Nonuniform Deformation Instability Mechanism of Gob-Side Entry Retained in Inclined Coal Seam and Stability Control

Abstract

In this study, the nonuniform deformation and failure of the goaf retaining roadway in an inclined coal seam due to repeated mining have been investigated by field verification, theoretical analysis and numerical simulation. As a case study, 3131 headentry of a coal mine in Sichuan province was considered. The deformation characteristics of the surrounding rock along the gob of inclined coal seam and the distribution characteristics and evolution of the plastic zone and stress field direction of gob-side entry retaining (GER) in 3131 coal faces during the service period were also studied. Based on the mechanical model of the plastic zone of surrounding rock, the stress field direction effect of nonuniform expansion of the plastic zone is explained, and the nonuniform deformation damage mechanism of the inclined coal seam along the empty tunnel is revealed. The results show that the plastic zone of the side always expands along the coal seam towards the side affected by mining during the whole service period of GER in the inclined coal seam, and the plastic zone of the roof and floor expands to the deep surrounding rock; and the expansion degree of the soft coal (rock) seam position of the roadway is the highest. At the same time, the direction of the surrounding rock stress field will be deflected during the service period of GER, and the plastic zone expands unevenly under the action of the coal seam dip angle and stress direction. The nonuniform expansion degree of the plastic zone is the largest when the angle between the maximum principal stress and the coal (rock) layer is 45° (±5°). A collaborative support method with “supporting and reducing span” as the core in GER is also proposed in this work. Field tests were also carried out. During the retaining period, the displacement of the roof and floor was reduced from 250 mm to 125 mm.

1. Introduction

An inclined coal seam is distributed in the southwest of China and is mostly high-quality and scarce coal. In order to increase production of high-quality coal resources and improve the tension between mining and excavation, gob-side entry retaining (GER) technology is often used in inclined coal seams [1,2]. After the GER in an inclined coal seam is affected by multiple minings, the law of mining pressure is significantly different from that of horizontal coal seam GER under the combined influence of the stress direction and the dip angle of the coal seam. The deformation and failure of the surrounding rock of the roadway are serious [3,4,5], exhibiting nonuniform deformation characteristics and significantly increasing the difficulty of roadway maintenance, making the stability of GER increasingly prominent [6,7,8]. Therefore, studying the nonuniform expansion mechanism and stability control method for the plastic zone in an inclined coal seam for the diffusion and application of GER technology is critically important.

In recent decades, many researchers have studied the deformation and failure characteristics and the stability control of surrounding rock in inclined coal seams. Researchers have found that there are differences in the bearing capacity of different positions in the GER, and the deformation and failure of the surrounding rock show obvious asymmetric characteristics [9,10,11]; moreover, the deformation of the surrounding rock is more sensitive to the influence of mining in the secondary mining stage, and the plastic failure zone of the surrounding rock at the edge of the goaf is larger [12,13]. It is further found that the greater the rotation angle of the principal stress direction in the regional stress field, the more obvious the alienation expansion of the plastic zone and the greater the degree of deformation and failure of the roadway, and the height of the hidden roof falls [14].

Therefore, based on the structural mechanics of key blocks in GER, scholars analyzed the influence of support resistance in roadway and roadside support resistance on the stability of key blocks and proposed that high-strength support should be used in roadways to reduce roof rotation and subsidence; further, roadside support should adopt filling materials with high early strength and fast resistance increasing speed [15,16,17] so as to adapt to the stage of increasing speed, decreasing speed and stable speed of surrounding rock deformation in GER [18]. The deformation of surrounding rock can be effectively controlled by the asymmetric coupling control technology of narrow flexible formwork wall partition [19].

Previously published studies have focused on the deformation characteristics and failure mechanism of GER, control technology and roadside support resistance. However, the studies on the deformation model of surrounding rock during the overall service period of GER and the common influence of coal seam dip angle and stress field direction on the surrounding rock failure of GER have been sparse. Therefore, the 3131 headentry of a mine in Sichuan is taken as the case study in this paper, focusing on the evolution law of the plastic zone of the surrounding rock and the direction of the principal stress in the stress field of the GER in inclined coal seams, revealing the nonuniform deformation mechanism of the GER in inclined coal seams and proposing control countermeasures.

The remaining part of the article proceeds as follows: In Section 3, the deformation law of surrounding rock along the GER is obtained, and the distribution patterns and evolution trend of the plastic zone and stress direction of surrounding rock in the full-service stage of the inclined coal seam along the GER are analyzed in Section 4. Section 5 explores the common influence trend of coal seam dip angle and the stress field direction of the surrounding rock on the deformation of the surrounding rock along the GER, revealing the nonuniform deformation and failure mechanism of the inclined coal seam in gob-side entry retaining. The idea of surrounding rock control of inclined coal seams in GER is put forward, and its effect is tested in Section 6. In Section 7, the control technology of inclined coal seams along the GER is proposed. Finally, the conclusion part briefly summarizes the research results.

2. Methods and Simulation Models

2.1. The Distribution of Plastic Zone and Stress Field Direction of Surrounding Rock in 3131 Roadway

Relevant research studies and engineering practices show that the caving gangue in the goaf of inclined coal seam coal face will form three areas with different compaction degrees of gangue under the action of gravity and overlying rock structure, i.e., complete compaction area, partial compaction area and loose area, which significantly impacts the resulting stress and damages the surrounding rock [20,21,22].

Therefore, in the relevant numerical simulation research, the compaction effect of gangue filling in goafs should be fully considered. The stress–strain relationship proposed by Salamon in the compression process of broken rock mass is widely used [23]. After continuous correction and improvement, the expression of compaction characteristics of rock mass in the caving zone was obtained, as given in Equation (1) [24,25].

$$\sigma =\frac{10.39{\sigma }_c^{1.042}}{b^{7.7}}\times \frac{\epsilon }{1-\frac{b}{b-1}\epsilon },$$

(1)

The theoretical solution of the stress–strain relationship was obtained from Equation (1), and the compression simulation test of the gangue in the goaf was carried out in combination with the FLAC3^D numerical calculation model. The stress–strain relationship fitting well with the theoretical solution was obtained by trial and error, as shown in Figure 1. The constitutive model parameters of gangue double-zone service in goaf obtained by numerical simulation trial-and-error inversion are shown in

Table 1. Parameters of constitutive model of gangue dual zone in goaf.

ρ/Kg·m−3	K/GPa	G/GPa	Rm/MPa	φ/(°)	C/MPa
2500	15	0.6	0	35	0.001

.

Considering the 3131 headentry of a coal mine in Sichuan province as the engineering case study, the model was established using FLAC3^D software (https://www.itasca.cl/software/FLAC3D, accessed on 1 July 2023), and the finite difference method is used for numerical calculation (

Table 2. Mechanical parameters of model.

Lithology	ρ/kg/m3	K/GPa	G/GPa	Rm /MPa	φ/°	C/MPa
Aluminous argillite	2750	6.41	4.03	4.17	43	5.00
Argillaceous limestone	2600	4.39	3.02	3.20	37	4.14
Sandy Mudstone	2500	3.97	1.94	3.00	35	3.50
K1 coal	1325	1.35	0.71	1.80	33	1.57
mudstone	2277	3.21	1.55	2.62	34	3.18
Sandy mudstone	2500	3.97	1.94	3.00	35	3.50
Aluminous argillite	2750	6.41	4.03	4.17	43	5.00
Gangue	2500	15	0.60	0	35	0.001

and Figure 2). The model size is 350 m in length, 100 m in width and 236 m in height, and it was divided into 4,224,550 units. The horizontal and vertical displacement constraint boundaries are applied around the model, and the vertical displacement constraint boundary is applied at the bottom of the model. The buried depth of the simulated coal seam was 400 m, and the equivalent load of 10 MPa was applied on the upper surface of the model. In order to accurately depict the filling of the goaf in an inclined coal seam, the goaf was divided into a complete compaction area, partial compaction area and loose area from bottom to top along the dip direction of the coal seam. In model calculation, the double-yield constitutive model was adopted for the caving gangue in the goaf, and the Mohr–Coulomb constitutive model was adopted for other rock masses.

2.2. Nonuniform Expansion Mechanism of Plastic Zone

The direction of principal stress in the stress field changes after the roadway along the inclined coal seam is affected by repeated mining. When the principal stress direction changes, the mechanical model of the plastic zone of the inclined coal seam in the non-hydrostatic pressure field can be divided into three non-hydrostatic pressure fields subjected to vertical and horizontal stresses, as shown in Figure 3.

2.3. Roadside Filling Support Effect

So as to analyze the supporting effect of roadside filling on the roof strata of GER in the inclined coal seam, according to the roof structure characteristics of GER in the inclined coal seam, the beam formed by the roof of GER was regarded as a simply supported beam structure. The roadside filling can be simplified by adding a bearing hinge support in the middle of the simply supported beam (Figure 4).

3. Deformation Patterns of GER in Inclined Coal Seam

3.1. Engineering Situations

The 3131 working face is mainly mining the K₁ coal seam. The dip angle of the coal seam is 26~32°, the average dip angle is 29° and the average coal thickness is 1.6 m. The 3131 headentry is designed as a special-shaped trapezoidal section. The low side of the roadway excavation section is 1.6 m, the high side is 4.0 m and the width is 4.2 m. The roof of the coal seam is dominated by sandy mudstone and argillaceous limestone, and the floor is dominated by mudstone and sandy mudstone (Figure 5). Due to the small thickness of the coal seam and the tension of the working face, GER is adopted as tailentry of 3112 working face in 3131 headentry (Figure 6). The supporting method is shown in Figure 7.

Under the existing support method, the deformation and failure of the 3131 headentry during the mining period are serious. There are obvious differences in the deformation and failure patterns of the different positions of the roof and the two sides. Different degrees of floor heave occur on the floor, and the surrounding rock presents nonuniform deformation and failure characteristics.

3.2. Deformation and Failure Characteristics of 3131 Headentry

So as to understand the deformation pattern of surrounding rock in 3131 headentry during the roadway excavation period, mining disturbance stage and GER stage, monitoring positions were arranged at 45 m from the setup entry of the 3131 coal face in the roadway.

Figure 8 shows the vertical displacement of the roof and floor of 3131 headentry in the driving period, mining disturbance stage and the GER stage. The relative displacements of the roof and floor showed a trend of continuous growth in the three periods. Also, the relative displacements of the low side of the roadway roof and floor are greater than the relative displacements of the middle side and the relative displacements of the high side. At the same time, the relative displacements of the roof and floor increased significantly during the mining disturbance and GER stages.

During the early stage of roadway excavation, the surrounding rock is affected by excavation, and the vertical displacement curve of the roof and floor shows a linear growth trend. The roof and floor deformation rates gradually slow down and stabilize with time.

During the one mining disturbance stage, the deformation curve of the roof and floor showed a sharp linear growth first and then a slow growth trend with the advancement of the 3131 coal face. At this stage, the roof and floor of the roadway produced a large amount of deformation. At the initial deformation stage, as the station is closer to the 3131 working face, the roof and floor increase drastically due to the influence of mining-induced stress, leading to the increased initial steep.

During the GER stage, as the 3131 coal face continues to advance, the monitoring positions are gradually away from the influence range of mining-induced stress, and the strain rate of the roof and floor gradually slows down. The relative displacements of the roof and floor is mainly affected by the adjustment and movement of large structures of roof strata in GER, and the relative displacements of the roof and floor increases sharply for the second time.

4. Evolution Law of Plastic Zone and Principal Stress Direction of GER

4.1. Expansion Law of Plastic Zone

Based on the numerical calculation model established in Section 2.1, the distribution of the plastic zone at 5 m in front of the working face of 3131 return airway in roadway excavation stage, mining disturbance stage, GER stage and repeated mining disturbance stage are obtained, as shown in Figure 9. The failure of the surrounding rock during excavation and first mining periods is primarily the shear failure. Only a small range of tensile failure occurs in the shallow part of the surrounding rock on the two sides of the roadway. Large-scale tensile failure occurs during the roadway retention period and the secondary mining period, which is mainly located in the filling and the roof positions of the goaf.

During the roadway excavation stage, the plastic zone distribution of the 3131 headentry is limited (Figure 9a). The maximum failure depth of the plastic zone at the lower side of the roof and the floor is about 2.5 m. The maximum failure depth of the high-side plastic zone of the roadway is 2 m, whereas the maximum failure depth of the plastic zone of the roadway is 1 m.

During the first mining disturbance stage, the distribution range of the plastic zone significantly increased, and the plastic zone of the low side and high side of the roof extended unevenly. The range of the plastic zone on the low side of the roof extended to the low side, and the maximum failure range increased by about 30%. The plastic zone on the high side expanded to the 3131 working face side along the coal seam, and the maximum damage depth increased significantly by about 5 m.

During the GER stage, the maximum failure range of the plastic zone on the high side of the roadway roof doubled, and it expanded along the coal seam tendency in the roof of the goaf. The plastic zone on the high side is connected with the goaf. The failure range of the plastic zone of the floor extended to the deep surrounding rock, increasing by about 30%.

During the repeated mining disturbance stage, the failure range of the plastic zone of the floor further extended to the deep surrounding rock, increasing by about 50%. The plastic zone of the low side extended along the coal seam towards the working face side, increasing by about 12 m, while the plastic zone on the high side was still connected with the goaf.

In summary, the plastic zone morphology of 3131 headentry shows nonuniform expansion during mining. During the whole service period of the roadway, the plastic zone near the side of the coal face is always extended along the coal seam towards the side of the coal face. The plastic zone of the roof and floor position expands to the deep. At different stages of the service period, there are clear differences in the expansion degree of different positions. The expansion degree of the weak coal (rock) layer is the highest. The changes in the plastic zone are shown in Figure 10.

4.2. Deflection Law of Principal Stress Direction

Studies have shown that the direction of the stress field affects the distribution of the plastic zone [26]. The mining activity causes the redistribution of the stress field in the surrounding rock, and the direction of the stress field is deflected to a certain degree [27], affecting the formation and expansion of the plastic zone in the surrounding rock. Therefore, in order to study the distribution characteristics of the stress field direction during the service period of the 3131 headentry, the angle between the principal stress direction and the horizontal direction at different positions of the gob-side entry at 5 m ahead of the working face during the roadway excavation stage, first mining disturbance stage, GER stage and repeated mining disturbance stage were obtained and plotted, as shown in Figure 11.

As shown in Figure 11, the direction of the maximum principal stress in the regional stress field of the roadway changes due to mining activities. However, the deflection degree of the maximum principal stress at different roadway surrounding rock positions differs in different service stages. For the roof and high side, the direction of the maximum principal stress is changed due to mining, and the large change in the direction of the maximum principal stress is mainly in the GER stage. At this stage, the change in the direction of the stress field of the surrounding rock of the roadway is away from the side of the goaf (Figure 11c). During the whole service period, the deflection degree of the direction of the maximum principal stress on the left side of the roof and the upper side of the high side is greater than that of other positions. For the low side of the roadway, the deflection degree of the maximum principal stress direction at different positions of the roadway is small during the whole server period after being affected by mining. For the floor, the deflection degree of the maximum principal stress direction during the repeated mining disturbance stage is more pronounced, and the deflection direction of the stress field is toward the side of the positive mining face (Figure 11d).

Based on the above analysis, it is deduced that mining activities affect the stress field direction in GER. However, the deflection degree and range of different service stages and different positions of roadways are significantly different. The deflection of the stress field direction is mainly on the left side of the roof and the upper side of the high side during the GER stage and the repeated mining disturbance stage. Therefore, it is inferred that the stress direction of the GER is more obviously affected by the primary mining, and the deflection direction of the stress field of the GER is always toward the side of the mining activity.

5. Nonuniform Expansion Mechanism of Plastic Zone

5.1. Mechanical Analysis of the Influence of Principal Stress Direction on Plastic Zone Expansion of Inclined Coal Seam Roadway

The principal stress direction will have a certain angle with the coal (rock) layer due to the influence of the occurrence angle of the coal seam, which affects the distribution and expansion of the plastic zone of the surrounding rock. Based on the mechanical model in Section 2.2, from the theory of elastic–plastic mechanics, the stress fields of surrounding rock in inclined rock roadway can be expressed as Equations (2)–(4).

$${\sigma }_r=\frac{p_z}{2}\left\{\begin{array}{l}\left[\frac{3\left(\eta +1\right)\sin \left(\alpha -\gamma \right)}{2}+\left(\eta +1\right)\cos \left(\alpha -\gamma \right)\right]\left(1-\frac{a^2}{r^2}\right)+\\ \left[\frac{3\left(\eta -1\right)\sin \left(\alpha -\gamma \right)}{2}+\left(\eta -1\right)\cos \left(\alpha -\gamma \right)\right]\left(1-4\frac{a^2}{r^2}+3\frac{a^4}{r^4}\right)\cos 2\theta \end{array}\right\},$$

(2)

$${\sigma }_{\theta }=\frac{p_z}{2}\left\{\begin{array}{l}\left[\frac{3\left(\eta +1\right)\sin \left(\alpha -\gamma \right)}{2}+\left(\eta +1\right)\cos \left(\alpha -\gamma \right)\right]\left(1-\frac{a^2}{r^2}\right)-\\ \left[\frac{3\left(\eta -1\right)\sin \left(\alpha -\gamma \right)}{2}+\left(\eta -1\right)\cos \left(\alpha -\gamma \right)\right]\left(1+3\frac{a^4}{r^4}\right)\cos 2\theta \end{array}\right\},$$

(3)

$${\tau }_{r\theta }=\frac{p_z}{2}\left\{\left[\frac{3\left(\eta -1\right)\sin \left(\alpha -\gamma \right)}{2}+\left(\eta -1\right)\cos \left(\alpha -\gamma \right)\right]\left(1+2\frac{a^2}{r^2}-3\frac{a^4}{r^4}\right)\sin 2\theta \right\},$$

(4)

From the relevant mechanical calculation formula of elastic–plastic theory, the principal stress at any point in polar coordinates can be expressed as Equations (5) and (6).

$${\sigma }_1=\frac{{\sigma }_r+{\sigma }_{\theta }}{2}+\frac{1}{2}\sqrt{{\left({\sigma }_r-{\sigma }_{\theta }\right)}^2+4{\tau }_{r\theta }^2},$$

(5)

$${\sigma }_3=\frac{{\sigma }_r+{\sigma }_{\theta }}{2}-\frac{1}{2}\sqrt{{\left({\sigma }_r-{\sigma }_{\theta }\right)}^2+4{\tau }_{r\theta }^2},$$

(6)

According to the MC criterion, the limit equilibrium condition can be expressed as the principal stress, as given in Equation (7).

$${\sigma }_1=2C\frac{\cos \phi }{1-\sin \phi }+\frac{1+\sin \phi }{1-\sin \phi }{\sigma }_3,$$

(7)

According to Equations (2)–(7), and combined with the cosine quartic implicit equation of the principal stress direction deflection angle and the polar coordinate position angle of the plastic zone [28], the expression of the angle between the maximum principal stress and the coal seam and the polar coordinate position of the plastic zone can be obtained from Equation (8).

$$\begin{array}{c}9{\left(1-\eta \right)}^2{\left(\frac{a}{r}\right)}^8-12{\left(1-\eta \right)}^2{\left(\frac{a}{r}\right)}^6+6\left(1-{\eta }^2\right){\left(\frac{a}{r}\right)}^6\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]+10{\left(1-\eta \right)}^2{\left(\frac{a}{r}\right)}^4\times \\ {\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]}^2-4{\left(1-\eta \right)}^2{\sin }^2\phi {\left(\frac{a}{r}\right)}^4{\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]}^2-2{\left(1-\eta \right)}^2{\left(\frac{a}{r}\right)}^4{\sin }^{2}2\left(\theta +\alpha -\gamma \right)\\ -4{\left(1-\eta \right)}^2{\left(\frac{a}{r}\right)}^2\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]+2\left(1-{\eta }^2\right)\left(1-2{\sin }^2\phi \right){\left(\frac{a}{r}\right)}^2\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]\\ -\frac{4C\left(1-\eta \right)\sin 2\phi }{P_z}{\left(\frac{a}{r}\right)}^2\left[2{\cos }^2\left(\theta +\alpha -\gamma \right)-1\right]+{\left(1-\eta \right)}^2-{\sin }^2\phi {\left(1+\eta +\frac{2C\sin 2\phi }{P_z\sin \phi }\right)}^2=0\end{array},$$

(8)

When calculating the plastic zone in heterogeneous layered rock strata, the redistribution of surrounding rock stress caused by the expansion deformation of the plastic zone was ignored. The relevant calculation program was written using Equation (5), and the parameters of each rock stratum were input for calculation and superposition. The equivalent calculation results of the plastic zone distribution under the different angle between the maximum principal stress and coal seam were obtained (Figure 12). In the calculation, the coal seam dip angle α was taken as 0° (horizontal coal seam) and 30° (inclined coal seam), respectively.

As shown in Figure 11, under different stress field conditions, the plastic zone expands nonuniformly under the action of coal seam dip angle and stress direction. When the angle is 45° (±5°), the degree of nonuniform expansion of the plastic zone is the largest (Figure 12(a-iv,b-iv)). The expansion degree of the plastic zone in the coal strata is affected by the lithology strength of the rock strata, and the expansion degree in the soft rock strata is higher than that in the hard rock strata.

5.2. Nonuniform Expansion Mechanism of Plastic Zone in GER in Inclined Coal Seam

For GER in the inclined coal seam, the stress field distribution of roadway surrounding rock significantly differed from that of the horizontal coal seam roadway due to the coal seam dip angle. Also, the principal stress direction in the stress field had a certain angle with the axial direction. When affected by mining, the stress field changes to some extent, and the direction of the surrounding rock stress field will deflect counterclockwise. Due to the formation of the plastic zone in the surrounding rock, the shallow surrounding rock has been destroyed, resulting in the pressure relief phenomenon, while the deeper surrounding rock is not totally destroyed. Therefore, the stress field of deep surrounding rock can be regarded as a regional stress field, which also affects the deformation and failure of the roadway surrounding rock in the next stage. Under the combined influence of the dip angle of the coal seam and the direction of the regional stress field, the plastic zone of the surrounding rock expands nonuniformly along the dip of the coal seam to the side of the working face in the soft rock layer (Figure 13). This leads to a further increase in the failure range and depth of the plastic zone, resulting in nonuniform deformation characteristics.

6. Support Span Reduction Effect of Roadside Filling Body

6.1. Roof Structure Analysis of GER

With the advancing coal face of the inclined coal seam, the surrounding rock of the goaf roof forms a caving zone due to the expansion of the plastic zone in the roof of GER in the inclined coal seam. When the roof of the caving zone collapses, the roof of the roadway side does not collapse, so a cantilever beam structure is formed. Thus, the cantilever beam structure has an elastic–plastic intersection position on one side above the solid coal [28,29]. When the cantilever beam length reaches the limit step distance, it breaks, rotates and sinks, touching the gangue, and the rock blocks squeeze each other to produce friction. Compared with the horizontal coal seam, the three-dimensional occlusion degree between the rock blocks is closer under gravity, forming a beam structure with a certain span between the roadway and the goaf [30,31,32] (Figure 14).

Under the combined influence of coal (rock) seam inclination and the direction of the stress field, the plastic zone on the high side of the roadway expands greatly near the goaf during the GER in the inclined coal seam and connects with the goaf. The plastic zone of the roof also expands to the roof of the goaf, increasing the span of the masonry beam structure between the roadway and the goaf. Therefore, the roadside filling can block the gangue of the goaf and support the roof, effectively controlling the deformation of the roof and ensuring the stability of the roadway during the GER to achieve a good effect of roadway retention.

6.2. Analysis of Supporting Span Reduction Effect

Based on the deflection curve of the simply supported beam under uniform load [33,34,35], the rotation angle equation and deflection (deformation) curve equation of the model shown in Figure 4a of Section 2.3 are obtained as given in Equations (9)–(11).

$$EI{w}^{″}=\frac{ql}{2}\cos \theta x-\frac{q}{2}\cos \theta x^2,$$

(9)

$$EI{w}^{\prime }=\frac{ql}{4}\cos \theta x^2-\frac{q}{6}\cos \theta x^3-\frac{q{L}^3}{24}\cos \theta ,$$

(10)

$$EIw=\frac{ql}{12}\cos \theta x^3-\frac{q}{24}\cos \theta x^4-\frac{q{L}^3}{24}\cos \theta x,$$

(11)

The equations for the rotation angle and deflection (deformation) of the model, as shown in Figure 4b of Section 2.3, are given as Equations (12)–(20).

$$EI{w}_1{}^{″}=qa\cos \theta x-\frac{q}{2}\cos \theta x^2,$$

(12)

$$EI{w}_1{}^{\prime }=\frac{qa}{2}\cos \theta x^2-\frac{q}{6}\cos \theta x^3-\frac{q{a}^3}{12}\cos \theta ,$$

(13)

$$EI{w}_1=\frac{qa}{6}\cos \theta x^3-\frac{q}{12}\cos \theta x^4-\frac{q{a}^3}{12}\cos \theta x,$$

(14)

$$EI{w}_2{}^{″}=\frac{qa}{2}\cos \theta (x-a)-\frac{q}{2}\cos \theta {(x-a)}^2,$$

(15)

$$EI{w}_2{}^{\prime }=\frac{qa}{4}\cos \theta {(x-a)}^2-\frac{q}{6}\cos \theta {(x-a)}^3+\frac{q\cos \theta b^2}{24}\left(b-2a\right),$$

(16)

$$EI{w}_2=\frac{qa}{12}\cos \theta {\left(x-a\right)}^3-\frac{q}{24}\cos \theta {\left(x-a\right)}^4+\frac{q\cos \theta b^2}{24}\left(b-2a\right)\left(x-a\right),$$

(17)

$$\omega \left(x\right)=\frac{ql{x}^3\cos \theta }{12EI}-\frac{q{x}^4\cos \theta }{24EI}-\frac{q{l}^{3}x\cos \theta }{24EI},$$

(18)

$${\omega }_1\left(x\right)=\frac{qa{x}^3\cos \theta }{6EI}-\frac{q{x}^4\cos \theta }{12EI}-\frac{q{a}^{3}x\cos \theta }{12EI}\hspace{1em}0 \le x \le a,$$

(19)

$${\omega }_2\left(x\right)=\frac{qa{\left(x-a\right)}^3\cos \theta }{12EI}-\frac{q{\left(x-a\right)}^4\cos \theta }{24EI}+\frac{q{b}^2\left(b-2a\right)\left(x-a\right)\cos \theta }{24EI}\hspace{1em}a \le x \le l,$$

(20)

In Equations (12)–(20), q is the load acting on the simplified beam, kN/m; l is the roadway roof span, m; θ is the dip angle of the coal seam, degrees; x is the distance from point A along the dip of the coal seam, m; f is the support force of the roadside filling wall, kN; a is the distance between the action point of roadside support force and point A, m; and b is the distance between the action point of roadside filling body and point B, m.

In order to quantitatively study the supporting role of the roadside support wall of the GER, the actual parameters of 3131 roadway were substituted into the Equations (9)–(11); the deformation of roadway roof with and without roadside support is calculated and compared. The results are shown in Figure 15.

Figure 15 shows that the overall subsidence (deformation) of the roof is significantly reduced when there is a roadside support body, and the maximum subsidence is reduced by about 85% in the roof compared with that without roadside support. For the inclined coal seam GER, when using the roadside filling to support the roof, the strength of the filling body can effectively support the roof. It also reduces the effective span of the roof, thus enhancing the stability of the roof. Therefore, compared with the horizontal coal seam, when the roadway side support is used in the GER of the inclined coal seam, the roadside filling fully supports and reduces the span.

7. Stability Control of 3131 GER

7.1. The Synergistic Effect of Roadway-in Support and Roadway-Side Support

After the GER in the inclined coal seam is affected by mining, the plastic zone of surrounding rock near the coal face greatly expands seriously under the combined influence of coal seam dip angle and stress field direction. Also, after the mining of the previous coal face, the roof significantly increases due to the rotation and sinking of the roof on the side of the goaf, severely deforming the roof. Therefore, based on the “support span reduction” of the roadside filling body, the synergistic support countermeasures of cable bolt reinforcement and roadway-side filling in the roadway are proposed.

(1) During the roadway excavation stage and the first mining disturbance stage, the plastic zone of the surrounding rock is less extended in the roof and high side. Therefore, the conventional bolt and cable-bolt-coordinated support are used to effectively control the deformation due to the expansion of the plastic zone.

(2) During the GER and the repeated mining disturbance stages, the plastic zone of the high side of the roadway is greatly extended, which is connected with the goaf, resulting in a significant increase in the roof span. Roadway-side filling technology reduces the roof span and improves overall stability.

7.2. Control Method of GER

7.2.1. Roadway-Side Support

1.

Backfill Strength.

While supporting the caving roof, the roadway-side filling body should be able to sustain the roof load and must have adequate early strength and deformation attributes. It should also have excellent mechanical properties in the later stage to ensure the long-term stability of the roadway. Therefore, the mixture ratio of stone powder:cement:water:special admixture = 770:770:480:1 was used to mix the roadway-side filling material. The compressive strength of the filling body reached 27.4 MPa after 5 days, while the final strength was 41.3 MPa after a 28-day age (Figure 16).

2.

Roadside Filling Scheme.

The 0.6 m wide and 2.4 m high roadside filling wall was cast in the goaf. The edge of the wall was 0.8 m away from the coal wall of the upper side of the roadway. Reinforcing bars were embedded in the wall, and anchor holes were placed. When casting concrete, anchor bolts were preset in the wall. The anchor bolts (anchor rods) were used to resist concrete lateral deformation and enhance its anti-dip-slip ability. The anchor bolt was Φ20 × 1100 mm rebar, and the two ends of the anchor bolt were rolled with a length of 100 mm. The density of the anchor bolts was 2 bolts per meter. The lower anchor bolt hole was 0.3 m from the bottom of the filling wall.

7.2.2. Roadway-in Support

Based on the original support method and support material of 3131 roadway, the optimization design of roadway support in gob-side entry retaining was carried out. The specific scheme is as follows: The supporting roof was reinforced with Φ20 mm × 2200 mm bars. The middle of the roof was provided with Φ15.24 mm × 7800 mm high strength anchor cables (row spacing 3600 mm). The Φ15.24 mm × 4300 mm high strength anchor cables were arranged on the lower side of the roof. The Φ15.24 mm × 7800 mm high strength anchor cables were arranged on the high side of the roof (row spacing 1800 mm). The two sides of the roadway had the Φ16 mm × 1800 mm shell bolts spaced at 800 mm × 800 mm and the corner bolts at 400 mm from the high side and 200 mm from the low side (Figure 17).

7.3. Mine Pressure Monitoring

So as to analyze the control effect of the support scheme on the GER in the inclined coal seam, the deformation of the roadway of the retaining section of the 3131 headentry is monitored on site after the influence of one mining (Figure 18).

Figure 18 shows that the deformation of the roadway section during GER process experienced three stages: rapid growth, slow growth and stabilization. In the first stage, the working face advances about 22 m, and the roadway deformation increases sharply. The deformation rates of the surrounding rock are faster, and the deformation increases. In the later phase of this stage, the deformation rate gradually slows down, and the convergence of the roof and floor reaches about 70 mm, while the convergence of the two sides reaches about 80 mm. In the second stage, the working face advances to about 90 m. At this stage, the deformation of the roadway is gradual, and the deformation rate of the surrounding rock is gradually reduced. In the third stage, the working face continues advancing, the roof and floor are stable, the roadway deformation is almost stable, the roof and floor convergence is constant at about 125 mm and the two sides’ convergence is stable at about 95 mm. Thus, roadway bolt (cable) support combined with roadside flexible formwork concrete wall-filling can effectively support the section of retaining roadway.

8. Conclusions

(1) During the service life of the roadway, the plastic zone near the side of the mining face is always extended along the coal seam towards the side of the mining. The plastic zone of the roof and floor expands to the deep part of the surrounding rock. There are significant differences in the expansion degree of the plastic zone at different positions in different service periods. The expansion degree of the soft coal (rock) layer is the highest.

(2) The direction of the stress field changes during the service period of GER. However, there are differences in the areas where the stress field direction changes in different periods. During the same period, the degree of change in the direction of the stress field at different positions of the roadway is also different. In addition, the deflection direction of the stress field of the GER is always toward the side of the mining activity.

(3) Under the action of coal seam dip angle and stress direction, the plastic zone expands nonuniformly. When the angle between the maximum principal stress and the coal (rock) layer is 45° (±5°), the nonuniform expansion degree of the plastic zone is the largest, and the expansion degree in the soft rock layer is higher than that in the hard rock layer.

(4) During the roadway excavation and the first mining periods, the plastic zone has a low degree of expansion on the roof and high side. The conventional bolt and anchor cable support is used inside the roadway. During the retaining period and the secondary mining period, the plastic zone of the surrounding rock on the high side of the roadway is significantly expanded and connected with the goaf. The roof span of the roadway is thus increased. The roadside filling technique reduces the roof span and improves its overall stability.

(5) The control scheme of the surrounding rock in the GER section of 3131 headentry was optimized. The method of roadway bolt (cable) support combined with roadside flexible formwork concrete wall-filling support was adopted. The width of the roadside filling body was 0.6 m, and the strength exceeded 40 MPa. The relative displacements of the roof and floor of the roadway were reduced from 250 mm to 125 mm, and the relative displacements on both sides were stabilized at 95 mm.