Theoretical Study on the Mechanism of Asymmetrical Large Deformation of Heading Roadway Facing Mining

Abstract

The problem of asymmetric large deformation of surrounding rock of heading roadways is prominent due to the superposition of mining stress in the mining intersection area. Therefore, on the basis of the background of 18,106 tailentry in the Xiegou Coal Mine, this paper establishes a mechanical model of surrounding rock deformation of mining roadways under the effect of advanced abutment pressure. In the model, we deduce the theoretical calculation formula of roadway full-section deformation and discuss the influence factors of roadway surrounding rock deformation. Accordingly, the deformation mechanism of surrounding rock of mining roadways and the engineering suggestions and measures are revealed. The main results and finding are threefold. Firstly, the increase of the stress concentration factor of the coal pillar rib and the increase of the width of the failure zone are the fundamental reasons leading to the aggravation of the surrounding rock deformation on the side of the coal pillar in the heading roadway. Secondly, the deformation of the coal pillar rib increases with the increase of stress concentration factor and decreases with the increase of coal cohesion, internal friction angle, elastic modulus, and roadway rib support resistance. Additionally, the deformation of the roadway roof and floor decreases with the increase of roadway rib support resistance and is inversely proportional to the cubic power of rock beam thickness and elastic modulus. The deformation rate of the roadway roof and floor increases with the increase of vertical stress concentration factor of the coal pillar rib, and the maximum deformation position shifts to the side of the coal pillar. Therefore, increasing the strength and stiffness of the roadway surrounding rock and the supporting resistance of surrounding rock can reduce the deformation of roadway surrounding rock and the influence of advanced abutment pressure on roadway deformation. In the end, the rationality and feasibility of the theoretical analysis is verified through an engineering example. Under the influence of advanced abutment pressure, the deformation of roadway floor heave is the most severe, the asymmetrical deformation on both sides of the roadway is remarkable, and the deformation of coal pillar side is about twice that of solid coal side.

1. Introduction

Coal-fired power generation accounts for more than 60% of China’s power structure [1]. Safe and efficient coal mining is of great significance to the sustainable development of economy and society. The smooth flow and stability of the roadway is essential for sustainable production in coal mining [2]. Clarifying the deformation and failure mechanism of surrounding rock of the roadway is the premise of controlling surrounding rock deformation, ensuring long-term stability of the roadway, and realizing sustainable production of coal mining. After roadway excavation, the stress in surrounding rock is redistributed and plastic failure occurs in a certain range. The surrounding rock in the failure area changes from three-dimensional stress to plane stress or one-way stress, and the confining pressure of surrounding rock decreased significantly. For rock materials, with the decrease of confining pressure, the rock strength and stiffness obviously decrease, the damage degree and damage evolution rate of rock increase sharply, and the rock properties gradually change from toughness to brittleness [3,4,5]. The increase of the scope and damage degree of the roadway surrounding rock failure areas will inevitably lead to the increase of roadway surrounding rock deformation [6], which is due to the decrease of rock mass-bearing capacity and anti-deformation capacity of the failure area. In view of the high space utilization rate of rectangular roadway, the cross section of coal mining roadway is mostly rectangular. The surrounding rock of mining roadway can be divided into roof, floor, and two sides, which interact and relate to each other, but whose deformation mechanisms and laws are not the same.

Numerous experts and scholars have carried out substantial theoretical research on roadway surrounding rock deformation and failure mechanism. In the aspect of the roadway roof, Zhang [7] and Fan [8] regarded roadway roof as fixed beam and Winkler foundation beam and derived the calculation equation of roadway roof deformation. On the basis of beam theory, Bai [9] established a dynamic mechanical model of roadway roof subsidence using mine pressure observation data and studied the deformation law of roadway roof. For the roadway ribs, Zhao [10] assumed that the coal seam interface is the slip surface of the relative movement between coal body and roof and floor strata, and the coal body in the plastic zone is in a critical sliding state. Therefore, the expression of the width of the plastic zone of the coal body in the roadway ribs is deduced. Yu [11] and Chen [12] determined a theoretical equation of the limit equilibrium zone and fracture zone width of coal ribs on the basis of the compression column model of coal wall at peak abutment pressure and obtained extrusion displacement of coal ribs according to the load transfer method. Wang [13] involved the strength-softening characteristics of the interface between coal seam and roof and floor on the basis of the load transfer method. They deduced analytical expressions of the width of plastic zone, coal stress, and displacement of gob-side entry as well. In the aspect of roadway floor, Shi [14] and Liu [15] proposed a mechanical model of the roadway floor along with the theory of fixed beam and axial load thin plate. In this way, the instability criterion of roadway floor strata was concluded. Yang [16] and Gong [17] applied the complex function method and semi-infinite body theory to calculate the floor heave in different positions of the roadway floor on the basis of stress distribution of the roadway floor.

Such studies have made significant contributions to the theoretical study of roadway stability. However, there are still some limitations when the methods are applied to solve the surrounding rock deformation problems in some real situations. For one, the research object is generally roadway roof, ribs, or floor under static load, and the influence of mining stress on roadway surrounding rock deformation is not considered. For another, the relationship among roadway roof, ribs, and floor is not involved; therefore, there is a lack of research on the deformation of the whole section of the roadway. With the continuous improvement of the advancing speed of the coal mining face, the problem of continuous tension in mining has become increasingly prominent [18]. Generally, it is necessary to dig the mining roadway in the lower section before the mining in the upper section of the working face is completed, as shown in Figure 1.

Currently, the research on the deformation and failure of surrounding rock of gob-side entry is based mainly on numerical calculation. Many scholars have studied the deformation and failure characteristics of the gob-side entry surrounding rock through FLAC^3D 5.0 software [19,20,21]. The results show that the surrounding rock deformation of gob-side entry is asymmetrical, and the deformation and failure degree of surrounding rock of coal pillar side is greater than that of solid coal side. Wang [22], Wang [23], and Jiang [24] have analyzed the surrounding rock deformation characteristics and coal pillar stress distribution of gob-side entry under different coal pillar widths. The influence mechanism of coal pillar width on roadway load deformation was systematically investigated. Zhang [25], Chang [26], and Wang [27] have explored the surrounding rock deformation, plastic zone development, and stress evolution of the mining roadway in the adjacent working face. In the intersection area affected by mining, under the influence of the advanced abutment pressure of the adjacent working face, the surrounding rock deformation of the roadway is severe, and the deformation speed is more than three times that of the roadway driving period. The strata of roof/floor and the coal seam of two ribs are activated under the excitation of mining stress. Once the coal and rock strata generate uncoordinated deformation, some structures such as separation and fracture will be shaped. The surrounding rock of roadway will also express the discontinuous deformation. The conventional mesh-based numerical approaches are invalid for the discontinuous deformation of surrounding rock, but the DLSM model can be applied to explore such a deformation [28,29]. However, there is little attention paid to theoretical research of the deformation mechanism of the heading roadway under the effect of advanced abutment pressure of the adjacent working face. Additionally, the superposition degree of coal mining and driving abutment pressure on the deformation and failure mechanism of the heading roadway should be further explored and examined.

To address the above issue, a mechanical model of the roadway facing mining is proposed to comprehensively investigate the asymmetric deformation characteristics and mechanism of the ribs, roof, and floor of the roadway under the effect of advanced abutment pressure. We analyze the factors of roadway surrounding rock deformation. The corresponding theoretical guidance and suggestions are presented for the deformation control of the mining roadway. The research findings are valuable for reducing the instability risk of mining roadway and improving the efficiency of coal mine production.

2. Characteristics of Stress Distribution in Surrounding Rock of Heading Roadway Facing Mining

With the influence of mining connection, there are a large number of heading roadways facing mining in the layout of a coal mining system. Under this circumstance, mining intersection is inevitable, which is bound to be affected by the advanced abutment pressure of the adjacent mining face. As shown in Figure 2, the upper section headentry is on the left side of the coal pillar, and the lower section tailentry is on the right. When the heading roadway is outside the area affected by the advanced abutment pressure, the vertical stress in the center of the coal pillar is equal to or slightly greater than the original rock stress γH. The abutment pressure formed by the upper section headentry does not spread to the peak stress position of the lower section tailentry, the vertical stress concentration factor K = K′, and the width of plastic zone A = A′, as graphically illustrated in Figure 2.

If the heading roadway is affected by the advanced abutment pressure, it will be influenced by the mining abutment stress. As a result, the vertical stress concentration factor of the coal pillar rib in the upper section headentry increases, and the influence range of the abutment pressure exceeds the peak stress of the lower section tailentry. Accordingly, the vertical stress concentration factor of the coal pillar rib in the lower section tailgate rises, and the width of the plastic zone expands. The solid coal rib is less affected by the mining of the upper section, and the stress distribution can be assumed to be consistent with the outside area affected by the advanced abutment pressure. Therefore, in the heading roadway, the vertical stress concentration factor K > K′, and the plastic zone width A > A′. On account of advanced abutment pressure, the increase of the heading roadway coal pillar rib plastic zone and stress concentration factor will inevitably increase roadway deformation of the coal pillar side. Consequently, there will be asymmetric deformation in both sides of the roadway.

3. Mechanical Analysis of Roadway Side

The coal body of roadway ribs as the bearing structure of roof strata and the loading structure of floor strata, as well as its stability, directly affects the deformation degree of roadway surrounding rock. The deformation monitoring of the two ribs of the mining roadway shows that under the influence of mining in the upper section, the deformation of the coal pillar rib is obviously larger than that of the solid coal rib. The deformation of the coal pillar rib can reach 1.52 to 2.85 times that of solid coal rib [30,31]. Clarifying the stress distribution and deformation law of coal body in roadway ribs is the premise of studying the asymmetric deformation mechanism of roadway surrounding rock under the effect of advanced abutment pressure.

3.1. Study on Deformation and Failure of Roadway Ribs

Considering the large axial direction of the roadway, the theoretical solution of the roadway deformation can be treated as a plane problem. The surrounding rock with unit thickness in the axial direction of the roadway is taken as the research object, as shown in Figure 3.

After the roadway excavation, the coal body within a certain depth of the two ribs enters a plastic failure state because of the excavation unloading effect. The coal body inside the plastic zone is in an elastic state, as shown in Figure 4. In this figure, P (Pa) is the resistance of roadway rib bolting; x₀ (m) is the width of the plastic zone of the roadway rib; x₁ (m) is the width of the elastic zone in the range of abutment pressure; γ (N/m³) is the average bulk density of the overlying strata of roadway; H (m) is the buried depth of roadway; h (m) is the roadway height; and K is the vertical stress concentration factor of side wall in roadway.

The elastic modulus of coal is smaller than that of the roof and floor, Poisson’s ratio is larger than that of roof and floor, and the cohesion and internal friction angle of the interface between roof and floor of the coal seam are lower than those of the two ribs coal body. Therefore, the coal in the plastic zone will be extruded from the interface of roof and floor. Taking the coal body in the plastic zone of the roadway rib as the research object, a coal microelement with a width dx (m) in the plastic zone is applied for force analysis, as shown in Figure 5a. In the figure, σ_x (Pa) and σ_y (Pa) are the horizontal stress and vertical stress on the microelement, respectively. T (N) is the friction force at the interface between the microelement and the roof and floor.

$$T=f{\sigma }_y\times t\times dx=f{\sigma }_{y}dx$$

(1)

where f is the interface friction coefficient between the coal body and the roof and floor, and t (m) is the thickness of the research object in the axial direction of the roadway. It is worth noting that the variable t will not appear in the subsequent derivation of the equation from stress to force because t is 1 m.

According to the condition of horizontal stress balance of microelement ${\displaystyle \sum F_x=0}$, we can obtain:

$$h({\sigma }_x+d{\sigma }_x)=h{\sigma }_x+2{\sigma }_{y}fdx$$

(2)

The limit equilibrium condition of coal in the plastic zone can be obtained by applying the Mohr–Coulomb strength theory:

$${\sigma }_y=\frac{1+\sin \phi }{1-\sin \phi }{\sigma }_x+\frac{2C\cos \phi }{1-\sin \phi }$$

(3)

where C (Pa) is cohesion of coal, and φ (°) is internal friction angle of coal. From Equation (3), we can obtain:

$$\frac{d{\sigma }_y}{d{\sigma }_x}=\frac{1+\sin \phi }{1-\sin \phi }$$

(4)

Introducing Equation (4) into Equation (2), according to the method of solving the differential equation with separable variables, Equation (5) can be obtained.

$$\ln {\sigma }_y=\frac{2fx}{h}\times \frac{1+\sin \phi }{1-\sin \phi }+C_1$$

(5)

Consider the boundary condition, that is x = 0 and σ_y = N, then C₁ = lnN can be obtained. The vertical stress expression of coal in the plastic zone of roadway rib is obtained by Equation (5).

$${\sigma }_y=N{e}^{\frac{2fx}{h}(\frac{1+\sin \phi }{1-\sin \phi })}$$

(6)

In the above equation, N (Pa) is the supporting capacity of the coal rib, which can be calculated by the supporting resistance P of the side wall from Equation (3):

$$N=\frac{1+\sin \phi }{1-\sin \phi }P+\frac{2C\cos \phi }{1-\sin \phi }$$

(7)

The horizontal stress expression of coal in the plastic zone of roadway rib is derived from Equations (3) and (6):

$${\sigma }_x=({\sigma }_y-\frac{2C\cos \phi }{1-\sin \phi })\frac{1-\sin \phi }{1+\sin \phi }$$

(8)

Introducing x = x₀ and σ_y = KγH into Equation (6), the width of the plastic zone of the side wall is calculated by:

$$x_0=\frac{h}{2f}\ln \frac{K\gamma H}{N}\times \frac{1-\sin \phi }{1+\sin \phi }$$

(9)

After the excavation of the roadway, the inner body of the plastic zone of the roadway rib is in a one-way stress state. According to Hooke’s law, the vertical strain of coal in the plastic zone of roadway ribs can be obtained by:

$${\epsilon }_y=\frac{{\sigma }_y}{E}$$

(10)

where E (Pa) is elastic modulus of coal. Under the Poisson effect, the horizontal strain of coal in plastic zone can be expressed as follows:

$${\epsilon }_x=\mu {\epsilon }_y$$

(11)

where μ is Poisson’s ratio of coal. After the plastic failure occurs in the coal body of the roadway ribs, its bearing capacity and anti-deformation capacity are significantly reduced. The deformation of roadway ribs is caused mainly by the deformation of coal in plastic zone. According to the load transfer method, the horizontal displacement of the roadway rib is:

$$u_0={\displaystyle {\int }_0^{x_0}\frac{\mu {\sigma }_y}{E}}dx=\frac{\mu h(1-\sin \phi )(K\gamma H-N)}{2f(1+\sin \phi )E}$$

(12)

Next, our research object is the coal body in the elastic zone of the roadway rib, and a microelement of coal and rock mass with a width dx in the elastic zone of the coal body is taken for force analysis, as shown in Figure 5b.

According to the horizontal stress equilibrium condition of the microelement:${\displaystyle \sum F_x=0}$, we can obtain:

$$h({\sigma }_x+d{\sigma }_x)=h{\sigma }_x-2{\sigma }_{y}f’dx$$

(13)

For the coal body in the elastic zone, the relationship between horizontal stress and vertical stress is:

$${\sigma }_x=\lambda {\sigma }_y$$

(14)

where λ is the lateral pressure coefficient of surrounding rock, and f′ can be presented as Equation (15). Consider the boundary conditions: $x=x_0$, $f’=f$, $x=x_0+x_1$, and $f’=0$, so set:

$$f’=\frac{(x_0+x_1-x)}{x_1}f$$

(15)

Replace Equations (14) and (15) into Equation (13), and the result is:

$$h\lambda \times d{\sigma }_y=-2{\sigma }_y\frac{x_0+x_1-x}{x_1}f\times dx$$

(16)

According to the method of solving the differential equation with separable variables, Equation (17) can be obtained:

$$\ln {\sigma }_y=\frac{f}{\lambda h{x}_1}[x^2-2(x_0+x_1)x]+C_2$$

(17)

Considering the boundary condition, that is, x = x₀ and σ_y = KγH, we can obtain $C_2=\ln K\gamma H+\frac{f}{\lambda h{x}_1}(x_0^2+2x_0{x}_1)$; substitute this into Equation (17) and obtain the vertical stress expression of coal body in the elastic zone of side wall:

$${\sigma }_y=K\gamma H{e}^{\frac{f}{\lambda h{x}_1}(x-x_0)(x-x_0-2x_3)}$$

(18)

Then, substituting x = x₀ + x₁ and σ_y = γH into Equation (18), the width of the elastic zone of the side wall is obtained as:

$$x_1=\frac{\lambda h}{f}\ln K$$

(19)

The specific parameters of roadway in the Xiegou Coal Mine are as follows. The average buried depth is 300 m, the width of the coal pillar is 20 m, the height of the roadway is 4 m, λ is 1.5, and f is generally 0.3. In line with the stress–strain curve of the complete coal sample under the uniaxial compression test shown in Figure 6, the coal in the roadway ribs has obvious elastic–plastic characteristics; the uniaxial compression strength of the sample ${\sigma }_{ci}=11.12\mathrm{MPa}$, and the elastic modulus E_i = 1.2 GPa.

This is quite different from the mechanical parameters measured by complete coal samples in the laboratory due to the size effect, joint crack, and groundwater effect of coal body. The elastic modulus of the coal in the plastic zone of the roadway is reduced to 10% of the standard specimen E_i, and the Poisson’s ratio μ is 0.5. The strength parameters, C and φ, of the roadway rib coal body are obtained by H-B strength criterion [32,33]. According to the integrity degree of coal body in the Xiegou Coal Mine, the geological strength index GSI is 65, H-B constant m_i is 7, and rock mass disturbance parameter D of roadway surrounding rock can be determined to be 0.5. The RocLab 1.0 software is used to calculated C = 0.605 MPa and φ = 27.19°. By substituting the values of C and φ into Equations (6) and (18), the vertical stress of the coal body at any position of the side wall can be attained.

The vertical stress distribution of the roadway rib under different stress concentration factors is illustrated in Figure 7. When the surrounding rock of roadway is not distracted by mining, the stress concentration factor of coal is minor, K is generally 1.5, the width of roadway rib plastic zone is 4 m, and the stress influence range is 12.11 m. With the growth of K, the width of the plastic zone of the coal body and the influence range of the vertical stress continue to increase. If K is 2.5, the width of the plastic zone is 4.7 m, and the stress influence range is more than 20 m. Owing to advanced abutment pressure of the upper section working face, the coal body of the coal pillar rib will inevitably be strongly obstructed. As a result, the plastic zone of the coal pillar rib is enlarged and the vertical stress concentration factor rises.

3.2. Influencing Factors of Roadway Rib Deformation

According to existing research [30,31], there is an elastic core with a certain width in the middle of the coal pillar if the width of the coal pillar is equal to 20 m. K on the coal pillar rib is more than 2.5, while K’ on the solid coal rib is generally less than 1.5. From Equation (12), the main factors affecting the deformation of the roadway ribs are: coal cohesion C, internal friction angle φ, coal body elastic modulus E, and roadway rib support resistance P. The influence of various factors on roadway rib deformation is demonstrated in Figure 8.

The stiffness and strength of the coal body have a great impact on the roadway rib deformation. The greater the stiffness and strength of the coal body is, the smaller the roadway rib deformation is. The deformation of roadway ribs is inversely proportional to the elastic modulus of coal. When K = 3, E increases from 0.1 GPa to 0.5 GPa, the deformation of the coal pillar rib is decreased from 251.60 mm to 50.20 mm, and the deformation of the coal pillar rib is reduced by 80%. The larger the E value is, the smaller the differential deformation between the two ribs of the roadway is. When K increases from 1.5 to 3.0, and when E is 0.1 GPa, 0.5 GPa, and 1.0 GPa, the deformation difference is 139.78 mm, 27.96 mm, and 13.98 mm, respectively.

Secondly, the wide friction angle of the coal body causes the minor deformation of the roadway ribs and the differential deformation of the two ribs. When K is 3 and φ increases from 20° to 40°, the deformation of the coal pillar rib decreases from 280.12 mm to 117.45 mm, and the deformation of the coal pillar rib reduces by 85.07%. When K increases from 1.5 to 3.0, and φ is 20° and 40°, the deformation difference is 153.22 mm and 67.95 mm, respectively.

Furthermore, roadway rib deformation decreases with the increase of coal cohesion and roadway rib support resistance, but the control of roadway rib deformation is limited. When K is 3 and cohesion increases from 0 MPa to 1.6 MPa, the deformation of the coal pillar rib decreases from 230.18 mm to 175.91 mm. In addition, when the support resistance of the roadway ribs increases from 0 MPa to 1 MPa, the deformation of the coal pillar rib decreases from 212.44 mm to 95.96 mm. The differential deformation of coal pillar rib and solid coal rib is not related to coal cohesion or roadway rib support resistance. Hence, when K increases from 1.5 to 3.0, no matter what the value of coal cohesion and support resistance is, the difference of deformation between the two ribs is 116.48 mm.

Accordingly, there are some implications of the above discovery. Strengthening the support of the roadway ribs and increasing the strength and stiffness of the coal body can effectively improve the stability of the roadway ribs. When the coal seam is soft and the elastic modulus of coal is small, only increasing the supporting resistance of the roadway ribs can reduce the roadway rib deformation, to a certain extent. However, it is difficult to control the asymmetric deformation of the two ribs of the roadway under the effect of advanced abutment pressure. Therefore, the grouting bolt support technology should be selected to improve the elastic modulus of coal and the angle of internal friction and reduce the differential deformation of the two ribs of the roadway.

4. Mechanical Analysis of Roadway Roof

Under the influence of advance abutment pressure, the asymmetry of roadway roof deformation is obvious. According to the surrounding rock deformation monitoring results of the mining roadway, the roof-to-floor convergence on the coal pillar side can exceed the 500 mm of the roof-to-floor convergence on the solid coal side, and the difficulty of roadway maintenance is significantly improved [19]. Therefore, it is of great significance to establish the mechanical model of roadway roof subsidence to provide a theoretical basis for roof control of mining roadway.

4.1. Deformation Analysis of Roadway Roof

After the roadway excavation, the plastic failure of the coal body in a certain range of the roadway ribs is produced. The coal body of the coal pillar rib is affected by mining; with the increase of the stress concentration degree, the range of the coal pillar rib plastic zone will expand, as shown in Figure 9. The immediate roof and immediate floor refer to the first layer of roof rock above the roadway and the first layer of floor rock below the roadway, respectively, and they are generally in immediate contact with the coal seam.

The roof strata of the roadway can be regarded as fixed beams at both ends when the width of the coal pillar is large and there is an elastic zone with a certain width in the middle of the coal pillar. In the plastic zone, the coal body in the stress reduction zone has vanished its bearing capacity, and it is relatively broken and easy to deform. Although the coal body in the plastic zone where the stress increases still has a certain bearing capacity, it has entered the post-peak stage, and thus, the deformation of the coal body is large. Additionally, for the coal body, the width of the plastic zone where the stress increases is small and the position is close to the elastic zone. Under the circumstances, the supporting role of the coal body in the plastic zone is ignored. The elastic–plastic boundary between the two sides of the roadway is taken as the fixed end of the beam, as shown in Figure 10.

In Figure 10, x₀ (m) and x_0′ (m) are the widths of the plastic zone of the coal pillar rib and the solid coal rib, respectively, and b (m) is the width of the roadway. The length of the fixed beam l (m) is equal to the sum of the roadway width and the plastic width of the two ribs. That is, l = b + x₀ + x_0′. The load q (Pa) on the clamped beam can be expressed as:

Q = γH_G

(20)

where γ is the average bulk density of rock strata within the range of roof balance arch height, and H_G (m) is the roof balance arch height [34,35]; it can be calculated as

$$H_G=\frac{b/2+x_0+x_0’}{\lambda }(\sqrt{(F/n{)}^2+\lambda }-\frac{F}{n})$$

(21)

where F is the Platts coefficient, and $F={\sigma }_{ci}/10=1.112$.

According to the mechanics of the materials [36], the bending moment at both ends of the clamped beam is

$$M_A=M_B=\frac{q{l}^2}{12}$$

(22)

The bending moment equation of roof strata in a coordinate system A-x′y′ is

$$M_x=F_{A}x-qx\times \frac{x}{2}+M_A=\frac{q}{12}(6lx-6x^2-l^2)$$

(23)

Introducing Equation (23) into the differential equation of the deflection curve of the beam, we obtain:

$$E_1{I}_1{w}_h’’=\frac{q}{12}(6lx-6x^2-l^2)$$

(24)

Equation (25) can be obtained after performing two consecutive integrals on Equation (24).

$$E_1{I}_1{w}_h=\frac{q}{12}(l{x}^3-\frac{1}{2}{x}^4-\frac{1}{2}{l}^2{x}^2)+C_{3}x+C_4$$

(25)

where w_h (m) is the deflection of the rock beam on the immediate roof of the roadway, E₁ (Pa) is the elastic modulus of the rock beam on the immediate roof of the roadway, and I₁ (m⁴) is the moment of inertia of the fixed beam facing the neutral axis. If the beam is taken as the unit width, then $I_1=d_1^3/12$, where d₁ (m) is the thickness of the rock beam. Considering the boundary condition: the deflection at the fixed end A and B is 0, C₃ = C₄ = 0 can be obtained; thus, the deflection curve equation is:

$$w_h=\frac{q}{2E_1{d}_1^3}(2l{x}^3-x^4-l^2{x}^2)$$

(26)

Translating the coordinate system origin in Figure 10 above the boundary of the left rib of the roadway, under the coordinate system O-xy, we obtain:

$$w_h=\frac{q{(x+x_0’)}^2}{2E_1{d}_1^3}[2l(x+x_0’)-{(x+x_0’)}^2-l^2]$$

(27)

The immediate roof of tailentry in the 18,106 panel of the Xiegou Coal Mine is a coal seam with a thickness of 2 m. The influence of mining stress on the solid coal rib of the roadway can be ignored, and the vertical stress concentration factor of the roadway solid coal rib is 1.5. The deformation evolution of the roadway roof when the vertical stress concentration factor of the coal pillar rib of the roadway increases from 1.5 to 5.0 is shown in Figure 11a.

As depicted in Figure 11a, under the effect of the advanced abutment pressure of the adjacent working face, the roadway roof is asymmetrically deformed, the roadway roof on the solid coal rib is slightly affected by mining, and the roadway roof on the coal pillar rib is significantly affected by mining. With the growth of the vertical stress concentration factor of the coal pillar rib, the displacement of each point of the roadway roof is increasing, and the roof subsidence on the coal pillar side is larger than that on the solid coal side. When K increases by 0.5, the subsidence of the left end of the roof is approximately 31.15 mm, that of the right end is approximately 13.25 mm, and the subsidence speed of the left end is approximately 2.35 times that of the right end. The maximum subsidence position of the roadway roof is constantly approaching the coal pillar side, and when K increases by 0.5, the maximum subsidence position moves approximately 0.21 m to the coal pillar side.

4.2. Relationship between Deformation of Roadway Roof and Width of Plastic Zone of Coal Pillar Rib

The increase of the vertical stress concentration factor of the coal pillar rib leads to the expansion of the width of the plastic zone of the coal pillar rib, and the span of the fixed beam of the immediate roof will be lengthened. In addition, the expanded plastic width of the coal pillar rib increases the height of the roof self-stable balance arch and the immediate roof load. The roof deformation enlarges under the combined action of the two. Therefore, the expansion of the plastic width of the coal pillar rib is paramount for the aggravation of the roadway roof subsidence. The relationship between the maximum subsidence of the roadway roof and the plastic width of the coal pillar rib is shown in Figure 11b. The functional relationship between the maximum roof subsidence and the width of the plastic zone of the coal pillar is fitted thorough an exponential function by Origin software. The maximum subsidence of roadway roof generally satisfies the relationship: $w_{h\max }=69.80e^{(x_0/4.08)}-79.16$. It can be explained by the following: with the expansion of the plastic width of the coal pillar rib, the subsidence of roadway roof rises, and the speed of roof subsidence is accelerated.

4.3. Influencing Factors of Roadway Roof Deformation

According to Equation (27), the main factors of the subsidence of roadway roof are: immediate roof thickness d₁, immediate roof elastic modulus E₁, roof rock Platts coefficient F, and roadway rib support resistance P. The influence of the factors on the roadway roof subsidence is shown in Figure 12.

On one hand, the maximum subsidence of roadway roof is inversely proportional to the cubic power of immediate roof thickness. When K is 3, the immediate roof thickness increases from 1 m to 2 m, the maximum roof subsidence decreases from 1626.58 mm to 203.36 mm, and the maximum subsidence is reduced by 77.5%. In addition, the thicker the immediate roof strata are, the less the roof subsidence is affected by the advanced abutment pressure. When K increases from 1.5 to 3.0, if the immediate roof thickness is 1 m and 2 m, the maximum roof subsidence increases by 753.61 mm and 94.20 mm, respectively.

On the other hand, the subsidence of roadway roof is inversely proportional to the elastic modulus of immediate roof. When the elastic modulus of the immediate roof is greater than 0.6 GPa, the increase of the elastic modulus of the immediate roof has little effect on the roof subsidence, but the influence is greater when it is lower than 0.6 GPa. When K is 3.0, the thickness of the immediate roof increases from 0.1 GPa to 0.6 GPa, the maximum roof subsidence decreases from 244.03 mm to 40.67 mm, and the maximum subsidence is reduced by 83.33%. The larger the elastic modulus of the immediate roof is, the less the roof subsidence is affected by the advanced abutment pressure. When K increases from 1.5 to 3.0, the elastic modulus is 0.1 GPa and 0.6 GPa, and the maximum roof subsidence increases by 113.04 mm and 18.84 mm, respectively.

With the increase of the Platts coefficient of the roof rock, the height of the self-stable equilibrium arch of the roadway roof, the immediate roof load, and the roof subsidence decrease. When K is 3.0, after the Platts coefficient of roof rock increased from 0.4 to 1.8, the maximum roof subsidence decreased from 233.73 mm to 99.22 mm, and the maximum subsidence was reduced by 57.55%. When the Platts coefficient of roof rock is greater than 1.8, the increasing rate of maximum roof subsidence tends to be stable. The larger the Platts coefficient of the immediate roof is, the less the roof subsidence is affected by the advanced abutment pressure.

As a result, increasing the support resistance of the roadway ribs can reduce the width of the plastic zone of the two ribs of the roadway and the height of the self-stabilizing equilibrium arch of the roadway roof. Thus, the span and load of the fixed beam and the roof subsidence are reduced. The control effect of increasing roadway rib support resistance on roof deformation is greater than that of the two ribs. When the roadway rib support resistance is 1 MPa, compared with no support, the deformation of the side wall is decreased from 134.79 mm to 107.01 mm, and the deformation is reduced by 20.61%, while the roof deformation is decreased from 178.64 mm to 30.77 mm, and the deformation is reduced by 82.78%. The greater the resistance of roadway rib support is, the less the roof subsidence is affected by the advanced abutment pressure.

Furthermore, the increase of the plastic width of the coal pillar rib will aggravate the subsidence of the roadway roof, and the stability of the two ribs of the roadway should be improved to control the subsidence of the roadway roof. Hence, the plastic width of the roadway ribs can be reduced by increasing the support resistance of the roadway ribs and the strength of the roadway side coal. It is of great importance to control the subsidence of the roadway roof. For the thin-layered weak roof roadway, increasing the immediate roof equivalent thickness through bolt support can significantly reduce the roof subsidence, and the bolt length should be not less than 2 m. In addition, increasing the stiffness and strength of the immediate roof strata can effectively reduce the roof subsidence of the roadway, and weaken the influence of advanced abutment pressure on roof subsidence.

5. Mechanical Analysis of Roadway Floor

The floor heave degree of roadway is affected by many factors, such as the nature of surrounding rock, mining conditions, geological structure, and groundwater. Due to the difference of geological conditions in a given roadway, the floor heave degree at different locations varies greatly. For example, when the floor rock layer is softened by water, its elastic modulus decreases significantly, and the maximum floor heave can even increase from 400 mm to more than 1000 mm [37]. Under the influence of the advance abutment pressure of the upper section working face, the stress state of roadway floor rock strata at the coal pillar side and the solid coal side is different, leading to the more complex floor heave of the roadway. Therefore, it is of great theoretical and engineering significance to establish a mechanical model and reveal the mechanism of roadway floor heave under the influence of advance abutment pressure on the upper section working face.

5.1. Deformation Analysis of Roadway Floor Heave

Asymmetric floor heave phenomenon is significantly ordinary in the roadway under the mining stress. The field observation suggests that the degree of the roadway floor heave on the coal pillar side is greater than that on the solid coal side, due to the different stress distributions between the two ribs of the roadway. In order to facilitate the calculation of the vertical stress of coal pillar rib and the solid coal rib in Figure 2, the stress distribution of the roadway floor is linearized, as shown in Figure 13a. Among them, O and O′ are the bottom angle of the coal pillar rib and the solid coal rib, respectively, and the length of OO′ is b, which is equal to the width of the roadway. The vertical displacement of the floor rock beam at O point and O′ point is constrained, but the cross-section rotation of the rock beam can still exist. Therefore, the O point and O′ points can be regarded as the simply supported ends. AO and AO′ are the widths of the plastic zone of the roadway pillar rib coal body and the solid coal rib coal body, respectively, and their lengths are x₀ and x₀′, respectively. According to the stress superposition principle, the stress distribution of the floor rock beam shown in Figure 13a can be decomposed into the superposition of the original rock stress shown in Figure 13b and the abutment pressure of the floor shown in Figure 13c. Obviously, the deformation of roadway floor heave is 0 under the action of original rock stress. Therefore, the deformation of roadway floor heave can be considered to be the result of floor abutment pressure. In this model, the position of the two floor corners of the roadway is the simply supported end of the immediate floor rock beam, and F_A (N), F_A′ (N), M_A (N·m), and M_A′ (N·m) are the reaction force and reaction moment of the elastic zone of the floor to the “floor beam” structure, respectively. Obviously, the smaller the F_A, F_A′, M_A, and M_A′ are, the greater the floor heave of the roadway is, and the more significant the asymmetric floor heave is. In this paper, the deformation of roadway floor heave under the limit condition is considered, so F_A, F_A′, M_A, and M_A′ are all 0.

According to the moment balance condition of point O, we can obtain:

$$\frac{1}{3}(K\gamma H-N)x_0^2+\frac{1}{2}\gamma H{b}^2+F_{O’}b+(\gamma H-N)(b{x}_0’+\frac{x_0{’}^2}{2})=\frac{1}{2}(\gamma H-N)x_0^2+\frac{1}{2}(K’\gamma H-N)(b{x}_0’+\frac{2}{3}{x}_0{’}^2)$$

(28)

Therefore, the reaction at the fixed end O’ is:

$$F_{O’}=\frac{3(\gamma H-N)(x_0^2-2b{x}_0’-x_0{’}^2)-3\gamma H{b}^2}{6b}+\frac{(K’\gamma H-N)(3b{x}_0’+2x_0{’}^2)-2(K\gamma H-N)x_0^2}{6b}$$

(29)

By the same token, the reaction at the fixed end O can be acquired:

$$F_O=\frac{3(\gamma H-N)(x_0{’}^2-2b{x}_0-x_0^2)-3\gamma H{b}^2}{6b}+\frac{(K\gamma H-N)(3b{x}_0+2x_0^2)-2(K\gamma H-N)x_0{’}^2}{6b}$$

(30)

According to the moment–balance conditions on any section of the beam O-O′ section, Equation (31) can be obtained:

$$\frac{1}{2}(K\gamma H-N)x_0(x+\frac{2}{3}{x}_0)-F_{O}x-\frac{1}{2}\gamma H{x}^2-(\gamma H-N)x_0(x+\frac{1}{2}{x}_0)+M_x=0$$

(31)

Hence, the bending moment equation of immediate floor is:

$$M_x=A_1{x}^2+A_{2}x+A_3$$

(32)

where A₁, A₂, and A₃ in Equation (32) are the coefficients which can be calculated as:

$$\left\{\begin{array}{l}{A}_1=\frac{1}{2}\gamma H\\ A_2=(\gamma H-\frac{1}{2}K\gamma H-\frac{1}{2}N)x_0+F_O\\ A_3=\frac{1}{2}(\gamma H-N)x_0^2-\frac{1}{3}(K\gamma H-N)x_0^2\end{array}\right.$$

(33)

Next, by introducing Equation (33) into the differential equation of the deflection curve of the beam, we can obtain:

$$E_2{I}_2{w}_f’’=A_1{x}^2+A_{2}x+A_3$$

(34)

where w_f (m) is the deflection of the immediate floor rock beam, E₂ (Pa) is the elastic modulus of the immediate floor rock beam, and I₂ (m⁴) is the moment of inertia of the cross-section of the rock beam facing the neutral axis. Equation (35) can be acquired obtained after two consecutive integrations to Equation (34):

$$E_2{I}_2{w}_f=\frac{1}{12}{A}_1{x}^4+\frac{1}{6}{A}_2{x}^3+\frac{1}{2}{A}_3{x}^2+A_{4}x+A_5$$

(35)

Consider the boundary conditions of the deflection of two simply supported ends: x = 0, w_f = 0, and x = b, w_f = 0. We can obtain: $A_5=0$ and $A_4=-A_1{b}^3/12-A_2{b}^2/6-A_{3}b/2$ based on Equation (35). After taking A₄ and A₅ back to Equation (35), we can obtain:

$$w_f=\frac{1}{E_2{I}_2}(\frac{1}{12}{A}_1{x}^4+\frac{1}{6}{A}_2{x}^3+\frac{1}{2}{A}_3{x}^2+A_{4}x)$$

(36)

If the beam is taken as the unit width, then $I_2=d_2^3/12$, where d₂ (m) is the immediate floor thickness:

$$w_f=\frac{1}{E_2{d}_2^3}(A_1{x}^4+2A_2{x}^3+6A_3{x}^2+12A_{4}x)$$

(37)

The thickness of the immediate floor strata of the Xiegou Coal Mine roadway is 2 m, and the elastic modulus E₂ should be 1.5 GPa, ignoring the influence of mining stress on the solid coal rib of the roadway. When the vertical stress concentration factor of the solid coal rib of the roadway is 1.5 and the vertical stress concentration factor of the coal pillar rib of the roadway increases from 1.5 to 5.0, the deformation evolution of the roadway floor heave is shown in Figure 14a.

Under the effect of the advanced abutment pressure of the adjacent working face, the roadway floor displays the characteristic of asymmetric deformation. When the vertical stress concentration factor of the coal pillar rib is equal to that of the solid coal rib, the floor heave of the roadway is symmetrical, and the maximum floor heave is located in the middle of the floor. With the increase of the vertical stress concentration factor of the coal pillar rib, the position of the maximum floor heave gradually shifts to the coal pillar side, the bulging amount of each point of the floor is increasing, and the deformation rate of the floor heave is accelerating.

5.2. Relationship between Floor Heave of Roadway and Width of Plastic Zone of Coal Pillar Rib

The increase of the plastic width of the coal pillar rib lengthens the OA section of the “floor beam” structure. The higher vertical stress concentration and larger range of action in the OA section directly lead to the aggravation of the roadway floor heave deformation. The relationship between the maximum floor heave and the plastic width of the coal pillar is shown in Figure 14b. The maximum floor heave of the roadway is related to the width index of the plastic zone of the coal pillar, and generally satisfies: $w_{f\max }=2.90e^{(x_0/1.25)}+2.79$. With the expansion of the plastic width of the coal pillar, the roadway floor heave rises, and the floor heave rate is accelerated.

5.3. Influencing Factors of Roadway Floor Heave Deformation

According to Equation (37), the main factors of roadway floor heave are immediate floor thickness d₂, immediate floor elastic modulus E₂, and roadway rib support resistance P. The influence of the factors on the deformation of the roadway floor is shown in Figure 15.

As illustrated in Figure 15, one item to note is that the maximum floor heave of the roadway is inversely proportional to the cubic power of the immediate floor thickness. When K = 3 and the immediate floor thickness increases from 1 m to 2 m, the maximum floor heave decreases from 2281.22 mm to 285.15 mm, and the maximum deformation is reduced by 77.5%. In addition, the thicker the immediate floor strata are, the less the floor heave is affected by the advanced abutment pressure. When K increases from 1.5 to 3.0, the maximum floor heave of the immediate floor with a thickness of 1 m and 2 m increases by 1642.99 mm and 205.37 mm, respectively.

Another item to note is that the amount of roadway floor heave is inversely proportional to the elastic modulus of immediate floor. When the immediate floor elastic modulus is less than 1.5 GPa, increasing the immediate floor elastic modulus can significantly reduce the floor heave. When K = 3.0, the elastic modulus of the immediate floor increases from 0.4 GPa to 1.5 GPa, the maximum floor heave decreases from 1069.32 mm to 285.15 mm, and the maximum floor heave is reduced by 73.33%. The larger the elastic modulus of the immediate floor is, the less the floor heave is affected by the advanced abutment pressure. When K increases from 1.5 to 3.0, the maximum floor heave of the immediate floor with elastic modulus of 0.4 GPa and 1.5 GPa increases by 770.15 mm and 205.37 mm, respectively.

Additionally, the greater the support resistance of the roadway ribs, the smaller the plastic width of the roadway, the shorter the length of the “floor beam” of the roadway, and the smaller the floor heave. When K = 3, compared with no support, the maximum floor heave of roadway rib support resistance of 1 MPa is decreased from 307.26 mm to 176.53 mm, and the deformation is reduced by 42.55%. The greater the roadway rib support resistance is, the less the floor heave is affected by the advanced abutment pressure. When K increases from 1.5 to 3.0, the roadway rib support resistance is 0 MPa and 1 MPa, and the maximum floor heave increases by 227.01 mm and 103.87 mm, respectively.

Based on the above observations, the stability of the roadway ribs will directly affect the floor heave deformation, and the expansion of the plastic width of the roadway ribs will dramatically affect the roadway floor heave degree. Furthermore, the coal body strength and the support resistance of the roadway ribs will be improved, which is helpful in controlling the roadway floor heave deformation. Strengthening the support of the roadway floor and increasing the immediate floor stiffness can effectively reduce the roadway floor heave. When the thickness of the immediate floor strata is small, increasing the immediate floor equivalent thickness through the floor bolt can significantly decrease the floor heave deformation.

6. Field Monitoring and Analysis

The head-on displacement measuring points of the roadway surface are arranged in the heading roadway 200 m away from the working face. As shown in Figure 16a, the approaching amounts of the roof and floor and the two ribs of the roadway are measured respectively. The measuring base points A, C, and D are based on the bolt heads of the top, left, and right ribs of the roadway, respectively; the floor is drilled 0.5 m deep, and short bolts are installed as the B base point. After the base point is installed, a red paint mark is sprayed to make use of the later observation and tie the engineering line to the bolt head.

The specific measuring methods are: tightening the rope between C and D, tightening the rope between A and B, using YHJ-100J mine intrinsically safe laser rangefinder (accurate to 1 mm when reading) to measure the values of OA, OB, OC, and OD, and monitoring the results of roadway surrounding rock deformation. The length changes of OA, OB, OC, and OD represent the deformation of roadway coal pillar rib, solid coal rib, roof, and floor, respectively. They are graphically depicted as Figure 16b.

When the roadway driving is outside the influence range of the advanced abutment pressure, the surrounding rock deformation of the roadway is smaller, and the deformation rate is slower. When the driving roadway enters the advanced abutment pressure affected area, the deformation speed of the surrounding rock of the roadway accelerates. When the roadway is located 50 m behind the working face of the upper section, the roadway deformation tends to be stable. As a result, roadway floor heave > coal pillar rib deformation > roadway roof subsidence > solid coal rib deformation. The coal pillar rib deformation is approximately 260 mm, and the deformation of solid coal rib is approximately 130 mm; the deformation of the coal pillar rib is twice that of the solid coal rib. The deformation degree of surrounding rock of roadway on the coal pillar side is greater than that on the solid coal side.

7. Conclusions and Future Works

In the advanced abutment-pressure-affected area, the superposition of mining stress leads to the prominent problem of asymmetric large deformation of surrounding rock of heading roadway facing mining. In this paper, the mechanical model of surrounding rock deformation of heading roadway facing mining is established. The roof, floor, and two ribs of roadway are connected, the deformation equation of the full section of roadway is obtained, and the deformation mechanism of the surrounding rock of the roadway under the effect of advanced abutment pressure that is studied with the help of K are analyzed systematically. Accordingly, the research findings are valuable for the coal production industry to perform more scientific and reasonable support methods. In this way, the safety and stability of the mining roadway are improved and the risk of instability caused by large deformation of the mining roadway is reduced. Additionally, our research provides pragmatic and viable ideas to effectively control the deformation of roadway surrounding rock. Hence, the repeated repair of the roadway can be reduced, and the production efficiency of the coal mine is improved, which accelerate the sustainable production of the coal mine.

(1) Under the effect of advanced abutment pressure, the deformation of surrounding rock of the roadway is intensified, and the deformation of the coal pillar side is larger than that of the solid coal side. The increase of the vertical stress concentration factor and the plastic width of the coal pillar rib is the fundamental reason for the asymmetric deformation of roadway.

(2) The deformation of roadway ribs decreases with the increase of coal cohesion, internal friction angle, elastic modulus, and roadway rib support resistance. Increasing the elastic modulus and internal friction angle of the roadway ribs can not only reduce the deformation of the roadway ribs but also reduce the differential deformation of the two ribs of the roadway.

(3) The increase of the plastic width of the coal pillar rib leads to the increase of the span of the fixed rock beam at both ends and the height of the roof balance arch, which generates the aggravation of the roof subsidence on the side of the coal pillar. The increase of load and length of the OA section of the roadway “floor beam” is the direct cause for the severe roadway floor heave.

(4) The deformation of roadway roof and floor decreases with the increase of roadway rib support resistance, which is inversely proportional to the cubic power of rock beam thickness and inversely proportional to the elastic modulus of rock beam. Increasing the equivalent thickness of immediate roof and immediate floor through bolt support and improving the strength and stiffness of roadway surrounding rock can reduce the deformation of roadway roof and floor and lessen the influence of advanced abutment pressure on roadway roof and floor deformation.

It is noteworthy that this study still has some shortcomings that warrant further research. Our theoretical study considers only the surrounding rock deformation of roadway under the condition of a large width of the coal pillar. Under the condition of a narrow coal pillar, the stress distribution and deformation law of roadway surrounding rock are quite different from those of a large coal pillar. In the future, we will establish the mechanical model of narrow coal pillar roadway deformation and further improve the relevant theory of surrounding rock deformation of coal mine roadways.