, roof cutting can be effectively used to reduce the displacement of roadside prop, limit the rotary subsidence of the main roof, which benefit the gob-side entry stability.

Roadside Prop Stress
As shown in Figure 5a, when adopting non-roof-cutting, the weight of the immediate roof F Z1 is While adopting roof cutting, as shown in Figure 5b, the weight of immediate roof F Z2 is where γ Z is the volumetric weight of immediate roof. γ E is the volumetric weight of main roof. The weight of main roof F E can be determined as follows.
Assuming that the bearing force of the gangues on the roof has a linear distribution, according to the rock dilatancy [52][53][54][55], the supporting resistance of the gangues in goaf for non-roof-cutting F G1 is as follows.
where L G1 is the gangues bearing length m on main roof for the non-roof-cutting condition.
With the lateral main roof subsidence, the contact point between the rock beam B edge and gangue in goaf moves to the left after the roof cutting. At this time, the bearing length of the gangue is L G2 : Therefore, the supporting resistance of gangues F G2 for roof-cutting condition is as follows: Assuming the roof load is uniformly applied to the roadside prop, and without considering the supporting resistance in the roadway, the mechanical equilibrium equation is established for non-roof-cutting in Figure 5a.
where P 1 is the support resistance of the roadside prop for the non-roof-cutting condition, kN. From Equation (16), we can obtain the following: Based on the above hypothesis, the mechanical equilibrium equation is established for roof-cutting as shown in Figure 5b.
where P 2 is the support resistance of the roadside prop for the roof-cutting condition, kN. According to Equation (18), the following can be obtained: Using Equations (2)-(4), the following can be obtained: Energies 2019, 12, 2032 9 of 25 Therefore, from Equation (20), it can be observed that The above analysis shows that after adopting roof-cutting, the roof is cut down and filled with the goaf. The bearing capacity of the gangues is improved, and they act as an active support to the upper strata weight. This reduces the pressure generated by the lateral roof subsidence and its sinking movement space, and fully exerts the bearing characteristics of gangues in goaf, which can greatly reduce the stress on the roadside prop and improve the surrounding rock stability and integration.

UDEC Model Criterion
Discontinuity will cause great defects to rock continuum mechanics. The discrete element method can be used to reflect the failure and mechanical features of surrounding rock in deep mining conditions. Additionally, the failure process can be better revealed by simulating the cracks and joints [60].
As the tensile strength of rock is much smaller than its compressive strength, the Mohr-Coulomb elastoplastic constitutive model is used to realise the tension failure of a block [60]. The failure criterion (σ 1 , σ 3 ) as illustrated in Figure 6.

UDEC Model Criterion
Discontinuity will cause great defects to rock continuum mechanics. The discrete element method can be used to reflect the failure and mechanical features of surrounding rock in deep mining conditions. Additionally, the failure process can be better revealed by simulating the cracks and joints [60].
As the tensile strength of rock is much smaller than its compressive strength, the Mohr-Coulomb elastoplastic constitutive model is used to realise the tension failure of a block [60]. The failure criterion ( 1 σ , 3 σ ) as illustrated in Figure 6. The failure process can be defined from points A to B by Mohr-Coulomb yield function.
where ϕ is the friction angle, c is the cohesion, and where t σ is the tensile strength.
In the contact model, the sliding or opening of the contact surface is realised by using Coulomb friction law, which is very appropriate to simulating the failure process. The contact behavior is simulated by spring slider, and the contact force can be divided into normal stress and shear stress. The contact constitutive behaviour is illustrated as Figure 7. The failure process can be defined from points A to B by Mohr-Coulomb yield function.
where ϕ is the friction angle, c is the cohesion, and N ϕ = 1+sin ϕ 1−sin ϕ . From points B to C, a tension yield function is expressed as follows.
where σ t is the tensile strength. In the contact model, the sliding or opening of the contact surface is realised by using Coulomb friction law, which is very appropriate to simulating the failure process. The contact behavior is simulated by spring slider, and the contact force can be divided into normal stress and shear stress. The contact constitutive behaviour is illustrated as Figure 7.
Depending on the stress state and the characteristics of the contact surface, damage can only occur along the contact by shearing or tension. In the vertical direction, the stress-displacement relationship is considered to be linear and controlled by stiffness k n , which is [60] ∆σ n = −k n ∆u n , where ∆σ n is the increment of effective normal stress; and ∆u n is normal displacement increment. The shear stress τ s is controlled by a constant shear stiffness in the shear direction, which is determined by contact characteristics, cohesion (c) and friction angle (φ). Therefore, if Then Then where ∆u s e is the elastic component in the shear displacement increment and ∆u s e is the total shear displacement increment. The failure process can be defined from points A to B by Mohr-Coulomb yield function.
where ϕ is the friction angle, c is the cohesion, and ϕ ϕ ϕ sin 1 . From points B to C, a tension yield function is expressed as follows.
where t σ is the tensile strength.
In the contact model, the sliding or opening of the contact surface is realised by using Coulomb friction law, which is very appropriate to simulating the failure process. The contact behavior is simulated by spring slider, and the contact force can be divided into normal stress and shear stress. The contact constitutive behaviour is illustrated as Figure 7.

Numerical Model Establishment and Modelling Procedures
A model was created by UDEC to simulate two key parameters of roof cutting (angles and heights) in the No. 2415 headentry. The simulation model is shown in Figure 8, which is based on the in-site lithological conditions illustrated in Figure 2 and Table 1 In the upper boundary, vertical stress was applied to simulate the overlying strata stress. In the two lateral boundaries, horizontal displacement were constrained. In the bottom boundary, the vertical and horizontal displacements were fixed. Before the excavation of roadway and working face, the model was equilibrium to produce the geostress. During the simulation, the "support" element was applied to simulate the roadside prop.
In addition, Monitoring Point 1 is set inside the coal wall to monitor the vertical stress and horizontal displacement of the coal wall. Monitoring Point 2 is arranged on the roadside prop to monitor the vertical stress and displacement after working face excavation.
The detailed simulation process was as follows ( A model was created by UDEC to simulate two key parameters of roof cutting (angles and heights) in the No. 2415 headentry. The simulation model is shown in Figure 8, which is based on the in-site lithological conditions illustrated in Figure 2 and Table 1. The numerical model was 240 m wide and 160 m high and contained 8045 blocks. The gob-side entry of 4.0 m width by 3.0 m height, and the 2415 working face with a 130 m length were simulated by excavating two rectangular openings in the middle respectively. In the upper boundary, vertical stress was applied to simulate the overlying strata stress. In the two lateral boundaries, horizontal displacement were constrained. In the bottom boundary, the vertical and horizontal displacements were fixed. Before the excavation of roadway and working face,  the model was equilibrium to produce the geostress. During the simulation, the "support" element was applied to simulate the roadside prop. In addition, Monitoring Point 1 is set inside the coal wall to monitor the vertical stress and horizontal displacement of the coal wall. Monitoring Point 2 is arranged on the roadside prop to monitor the vertical stress and displacement after working face excavation.

Cutting Angle
We define the cutting angle as the angle between the cutting borehole and the horizontal line. After adopting the directional roof-cutting boreholes, the boreholes are mutually conductive to form the weak surface structure. After the mining, the roof breaks along the weak surface and collapses to the goaf under self-weight and the overlying strata load. In the numerical simulation, the cutting angles are selected as 90°, 80°, 70°, 60°, and 50°, the cutting height is designed as 5 m, as shown in Figure 10.
(a) (b) Figure 9. Flowchart of numerical modeling for optimal roof cutting parameters.

Cutting Angle
We define the cutting angle as the angle between the cutting borehole and the horizontal line. After adopting the directional roof-cutting boreholes, the boreholes are mutually conductive to form the weak surface structure. After the mining, the roof breaks along the weak surface and collapses to the goaf under self-weight and the overlying strata load. In the numerical simulation, the cutting angles are selected as 90 • , 80 • , 70 • , 60 • , and 50 • , the cutting height is designed as 5 m, as shown in Figure 10.
The vertical stress contours and monitoring points curves of the numerical simulation are shown in Figures 11 and 12. With the change of cutting angle, the stress and displacement of coal wall and roadside prop also change in varying degrees. When the cutting angle is 90 • (Figure 11a), there is an obvious stress concentration area at the left side of the coal wall after excavation, which is large in scope and near the coal wall surface. Moreover, the roadside prop are subjected to a large compressive stress. The vertical stress peak value at the coal wall is 12.13 MPa, and the horizontal displacement is 360 mm. Meanwhile, the vertical stress peak value at the roadside prop is 33.74 MPa, and the vertical displacement is 330 mm. At this time, the lateral roof of the gob-side entry is only cut down by approximately half, and the roof-cutting performance is poor. When the cutting angle changes from 90 • to 80 • (Figure 11b), the range of the stress concentration area and stress peak value of the coal wall decrease gradually, and the stress peak value of the roadside prop also exhibits a downward trend. As compared with the cutting angle 90 • , the vertical stress peak values at the coal wall and roadside prop decreased by 6.7% and 25.1%, respectively. In terms of displacement, the coal wall horizontal displacement and roadside prop vertical displacement decreased by 11.1% and 9.1%, respectively. At this time, it is more suitable to cut the lateral roof along the gob-side entry; however, the hard roof still cannot be completely cut down. When the cutting angle changes from 80 • to 70 • (Figure 11c), the vertical stress peak values at the coal side and roadside prop further decreases. As compared with the cutting angle of 80 • , the stress peak values at the coal wall and roadside prop decreased by 6.7% and 20.3%, respectively. In terms of displacement, the coal wall horizontal displacement and the roadside prop vertical displacement decreased by 14.1% and 10.0%, respectively. At this time, the lateral roof of the gob-side entry is completely cut off, the coal side and roadside prop displacement is small, and the vertical stress peak value is effectively reduced.

Cutting Angle
We define the cutting angle as the angle between the cutting borehole and the horizontal line. After adopting the directional roof-cutting boreholes, the boreholes are mutually conductive to form the weak surface structure. After the mining, the roof breaks along the weak surface and collapses to the goaf under self-weight and the overlying strata load. In the numerical simulation, the cutting angles are selected as 90°, 80°, 70°, 60°, and 50°, the cutting height is designed as 5 m, as shown in Figure 10. The vertical stress contours and monitoring points curves of the numerical simulation are shown in Figures 11 and 12. With the change of cutting angle, the stress and displacement of coal wall and roadside prop also change in varying degrees. When the cutting angle is 90° (Figure 11a), there is an obvious stress concentration area at the left side of the coal wall after excavation, which is large in scope and near the coal wall surface. Moreover, the roadside prop are subjected to a large compressive stress. The vertical stress peak value at the coal wall is 12.13 MPa, and the horizontal displacement is 360 mm. Meanwhile, the vertical stress peak value at the roadside prop is 33.74 MPa, and the vertical displacement is 330 mm. At this time, the lateral roof of the gob-side entry is only cut  (Figure 11c), the vertical stress peak values at the coal side and roadside prop further decreases. As compared with the cutting angle of 80°, the stress peak values at the coal wall and roadside prop decreased by 6.7% and 20.3%, respectively. In terms of displacement, the coal wall horizontal displacement and the roadside prop vertical displacement decreased by 14.1% and 10.0%, respectively. At this time, the lateral roof of the gob-side entry is completely cut off, the coal side and roadside prop displacement is small, and the vertical stress peak value is effectively reduced.  However, the vertical stress peak values at the coal wall and roadside prop exhibit an upward trend with a further reduction in the cutting angle. When the cutting angle changes from 70 • to 60 • (Figure 11d), the stress peak values at coal wall and roadside prop also increase gradually. As compared with the cutting angle of 70 • , the vertical stress peak values increase by 5.1% and 20.9%, respectively. In addition, the displacement also increased in varying degrees. The coal wall horizontal displacement and the roadside prop vertical displacement increased by 12.7% and 7.4%, respectively. At this time, the roof can be completely cut off, but the length of the hanging roof also increases, which lead to the stress and displacement increased in the coal wall and roadside prop. When the cutting angle is changed from 60 • to 50 • (Figure 11e), the stress peak values at the coal wall and roadside prop continued to rise and showed an increase of 3.2% and 20.7%, respectively, as compared with those at the cutting angle of 60 • . Furthermore, the coal wall horizontal displacement and the roadside prop vertical displacement increased by 9.7% and 10.3%, respectively.
As shown in Figure 13, the results can be obtained according to the numerical calculation results above.

•
When the cutting angle is 90 • , i.e., in the case of vertical roof cutting, the immediate roof is bent and deformed under self-weight and the overlying strata load. Moreover, extrusion friction occurs at the cutting line, which means that the roof is required to overcome the larger rock shear force in order to collapse, and hence, the immediate roof cannot be completely cut off. Therefore, the stress transmission between the roof in the goaf and roadway is still maintained, which results in a large stress and deformation in the gob-side entry. In addition, the roadside prop is subjected to a large compressive stress, which causes severe deformation and damage.

•
With the reduction in the cutting angle, the peak stress and displacement at the coal wall and roadside prop decrease correspondingly when the cutting angle is 80 • . This indicates that the immediate roof will be more easily cut off when the cutting roof deflects to the goaf at a certain angle. However, the roof in the goaf still experiences some extrusion friction on the roadway roof during the process of collapsing, which results in insufficient cutting.

•
With a further reduction in the cutting angle, the stress and displacement at the coal wall and roadside prop are minimised when the cutting angle reaches 70 • . This indicates that the extrusion friction at the roof cutting surface can be effectively eliminated, and the stress transmission between the roof in the goaf and roadway is thoroughly cut off, which is beneficial to surrounding rock stability and protecting the roadside prop. • However, as the cutting angle continues to decrease, the stress and displacement at the coal wall and roadside prop increase to varying degrees when the cutting angle is 60 • and 50 • . This is because, as the cutting angle decreases, the extrusion friction at the cutting surface will not have a direct impact on the roof cutting effect, but at this time, the length of the hanging roof increases, which increases the roof load as well as the compressive stress on the roadside prop. Therefore, effective pressure relief cannot be achieved. However, the vertical stress peak values at the coal wall and roadside prop exhibit an upward trend with a further reduction in the cutting angle. When the cutting angle changes from 70° to 60° because, as the cutting angle decreases, the extrusion friction at the cutting surface will not have a direct impact on the roof cutting effect, but at this time, the length of the hanging roof increases, which increases the roof load as well as the compressive stress on the roadside prop. Therefore, effective pressure relief cannot be achieved.  Based on the comprehensive numerical calculation results, the optimum cutting angle is 70° for the mining conditions of 2415 working face.

Cutting Height
We define the cutting height as the maximum vertical height of the roof cutting borehole. According to the theoretical analysis [55][56][57][58], the cutting height has great impact on the cutting effect. In the numerical simulation, various cutting heights of 3, 4, 6, 7, 8, and 9 m are adopted. The cutting angle is designed as 70° in order to determine the optimum cutting height, as shown in Figure 14.

Cutting Height
We define the cutting height as the maximum vertical height of the roof cutting borehole. According to the theoretical analysis [55][56][57][58], the cutting height has great impact on the cutting effect. In the numerical simulation, various cutting heights of 3, 4, 6, 7, 8, and 9 m are adopted. The cutting angle is designed as 70 • in order to determine the optimum cutting height, as shown in Figure 14.
To simulate the fracture zone in the main roof strata, we use Voronoi tessellation in UDEC to provide randomly sized polygonal blocks. The fracture zone of the main roof is represented by a combination of triangular blocks and interval contact. By dividing each block into a triangular finite difference region, it will not fail due to its elasticity. According to the stress state and the characteristics of the contact surface, the failure only occurs along the contact surface in shear or tension.
The numerical simulation of the vertical stress contours and the monitoring points curves are shown in Figures 15 and 16. On comparing the various cutting height schemes, the following can be observed.
When the cutting height is 3 m (Figure 15a), the vertical stress peak values at the coal wall and roadside prop are 11.12 and 34.41 MPa, respectively, and the coal wall horizontal displacement and roadside prop vertical displacement are 350 and 340 mm, respectively. At this time, the lateral roof of the gob-side entry cannot be completely cut off because of the small cutting height, which is unsatisfactory. When the cutting height increases to 4 m (Figure 15b), the vertical stress peak values at the coal wall and roadside prop decrease by 5.8% and 17.6%, respectively. In terms of displacement, the coal wall horizontal displacement and roadside prop vertical displacement decrease by 7.1% and 13.3%, respectively. At this time, it is easier to cut off the hanging roof, but the stress transmission between the roof in goaf and roadway is still maintained. In addition, the collapsed gangue cannot fill the goaf to support the overlying strata. Therefore, the cutting height should continue to increase to the main roof strata.

Cutting Height
We define the cutting height as the maximum vertical height of the roof cutting borehole. According to the theoretical analysis [55][56][57][58], the cutting height has great impact on the cutting effect. In the numerical simulation, various cutting heights of 3, 4, 6, 7, 8, and 9 m are adopted. The cutting angle is designed as 70° in order to determine the optimum cutting height, as shown in Figure 14.  When the cutting height is 6 m (Figure 15c), the vertical stress peak values at the coal wall and roadside prop continue to decrease-2.3% and 4.2% lower than those at 4 m-and the displacements decrease by 18.8% and 23.3%, respectively. When the cutting height is 7 m (Figure 15d), the vertical stress peak values decrease by 5.0% and 14.1%, respectively, and the displacement decreases by 33.3% and 13.0%, respectively. When the cutting height is 8 m (Figure 15e), vertical stress peak values of the coal wall and roadside prop are 8.82 and 19.87 MPa, respectively, and the coal wall horizontal displacement and roadside prop vertical displacement are 162 and 150 m, respectively. At this time, the stress peak values at the coal wall and roadside prop reach a minimum, the stress concentration area is smallest far away from the roadway. Moreover, the displacement of coal wall and roadside prop are small, which indicates that the roof cutting has achieved good results at this cutting height.
However, the stress peak values at the coal wall and roadside prop exhibit an upward trend with a further increase in the cutting height. When the cutting height increases to 9 m (Figure 15f), the stress peak value at the coal wall and roadside prop increase gradually by 15.1% and 18.9%, respectively, as compared with those at 8 m. The displacement also increases in varying degrees.
The coal wall horizontal displacement and roadside prop vertical displacement increase by 38.3% and 40.0%, respectively.
To simulate the fracture zone in the main roof strata, we use Voronoi tessellation in UDEC to provide randomly sized polygonal blocks. The fracture zone of the main roof is represented by a combination of triangular blocks and interval contact. By dividing each block into a triangular finite difference region, it will not fail due to its elasticity. According to the stress state and the characteristics of the contact surface, the failure only occurs along the contact surface in shear or tension.
The numerical simulation of the vertical stress contours and the monitoring points curves are shown in Figures 15 and 16. On comparing the various cutting height schemes, the following can be observed. When the cutting height is 3 m (Figure 15a), the vertical stress peak values at the coal wall and roadside prop are 11.12 and 34.41 MPa, respectively, and the coal wall horizontal displacement and roadside prop vertical displacement are 350 and 340 mm, respectively. At this time, the lateral roof of the gob-side entry cannot be completely cut off because of the small cutting height, which is unsatisfactory. When the cutting height increases to 4 m (Figure 15b), the vertical stress peak values at the coal wall and roadside prop decrease by 5.8% and 17.6%, respectively. In terms of displacement, As shown in Figure 17, according an analysis of the above numerical calculation results, the following can be determined.

•
When the cutting height is 3 and 4 m, the hanging roof cannot be completely cut off because of the insufficient cutting height. In addition, the collapsed gangues cannot fill the goaf, which cannot exert the bearing capacity to restrict the main roof movement. Therefore, the stress concentration area of coal wall is large, and the stress peak value is high. Moreover, the roadside prop is subjected to a large compressive stress and suffers obvious deformation.

•
When the cutting height is greater than the immediate roof thickness, which means that part of main roof is cut off, the stress peak values and displacement of the coal wall and roadside prop are reduced correspondingly. This is because the immediate roof is cut off, which fundamentally eliminates the inside stress transmission. In addition, the gangues cut from the main roof can be further filled with the goaf according to the rock dilatancy, such that it can limit the movement of the overlying strata, which is beneficial for the stability to roadway surrounding rock. When cutting height is 8 m, the stress peak values and displacement of coal wall and roadside prop roadway are minimised, which effectively controls the deformation and failure at the gob-side entry and greatly reduces the stress on the roadside prop. Roof cutting achieved in this case exhibits the best results. • However, for a larger cutting height the obtained roof-cutting result is not better. When the cutting height is increased to 9 m, the stress and displacement at the coal wall and roadside prop tend to increase. This is because the cutting height is sufficiently large to destroy the structure of the main roof rock beam, which loses its bearing capacity with respect to the overlying strata. Meanwhile, the upper part of the main roof is compressed and greatly deformed during the process of rotary subsidence, which is not conducive to effective roof cutting.

•
Based on the comprehensive numerical calculation results, the optimum cutting height is 8 m for the mining conditions of 2415 working face. the coal wall horizontal displacement and roadside prop vertical displacement decrease by 7.1% and 13.3%, respectively. At this time, it is easier to cut off the hanging roof, but the stress transmission between the roof in goaf and roadway is still maintained. In addition, the collapsed gangue cannot fill the goaf to support the overlying strata. Therefore, the cutting height should continue to increase to the main roof strata. When the cutting height is 6 m (Figure 15c), the vertical stress peak values at the coal wall and roadside prop continue to decrease-2.3% and 4.2% lower than those at 4 m-and the displacements decrease by 18.8% and 23.3%, respectively. When the cutting height is 7 m (Figure 15d), the vertical stress peak values decrease by 5.0% and 14.1%, respectively, and the displacement decreases by 33.3% and 13.0%, respectively. When the cutting height is 8 m (Figure 15e), vertical stress peak values of the coal wall and roadside prop are 8.82 and 19.87 MPa, respectively, and the coal wall horizontal displacement and roadside prop vertical displacement are 162 and 150 m, respectively. At this time, the stress peak values at the coal wall and roadside prop reach a minimum, the stress concentration area is smallest far away from the roadway. Moreover, the displacement of coal wall and roadside prop are small, which indicates that the roof cutting has achieved good results at this cutting height.
However, the stress peak values at the coal wall and roadside prop exhibit an upward trend with a further increase in the cutting height. When the cutting height increases to 9 m (Figure 15f), the stress peak value at the coal wall and roadside prop increase gradually by 15.1% and 18.9%, respectively, as compared with those at 8 m. The displacement also increases in varying degrees. The coal wall horizontal displacement and roadside prop vertical displacement increase by 38.3% and 40.0%, respectively.  tend to increase. This is because the cutting height is sufficiently large to destroy the structure of the main roof rock beam, which loses its bearing capacity with respect to the overlying strata. Meanwhile, the upper part of the main roof is compressed and greatly deformed during the process of rotary subsidence, which is not conducive to effective roof cutting.  Based on the comprehensive numerical calculation results, the optimum cutting height is 8 m for the mining conditions of 2415 working face.

Field Application
According to the key parameters of roof cutting determined by the above research, field implementation was conducted at No. 2415 headentry in the Suncun coal mine. As the change in the roadside prop can directly reflect the roof and floor movement, the roadside prop stress and displacement are monitored separately to analyse the roof cutting effect. The monitoring curves of roadside prop are shown in Figure 18.

Field Application
According to the key parameters of roof cutting determined by the above research, field implementation was conducted at No. 2415 headentry in the Suncun coal mine. As the change in the roadside prop can directly reflect the roof and floor movement, the roadside prop stress and displacement are monitored separately to analyse the roof cutting effect. The monitoring curves of roadside prop are shown in Figure 18.
As illustrated in Figure 18a, It can be concluded that within the range of 34 m ahead of the working face, the stress and displacement of the roadside prop begin to increase, from which it can be inferred that this range is the area affected by the advance abutment pressure. After the working face is excavated, the displacements of roadside props are continuously monitored. Within 10 m behind the working face, a large deformation of the surrounding rock occurs owing to the main roof rotary subsidence. Beyond It can be concluded that within the range of 34 m ahead of the working face, the stress and displacement of the roadside prop begin to increase, from which it can be inferred that this range is the area affected by the advance abutment pressure. After the working face is excavated, the displacements of roadside props are continuously monitored. Within 10 m behind the working face, a large deformation of the surrounding rock occurs owing to the main roof rotary subsidence. Beyond 10 m lagged the working face, the hanging roof collapses along the cutting line under the periodic roof pressure. The gangues in goaf exert the bearing capability on the roof, which reduces the stress of the roadside prop and slows down its deformation rate. Then, as the main roof continues to rotate and sink, the gangues in the goaf are gradually compacted, and the stress of roadside prop increases slightly and eventually stabilises.
The monitoring results show that the stress and displacement of the roadside props are small, which indicates that the hanging roof is effectively cut off after the excavation of the working face, and the roof-cutting effect is remarkable. It also reflects that the deformation of the roof and floor of the gob-side entry is small, as shown in Figure 19, the surrounding rock has been effectively controlled, and the deformation is small, which meets the normal production requirements. the gob-side entry is small, as shown in Figure 19, the surrounding rock has been effectively controlled, and the deformation is small, which meets the normal production requirements.

Discussion
In this paper, we theoretically confirmed the necessity and significance of roof cutting using GER technology in coal mines, revealed the influences of the cutting parameters on the stability of the surrounding rocks of the gob-side entry, and determined the optimal values of two key parameters, the cutting angle and height, of a typical deep coal seam in the Suncun coal mine.

Discussion
In this paper, we theoretically confirmed the necessity and significance of roof cutting using GER technology in coal mines, revealed the influences of the cutting parameters on the stability of the surrounding rocks of the gob-side entry, and determined the optimal values of two key parameters, the cutting angle and height, of a typical deep coal seam in the Suncun coal mine.
Currently, some scholars have built structural mechanical models [53][54][55][56] for roof cutting, such as the transfer rock beam mechanical model [53], mechanical model of fracturing roofs to maintain entry approach [54], dynamic pressure area mechanical model [55], and main roof breaking upon retracement channel mechanical model [56]. These mechanical models revealed the role of various supporting structures, such as roadside backfill and coal support, and the basic characteristics of the main roof movement in GER. However, these mechanical models are mainly focused on the after-roof-cutting mechanical analysis. In this paper, the significance and necessity of roof cutting were clarified by establishing two mechanical models of non-roof-cutting and roof-cutting conditions. We deduced the stress and displacement of the roadside prop in the two models according to the theoretical mechanics and material mechanics. This method laid a theoretical foundation for roof cutting in GER.
In addition, the roof cutting parameters play a significant role in the process of roof cutting. Currently, roof cutting parameters are mostly based on field engineering experience or empirical formulas [54][55][56], which limit its application scope. Moreover, the FLAC3D software is used to determine the parameters of roof cutting [57,58]. However, as compared with the FEM, the DEM can not only reflect the fractured form of deep roadway, but also show the failure process of surrounding rock. In this paper, we obtained the optimal roof cutting parameters for No. 2415 headentry of Suncun coal mine by using UDEC numerical simulation software and obtained better application. Additionally, the variable-controlling approach was applied in the process of optimization. In this approach, firstly, we kept vertical cutting height constant, and changed the cutting angle to obtain its optimal angle. Then, we maintained the optimal constant cutting angle and varied cutting heights to obtain the optimal height eventually. This approach avoids blindness in choosing roof-cutting schemes, fully considers the factors of cutting angle and height, and provides references for similar mining conditions.
It should be noted that we only impose a constant static load on the upper boundary of the model without considering the influence of the dynamic load inside the numerical model, which also has great influence to the stability of the surrounding rock in GER [27,28,43]. In addition, the discontinuities have a direct impact on the mechanical properties of the rock mass. Although the mechanical properties of the rock mass are appropriately modified, it is difficult to characterise the mechanical behaviour of the discontinuities in complex geological conditions. In future work, we intend to study the UDEC numerical simulation model further, and gradually improve the design scheme of the key roof cutting parameters in order to make it more widely used.

Conclusions
The aim of this research was to confirm the necessity and significance of roof cutting theoretically and determine the optimal values of two key parameters (cutting angle and height), by establishing UDEC numerical models. As compared with the current published works, this work has at least two original aspects: • Two mechanical models of gob-side entry for non-roof-cutting and roof-cutting cases were established, and the necessity and significance of roof cutting for GER were theoretically revealed.

•
The UDEC numerical simulation software was used to simulate the roof cutting process. The key parameters of roof cutting (cutting angle and height) were quantitatively determined by comparing and analysing the simulation results.
With respect to theory, the stress and displacement of the roadside prop were reduced after the roof cutting, which proved the necessity and importance of roof cutting for the surrounding rock stability.
The simulation results showed that cutting angle and height had a significant influence on the surrounding rock stability. (1) As the cutting angle decreased, the amount of stress and displacement at the coal wall and roadside prop decreased first and then increased. When the cutting angle was 70 • , the stress and displacement the at coal wall and roadside prop were the smallest. The vertical peak stress values were 10.56 and 20.15 MPa, respectively, i.e., 12.9% and 40.3% lower than those at the cutting angle of 90 • . The horizontal displacement of the coal wall and vertical displacement of the roadside prop were 275 and 270 mm, respectively, which were 23.6% and 18.2% less than those at the cutting angle of 90 • . When the cutting angle was 50 • , the stress at the coal wall and roadside prop increased by 8.4% and 46.1%, respectively, as compared with those at the cutting angle of 70 • , and the coal wall horizontal displacement and the roadside prop vertical displacement increased by 23.6% and 18.5%, respectively. (2) As the cutting height increased, the amount of stress and displacement at the coal wall and roadside prop also decreased first and then increased. When the cutting height is 8 m, the stress and displacement at the coal wall and roadside prop are the least, and the vertical peak stress values were 8.82 and 19.87 MPa, respectively, which were 20.7% and 42.3% lower than those at the cutting height of 3 m. The coal wall horizontal displacement and roadside prop vertical displacement were 162 and 150 mm, respectively, which were 53.7% and 55.9% less than those at the cutting height of 3 m. When the cutting height was 50 • , the stress at the coal wall and roadside prop increased by 15.1% and 18.9%, respectively, as compared with those at the cutting height of 8 m, and the horizontal displacement of the coal wall and vertical displacement of the roadside prop increased by 38.3% and 40.0%, respectively. Therefore, it can be observed that the influence of the cutting height is more significant than the cutting angle at the selected level, and the optimum cutting parameters can be determined as a cutting angle of 70 • and cutting height of 8 m.
Field practice and the monitoring results showed that the stress of the roadside prop increased first and then decreased, and finally stabilised at 19 MPa with a slight rise at 32 m behind the working face. The deformation rate of the roadside prop increased from small to large, then became small, and finally stabilised at 145 mm, which is consistent with the numerical simulation results. The monitoring results showed that the stress transmission inside the immediate roof was fundamentally eliminated on applying the optimal roof cutting parameters determined in the numerical simulation. In addition, the gangues cut down from the main roof filled the goaf according to the dilatancy of the rock, such that it could limit the movement of the main roof and the overlying strata. The stress and displacement of the roadside prop were small, which effectively controlled the deformation and failure of the surrounding rock.
Although the optimal key parameters of the roof were determined, and good field application results have been achieved, it should be noted that the influence of the dynamic load is not taken into consideration in this numerical simulation. In future work, this factor will be taken into consideration, which could make the key parameters more widely applicable.