Breakage Patterns of High-Level Thick Weakly Cemented Overburden for Coal Safe and Sustainable Mining

Abstract

The breakage of massive thick weakly cemented rock layer is likely to cause strong mine earthquakes, which threatens the safe and sustainable production of the mine. In order to reveal the breakage law of high-level giant-thickness weakly cemented overburden rock and prevent the occurrence of mine earthquakes, we took the 2201 and 2202 working faces of Yingpanhao Coal Mine as the research object, established the mechanical calculation model of breakage of the high-level giant-thickness weakly cemented overburden, and used the methods of medium-thickness plate and short-beam function to solve the breakage law of high-level giant-thickness weakly cemented overburden rock. The findings indicate that during initial mining operations of high-level giant-thickness weakly cemented overburden rock, the applied force remains well below its bearing capacity. This condition ensures the stability of the overburden, effectively suppressing energy release events and minimizing surface subsidence. However, as mining progresses and approaches its operational limits, the overburden experiences both tensile and shear failures. This results in substantial increases in surface subsidence and the occurrence of frequent high-energy events. Finally, the model is verified against the surface-measured data and microseismic data of Yingpanhao Coal Mine, which proves the reliability of the model. The research results have important practical significance for mine earthquake prevention and safe and sustainable mining in similar geological conditions.

1. Introduction

Coal mining can cause surface subsidence [1,2,3], leading to the destruction of land resources and deterioration of the ecological environment [4,5]. The sedimentary environment and subsidence processes in western mining areas such as Inner Mongolia, Yulin, Shendong, and northern Shaanxi have unique characteristics. Most coal mines primarily extract Jurassic coal seams, with the overlying rocks commonly consisting of multiple layers of thick or massive quartz–feldspar sandstones of different grain sizes. The fundamental characteristics of these rocks include low strength, poor cementation, susceptibility to weathering, and the absence of significant faulting or undeveloped jointing [6,7,8,9,10]. Although the strength of this type of rock layer is not high, its substantial thickness and good integrity result in notable small anomalous characteristics of surface subsidence when the degree of mining is reduced. This phenomenon is primarily attributed to the controlling effect of the massive, thick, and weakly cemented rock layer. However, as the mining area expands, if this massive, thick, and weakly cemented rock layer fractures, it is highly likely to cause severe mine quakes and significant ground deformation. These events pose a serious threat to the safe and sustainable production of the coal mine. Therefore, it is imperative to elucidate the fracture mechanisms of the high-level, giant-thickness, weakly cemented overburden rock to provide technical support for safe and sustainable mining in the region.

Currently, both domestic and international scholars have undertaken extensive research on the fracture models and mechanics of massive thick rock layers, achieving substantial advancements through various theoretical analysis methods. These efforts have significantly contributed to the resolution of related geological and engineering challenges. Specifically, within the domain of beam theory, an initial fracture mechanics model for thick and hard rock layers has been developed based on long-beam theory. This model facilitates the calculation of the primary weighted characteristic and the ultimate fracture step distance, providing a robust framework for understanding the fracture behavior of these geological formations [11]. It was discovered that the mid-span moment in the rock layer exceeds the end moment, resulting in crack initiation in the middle before fracture occurs. A mechanical model of an elastic foundation beam was established to analyze the fracture of hard thick rock [12]. In the field of thin plate theory, based on the theory of thin plates, a mechanical model of the roof was established, the distributions of deflection, stress, and internal force were discussed, and the main factors affecting the stability of the roof were analyzed by FLAC3D numerical simulation [13]. Based on the theory of four-sided fixed thin plate, a mechanical model was established to analyze the failure law of overlying thick hard rock, and the reliability of the model was verified by numerical simulation and ground measurement data [14]. In the context of thick plate theory, addressing the challenge of uniformly describing the fracture modes of rock strata of varying thickness, a corresponding mechanical model was established based on the theory of medium and thick plates. This model was employed to analyze the fracture modes of rock strata of different thicknesses. Through numerical simulation, the mechanical mechanisms and fracture modes of these rock strata were elucidated [15]. Based on the theory of thick plates, considering the different boundary conditions that occur when a thick hard roof breaks, the spans of the first fracture and periodic fracture were analyzed and deduced. It was found that the accuracy was higher than that of the traditional beam theory [16]. These research achievements provide valuable insights for studying the fracture movement laws of high-thickness and massive weakly cemented overlying rocks.

To elucidate the fracture mechanism of high-level, thick, weakly cemented overburden, this paper examines the 2201 and 2202 working faces of Yingpanhao Coal Mine as the focal point of its research. It delves into and formulates a fracture mechanics calculation model tailored specifically for these high-level, thick, weakly cemented strata. Subsequently, the paper analyzes the mechanical conditions governing the fracture motion of sub-energy within these strata and identifies the primary failure modes. Furthermore, it sheds light on the fracture evolution process in the continuous mining process of the working face for high-level, thick, weakly cemented strata. The research is validated through the analysis of surface-measured data and microseismic monitoring data. Consequently, the findings of this study hold significant guiding value for the prevention and management of dynamic disasters, as well as for ensuring the safe and sustainable extraction of coal in similar geological settings.

2. Establishment and Fracture Analysis of the Mechanical Model for Thick Weakly Cemented Overburden Rocks

Currently, theoretical studies on the fracture of overlying rock layers predominantly employ beam theory or plate theory. Beam theory, which simplifies the roof strata as fixed-end beams, is usually applied to analyze the initial fracture of rock layers in a two-dimensional plane. However, practical scenarios often involve three-dimensional spatial problems. Considering the large thickness, good integrity, and significant distance from the stope of the thick and weakly cemented sandstone group, as well as the occurrence characteristics of the rock strata, it is more reliable to use plate theory for analysis.

2.1. Engineering Overview

The Yingpanhao Coal Mine is situated in Wushen Banner, Ordos City, nestled within the Inner Mongolia Autonomous Region. It stands prominently in the midst of the Mu Us Desert, perched on the expansive Ordos Plateau. The terrain is characterized by its relative flatness, adorned with beaches and dunes, spanning approximately 14.70 km from south to north and 8.10 km from east to west.

The mine’s surface is predominantly covered by modern aeolian sand and lacustrine sand, reflecting the diverse geological strata that range from ancient to recent formations. These include the Upper Triassic Yanchang Formation, the Middle and Lower Jurassic Yan’an Formation, the Middle Zhiluo Formation, the Anding Formation, the Lower Cretaceous Zhidan Group, and the Quaternary Upper Pleistocene Malan Formation. Additionally, there are residual slope deposits, Holocene alluvial deposits, swamp sediments, and aeolian sand, all contributing to the mine’s unique geological makeup. The fractured confined aquifer of the Upper Yan’an Formation is mainly composed of gray white fine-grained sandstone, with a thickness of 2.00–33.00 m and an average thickness of 16.90 m.

The mine’s primary focus is the extraction of coal from the 2-2 coal seams, which lie at an average burial depth of 720 m. These seams are nearly horizontal, boasting an average thickness of 6.67 m. The 2201 working face extends for 2502 m, with a tendency of 300 m, while the 2202 working face spans 2077 m, also with a tendency of 300 m. Notably, the 2201 and 2202 working faces are adjacent to each other, with mining operations on the 2201 face concluding in July 2019 and mining activities commencing on the 2202 face in August 2019. By June 2021, approximately 1317 m had been mined at the 2202 face, as depicted in Figure 1, highlighting the mine’s productivity and efficiency.

2.2. Establishment of Mechanical Model of Thick Weakly Cemented Overburden Rock

According to the actual geological data, the overlying thick rock layer of Yingpanhao Coal Mine is at a high position and the thickness reaches 300 m. Combined with the existing microseismic data and a literature analysis, the ratio of the thickness of the rock layer to its fracture span is greater than 1/5. Compared with elastic thin plates, it is more appropriate to establish the structural mechanics model of the thick rock layer by using the relevant theory of thick plates.

With the continuous expansion of the mining scope, the boundary conditions of the thick rock strata will also change post-fracture, as shown in Figure 2. There are four sides fixed, three sides fixed and one long side simply supported, three sides fixed and one short side simply supported, and adjacent fixed and adjacent simply supported [17].

Considering that different boundary conditions caused by rock fracture lead to an inconsistent mechanical analysis, the short-beam function solution of rectangular elastic medium-thick plate [18] is used to solve the problem. This method can ignore this issue, and the established basis function system can satisfy all the displacement boundary conditions of the medium-thick plate.

If x = a is a clamped boundary, then we have

$$\{\begin{array}{l}w=e{w}_x(a)w_y(y)=0\\ {\psi }_x=f{\phi }_x(a)w_y(y)=0\\ {\psi }_y=g{\phi }_y(y)w_x(a)=0\end{array}$$

(1)

where w is the deflection function of the plate, $w_x$ is the short-beam function along the X-axis direction, $w_x$ is the short-beam function along the Y-axis direction, ${\phi }_x$ is the corner in the X direction, ${\phi }_y$ is the corner in the Y direction, ${\psi }_x$ is the corner of the medium-thick plate in the X direction, ${\psi }_y$ is the corner of the medium-thick plate in the X direction, and $e$, $f$, $g$ are undetermined coefficients.

If x = a is a simply supported boundary, then we have

$$\{\begin{array}{l}w=e{w}_x(a)w_y(y)=0\\ {\psi }_y=g{\phi }_y(y)w_x(a)=0\\ M_x=-D(\frac{\partial {\psi }_x}{\partial x}+v\frac{\partial {\psi }_y}{\partial y})=0\end{array}$$

(2)

where $M_x$ represents the bending moment in the Y direction of the roof strata, $D=E{h}^3/[12(1-{\nu }^2)]$.

Hence, if there are no free boundaries, this equation can fulfill all the boundary conditions of the medium-thick plate.

Taking the high-position thick weakly cemented sandstone of Yingpanhao Coal Mine as the research object, the mechanical model is established as shown in Figure 3. In the model, the x-axis represents the direction of inclination of the working face, while the y-axis represents the advancement direction of the working face along the strike. The mid-plane of the rock layer serves as the reference plane, with the origin O situated at the intersection point of the three axes within the thick plate. Several parameters are defined: h represents the thickness of the weakly cemented sandstone, $a$ denotes the extent of inclined overhang during rock fracture, $b$ signifies the extent of strike overhang during rock fracture, and $q(x,y)$ represents the uniformly distributed load acting on the weakly cemented sandstone layer.

2.3. Fracture Mechanics Analysis of Thick Weakly Cemented Overburden Rock

Taking the high-thickness weakly cemented overburden rock of Yingpanhao Coal Mine as the research subject/object of study. Firstly, the short-beam function considering transverse shear stress is established, as shown in Equation (3):

$$\{\begin{array}{l}{\omega }_x=6ix(1-\frac{x}{a})+0.5a(\frac{x^2}{a^2}-\frac{2x^3}{a^3}+\frac{x^4}{a^4})\\ {\phi }_x=\frac{x}{a}-\frac{3x^2}{a^2}+\frac{2x^3}{a^3}\\ {\omega }_y=6jy(1-\frac{y}{b})+0.5b(\frac{y^2}{b^2}-\frac{2y^3}{b^3}+\frac{y^4}{b^4})\\ {\phi }_y=\frac{y}{b}-\frac{3y^2}{b^2}+\frac{2y^3}{b^3}\end{array}$$

(3)

In the equation, $a$, $b$, and $h$, respectively, represent the inclination overhang length, strike overhang length, and thickness of the rock layer. $i={\left(h/a\right)}^2/\left(5-5v\right)$ $j={(h/b)}^2/(5-5\nu )$.

The deflection function and rotation function of the medium-thick plate are as follows:

$$\{\begin{array}{l}\omega =e{\omega }_x{\omega }_y\\ {\psi }_x=f{\phi }_x{\omega }_y\\ {\psi }_y=g{\phi }_y{\omega }_x\end{array}$$

(4)

By applying the minimum potential energy principle to the functional form of the medium-thick plate, Equations (3) and (4) are substituted into Equation (5).

$$\{\begin{array}{l}II={\displaystyle {\iint }_{\mathsf{\Omega }}(U_M+U_Q-q\omega )d\mathsf{\Omega }}\\ U_M=\frac{1}{2}D\left[\frac{\partial {{\psi }_X}^2}{\partial x}+\frac{\partial {{\psi }_y}^2}{\partial y}+2v\frac{\partial {\psi }_x}{\partial x}\frac{\partial {\psi }_y}{\partial y}+\frac{1}{2}(1-v){(\frac{\partial {\psi }_x}{\partial x}+\frac{\partial {\psi }_y}{\partial y})}^2\right]\\ U_Q=\frac{1}{2}C\left[{(\frac{\partial \omega }{\partial x}-{\psi }_x)}^2+{(\frac{\partial \omega }{\partial y}-{\psi }_y)}^2\right]\end{array}$$

(5)

In the equations, $II$ represents the total potential energy, $U_M$ represents the strain energy, $U_Q$ represents the work done by shear forces, and $C$ represents the shear stiffness, $C=5Eh/[12(1+\nu )]$.

By taking the partial derivative of $II$, we obtain

$$\{\begin{array}{l}\frac{\partial II}{\partial e}=0\\ \frac{\partial II}{\partial f}=0\\ \frac{\partial II}{\partial g}=0\end{array}$$

(6)

By solving Formula (6), the values of the undetermined coefficients can be determined. Substituting the determined coefficients e, f, g, into Equation (4) provides the deflection approximate function and the rotation angle approximate function of the roof strata. This enables us to derive the internal force equation of the roof strata:

$$\{\begin{array}{l}{M}_x=-D(\frac{\partial {\psi }_x}{\partial x}+v\frac{\partial {\psi }_y}{\partial y})\\ M_y=-D(\frac{\partial {\psi }_y}{\partial y}+v\frac{\partial {\psi }_x}{\partial x})\\ Q_x=C(\frac{\partial \omega }{\partial x}-{\psi }_x)\\ Q_y=C(\frac{\partial \omega }{\partial y}-{\psi }_y)\\ M_{xy}=-\frac{1}{2}D(1-v)(\frac{\partial {\psi }_x}{\partial y}+\frac{\partial {\psi }_y}{\partial x})\end{array}$$

(7)

In the equations, $Q_x$ represents the shear force in the Y direction of the roof strata, $Q_y$ represents the shear force in the X direction of the roof strata, $M_y$ represents the bending moment in the X direction of the roof strata, and $M_{xy}$ represents the torsional moment of the roof strata.

The stress exerted on the roof strata is

$$\{\begin{array}{l}{\sigma }_x=\frac{12M_x}{h^3}z\\ {\sigma }_y=\frac{12M_y}{h^3}z\\ {\sigma }_z=-2q{(\frac{1}{2}-\frac{z}{h})}^2(1+\frac{z}{h})\end{array}\{\begin{array}{l}{\tau }_{xz}=\frac{3Q_x}{2h}\left[1-{(\frac{z}{h/2})}^2\right]\\ {\tau }_{yz}=\frac{3Q_y}{2h}\left[1-{(\frac{z}{h/2})}^2\right]\\ {\tau }_{xy}=\frac{12z}{h^3}{M}_{xy}\end{array}$$

(8)

In the equations, ${\sigma }_x$ represents the tensile stress along the short edge, ${\sigma }_y$ represents the tensile stress along the long edge, ${\sigma }_z$ represents the tensile stress in the vertical direction, ${\tau }_{xz}$ represents the vertical shear stress along the short edge, ${\tau }_{yz}$ represents the vertical shear stress along the long edge, and ${\tau }_{xy}$ represents the transverse shear stress.

Due to the significant distance between the thick, weakly cemented rock layer and the coal seam in engineering scenarios, there is a difference in the size of the rock fracture overhang compared to the dimensions of the goaf. It is essential to consider the impact of the rock fracture angle. The relationship between the dimensions of the rock fractures and the spatial dimensions of the goaf is as follows:

$$\{\begin{array}{l}A=a+\frac{2H}{\tan \alpha }\\ B=b+\frac{2H}{\tan \alpha }\end{array}$$

(9)

In the equations, A represents the length of the goaf in the inclination direction, B represents the length of the goaf in the strike direction, H represents the distance between the coal seam and the chalk rock layer, $\alpha$ represents the rock fracture angle.

Based on the theoretical formulas mentioned above, let us analyze the thick, weakly cemented overlying strata with a thickness of 300 m in the Yingpanhao Coal Mine. According to relevant geological data and the literature, we assume the tensile strength of the rock layer is 1.35 MPa, the Poisson’s ratio is 0.383, and the elastic modulus is 12.2 GPa. We substitute these mechanical parameters into Formula (8) for calculations to determine the stress conditions of the rock layer under different advancing distances. Consider that during single-panel mining, the panel width is 300 m. Based on [19], the height of overlying strata failure is approximately half the length of the short edge, which is about 150 m without affecting the thick weakly cemented overlying strata. Moreover, according to surface monitoring data, when panel 2201 completed its mining, the surface subsidence was only 326 mm. Therefore, the stability of the rock layer remains good. According to the above theoretical formula, when the width of the working face is 300 m (i.e., when a single working face is mined), the maximum tensile stress of the rock stratum is approximately 2300 Pa, which is well below its tensile strength. At this point, the structure of the rock stratum is stable and will not fracture.

When the 2202 working face begins advancing, the adjacent 2201 working face has already been mined. At this stage, the width of the goaf can be considered as 600 m. According to formula (9), the hanging length of the rock stratum is calculated to be 310 m. Stress curves of rock strata with different exposed lengths are plotted based on the rock stratum stress, as shown in Figure 4. From Figure 4, it is evident that as the 2202 working face advances, the stress in the rock strata within a specific range follows the order: strike-edge shear stress > dip-edge tensile stress > middle tensile stress > strike-edge tensile stress.

3. Fracture Evolution Law of Extremely Thick Weakly Cemented Overburden Rock

Different failure modes may occur in large-thickness rock strata under stress [20]. Cracking occurs along the fracture surface, shear failure manifests along a specific layer within the rock stratum, and the rock stratum in the negative bending moment zone of the load undergoes separation. According to the mechanical judgment of different failure modes, the failure mode of extremely weak cemented overburden rock is further analyzed.

(1)

Shear failure at a certain level

According to Formula (8), the shear stress on the rock stratum is greatest at the midpoint of the rock stratum. Ignoring the weak surface or weak interlayer of the rock stratum, if the rock stratum reaches its shear strength, shear failure will occur at the middle level, according to the shear failure criterion:

$${\tau }_{\theta }=\tan \phi {\sigma }_{\theta }+c$$

(10)

(2)

Compression shear damage

According to the Mohr–Coulomb strength criterion, it is known that the angle between the direction of the rupture surface of the rock formation and the direction of the maximum principal stress is $\theta ={45}^{°}-\frac{\beta }{2}$, where $\beta$ is the friction angle, then the stress on the failure surface is

$$\{\begin{array}{l}{\sigma }_{\theta }=\frac{1-\sin \beta }{2}({\sigma }_x)\\ {\tau }_{\theta }=\frac{\cos \theta }{2}({\sigma }_x)\end{array}$$

(11)

Combined with the shear failure criterion, the relationship between the shear stress of the rock layer on the failure surface and the length of the suspension is drawn into a curve, as shown in Figure 5. It can be observed from the figure that the weakly cemented overburden does not experience compression-shear failure within a specific range.

(3)

Tensile failure

According to Formula (8), the tensile stress in the rock layer typically peaks near the ends of the upper and lower surfaces, particularly at the midpoint. Therefore, if the rock layer reaches its tensile strength, it may undergo fracturing and form an articulated structure. For an exposed length of 220 m, the inclined side of the rock layer will experience tensile failure; at 300 m exposed length, the middle of the rock layer will be susceptible to tensile failure; and with an exposed length of 680 m, the edge of the rock layer will be prone to tensile failure.

Statistics of the overhanging distance when the stress on the rock layer reaches strength and the advancement distance of the working face calculated according to Formula (9) are shown in

Table 1. The relationship between failure mode and location of weakly consolidated sandstone and its overhanging length and advancing distance of working face.

Destruction Mode	Destruction Location	Overhang Length/m	Pushing Distance/m
Tensile failure	Hypotenuse	220	510
	Central section	300	590
	Move towards the edge	680	970
Shear failure	Move towards the edge	360	650

.

In summary, by applying mechanical analysis of various failure modes and combining it with theoretical stress calculations of the thick and weakly cemented overburden in the second section, possible failure modes are further examined. According to the data in Table 1, as the working face advances, the extremely thick weakly cemented overburden initially experiences tensile failure at the inclined edge and in the middle. Subsequently, shear failure occurs at the strike edge of the middle layer of the rock stratum, followed by tensile failure at the strike edge.

The stress surface diagrams on different surfaces of the giant thick weakly cemented rock layer are shown in Figure 6 (the yellow plane in the figure represents the ultimate tensile strength of the rock layer). It can be seen that at the advancing distance of 510 m, the stress value at the midpoint of the upper surface edge of the inclination is 1.37 MPa, where it reaches its tensile strength and produces cracks. After that, the stress in the middle of the lower surface of the rock layer reaches the tensile strength, and expands to the surrounding with the advancement, forming X-shaped damage. When the working face advances to 650 m, the shear stress on the middle surface of the rock layer reaches 4.78 MPa, surpassing its shear strength, resulting in damage at the midpoint of the strike edge. As the working face further advances, the tensile stress at the midpoint of the upper surface edge of the rock layer reaches its limit, leading to failure.

Through the analysis of the stress surface diagramd of the rock stratum advancing with the working face, the evolution of the failure mode of the extremely thick and weakly cemented rock stratum can be obtained, as shown in Figure 7. As the 2202 working face advances, the extremely thick weakly cemented rock stratum gradually deteriorates. At distances of 510 m and 590 m into the advance, the rock stratum reaches its tensile strength limit on the upper surface and in the middle of the lower surface, respectively, leading to damage. Then, when the working face advances to 650 m, the rock stratum undergoes shear failure at the edge of the strike direction of the middle surface. Finally, when the working face is advanced to 970 m, the rock layer is damaged at the edge of the surface in its strike direction. Under the combined action of tensile and shear stresses, the rock stratum undergoes progressive damage across various levels, eventually leading to collapse. Since the rock layer experiences tensile failure first at its inclined edge and middle, it is predominantly characterized by tensile fracturing.

4. Validation of Surface-Measured Data and Microseismic Data from Key Workings for Breakage of Thick Weakly Cemented Overburden Rocks

The correctness of the above theoretical analysis is verified by collating and analyzing the existing surface-measured data. Three surface rock movement observation lines (B, C, E measurement lines) arranged above the 2201 and 2202 working faces, and the specific monitoring point arrangement, are shown in Figure 8.

The first observation uses the existing E-level GPS control points in the mining area, with the instrument used being HITARGET V96 (Guangzhou, China). The plane coordinate first-level wire (the mean square error of distance measurement on each side does not exceed 15 mm, and the mean square error of angle measurement does not exceed 5″), and then, uses the polar coordinate measurement method to measure the coordinates of the remaining points based on the first-level wire. The elevation adopts the third-order leveling; the total mean square error of the height difference per kilometer does not exceed 6 mm. In daily observation, the elevation is measured by the fourth-order leveling method. The total mean square error of the height difference per kilometer does not exceed 10 mm. The observation data are mainly divided into two parts. The first part is until the end of 2019, when the 2201 working face and the 2101 working face are completed, and the 2202 working face adjacent to the 2201 working face is advanced by about 300 m. The second part is from 2020 to mid-2022, during which the 2202 working face is gradually advanced. The specific times and advance distances are shown in

Table 2. Surface observation times and advance distances of 2202 working face.

Observation Period	Observation Year	Observation Date	Pushing Distance/m
1	2020	6 January
2	2020	6 March	567
3	2020	10 April
4	2020	18 May	917
5	2020	17 June
6	2020	22 July	1008
7	2020	28 August
8	2020	30 November	1073
9	2021	8 March	1318
10	2021	8 August	1318
11	2022	15 May	1931

.

The surface mobile observatory at Yingpan Trench Coal Mine commenced full observation on 8 May 2017. By 3 January 2019, a total of 22 observations had been conducted, primarily focused on monitoring the surface deformation of the first mining face of 2201. The most recent observation occurred on 15 May 2022. The initial observation took place on 6 January 2020, following the completion of mining on the 2201 working face. Subsidence curves for the following observation lines were obtained through the processing of observation results, although those for observation line B2 could not be plotted due to significant missing data.

At present, we have measured data, as shown in Figure 8, from observation lines C, E, and B, the strike observation line of 2201 face, the strike observation line of the 2201 and 2202 faces of the mining area, and its two tendency observation lines, respectively. According to the existing surface movement observation data, the surface subsidence curve is plotted, and the maximum subsidence value of each observation line in each period is recorded, as shown in Figure 9 and

Table 3. Maximum sinking value of each phase of different observation lines.

Observation Period	Maximum Subsidence of Observation Line C/mm	Maximum Subsidence of Observation Line E/mm	Maximum Subsidence of Observation Line B1/mm
1	510	27	10
2	822	502	61
3		663	208
4	960	733	442
5	1006	793	674
6	1039	824	792
7	1063	837	818
8	1091	857	932
9	1120	949	1017
10	1148	970	1230
11			1343

.

The 2201 working face was completed in mid-2019, and mining activities on the 2202 working face continued from 2019 to 2022. Therefore, the data reflect a series of surface subsidence events resulting from the mining of the 2202 working face. As of the tenth observation, by analyzing the surface subsidence curve, the subsidence curve of the 2201 working face is shown in Figure 9a, and the point number is C09~C53. The distribution direction is from east to west, aligning with the direction of advancement. From the diagram, it is evident that the subsidence of the 2201 working face follows the pattern expected during full mining. The subsidence basin appears along the strike direction, and its subsidence stabilizes temporarily at approximately 1 m. With the advancement of the 2202 working face, the scope of the subsidence basin also expands. The maximum surface subsidence point is C46, the subsidence value is 1148 mm, and the surface subsidence coefficient is about 0.191.

The strike subsidence curve of the two working faces, represented by observation line E, is depicted in Figure 9b. The points are labeled E1 to E35, and the distribution direction is from west to east. Initially, during the early stages of mining the 2202 working face, points E1 to E20 show minimal surface subsidence because they are distant from the goaf. It was only after the 2202 working face advanced beyond 1300 m that significant subsidence became noticeable. The maximum subsidence point on the surface was observed at E27, with a subsidence value of 970 mm and a surface subsidence coefficient of approximately 0.162.

The tendency observation line B1 is shown in Figure 9c, point number B1~B58, distribution direction from north to south. From the figure, it can be seen that the bottom of the subsidence curves of each period in the tendency direction is a gentle curve, which has not reached the full mining, and the shape of the surface moving basin is in the shape of a “V”. The maximum subsidence value is 1230 mm, located near B37, and the surface subsidence coefficient is about 0.205. In a word, the surface subsidence coefficient in the direction of strike and tendency is small, and with the advance of the working face and the expansion in the mining area, it may lead to the continuous bending and subsidence of the rock layer.

In order to better analyze the movement of overburden rock through surface subsidence data, the surface subsidence rate in the process of working face advancing is calculated. The calculation formula is as follows:

$$v_m=\frac{W_{m+1}-W_m}{t}$$

(12)

where $W_{m+1}$ is the subsidence of the observation station measured for the m + 1th time; $W_m$ is the subsidence of observation station n measured for the mth time; and $t$ is the number of days between two observations.

The surface subsidence rate curves for each observation line were computed using the formula described earlier and are displayed in Figure 10.

The maximum surface subsidence rate of observation line C is approximately 10.62 mm/day. Initially observed in front of the working face during the second observation, the maximum subsidence rate point subsequently shifted towards the direction of the open-off cut. It is speculated that the reason for this phenomenon is that during the mining of the 2201 working face, according to the microseismic data in the literature [21], the overlying thick weakly cemented sandstone has been damaged to a certain extent. Therefore, the disturbance and subsidence observed during the mining of the 2202 working face, followed by a shift towards the direction of the open-off cut, can be attributed to the formation of a large-scale goaf resulting from the mining activities of both the 2201 and 2202 working faces during the advancement process. The maximum surface subsidence rate of observation line E is about 9.76 mm/d, which appears in the third observation. It is speculated that due to the expansion of the mining scope, the subsidence rate caused by the destruction of the overlying thick weakly cemented sandstone becomes larger. The position of the observation line B1 is a certain distance from the open-off cut, so the surface subsidence velocity reaches a maximum of about 8.07 mm/d at the fourth observation. Compared with the surface subsidence data of the 2201 working face mining, the mining of the 2202 working face makes the surface subsidence rate increase significantly, and the maximum subsidence rate increases from 1.4 mm/d to 10.62 mm/d.

In summary, combining the theoretical results analyzed in the previous section with the microseismic data in the literature [22], it can be obtained that:

(1) When the 2202 working face advances to 567 m, it marks the peak surface subsidence rate observed during the monitoring period. At this point, the surface subsidence values for observation line C and observation line E have increased by 312 mm and 475 mm, respectively, compared to the previous period. As the working face progresses from 551 m to 682 m, there are frequent occurrences of large-energy events. This is close to the the theoretically calculated workface advance distances of 510 m, 590 m, and 650 m for the rock strata reported in Table 1, with tensile failure at the inclined side and the middle, and shear failure at the middle of the strike side.

(2) When the 2202 working face advanced from 1008 m to 1073 m, the surface subsidence increased by 52 mm for observation line C, 33 mm for observation line E, and 140 mm for observation line B1. During the mining process from 879 m to 1049 m, frequent large-energy events occurred, exceeding 106 J multiple times. This is closely aligned with the theoretical calculation results indicating tensile failure of the rock layer at the strike edge for a mining distance of 970 m, as shown in Table 1.

5. Conclusions

(1) Based on the thick plate theory, a mechanical model of super-thick weakly cemented overburden rock breaking is established. The short-beam function solution of rectangular elastic medium-thick plate is used to calculate the stress of the rock stratum in the process of advancing.

(2) The main damage mode of high-level thick and weakly cemented overburden is tensile failure, and it is calculated that when the working face of 2202 advances to 510 m and 590 m, the rock layer will be damaged in shear at the edge of its strike direction; when the working face advances to 970 m, the rock layer will be damaged in tension at the edge of the upper surface of its strike direction. When the mining area reaches the limit, it will result in the occurrence of tensile and shear damage of the thick and weakly cemented overburden rock, which will lead to the obvious increase of surface subsidence and the frequent occurrence of high-energy events.

(3) Compared with a single working face, the amount and rate of surface subsidence in the mining process of the two working faces increased significantly, and the maximum subsidence rate increased from 1.4 mm/d to 10.62 mm/d. The measured data are consistent with the analysis results of the theoretical model, which verifies the correctness of the established high-level thick weakly cemented overburden fracture model and provides a theoretical basis for the safe and sustainable mining of regional coal mines.