Mechanism of Stability Control for Gob-Side Entry Retaining via Artificial Regulation of Main Roof Fracture Position

Abstract

To address severe stress concentration, excessive convergence, and instability of the roadside backfill body (RBB) in gob-side entry retaining (GER) under thick and hard roof conditions, this study investigates the control mechanism of main roof fracture position on surrounding rock stability, using the 3⁻¹01 working face of Huoluowan Coal Mine as a case study. A combined approach integrating theoretical analysis, numerical simulation, and field investigation is adopted. A statically indeterminate mechanical model based on masonry beam theory is established to characterize the lateral roof fracture behavior. The deflection and bending moment distributions are derived, and a criterion for fracture position determination is developed based on the maximum bending moment condition. The theoretical results indicate that the natural fracture position is located approximately 9.4–11.2 m inside the gob boundary. Numerical simulations using UDEC Trigon under different fracture positions (−2 m, 1 m, 5 m, and 9 m) show that fracture location significantly affects the mechanical response of GER. Fractures occurring above the roadway or RBB induce large deformation levels and more extensive plastic zones, while gob-side fracture conditions correspond to relatively lower disturbance levels and improved structural stability. The RBB exhibits shear-dominated failure characteristics, and the displacement distribution is non-uniform along height, with larger deformation in the middle-to-upper region. To improve stability, a coordinated control strategy combining anchor cable reinforcement and directional long-distance hydraulic fracturing (HF) is proposed to regulate the main roof fracture position through the formation of artificial weak planes. Field monitoring results show that the maximum displacements of the roof, floor, and ribs are 558 mm, 233.5 mm, and 71.3 mm, respectively, with a convergence ratio of 19.8%. Borehole imaging confirms the development of hydraulic fractures within the designed roof stratum, supporting the effectiveness of the proposed control approach. These results demonstrate that the fracture position of the main roof plays a key role in controlling GER stability, and its regulation provides an effective means for improving roadway performance under complex geological conditions.

1. Introduction

Gob-side entry retaining (GER) is a key technology in pillarless mining systems and has played an increasingly important role in achieving efficient, safe, and green coal mining in recent years. Its fundamental principle lies in maintaining and reusing the roadway adjacent to the goaf by establishing a stable coupling system between the surrounding rock and support structures [1,2,3,4]. Compared with conventional coal pillar retention methods, GER significantly improves coal recovery, reduces roadway drivage, and effectively mitigates stress concentration and associated dynamic disasters such as rock bursts. In addition, it provides favorable conditions for gas drainage, making it particularly advantageous in multi-seam mining systems. However, under thick and hard roof conditions or intense mining disturbances, the surrounding rock structure is subjected to long-term superimposed mining-induced stresses. When the main roof fails to cave in a timely and sufficient manner, large-span cantilever structures are easily formed, leading to continuous load transfer from the overburden to the roadway and RBB. This results in severe roof subsidence, rib extrusion, and backfill instability, which has become a major bottleneck restricting the wide application of GER [5,6,7,8].

From the perspective of strata structural evolution, the stability of GER is fundamentally governed by the fracture mode of the main roof and the movement characteristics of key blocks. According to key strata theory, the overlying strata typically exhibit an “O–X” fracture pattern during mining and form a lateral arc-shaped triangular block structure along the goaf boundary, which transfers the overburden load through rotation and articulation [9,10]. Engineering practice indicates that the fracture position of this arc-shaped triangular block directly determines the effective bearing length and load transfer path of the roof structure. Meanwhile, the resistance provided by roadside support influences the rotation mode and secondary fracture behavior of key blocks. These two factors jointly control the deformation characteristics and stress distribution of the surrounding rock [11,12,13]. Therefore, the fracture position of the main roof is not only a key parameter in roof structural evolution but also a governing variable for GER stability.

Extensive studies have been conducted to investigate the mechanical behavior of roof structures. Smart [14] proposed an inclined roof mechanical model, identifying the roof inclination angle and rotational hinge position as critical parameters for roadside support design. Wu [15] demonstrated, based on elastic foundation beam theory, that the fracture position of lateral cantilever structures migrates deeper with increasing rock mass strength. Li Huamin [16] simplified the roof as a laminated bending plate model and introduced a strip segmentation method to describe load distribution. Han Changliang and Zhang Nong [17,18] further established a composite bearing model of the “roof–wall–floor” system, emphasizing that the overall system stiffness controls roadway stability. Although these studies have revealed important aspects of roof structural response, they are largely limited to passive analysis under predefined fracture conditions, focusing on deformation and failure behavior rather than the active regulation of fracture processes.

With the advancement of stress field theory, Wang and Jiang [19,20] analyzed surrounding rock failure from the perspective of deviatoric stress distribution, highlighting the role of stress gradients in plastic zone evolution. Nevertheless, whether based on structural models or stress analysis, most existing studies have not fully elucidated the coupling relationship among fracture position, structural reconfiguration, and stress transfer paths. In particular, a systematic theoretical framework for the quantitative prediction and active regulation of main roof fracture position remains lacking.

In engineering practice, the stability of GER is typically achieved through the cooperative bearing of the RBB and support system [21,22,23,24]. Previous studies have shown that increasing the backfill ratio or optimizing support parameters can improve the load-bearing capacity of surrounding rock and reduce deformation. However, due to the limited strength and deformation capacity of high-water materials or concrete, passive support alone is insufficient to effectively control roof movement under deep and high-stress conditions [25,26,27]. Therefore, modifying the roof structure through artificial intervention to reconstruct the stress transfer path has become an important research direction.

For hard roof control, both blasting and HF techniques have been widely applied [28,29,30,31,32]. Among them, HF has gradually become the dominant method due to its advantages of long influence range, low disturbance, and high safety. Existing studies indicate that directional HF can weaken roof integrity and induce fracture along predefined weak planes, thereby reducing the cantilever length and redistributing stress. However, the effectiveness of this technique is highly dependent on the spatial position of roof fracture. Improper fracture positioning may not only fail to achieve pressure relief but also exacerbate surrounding rock instability. Consequently, determining and regulating the fracture position of the main roof has emerged as a key scientific issue linking theoretical research and engineering application.

Based on the above considerations, this study takes the GER of the 3⁻¹01 working face in Huoluowan Coal Mine as the engineering background and focuses on the main roof fracture position as the core variable. First, a statically indeterminate mechanical model considering the inner and outer fracture positions of the roadside roof is established based on masonry beam theory, and the deflection and bending moment distributions are derived to determine the fracture position. Then, UDEC Trigon numerical models are developed to analyze the deformation and damage evolution of the surrounding rock and backfill body under different fracture conditions. On this basis, a coordinated control technology integrating anchor cable reinforcement and directional long-distance HF is proposed to actively regulate the fracture position. Finally, field application and mine pressure monitoring are conducted to verify the effectiveness of the proposed method.

This study elevates the main roof fracture position from a passive response parameter to a controllable variable, enabling the reconstruction of the surrounding rock stress environment from the perspective of structural evolution. The findings provide new theoretical insights and technical approaches for stability control of GER under complex geological conditions.

2. Deformation and Failure Characteristics of Gob-Side Entry Retaining in Huoluowan Coal Mine

2.1. Geological and Engineering Conditions

Huoluowan Coal Mine is located in the Shendong mining area, China, where the 3⁻¹ upper coal seam is currently being extracted. The seam has an average thickness of 3.7 m and a dip angle of 1–3°, indicating a nearly horizontal occurrence, with an average burial depth of 173.5 m. The immediate roof consists of 3.0 m thick sandy mudstone, while the main roof is composed of 8.3 m thick fine-grained sandstone. The comprehensive stratigraphic column is shown in Figure 1b. The GER test section is located in the tailgate of the 3⁻¹01 working face, which is the first panel mined in the south wing of the main roadway. The retained entry is designed to be reused as the headgate of the adjacent 3⁻¹02 working face. The layout of the GER system in the 3⁻¹01 working face is illustrated in Figure 1c. A high-water rapid solidification material is adopted as roadside support, and the RBB is arranged along the floor on the gob side. The RBB has a width of 2.0 m, while the roadway cross-section remains unchanged before and after retaining, with a height of 3.7 m and a width of 5.4 m.

Figure 1. Engineering background: (a) Layout and gob-side entry retaining (GER) system of the 3⁻¹01 working face; (b) A–A cross-section of the 3⁻¹01 working face; (c) Stratigraphic column.

The support scheme of the tailgate in the 3⁻¹01 working face is shown in Figure 2. The roof is reinforced using a bolt–mesh–cable support system. Roof bolts are Φ20 × 2200 mm left-handed ribbed steel bolts (MG500 grade), installed with M22 × 2.5 damping nuts. The bolt spacing is 900 mm × 900 mm, with six bolts arranged per row. Adjacent bolts are connected by Φ14 mm steel ladder beams to improve the integrity of the support structure. Roof cable bolts with a specification of Φ18.9 × 6300 mm are installed in a “2–0–2” pattern along the roof, with a spacing of 1800 mm × 1800 mm. The sidewalls are fully supported by bolts with a spacing of 800 mm × 900 mm, with five bolts arranged per row. Adjacent bolts are connected using steel ladder beams to enhance the lateral confinement and load transfer capacity.

Figure 2. Support configuration of the tailgate cross-section in the 3⁻¹01 working face: (a) Cross-sectional view; (b) Plan view; (c) Side view.

2.2. Mine Pressure Behavior and Deformation Characteristics of GER in the 3⁻¹01 Working Face

At present, the length of the GER section in the 3⁻¹01 working face is approximately 300 m. With the advancement of the working face, the overall performance of the retained entry is unsatisfactory, exhibiting severe deformation and structural damage, which makes roadway reuse difficult. Field observations indicate that the deformation of the surrounding rock and the roadside support system in the tailgate shows pronounced asymmetry. The roadside support structure undergoes progressive inclination and gradually loses its load-bearing capacity, which in turn induces rib deformation and floor heave. The development of floor heave further aggravates the inclination of the roadside support and increases the extrusion of the coal rib, forming a coupled deterioration process. The overall deformation profile of the surrounding rock after instability is shown in Figure 3, and the main failure characteristics can be summarized as follows:

Figure 3. Overall contour of surrounding rock after deformation of GER: ① roof subsidence; ② solid coal rib deformation; ③ RBB instability; ④ floor heave.

(1) The roof exhibits cutting-induced subsidence along the inner side of the roadside support. Significant inward deformation occurs at the shoulder of the coal rib. The roof metal mesh and steel strips show obvious bending and torsion, and some bolts and cable bolts experience local breakage and failure.

(2) The coal rib undergoes pronounced extrusion into the retained entry space. The ladder beams and metal mesh are subjected to tensile deformation and cracking. A large number of sidewall bolts are pulled out together with the overall movement of the coal rib, resulting in a complete loss of rib support capacity.

(3) The RBB shows evident inclination, and some high-water material bags are damaged due to roof compression, leading to a substantial reduction in its load-bearing capacity.

(4) The floor of the retained entry experiences localized bending and heave, which adversely affects the normal movement and operation of the end supports at the working face.

These observations indicate that the instability of GER is closely related to the unfavorable evolution of the main roof structure, particularly the fracture position, which governs the load transfer path and deformation pattern of the surrounding rock.

3. Deformation and Failure Mechanism of Gob-Side Entry Retaining

3.1. Fracture Characteristics of the Main Roof

The extraction of the 3⁻¹01 working face induces movement of the overlying strata, disrupting the original stress equilibrium and generating a mining-induced stress field. As the retained entry is located at the edge of the goaf, the main roof is subjected to dynamic loading, leading to the formation of a lateral arc-shaped triangular block structure. This structure serves as the primary load-bearing system that transfers the dynamic load of the overlying strata to the surrounding rock and the roadside support system. The structure consists of three key blocks. Block A is fixed at one end within the deep solid coal, block B is hinged between blocks A and C, and block C is supported by caved gangue while its other end is hinged to the stable rock mass in the goaf.

During the advancement of the working face using GER technology, the main roof on the gob side undergoes fracture, rotation, and subsidence under the combined effects of its self-weight and the support resistance of the RBB [33,34]. Among these factors, the fracture position of the main roof above the retained entry—corresponding to the failure position of key block B—has a decisive influence on roadway stability. Depending on the mechanical properties of the surrounding rock and the occurrence conditions of the overlying strata, the lateral fracture position of the main roof above the retained entry can be classified into four typical cases: solid coal side, above the roadway, above the backfill body, and gob side, as illustrated in Figure 4.

Figure 4. Fracture positions of the main roof in GER: (a) solid coal side; (b) above the roadway; (c) above the backfill body; (d) gob side.

The four fracture modes of the main roof:

(1) Fracture on the gob side: When the fracture occurs on the gob side, the main roof fracture and key block movement are primarily confined to the goaf area, making it difficult to form a stable load-bearing structure acting on the retained entry. Consequently, the load imposed on the retained entry is significantly reduced, and the surrounding rock is subjected to minimal mining-induced disturbance. The roadway deformation is effectively controlled, making this the most favorable fracture mode for GER stability.

(2) Fracture above the roadway or the RBB: When the fracture occurs above the roadway or the RBB, key block B directly acts on the retained entry structure, representing the most unfavorable condition. During the rotation and subsidence of the fractured block, most of the overburden load is directly transferred to the surrounding rock and the RBB. This leads to intensified roof subsidence, pronounced rib convergence, and strong non-uniform compression of the RBB, resulting in severe stress concentration and significant expansion of the plastic failure zone.

(3) Fracture on the solid coal side: When the fracture occurs on the solid coal side, key block B shifts toward the coal mass and forms a new load-bearing structure. The overlying strata load is primarily carried by the solid coal, while the RBB shares a secondary portion of the load. Compared with the cases where fracturing occurs above the backfill body or above the roadway, the direct loading on the GER system is reduced under this condition; however, this does not indicate that the roadway is in a stable state. Due to the formation of a cantilever beam structure above the roadway after lateral breakage of the main roof, a sustained asymmetric additional load is generated during its rotation and subsidence toward the goaf. Consequently, progressive deformation still develops, including stress concentration in the solid coal rib, inward movement of the coal rib, tilting of the backfill body, and floor heave. Therefore, this condition represents a relatively sub-stable state, and its stability is significantly lower than that of the goaf-side fracture condition.

3.2. Mechanical Model of Lateral Fracture Position of the Main Roof

To ensure the stability of the surrounding rock in gob-side entry retaining (GER), a statically indeterminate mechanical model based on masonry beam theory is established to characterize the lateral roof fracture behavior.

In this model, the overlying strata system is simplified as a combination of a semi-infinite elastic foundation beam on the solid coal side and a masonry-type rock beam spanning the goaf. The Winkler-type elastic foundation assumption is adopted to represent the supporting effect of the coal–rock mass, while the masonry beam idealization is used to describe the key stratum behavior through rigid block rotation and fracture. The governing differential equations of the deflection curve for the coupled beam system are derived, and the corresponding expressions for the bending moment and deflection distribution of the lateral roof are obtained. Furthermore, based on the maximum tensile stress criterion, a quantitative criterion for determining the fracture position of the main roof in GER is proposed [35,36]. The elastic foundation beam model of the overlying strata structure in GER is illustrated in Figure 5.

Figure 5. Structural configuration and loading conditions of the overlying strata prior to main roof fracture in GER.

These formulations are based on the following assumptions: the rock mass is treated as an equivalent continuous medium with linear elastic foundation response; the key stratum is simplified as rigid blocks with discrete rotational interfaces; and the system response is analyzed under quasi-static conditions, neglecting three-dimensional stress redistribution and progressive damage evolution associated with dynamic mining processes.

3.2.1. Mechanical Analysis of Load Distribution Prior to Main Roof Fracture

The load acting on the side of the working face is greater than the far-field uniformly distributed load. As the distance from the coal wall increases, the roof load gradually approaches uniform distributions $q_1$ and $q_2$, respectively. The distributed load acting on the roof is described using a Weibull distribution function:

$$f(x)=Ax{e}^{-{\displaystyle \frac{x}{x_c}}}$$

(1)

where A is the initial slope of the function $f\left(x\right)$.

Taking the derivative of both sides of Equation (1) yields: $f^{\prime }\left(x\right)=\left(A-{\displaystyle \frac{Ax}{x_c}}\right)e^{-{\displaystyle \frac{x}{x_c}}}$. Let $f^{\prime }\left(x\right)$ = 0, then $x=x_c$ can be obtained. Meanwhile, when $x>x_c, f^{\prime }\left(x\right)<0$. Therefore, $f\left(x\right)$ reaches its maximum value at this point, and $f^{\prime }\left(x_c\right)$ = 0. Let $f\left(x_c\right)=f_c$ According to Equation (1), $A={\displaystyle \frac{f_{c}e}{x_c}}$, can be derived. Substituting this into Equation (1), the expression can be rewritten as:

$$f(x)={\displaystyle \frac{f_{c}e}{x_c}}x{e}^{-{\displaystyle \frac{x}{x_c}}}$$

(2)

From Equation (2), it can be observed that a larger $f_c$ leads to a higher peak value of the function $f\left(x\right)$. Therefore, the peak magnitude of the incremental load can be regulated by adjusting $f_c$. Meanwhile, the rate of variation of $f\left(x\right)$ as $x\to \mathrm{\infty }$ can be controlled by increasing or decreasing $x_c$, which governs the smoothness or abruptness of the decay behavior. Accordingly, the incremental load distributions of the roof on the gob side and the solid coal side can be assumed as follows:

$$\{\begin{array}{c}{f}_1(x)=k_1(x+x_{c1})e^{-{\displaystyle \frac{x+x_{c1}}{x_1}}}={\displaystyle \frac{f_{c1}e}{x_{c1}}}(x+x_{c1})e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}} (0\le x\le L)\\ f_2(x)=k_2(x_{c2}-x)e^{{\displaystyle \frac{x-x_{c2}}{x_{\mathrm{c}2}}}}={\displaystyle \frac{f_{c2}e}{x_{c2}}}(x_{c2}-x)e^{{\displaystyle \frac{x-x_{c2}}{x_{\mathrm{c}2}}}} (x\le 0)\end{array}$$

(3)

Substituting $f_{c1}=f_{c2}=15$, $x_{c1}=2$, and $x_{c2}=5$ into Equation (3), the post-peak curves of $f_1\left(x\right)$ and $f_2\left(x\right)$ are plotted, as shown in Figure 6. The reason for selecting $x_{c1}=2$ and $x_{c2}=5$ as the parameters for the incremental load above the goaf and the coal-wall side, respectively, is that the roof above the goaf undergoes larger subsidence and thus exhibits a faster decay of incremental load, whereas the roof above the coal-wall side is jointly supported by the coal seam and the immediate roof, resulting in smaller subsidence and a slower decay rate of the incremental load.

Figure 6. Forms of incremental load of the roof on the solid coal side and the goaf side of the working face.

Taking the coal wall as the horizontal reference point, the loads acting on the roof above the gob side and the solid coal side can be expressed as follows:

$$\{\begin{array}{c}{F}_1\left(x\right)=q_1+k_1(x+x_{c1})e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}} (0\le x\le L)\\ F_2\left(x\right)=q_2+k_1\left(x_{c2}-x\right)e^{{\displaystyle \frac{x-x_{c2}}{x_{\mathrm{c}2}}}} \left(x\le 0\right)\end{array}$$

(4)

where $q_1$ and $q_2$ denote the incremental roof load distributions on the gob side and coal side, respectively. Since the load distribution is continuous, we have $F_1\left(0\right)=F_2\left(0\right)$, thus:

$$q_1+f_{c1}=q_2+f_{c2}$$

(5)

Let the hanging length of the arc-shaped triangular block before initial fracture be $L$. Equations (4) and (5) describe a continuous and smooth load distribution. When $x\to L$, $F_1\left(x\right)\approx q_1$; when $x\to -\mathrm{\infty }$, $F_2\left(x\right)\to q_2$.

Based on Equation (4), a free-body diagram of the hard roof prior to initial fracture is constructed, as shown in Figure 7.

Figure 7. Free-body diagram of the main roof prior to fracture: (a) solid coal side; (b) gob side.

Goaf-side analysis: Taking moments of all loads about a cross-section at position $x$, As shown in Figure 6, t is the integration variable along the axis of the gob-side roof beam, representing the position of the distributed load. The differential equation governing the deflection curve of the roof beam on the goaf side can be obtained as:

$$EI{y}_1^{″}\left(x\right)=M_0+Q_{0}x+{\displaystyle \frac{1}{2}}{q}_1{x}^2+{\int }_0^x{k}_1\left(t+x_{c1}\right)e^{-{\displaystyle \frac{t+x_{c1}}{x_{c1}}}}\left(x-t\right)dt (0\le t\le x\le L)$$

(6)

where $Q_0$ and $M_0$ are the internal shear force and bending moment at the section x = 0, respectively; E is the elastic modulus of the main roof; I is the standard second moment of area of a rectangular section about its neutral axis, defined as $I={\displaystyle \frac{1}{12}}b{h}^3$, where b and h denote the width of the beam and the thickness of the main roof, respectively.

On the coal wall side, the roof is modeled as a semi-infinite beam resting on a Winkler elastic foundation under the distributed load $F_2\left(x\right)$. The coal seam and immediate roof jointly constitute the elastic foundation. The foundation reaction $q_c$ is proportional to the vertical displacement $y$ of the beam:

$$q_c=-Cy$$

(7)

Solid coal side: According to Equations (4) and (7), the governing differential equation of the deflection curve for the semi-infinite elastic foundation beam on the coal wall side under the action of $F_2\left(x\right)$ can be written as:

$$EI{y}_2^{\left(4\right)}\left(x\right)=q_2+k_2\left(x_{c2}-x\right)e^{{\displaystyle \frac{x-x_{c2}}{x_{\mathrm{c}2}}}}-C{y}_2(x)$$

(8a)

Let $\beta ={\left({\displaystyle \frac{C}{4EI}}\right)}^{{\displaystyle \frac{1}{4}}}$, Equation (8a) can be rewritten as:

$$y_2^{\left(4\right)}\left(x\right)+4{\beta }^4{y}_2\left(x\right)={\displaystyle \frac{q_2}{EI}}+{\displaystyle \frac{k_2}{EI}}\left(x_{c2}-x\right)e^{{\displaystyle \frac{x-x_{c2}}{x_{\mathrm{c}2}}}}$$

(8b)

The analytical expression of the last integral term on the right-hand side of Equation (3) is given by:

$$\sum =k_1{x}_{c1}^3\left[\left(2+{\displaystyle \frac{x+x_{c1}}{x_{c1}}}\right)e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}}-\left(5-2{\displaystyle \frac{x+x_{c1}}{x_{c1}}}\right)e^{-1}\right]$$

(9)

Substituting Equation (9) into Equation (6) and integrating twice yields the deflection equation of the roof beam above the goaf:

$$EI{y}_1\left(x\right)={\displaystyle \frac{q_1}{24}}{x}^4+{\displaystyle \frac{M_0}{2}}{x}^2-{\displaystyle \frac{Q_0}{6}}{x}^3+k_1{x}_{c1}^5\left\{\left(4+{\displaystyle \frac{x+x_{c1}}{x_{c1}}}\right)e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}}-\left[{\displaystyle \frac{3}{2}}{\left({\displaystyle \frac{x}{x_{c1}}}\right)}^2-{\displaystyle \frac{1}{3}}{\left({\displaystyle \frac{x}{x_{c1}}}\right)}^3\right]e^{-1}\right\}+c_{1}x+c_2$$

(10)

Equation (8) is a fourth-order linear non-homogeneous differential equation with constant coefficients. Its solution consists of the general solution $Y_2\left(x\right)$ of the corresponding homogeneous equation (Equation (8b)) and a particular solution $y_2^{*}\left(x\right)$ corresponding to Equation (8b). Since Equation (8) is a linear differential equation, the superposition principle can be applied to separately determine the particular solutions $y_{21}^{*}\left(x\right)$ and $y_{22}^{*}\left(x\right)$, corresponding to the first term $q_2/EI$ and the second term on the right-hand side of Equation (8b), respectively. Therefore, the solution of Equation (8) can be expressed as:

$$y_2\left(x\right)=Y_2\left(x\right)+y_{21}^{*}\left(x\right)+y_{22}^{*}\left(x\right)$$

(11)

By solving the fourth-order non-homogeneous linear differential equation with constant coefficients, the deflection function of the elastic foundation beam on the working face side is obtained as:

$$y_2\left(x\right)=e^{\beta x}\left[B_3\cos \left(\beta x\right)+B_4\sin \left(\beta x\right)\right]+{\displaystyle \frac{q_2}{4{\beta }^{4}EI}}+{\displaystyle \frac{k_2}{EI}}{\displaystyle \frac{x_{c2}^4}{1+4{\beta }^4{x}_{c2}^4}}\left(x_{c2}-x+{\displaystyle \frac{4x_{c2}}{1+4{\beta }^4{x}_{c2}^4}}\right)$$

(12)

The first-, second-, and third-order derivatives of $y_1\left(x\right)$ in Equation (10) are given by:

$$EI{y}_1^{\prime }\left(x\right)={\displaystyle \frac{q_1}{6}}{x}^3-{\displaystyle \frac{Q_0}{2}}{x}^2+M_{0}x-k_1{x}_{c1}^4\left\{\left(3+{\displaystyle \frac{x+x_{c1}}{\overline{x_{c1}}}}\right)e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}}+\left[3{\displaystyle \frac{x}{x_{c1}}}-{\left({\displaystyle \frac{x}{\overline{x_{c1}}}}\right)}^2\right]e^{-1}\right\}+B_1$$

(13)

$$EI{y}_1^{″}\left(x\right)={\displaystyle \frac{q_1}{2}}{x}^2+Q_{0}x+M_0+k_1{x}_{c1}^3\left\{\left(2+{\displaystyle \frac{x+x_{c1}}{x_{c1}}}\right)e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}}-\left(3-2{\displaystyle \frac{x}{x_{c1}}}\right)e^{-1}\right\}$$

(14)

$$EI{y}_1^{‴}\left(x\right)=q_{1}x-Q_0{k}_1{x}_{c1}^2\left\{\left(1+{\displaystyle \frac{x+x_{c1}}{x_{c1}}}\right)e^{-{\displaystyle \frac{x+x_{c1}}{x_{c1}}}}-2e^{-1}\right\}$$

(15)

Since the rock beam above the goaf and the elastic foundation beam on the coal wall side form a statically indeterminate continuous system (as shown in Figure 5), Equations (6) and (8) constitute the governing differential equations of the coupled system. The natural boundary conditions and continuity conditions of the continuous beam shown in Figure 5, Figure 6 and Figure 7 are relatively complex and can be listed from left to right as follows:

$$\{\begin{array}{c}\begin{array}{c}{y}_2\left(-\infty \right)={\displaystyle \frac{q_2}{C}}={\displaystyle \frac{q_2}{4EI{\beta }^4}}\\ y_1^{\prime }\left(-\infty \right)=0\\ y_2\left(0\right)=y_1\left(0\right)\end{array}\\ \begin{array}{c}{y}_2^{\prime }\left(0\right)=y_1^{\prime }\left(0\right)\\ y_2^{″}\left(0\right)=y_1^{″}\left(0\right)\\ y_2^{‴}\left(0\right)=y_1^{‴}\left(0\right)\end{array}\\ \begin{array}{c}{y}_1^{\prime }\left(L\right)=0\\ y_1^{‴}\left(L\right)=0\end{array}\end{array}$$

(16)

According to Equation (13), the third derivative of the deflection function at x = 0 can be expressed as:

$$y_2^{‴}\left(0\right)=2{\beta }^3\left(-B_3+B_4\right)+{\displaystyle \frac{k_2}{EI}}{\displaystyle \frac{x_{c2}^2{e}^{-1}}{1+4{\beta }^4{x}_{c2}^4}}\left({\displaystyle \frac{4}{1+4{\beta }^4{x}_{c2}^4}}-2\right)$$

(17)

By solving the system of equations based on the boundary conditions given in Equation (16), the coefficients can be obtained as:

$$B_3={\displaystyle \frac{1}{2{\beta }^3}}\left[D_1-D_3-{\displaystyle \frac{\beta }{1+\beta L}}\left(D_2-D_3\right)\right]$$

(18)

$$B_4={\displaystyle \frac{D_2-D_3}{2{\beta }^3\left(1+\beta L\right)}}$$

(19)

where $D_1$, $D_2$, and $D_3$ are auxiliary expressions determined by the loading and structural parameters, as given in Equations (20)–(22).

$$D_1={\displaystyle \frac{k_2}{EI}}{\displaystyle \frac{x_{c2}^2{e}^{-1}}{1+4{\beta }^4{x}_{c2}^4}}\left({\displaystyle \frac{2-4{\beta }^2{x}_{c2}^2}{1+4{\beta }^4{x}_{c2}^4}}-1\right)-{\displaystyle \frac{4k_1{\beta }^2{x}_{c1}^4{e}^{-1}}{EI}}+{\displaystyle \frac{Q_0}{2EI}}$$

(20)

$$D_2=-{\displaystyle \frac{k_2{L}^2}{EI}}{\displaystyle \frac{x_{c2}^2{e}^{-1}}{1+4{\beta }^4{x}_{c2}^4}}\left({\displaystyle \frac{2-4{\beta }^2{x}_{c2}^2}{1+4{\beta }^4{x}_{c2}^4}}-1\right)-{\displaystyle \frac{4k_1{\beta }^2{x}_{c1}^4{e}^{-1}}{EI}}-{\displaystyle \frac{Q_0}{2EI}}$$

(21)

$$D_3={\displaystyle \frac{{\beta }^2}{EI}}\left\{{\displaystyle \frac{q_1{L}^3}{6}}-{\displaystyle \frac{Q_0{L}^2}{2}}-k_1{x}_{c1}^4\left[\left({\displaystyle \frac{3L}{x_{c1}}}-{\displaystyle \frac{L^2}{x_{c1}^2}}\right)e^{-1}+\left(4+{\displaystyle \frac{L}{x_{c1}}}\right)e^{-{\displaystyle \frac{L+x_{c1}}{x_{c1}}}}\right]+{\displaystyle \frac{k_{2}L{x}_{c2}^3{e}^{-1}}{1+4{\beta }^4{\overline{x}}_{c2}^4}}\left({\displaystyle \frac{4}{1+4{\beta }^4{x}_{c2}^4}}-1\right)\right\}$$

(22)

Once these coefficients are determined, the bending moment distribution of the coal-wall-side beam can be expressed as:

$$M_2\left(x\right)=EI{y}_2^{″}\left(x\right)=2EI{\beta }^2{e}^{\beta x}\left[-B_3\sin \left(\beta x\right)+B_4\cos \left(\beta x\right)\right]+{\displaystyle \frac{k_2{x}_{c2}^3}{1+4{\beta }^4{x}_{c2}^4}}\left({\displaystyle \frac{4}{1+4{\beta }^4{x}_{c2}^4}}-{\displaystyle \frac{x+x_{c2}}{x_{c2}}}\right)e^{{\displaystyle \frac{x+x_{c2}}{x_{c2}}}}$$

(23)

The fracture of the main roof is governed by the maximum bending moment criterion. Specifically, tensile failure occurs when the tensile stress induced by the peak bending moment exceeds the tensile strength of the rock mass, leading to brittle fracture of the roof structure.

3.2.2. Calculation and Analysis of the Main Roof Fracture Position in the 3⁻¹01 Tailgate

Based on the field parameters of the 3⁻¹01 working face in Huoluowan Coal Mine, the main roof thickness is 8.3 m, ${\gamma }_w$ = 25 kN/m³, $E$ = 22 GPa, $L$ = 17 m, $EI$ = 1048 × 10⁹ N·m², $f_{c1}$ = 30 × 10⁶ N·m, $f_{c2}$ = 15 × 10⁶ N·m, $q_1$ = 0.6 × 10⁶ N·m, $q_2$ = 4.0 × 10⁶ N·m, $x_{c1}$ = 2 m, $x_{c2}$ = 5 m, $k_1$ = 8.04 × 10⁷ Pa, $k_2$ = 1.43 × 10⁷ Pa. The foundation stiffness of coal measure strata generally ranges from 0.25 to 1.00 GPa. By assigning $C=0.6, 0.7, 0.8, 0.9$, and 1.0 Gpa, the governing equations were solved using Mathematica, and the deflection and bending moment curves of the main roof in GER were obtained, as shown in Figure 8.

Figure 8. Deflection and bending moment curves of the main roof in GER.

As shown in Figure 8, when C varies from 0.6 to 1.0 GPa, the peak bending moments of the rock beam occur at positions x = 11.2 m, 10.7 m, 10.2 m, 9.7 m, and 9.4 m, respectively, with corresponding peak values of 5.54 × 10⁸ N·m, 5.15 × 10⁸ N·m, 4.78 × 10⁸ N·m, 4.45 × 10⁸ N·m, and 4.15 × 10⁸ N·m. When C = 0.6 GPa, both the fracture length and peak bending moment are relatively large, indicating a greater tendency for roof deformation. In contrast, when C = 1.0 GPa, both the fracture length and peak bending moment decrease significantly, demonstrating that higher foundation stiffness effectively suppresses roof deformation. As $x\to -30\hspace{0.17em}\mathrm{m}$, all bending moment curves gradually approach 0.

Theoretical analysis indicates that after the extraction of the 3⁻¹01 working face, the natural fracture of the main roof predominantly occurs within the elastoplastic transition zone inside the coal mass (approximately 9.4–11.2 m). This result only represents the most probable fracture location and does not directly imply the stability of the gob-side entry retaining system.

Following lateral fracturing on the solid coal side, a cantilever beam structure forms above the roadway, extending toward the goaf. During its rotation and subsidence, this structure imposes a sustained and asymmetric additional load on the surrounding rock and the RBB. Although this condition induces a weaker direct disturbance to the roadway compared with fractures occurring above the roadway or above the backfill body, it still triggers pronounced progressive deformation and structural instability, manifested by asymmetric failure characteristics such as roof subsidence, coal rib extrusion, and tilting of the backfill body.

4. Numerical Simulation Study

4.1. Numerical Modeling

4.1.1. UDEC Trigon Numerical Model

The Trigon model is an improved discrete element modeling approach implemented in UDEC, in which conventional Voronoi polygonal blocks are further subdivided into randomly distributed triangular elements to enhance the representation of material heterogeneity and fracture development in coal and rock masses [11]. In this model, the triangular blocks are treated as elastic bodies, and no failure occurs within the blocks themselves. The nonlinearity of the system arises from the mechanical response of the contacts between adjacent blocks. Under external loading, deformation and failure of the coal–rock mass occur exclusively along the interfaces between blocks, primarily in the form of shear slip and tensile separation. The strength behavior of these interfaces follows the Mohr–Coulomb failure criterion [37,38]. Compared with conventional continuum or block-based models, the Trigon approach, characterized by randomly distributed triangular blocks and a dense contact network, provides a more realistic simulation of crack initiation, propagation, and coalescence. Based on this framework, the Trigon model is adopted in this study to investigate the fracture characteristics of the roof and the deformation and failure mechanisms of gob-side entry retaining (GER). The mechanical criteria governing the interactions between triangular blocks are summarized in Table 1.

Table 1. Failure criteria of triangular blocks in the Trigon model.

In the normal direction $∆{\sigma }_n=-k_n∆u_n$ Where $∆{\sigma }_n$ and $∆u_n$ are the effective normal stress increment and normal displacement increment, respectively, and $k_n$ is the normal stiffness of contacts. In the shear direction, if $\left|{\tau }_s\right|\le c+{\sigma }_n\mathrm{t}\mathrm{a}\mathrm{n}\phi ={\tau }_s^{max}$ then $∆{\tau }_s=-k_s∆u_s^e$ or else, if $\left|{\tau }_s\right|>{\tau }_s^{max}$ then ${\tau }_s=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(∆u_s){\tau }_s^{max}$ Where $\phi$ and c are the cohesion and friction angle of the contact, respectively. $∆u_s^e$ and $∆u_s$ are the elastic component of the incremental shear displacement and total incremental shear displacement, respectively.

(a) Micro-contacts yielding process in Trigon model

(b) Coulomb friction law

4.1.2. Calibration of Model Parameters

(1) Calibration of Rock Mass Parameters

The mechanical parameters obtained from laboratory tests primarily represent the properties of intact rock specimens, whereas the UDEC numerical model requires parameters corresponding to the rock mass. Due to the widespread presence of joints and fractures in the rock mass, its overall mechanical properties are generally lower than those measured in laboratory conditions. Therefore, it is necessary to reduce and calibrate the laboratory-derived parameters to more accurately reflect the in situ mechanical behavior of the rock mass and to provide reliable input parameters for numerical simulation.

According to the studies of Zhang and Singh M [39,40], the elastic modulus of the rock mass can be estimated from the RQD using Equation (25), and the results are presented in Table 2. The tensile strength of the rock mass is assumed to be one-tenth of its uniaxial compressive strength.

$${\displaystyle \frac{E_m}{E_r}}={10}^{0.0186RQD-1.91}$$

(24)

where $E_m$ and $E_r$ represent the elastic modulus of the rock mass and intact rock.

$${\displaystyle \frac{{\sigma }_{cm}}{{\sigma }_c}}=({\displaystyle \frac{E_m}{E_r}}{)}^n$$

(25)

where ${\sigma }_{cm}$ and ${\sigma }_c$ denote the uniaxial compressive strength of the rock mass and intact rock, respectively (MPa). The exponent $n$ varies depending on the failure mode, with typical values of 0.56, 0.56, 0.66, and 0.72 corresponding to splitting, shearing, sliding, and rotational failure modes, respectively. Considering that the failure process of coal is highly complex and involves multiple failure mechanisms [41], a representative value of n = 0.63 is adopted in this study.

Table 2. Mechanical parameters of intact rock specimens and calibrated rock mass parameters.

Lithology	Intact Rock		RQD	Rock Mass
	Modulus ${\mathit{E}}_{\mathit{r}}$ (GPa)	UCS ${\mathit{\sigma }}_{\mathit{c}}$ (MPa)		Modulus ${\mathit{E}}_{\mathit{m}}$ (GPa)	UCS ${\mathit{\sigma }}_{\mathit{c}\mathit{m}}$ (MPa)	Tensile Strength ${\mathit{\sigma }}_{\mathit{t}\mathit{m}}$ (MPa)
Fine sandstone	8.49	38.05	93	4.93	27.02	2.70
Siltstone	5.52	33.07	86	2.70	21.08	2.11
Sandy mudstone	3.34	21.92	78	1.16	11.26	1.13
coal	1.87	9.14	60	0.30	2.89	0.29

A calibration model with dimensions of 2 m × 4 m (width × height) was established using the Trigon model. Rigid loading platens were arranged at the top and bottom of the specimen, and displacement-controlled loading was applied at a rate of 0.01 m/s. A series of uniaxial compressive strength tests were conducted by iteratively adjusting the mechanical parameters of the model through a trial-and-error procedure until the numerical results were consistent with the target (calibrated) values.

In the calibration model, the elastic modulus of the blocks was set equal to that of the rock mass. The normal stiffness of the joints, $K_n$, was determined according to Equation (26) [11], and the ratio of shear to normal stiffness was taken as $K_s/K_n$ = 0.4.

$$\{\begin{array}{c}{K}_n=n\left[{\displaystyle \frac{K+(4/3)G}{∆Z_{min}}}\right]1\le n\le 10\\ K={\displaystyle \frac{E}{3\left(1-2\mu \right)}}\\ G={\displaystyle \frac{E}{2\left(1+\mu \right)}}\end{array}$$

(26)

where $E$, $K$, and $G$ denote the elastic modulus, bulk modulus, and shear modulus of the blocks, respectively; $\Delta Z_{\mathrm{m}\mathrm{i}\mathrm{n}}$ represents the minimum spacing of adjacent joint elements in the normal direction; and $\mu$ is the Poisson’s ratio of the blocks.

A series of uniaxial compression simulations were conducted using the calibrated model, and the stress–strain curves of fine-grained sandstone, siltstone, sandy mudstone, and coal seam were obtained, as shown in Figure 9. The calibrated mechanical parameters of blocks and joints in the Trigon model are listed in Table 3, and the calibration results are summarized in Table 4. The deviation between the calibrated values and the target values is within 10%, indicating that the calibrated parameters are sufficiently accurate and can be reliably used in large-scale numerical models to simulate the deformation and failure behavior of in situ rock mass.

Figure 9. Calibration of rock mass mechanical parameters based on numerical simulations: (a) Uniaxial compression simulation results; (b) coal; (c) Sandy mudstone; (d) Siltstone; (e) Fine sandstone.

Table 3. Correction of mechanical parameters for blocks and joints in the Trigon model after calibration.

Lithology	Matrix Properties			Contact Properties
	Density (kg/m3)	$\mathit{E}$ (GPa)	Poisson’s Ratio	${\mathit{K}}_{\mathit{n}}$ (GPa/m)	${\mathit{K}}_{\mathit{s}}$ (GPa/m)	Cohesion (MPa)	Friction Angle (°)	Tensile Strength (MPa)
Fine sandstone	2350	4.93	0.288	36.54	14.62	4.58	29	3.57
Siltstone	2260	2.70	0.254	20.85	8.34	3.27	23	3.31
Sandy mudstone	2155	1.16	0.277	13.01	5.20	2.56	20	2.69
coal	1265	0.30	0.253	11.08	4.43	1.32	18	1.88

Table 4. Parameter calibration results in the Trigon model.

Lithology	E (GPa)		Error (%)	Compressive Strength (MPa)		Error (%)
	Target	Calibrated		Target	Calibrated
Fine sandstone	4.93	5.11	2.10	27.02	27.19	0.63
Siltstone	2.70	2.73	1.11	21.08	21.27	0.90
Sandy mudstone	1.16	1.17	0.86	11.26	11.66	3.55
coal	0.30	0.31	0.33	2.89	2.72	−5.8

(2) Calibration of RBB Parameters

Considering the characteristics of the high-water material used in the RBB for gob-side entry retaining in the 3⁻¹01 working face, it is necessary to reasonably determine its mechanical parameters and to appropriately account for post-peak strain softening behavior to improve the accuracy of numerical simulations and to better capture the damage and fracture processes of the surrounding rock [42]. Based on the UDEC Trigon model, a uniaxial compression specimen with dimensions of 2 m (height) × 4 m (width) was constructed, in which the backfill material was modeled using a strain-softening constitutive model. Through iterative adjustment of the model parameters, the simulated stress–strain curves were calibrated to match the laboratory test results corresponding to a water–cement ratio of 1.5:1.0, thereby validating the rationality of the selected parameters, as illustrated in Figure 10. The calibrated mechanical parameters of the backfill material are summarized in Table 5, which can be used for subsequent numerical analysis of roof fracture characteristics in GER.

Figure 10. Stress–strain curves of high-water backfill material under uniaxial compression.

Table 5. Calibrated mechanical parameters for numerical simulation.

Matrix Properties					Contact Properties
Density (kg/m3)	E (GPa)	Cohesion (MPa)	Friction Angle (°)	Tensile Strength (MPa)	${\mathit{K}}_{\mathit{n}}$ (GPa/m)	${\mathit{K}}_{\mathit{s}}$ (GPa/m)	Cohesion (MPa)	Friction Angle (°)	Tensile Strength (MPa)
1400	0.15	2.0	33	1.8	583.3	233.3	2.5	30	1.5

4.1.3. Model Establishment

Based on the actual geological conditions of the 3⁻¹01 working face in Huoluowan Coal Mine, a UDEC numerical model was established, as presented in Figure 11. The model dimensions are 120 m × 48.5 m (length × height). The excavation cross-section of the 3⁻¹01 tailgate is 5.4 m × 3.7 m.

Figure 11. UDEC numerical model for GER.

In the model, “Cable” elements are used to simulate rock bolts and cable bolts, while “Beam” elements are adopted to represent steel mesh and ladder beams. The detailed parameters of the support components are listed in Table 6 [37]. A vertical stress of 3.75 MPa is applied to the top boundary of the model, and the horizontal in situ stress is set to 4.5 MPa. The bottom boundary is constrained with a fixed condition. The blocks in the model are assigned a Mohr–Coulomb constitutive model, and the joints and fractures are governed by the Mohr–Coulomb slip criterion.

Table 6. Properties of support elements in UDEC Trigon models [37].

Type	Value
Cable
Elastic modulus (GPa)	200
Stiffness of the grout (N/m2)	2 × 109
Cohesive capacity of the grout (N/m)	4 × 105
Structural beam
Elastic Modulus (GPa)	200
Tensile yield strength (MPa)	500
Compressive yield strength (MPa)	500
Interface normal stiffness (GPa/m)	10
Interface shear stiffness (GPa/m)	10

4.2. Analysis of Numerical Simulation Results

Based on the analysis presented in Section 3 and considering the significant influence of the main roof fracture position on GER stability, four representative scenarios are established and simulated using the UDEC Trigon model. The coordinate origin is defined at the gob boundary (x = 0), with positive values indicating the coal side and negative values indicating the goaf side. The distance between the pre-defined weakened structural zone and the gob boundary is set to −2 m, 1 m, 5 m, and 9 m, corresponding to fracture-prone locations on the gob side, above the RBB, above the roadway, and within the solid coal side, respectively. This treatment allows the potential instability location of the main roof to be governed by the mechanical response of the pre-defined weak domain under identical geological and boundary conditions.

To ensure comparability among different scenarios, all numerical models are advanced to the same mining progression stage rather than being compared at equilibrium termination or a fixed number of calculation steps. This ensures that all cases are evaluated under identical disturbance conditions, allowing consistent comparison of roof fracture evolution and load transfer behavior induced solely by variations in the weak zone position. The simulation scheme is shown in Figure 12.

Figure 12. Roof fracture characteristics under different fracture positions in GER: (a) gob side; (b) above the RBB; (c) above the roadway; (d) solid coal side.

4.2.1. Overall Deformation Characteristics of the Roadway

As shown in Figure 13, under different main roof fracture positions, the surrounding rock exhibits significant coupled differences in vertical stress distribution, horizontal displacement evolution, and plastic zone development. These differences fundamentally arise from the reconfiguration of load transfer paths and the redistribution of the global mechanical state induced by the movement of the overlying key blocks.

Figure 13. Numerical simulation results: (a) vertical stress distribution characteristics; (b) horizontal displacement distribution characteristics; (c) plastic zone distribution characteristics.

When the main roof fractures on the goaf side (−2 m), the structural integrity above the roadway remains relatively high, and the direct load transfer path from the overlying strata to the roadway is weakened. Consequently, the overall vertical stress level is low, with stress concentration mainly occurring in the far-field region near the goaf boundary. Horizontal displacement is characterized by weak convergence toward the goaf, with a maximum value of approximately 0.18–0.22 m, indicating limited deformation. The plastic zone is primarily distributed on both the goaf side and the solid coal side, while the RBB mainly exhibits plastic bearing behavior, resulting in relatively high overall stability of the roadway system.

When the fracture occurs above the backfill body (0 m), the overlying load begins to transfer through the backfill body to the roadway structure. Vertical stress is significantly intensified at the backfill–roof interface and progressively extends into the roadway, indicating a marked increase in stress concentration. Horizontal displacement is dominated by compressive deformation in the central region, reaching approximately 0.25–0.28 m, which is notably higher than in the −2 m case. The plastic zone expands from the goaf side toward both the backfill body and the roof, indicating that the surrounding rock enters a stage of coupled load-bearing and progressive deformation.

When the main roof fractures above the roadway (5 m), the key block directly acts on the roadway system. A pronounced high-stress concentration zone forms in the roof and both ribs, with a significant increase in peak vertical stress. Horizontal displacement reaches its maximum value of approximately 0.30–0.33 m. The backfill body exhibits obvious lateral bulging, while both ribs converge synchronously inward, leading to severe overall deformation of the roadway. The plastic zone rapidly coalesces and propagates into the deep surrounding rock, covering the roof, ribs, and floor, indicating a globally deteriorated structural state approaching instability.

When the fracture position shifts to the solid coal side (9 m), the stress redistribution of the surrounding rock shows a clear lateral migration tendency. The vertical stress concentration zone shifts from the roadway toward the coal rib side. Although the overall stress level in the roadway decreases compared with the 5 m case, the stress in the coal rib increases significantly. Horizontal displacement ranges from approximately 0.24–0.27 m and exhibits an asymmetric convergence pattern biased toward the solid coal side. The plastic zone predominantly develops within the deep coal rib, while damage intensity within the roadway is relatively reduced.

4.2.2. Deformation Characteristics of the RBB

(1) Fracture Evolution Characteristics

The evolution of tensile and shear cracks within the RBB under different fracture position scenarios is statistically analyzed (Figure 14), revealing the damage characteristics induced by mining disturbance. Overall, the number of shear cracks within the RBB is significantly higher than that of tensile cracks. Shear cracks exhibit rapid growth during the early stage (approximately 0–4000 steps), followed by a gradual accumulation phase. In contrast, tensile cracks show a clear lag in development, with their total number accounting for only about 30–40% of shear cracks. This indicates that the RBB is dominated by shear failure, while tensile failure mainly results from local stress release or structural bending, forming a composite failure mode characterized by “shear-dominated with tensile assistance”.

Figure 14. Evolution characteristics of tensile and shear cracks within the RBB under different fracture positions.

From the perspective of different scenarios, the 5 m case (fracture located above the roadway) shows the fastest growth rate and highest accumulation of shear cracks, indicating the most severe damage. The 9 m case, although slightly lower than the 5 m case, still maintains a relatively high level, reflecting significant lateral compression induced by stress transfer toward the solid coal side. In the 1 m case, crack evolution is relatively moderate, suggesting a more distributed stress state. In contrast, the −2 m case exhibits the lowest crack quantity and tends toward stabilization, indicating that fracture on the gob side imposes the weakest disturbance on the RBB.

(2) Horizontal Displacement Characteristics

As presented in Figure 15, the horizontal displacement of the RBB exhibits a pronounced asymmetric distribution along its height and varies significantly with the fracture position of the main roof. In general, the displacement at the bottom is close to zero, indicating strong constraint from the floor. With increasing height, the displacement gradually increases, and deformation is mainly concentrated in the middle–upper region. On the gob side of the RBB, the maximum horizontal displacement at the upper portion reaches approximately 253 mm. Among all scenarios, the −2 m case shows the largest overall displacement magnitude, indicating that when the fracture occurs on the gob side, the rotation of the key block toward the goaf induces a dragging effect on the upper part of the RBB. As the fracture position shifts toward the roadway and the solid coal side (1 m, 5 m, and 9 m), the displacement gradually decreases and approaches zero, suggesting that the disturbance induced from the goaf side is progressively weakened. On the solid coal side of the RBB, a pronounced displacement peak is observed in the mid-height region, with a maximum value of approximately 321 mm. This feature is most prominent in the 5 m case, exhibiting a typical “mid-height bulging” pattern. This indicates that when the fracture occurs above the roadway, the direct rotation and subsidence of the key block impose strong lateral compression on the RBB, leading to concentrated deformation in the middle portion.

Figure 15. Horizontal displacement distribution characteristics of the RBB: (a) on the gob side of the RBB; (b) on the solid coal side of the RBB.

Overall, the deformation behavior of the RBB evolves with the change in fracture position, exhibiting a transition from “gob-side traction control” to “strong compression control above the roadway,” and further to “stress transfer toward the solid coal side.” Correspondingly, the displacement distribution shows a characteristic pattern of “bottom constraint–mid-height concentration–upper dominance.” This result indicates that when the fracture occurs above the roadway, the internal stress distribution within the RBB becomes highly non-uniform, making it more susceptible to large deformation and structural instability.

4.2.3. Evolution of Displacement Vector Field of Surrounding Rock in GER

From Figure 16, results indicate that the movement patterns and load transfer paths of the surrounding rock–RBB system vary significantly under different main roof fracture positions. Overall, as the fracture position shifts from the gob side toward the solid coal side, the system response evolves from “goaf-dominated rotation” to “concentrated disturbance above the roadway,” and further to “load transfer toward the solid coal side.” Specifically, in the −2 m case, the displacement vectors are predominantly directed toward the goaf and characterized by subsidence, while the deformation of the RBB remains relatively small. The system behavior is therefore governed by goaf-side stress release, with a weak response in the roadway. In the 1 m case, the movement of the overlying strata transitions into a combined mode of “subsidence–lateral compression.” The displacement vectors at the top of the RBB increase noticeably, indicating that the RBB begins to undertake a primary load-bearing role. In the 5 m case, the vector magnitudes increase significantly and exhibit a disordered distribution. A concentrated deformation zone develops above the roadway, and the RBB shows a pronounced bulging deformation toward the solid coal side, accompanied by convergence of the two ribs. The surrounding rock undergoes substantial deformation, representing the most unfavorable condition. In the 9 m case, the region of maximum displacement shifts toward the solid coal side. The deformation of the RBB is alleviated to some extent; however, dense vector distributions within the coal mass indicate that stress concentration propagates deeper into the coal body.

Figure 16. Evolution of displacement vector field of surrounding rock in GER under different fracture positions: (a) gob side; (b) above the RBB; (c) above the roadway; (d) solid coal side.

Therefore, in practical engineering applications, it is not sufficient to focus solely on the strength and deformation capacity of the RBB. From the perspective of roof structure control, it is essential to regulate the fracture position or weaken the rotational effect of the key block. By reducing the direct impact of concentrated displacement vector zones on the roadway, the overall stability of the surrounding rock system in GER can be effectively improved.

5. Control Technology for Deformation and Failure of GER

Based on the preceding analysis, when the main roof fracture occurs on the gob side (−2 m), the tailgate of the 3⁻¹01 working face experiences relatively low disturbance induced by lateral roof fracture. Under this condition, the coal rib and RBB exhibit comparatively stable deformation behavior, providing a relatively favorable state for GER. However, field observations indicate that deformation and instability may still develop under complex loading and support conditions, highlighting the necessity of targeted control measures. To mitigate deformation and improve the stability of GER, an integrated control strategy combining in-entry support optimization and roof structure regulation is proposed.

(1) Optimization of in-entry support system: By improving the support strength and deformation resistance capacity of GER through optimized support design, the integrity of the coal rib and roof can be enhanced.

(2) Directional HF for fracture position control: By means of artificial intervention, the lateral fracture position of the main roof on the gob side is regulated. Pre-fracturing is conducted to create weak planes in the main roof, promoting fracture at predetermined locations. This effectively eliminates the adverse influence of the lateral cantilever structure formed above the retained entry, thereby improving the stability of GER.

5.1. Reinforced Support of Solid Coal Rib Using Anchor Cables

During the application of GER in the 3⁻¹01 working face, controlling the deformation of the roof and the solid coal rib is critical for maintaining the stability of the surrounding rock. During panel retreat, the retained entry is subjected to the combined effects of mining-induced stress and advanced abutment pressure, which often lead to non-uniform failure. Properly designed bolt and anchor cable support systems can reinforce the plastic zone of the surrounding rock and enhance its overall load-bearing capacity, thereby effectively inhibiting the large-scale propagation of the plastic zone into the coal rib and suppressing excessive deformation of the roadway [43].

Based on the above analysis, in order to improve the load-bearing capacity of the solid coal rib while restraining the development of the fractured zone and the outward displacement of the anchorage system, additional anchor cable reinforcement is implemented on the basis of bolt support. This approach anchors the shallow plastic coal mass into the deeper elastic coal mass, thereby enhancing both the peak strength and residual load-bearing capacity of the shallow coal.

Specifically, for roof reinforcement in the 3⁻¹01 tailgate, one additional anchor cable with a specification of Φ18.9 × 6300 mm is installed at the central position, arranged in a “2–1–2” pattern along the roof. For the solid coal rib, two anchor cables with a specification of Φ15.24 × 4.3 m are installed per row, with a spacing of 800 mm. The reinforced support configuration of the roadway cross-section is illustrated in Figure 17.

Figure 17. Reinforcement support scheme for the 3⁻¹01 tailgate in GER: (a) Cross-sectional view; (b) Plan view; (c) Side view.

5.2. Advanced Directional Long Horizontal Drilling for Roof Cutting and Pressure Relief

Considering that HF can effectively weaken the integrity and stability of rock strata, the lateral roof of the 3⁻¹01 working face can be directionally cut through artificial intervention. This approach optimizes the stress environment of GER, shortens the cantilever length of the main roof above the RBB, and promotes fracture of the main roof outside the RBB (toward the gob side). As a result, the high stress carried by the coal–rock mass is significantly reduced, allowing the retained entry to operate within a low-stress environment.

According to Chen [44,45], conventional short-hole HF often results in insufficient fracturing depth and excessive roof fragmentation, which may adversely affect the movement of supports at the working face. Therefore, a high-level directional long horizontal borehole HF technique is adopted in the 3⁻¹01 working face of Huoluowan Coal Mine to achieve effective pressure relief.

5.2.1. Fracturing Parameter Design

(1) Determination of fracturing height

Artificial weak planes are created through HF to induce fracture of the main roof at predetermined locations. In this process, the design of an appropriate roof-cutting height is of critical importance. It is necessary to ensure that, after roof cutting, both the main roof and the immediate roof can collapse smoothly into the goaf, thereby forming a supporting structure for the overlying strata and accommodating the large-scale transferred abutment pressure generated during downward bending deformation.

The caving height of the roof is closely related to the bulking factor of the broken rock mass. Accordingly, the required caving height $h$ can be calculated using Equation (27).

$$h={\displaystyle \frac{M}{K_z-1}}$$

(27)

where M denotes the mining height, and $K_Z$ represents the residual bulking factor of the roof strata.

For the 3⁻¹01 working face, the mining height is 3.7 m. Considering the recovery ratio of the 3⁻¹ upper coal seam, the bulking factor is taken as 1.3. Based on the above equation, the required caving height to fully fill the goaf is calculated to be approximately 12.3 m.

When the drilling borehole is located in the lower part of the main roof, hydraulic fractures tend to concentrate within the lower roof strata, making it difficult to effectively cut through the main roof. As a result, the cantilever length of the main roof cannot be effectively reduced, and the lateral abutment pressure acting on the retained entry remains relatively high. When the borehole elevation exceeds the main roof, fracture propagation is more likely to be influenced by bedding planes, thereby weakening the effectiveness of roof cutting and pressure relief.

Considering that the combined thickness of the immediate roof and main roof in the 3⁻¹ upper coal seam is approximately 11.3 m, and the calculated caving height is 12.3 m, the main roof can theoretically collapse completely. By placing the borehole in the upper-middle portion of the main roof (approximately 9 m above the coal seam roof), the hydraulic fractures can be positioned near the key fracture plane of the main roof, thereby promoting directional failure along the pre-induced weak plane under periodic weighting of the mining face. This elevation not only ensures effective penetration of fractures through the main roof, but also avoids reduced fracturing efficiency caused by excessive borehole height.

(2) Determination of HF Borehole Spacing

The determination of borehole spacing depends on the effective fracture propagation radius of a single HF borehole, as shown in Equation (28). According to the Perkins–Kern–Nordgren (PKN) fracture propagation model, the fracture half-length $L_f$ is expressed as:

$$L_f={\left({\displaystyle \frac{Q\mu E}{\pi (1-{\nu }^2)\Delta P}}\right)}^{1/2}\cdot t^{1/2}$$

(28)

Substituting the mechanical parameters of the fine-grained sandstone in the working face (elastic modulus E = 8.49 GPa, Poisson’s ratio v = 0.21, designed pumping pressure $P_w$ = 30 MPa, minimum horizontal principal stress ${\sigma }_h$ = 4.5 MPa, net pressure $\Delta P=P_w-{\sigma }_h=25.5\hspace{0.17em}\mathrm{MPa}$, single-hole injection rate $Q=300\hspace{0.17em}\mathrm{L}/\min$, and fracturing duration t = 30 min), the effective fracture propagation radius of a single borehole is calculated to be approximately $L_f\approx 5.3\hspace{0.17em}\mathrm{m}$. Therefore, the borehole spacing should be less than $2L_f$, and a spacing of 10 m is selected for the directional long-distance HF zone.

5.2.2. Layout of HF Boreholes

HF operations should be arranged in advance of the working face to avoid interference with normal mining activities. Based on the above analysis, one long-distance horizontal fracturing borehole is designed within the fine-grained sandstone roof stratum at a height of approximately 9 m in the 3⁻¹01 working face, as illustrated in Figure 18. Considering that the strike length of the working face is 2600 m and the distance from the stopping line to the main roadway is 50 m, three drilling sites are arranged on the coal rib side of the tailgate at a location approximately 150 m ahead of the working face (which has currently advanced to about 300 m from the open-off cut). A total of six directional long-distance boreholes are constructed, designated as D1–D6. Each drilling site has a horizontal length of 400 m. Directional drilling rigs are employed at each drilling site to construct the HF boreholes. After fracturing, a “two-plug and one-injection” sealing technique is adopted to ensure effective sealing and fluid injection, thereby achieving efficient fracturing within the fine-grained sandstone roof above GER in the 3⁻¹01 working face.

Figure 18. Layout and configuration of HF boreholes: (a) plan view; (b) dip-direction section; (c) strike-direction section.

6. Field Application Performance

6.1. Roadway Displacement Monitoring

To comprehensively evaluate the field performance of the coordinated control technology combining anchor cable reinforcement support and directional long-distance HF pressure relief in the 3⁻¹01 tailgate, a fixed monitoring station was installed at a position 20 m ahead of the working face within the tailgate. A cross-layout monitoring method was adopted to systematically measure the convergence of the roof and floor, the deformation of the solid coal rib, and the lateral deformation of the RBB within the same roadway cross-section. As the working face advanced, when the monitoring station entered the goaf area behind the face, displacement sensors were embedded within the constructed RBB to achieve real-time monitoring of the full deformation process of the roadway section, covering a range from 20 m ahead of the working face to 120 m behind the goaf. The monitoring results are presented in Figure 19.

Figure 19. Deformation characteristics of surrounding rock in the 3⁻¹01 tailgate.

Results show that, after HF, the maximum displacements of the roof and floor, solid coal rib, and RBB side in the 3⁻¹01 tailgate are 558 mm, 233.5 mm, and 71.3 mm, respectively. The roadway convergence ratio is approximately 19.8%, indicating that the overall deformation is effectively controlled. Based on the relative distance between the advancing working face and the monitoring station, the deformation of the roadway can be divided into three distinct stages. Within the range of 20 m ahead to 20 m behind the working face, the deformation of the roof, floor, and both sides of GER increases significantly. At distances of 40–100 m behind the working face, the deformation rate gradually decreases. The convergence rates of the roof and floor, solid coal rib, and RBB side reduce to 3.39 mm/m, 1.7 mm/m, and 0.7 mm/m, respectively. When the working face has advanced more than 100 m beyond the monitoring station, the deformation tends to stabilize, and all displacement values remain within an acceptable range for GER.

6.2. Field Test Results

To verify the effectiveness of directional long-distance HF, borehole imaging was conducted in the main roof above the gob-side backfill of the 3⁻¹01 tailgate.

As presented in Figure 20a, a distinct fracture was observed at approximately 13.89 m, showing a continuous crack morphology consistent with the pre-designed weak zone. The fracture exhibits a preferential extension toward the gob side, indicating that HF promotes directional weakening of the main roof. Based on the in situ monitoring results shown in Figure 20b,c, the surrounding rock and backfill body exhibit coordinated deformation characteristics without evidence of large-scale uncontrolled collapse. The observed structural behavior is consistent with the expected roof weakening and controlled deformation pattern induced by HF. This indicates that, after adopting the coordinated control technology of anchor cable reinforcement support combined with directional long-distance HF for pressure relief in the 3⁻¹01 GER, no significant deformation occurs in the roadway, and the reuse efficiency of the entry can be effectively improved.

Figure 20. Field application results of GER: (a) Borehole inspection results; (b) RBB condition; (c) cross-sectional view of the 3⁻¹01 tailgate.

7. Discussion

7.1. Mechanism of Fracture Position Controlling GER Stability

The stability of GER is fundamentally governed by the evolution of the main roof load transfer path and its coupling degree with the roadway–backfill system, rather than the geometric position of the fracture alone. From the perspective of load-transfer behavior, the system can be classified into load-decoupled and load-coupled states (Figure 21).

Figure 21. Unified Mechanism of Load Transfer Path and Stability Evolution of GER under Four Main Roof Fracture Scenarios.

Under the load-decoupled condition (gob-side fracture), the overburden load is predominantly transferred into the goaf, resulting in limited perturbation to the retained roadway. Conversely, under load-coupled conditions (fractures occurring above the roadway or RBB), the overburden load is directly transmitted into the support system, inducing pronounced stress concentration, deformation localization, and accelerated structural degradation.

The solid coal-side fracture represents an intermediate transitional state, in which asymmetric load redistribution is induced by cantilever beam formation and rotational subsidence of key blocks above the roadway. Accordingly, GER stability is primarily controlled by the evolution of the load transfer pathway rather than the fracture location itself.

7.2. Reconciliation Between Theoretical Prediction and Field Observations

The theoretical analysis indicates that the natural fracture position of the main roof is located within the solid coal side at approximately 9.4–11.2 m. However, field observations reveal pronounced deformation and instability of the retained roadway, which appears inconsistent with a relatively less unfavorable fracture scenario.

This apparent inconsistency is resolved by considering the post-fracture structural evolution of the overlying strata. Following lateral fracture in the solid coal side, a cantilever beam structure forms above the retained roadway and undergoes rotation and subsidence toward the goaf. This process generates continuous asymmetric loading on the surrounding rock mass and RBB, thereby triggering progressive deformation responses, including coal rib extrusion, backfill inclination, roof subsidence, and floor heave.

Therefore, the field failure behavior is fully consistent with the theoretical prediction when the load-transfer mechanism and structural evolution of the post-fracture system are explicitly considered.

7.3. RBB Failure Mechanism and Displacement Field Coupling

Numerical results indicate that shear cracks dominate the failure process of the RBB, whereas tensile cracks play a secondary role. This observation is consistent with existing studies on high-water backfill and roof-cutting GER systems, which identify shear-controlled failure as the dominant instability mode under high-stress asymmetric loading conditions.

Furthermore, a strong correlation is observed between shear localization and displacement field concentration. Regions exhibiting high displacement gradients coincide with shear crack initiation and propagation zones, indicating a pronounced coupling between kinematic response and damage evolution.

This finding extends existing knowledge by explicitly clarifying the mechanical linkage between displacement field evolution and shear failure localization in GER systems.

8. Conclusions

(1) This study clarifies the influence mechanism of main roof fracture position on the stability of GER and establishes a quantitative framework for fracture position determination based on a statically indeterminate mechanical model combined with UDEC Trigon numerical simulations. The results indicate that the natural fracture position of the main roof in the 3⁻¹01 working face is located approximately 9.4–11.2 m inside the gob boundary. Different fracture locations lead to distinct structural responses of the surrounding rock system, among which gob-side fracture conditions are associated with relatively more favorable stability characteristics compared with roadway-side or RBB-side fracture scenarios.

(2) The deformation characteristics of the RBB and surrounding rock under different fracture positions are systematically analyzed. The RBB exhibits shear-dominated failure behavior, and the horizontal displacement shows a non-uniform distribution along height, characterized by mid-to-upper concentration. Under gob-side fracture conditions, the maximum RBB displacement is approximately 253 mm, while roadway-side fracture induces more pronounced deformation, with a maximum value of approximately 321 mm. The evolution of cracks and deformation indicates that fracture position significantly affects the redistribution path of mining-induced stress.

(3) A coordinated control approach combining anchor cable reinforcement and directional long-distance HF is proposed to regulate the main roof fracture position through artificial weak planes. Field monitoring and borehole observation confirm that the proposed method can effectively influence the fracture development behavior of the main roof and improve roadway stability. The maximum measured displacements of the roof, floor, and ribs are 558 mm, 233.5 mm, and 71.3 mm, respectively, with a convergence ratio of 19.8%, meeting the requirements for gob-side entry reuse under the studied conditions.

(4) The theoretical model is based on the Winkler elastic foundation assumption and masonry beam idealization, which simplifies the three-dimensional stress redistribution and dynamic fracture evolution of the overlying strata. In addition, the numerical and field results are mainly obtained under the geological conditions of the 3⁻¹01 working face. Future studies should further consider different roof lithologies, mining depths, support parameters, and hydraulic fracturing schemes, combined with long-term field monitoring, to improve the general applicability of the proposed stability control framework.