Fracture Characteristics and ZoningModel of Overburden during Longwall Mining

+e fracture characteristics and zoning model of overburden during longwall mining are the basis of coal mine disaster prevention. However, the existing theoretical model is inconsistent with the field measurement. In order to further research into the strata’s fracture characteristics and optimize the overburden’s zoning model, we used the elasticity and Winkler foundation theory to establish first fracture and periodic fracture mechanics models of clamped boundary supported by an elastic foundation with a key stratum as the research object. We analyzed the stress distribution characteristics and fracture evolution pattern of the mining-induced key stratum. We analyzed the zoning characteristics of mining-induced overburden and established the zoning model according to different fracture mechanisms. +e results show that the key stratum formed a double “O-X” shaped interconnected fracture zone after the first fracture. +e key stratum formed a double “C-K” shaped interconnected fracture zone after the periodic fracture. We divided the mining-induced overburden into three zones along the horizontal direction: the original rock zone, the inverted triangular compression-shear fracture zone, and the trapezoidal tensile fracture zone. +e study revealed the mechanism of inverted step fracture in the separation zone, explained the fracture mechanism of the coal pillar support zone, and has significant theoretical value for the prevention and control of water disasters, gas outbursts, and strata movement.


Introduction
e deformation and fracture process of mining-induced overburden is the main reason for coal mine production accidents [1][2][3][4]. erefore, it is necessary to conduct indepth research on the fracture characteristics and zoning model of mining-induced overburden. Currently, strata mechanical models are widely using the plate theory and beam theory. Zuo et al. simplified the roof strata into the fixed beam and cantilever beam with uniform load. e principal tensile stress contour revealed the first oblique tensile fracture mechanism on both sides of the fixed beam's lower edge and the periodic oblique tensile fracture mechanism of the upper edge of the cantilever beam's fixed end [5]. He et al. established the mechanical model of elastic foundation beam, calculated the ultimate fracture distance of the main roof, and revealed the fracture characteristics of the advanced coal wall of the main roof [6]. Qian et al. regarded the main roof as a fixed elastic thin plate and revealed the "O-X" fracture characteristics according to the bending moment distribution of the main roof [7]. Based on plastic mechanics, Jiang et al. judged that the plastic yield line of roof strata presented "O-X" structure characteristics according to energy dissipation [8]. Elastic foundation beam theory can only analyze the fracture characteristics of the roof section. It cannot analyze the roof's overall structure. e mechanical models of a thin elastic plate with fixed and simple support ignore the influence of elastic support of coal seam (rock strata) on the roof [9]. e vertical coal seam direction is widely recognized in the three-zone theory based on the continuity of mining-induced overburden, as shown in Figure 1. In parallel coal seam direction, the three-zone theory divided according to the carrying characteristics of overburden is shown in Figure 2. Zuo et al. established an analogous hyperbola subsidence model (AHSM) according to the fracture boundary of overburden in the three-zone theory. It is considered that the strata movement boundary is two inner concave curves, which are symmetrical along the center of goaf [10][11][12]. Xu et al. established a trapezoidal caving model of strata movement induced by coal mining according to the inverted step fracture form of overburden in the three-zone theory [13]. Guo et al. established a new method of predicting the fractured water-ducting zone (FWCZ) height due to longwall coal mining according to the trapezoidal fracture zone in the three-zone theory [14].
However, the above-mentioned overburden's zoning model is inconsistent with the measured results. e measured results show that the fracture area of mininginduced overburden is larger than the exploitation area [16][17][18]. Chen et al. carried out microseismic monitoring on the coal mining panel. e microseismic activity caused by longwall mining was mainly distributed in the coal pillar support zone and separation zone. e peak value of the microseismic events near the panel is located in front of the coal wall, consistent with the peak value of the front abutment pressure. In the depth direction, the microseismic activity is mainly distributed in the lower part of the continuous deformation zone [19]. Yu et al. arranged detection boreholes in front of the longwall panel. e digital panoramic imaging (DPI) technique was used to observe the internal fracture at different relative positions between the borehole and the longwall panel, which confirmed an advanced fracture in the roof strata [20]. Shi et al. carried out microseism and stress monitoring in deep mining. e strata movement range in deep mining was expanded. e influence distance in front of the longwall panel was far more than the influence distance in shallow mining [21]. Palchik measured the amount of natural gas emission in overburden during longwall coal excavation by drilling. He studied the distribution of mining-induced fractures based on the change in natural gas emissions. When the longwall panel did not exceed the drilling, the roof produced interconnected fractures, resulting in the emission of natural gas [22]. Hosseini et al. used the double-difference passive seismic velocity tomography to evaluate stress changes around the longwall mining panel. ey found that the increase of front abutment pressure and side abutment pressure led to the expansion of fracture [23]. Cheng et al. used the microseismic monitoring technique to investigate the distribution law of strata movement released by coal mining. It was revealed that shear fracture mainly occurs in pillar support zone and tensile fracture mainly occurs in separation zone [24]. e deformation and fracture process of mining-induced overburden is the main factor of surface subsidence, roadway instability, mine water, coal and gas outburst (CGO), and rockburst [2][3][4]. erefore, it is necessary to clarify the mechanism of overburden fracture and the fracture characteristics of different regions and provide a theoretical basis for the prevention and control of mine disasters. We established the overall mechanical model of mining-induced strata supported by the elastic foundation with the Winkler foundation. We analyzed the characteristics and dynamic evolution law of stress field and fracture field of mining-induced strata. According to the different fracture mechanisms of roof strata in different zones, we analyzed the zoning characteristics of mining-induced overburden and established a mining-induced overburden zoning model.

Mechanical Model of KS First Fracture.
e physical and mechanical parameters of sedimentary rock are not uniform in the vertical direction. If there are hard and thick strata in the overburden, they control the deformation and fracture of the overburden, which are called the key strata [25]. e key strata (KS) theory has been widely accepted and used in academia and industry [26,27]. e key strata move synchronously with the strata they control. According to the control range of the key strata, they can be divided into the primary key stratum (PKS) and the inferior key stratum (IKS) [25]. According to the key strata theory, the strata movement is grouped from bottom to top. e boundary between two zones is usually the key stratum [28]. Studying the fracture characteristics of the key strata can clarify the fracture characteristics of the overburden [29]. If the overburden is weak strata, there are no key strata, which is not in the scope of this article. e immediate roof fractures first due to the lower strength during longwall mining. e KS is in a state of suspension due to the loss of support. e boundary condition of KS is elastic clamped because the KS is tied by relatively weak rock strata [9,25,30]. e KS fracture's size generally meets the basic assumption of elasticity [31]. e first fracture thin plate mechanical model of KS is shown in Figure 3. e x-axis is the direction of the longwall panel, and the y-axis is the direction of excavation. e A 1 B 1 C 1 D 1 area is in a suspended state called an unsupported zone below the goaf.
e ABCD area is clamped by the relatively weak rock strata called the elastic foundation-supported zone [9].
ere is a fixed boundary far from the elastic foundation-supported zone. e section figure of the KS structure indicates its stress state. e load of the unsupported zone is q 1 , which is the sum of self-weight and controlled weak rock strata load. e elastic foundation-supported zone load is q 2 , which is the sum of the transfer load of the unsupported zone and the field stress [30]. e basic differential equations of unsupported zone and elastic foundation-supported zone are as follows [31]: 2 Shock and Vibration where w 1 and w 2 are the deflection function of unsupported zone and elastic foundation-supported zone and D is the flexural rigidity of KS, GPa·m 3 .
In order to characterize the movement and deformation of elastic foundation, introducing the Winkler foundation model, the foundation modulus k is as follows [6,30]: where k c and k i are the elastic coefficients of coal seam and other strata, GPa/m. e load q 1 of the unsupported zone is as follows [25]:

Shock and Vibration
where δ 1 , δ 2 , . . ., δ n are the thickness of the KS and controlled rock strata, m; c 1 , c 2 , . . ., c n are the volume force of the KS and controlled rock strata, MN/m 3 ; and E 1 , E 2 , . . ., E n are the elastic modulus of the KS and controlled rock strata, GPa. e transfer load of the elastic foundation support area can be obtained by inversion of its subsidence value [30]. e load q 2 of elastic foundation-supported zone is as follows: where w is the subsidence value of the elastic foundation, m; c is the average volume force of overburden, MN/m 3 ; and H d is the depth of KS, m. e differential equations of the fixed boundary conditions are as follows [30]:

Mechanical Model of KS Periodic
Fracture. When the KS first fractures, with the excavation of the longwall panel, the KS will fracture periodically; the mechanical model is shown in Figure 4. e C 1 D 1 of the unsupported zone and the D 1 D 2 and C 1 C 2 of goaf are free boundaries. Other boundaries of the unsupported zone are clamped boundary conditions. e load of the unsupported zone is q 1 , which is the sum of self-weight and controlled weak rock strata load. e elastic foundation-supported zone load is q 2 , which is the sum of the transfer load of the unsupported zone and the field stress. e differential equations of the free boundary conditions are as follows:

Differential Equation Solution Method: Finite Difference
Method. It is challenging to acquire the unified functional expression because the basic differential equations of the unsupported zone and the elastic foundation-supported zone are different. e finite difference method uses difference equations to express the differential equations [9,30,31]. Finite difference grid is shown in Figure 5; the intersection of the grid is called the node with equal spacing h. Using MATLAB software to solve the difference equations can get the deflection value of each node [30][31][32]. e solving process is shown in Figure 6. e stress value of each node is calculated according to the deflection value. e principal stress calculation equation of xy plane is as follows [33]: where σ 1 is the major principal stress (MPa) and σ 3 is the minor principal stress (MPa). e principal stress equations for the xz plane and yz plane are the same as equation (7) and are no longer listed.  Figure 7. e stress range of KS is larger than the mining area. e middle of the unsupported zone is subjected to compressive stress. e area around the elastic foundationsupported zone is subjected to tensile stress. e maximum tensile stress is close to the junction of two zones and is located above the coal seam (rock strata) around the goaf, called advanced tensile stress. e stress direction of the advanced tensile stress distributed along the x-axis is perpendicular to the x-axis. e stress direction of the advanced tensile stress distributed along the y-axis is perpendicular to the y-axis, as shown in Figure 7. e major principal stress distribution at the lower surface of the xy plane of the KS first fracture model is shown in Figure 8. e middle of the unsupported zone is subjected to tensile stress. e area around the elastic foundationsupported zone is subjected to compressive stress. e maximum tensile stress is located in the middle of the lower surface of the unsupported zone, which is called the middle tensile stress. When the middle tensile stress contour is decreased to the periphery, it is deflected in the four corner regions.

Fracture Characteristics of KS and Overburden Zoning Model
e stress direction of the tensile stress in the middle of the lower surface of the unsupported area is parallel to the x-axis. e stress direction of the tensile stress near the coal wall deflects to the corner, as shown in Figure 8.
e KS first fracture model's major principal stress distribution on xz and yz sections is shown in Figures 9 and 10.

KS
Unsupported zone Winkler Foundation   Figure 9: Major principal stress on xz section of first fracture model. 6 Shock and Vibration

Stress Distribution of KS Periodic Fracture.
e major principal stress distribution at the upper surface of the xy plane of the KS periodic fracture model is shown in Figure 11. e stress range of KS is also larger than the mining area. e middle of the unsupported zone is subjected to compressive stress. e area around the elastic foundation-supported zone is subjected to tensile stress. e advanced tensile stress is close to the junction of two zones and is located in front of the longwall panel and two corners of the free boundary. e stress direction of the advanced tensile stress in front of the longwall panel is perpendicular to the x-axis and points to the goaf. e stress direction of the tensile stress in the two corners of the free boundary deflects to the inner side of the coal wall, as shown in Figure 11. e major principal stress distribution at the lower surface of the xy plane of the KS periodic fracture model is shown in Figure 12. e middle of the unsupported zone is subjected to tensile stress. e elastic foundation-supported zone in front of the longwall panel is subjected to compressive stress. e maximum tensile stress is located at the free boundary of the unsupported zone's lower surface and central symmetric distribution along the x-axis. e contour line of edge tensile stress deflects to the corner on both sides of the longwall panel.
e transition line of tensile and compressive stress near the coal wall deflects to the center, as shown in Figure 12.
e KS periodic fracture model's major principal stress distribution on xz and yz sections is shown in Figures 13 and  14. e elastic foundation-supported zone is subjected to tensile stress on the upper surface and compressive stress on the lower surface. e unsupported zone is subjected to compressive stress on the upper surface and tensile stress on the lower surface. e maximum tensile stress at the lower surface of the unsupported zone of the xz section is located on both sides of the x-axis center. e tensile-compressive stress transition line near the coal wall deflects to the center. e maximum tensile stress at the upper surface of the yz section is located in the elastic foundation-supported zone and gradually decreases to the unsupported zone. e tensile-compressive stress transition line near the coal wall deflects obliquely. erefore, the upper surface of the elastic foundationsupported zone and the unsupported zone is in the biaxial compressive-tensile state. e lower surface of the unsupported zone is in the uniaxial tensile state.

KS Fracture Characteristics.
According to the stress distribution law of KS and the Mohr-Coulomb strength criterion, the fracture positions of the KS are mainly concentrated in the upper surface of the elastic foundationsupported zone near the goaf boundary, the middle of the lower surface of the unsupported zone, and the lower zone of the unsupported zone near the coal wall. According to the Mohr-Coulomb strength criterion, when the normal stress is compressive, shear yield will occur in the KS. When the normal stress is tensile, tensile yield will occur in the KS [33]. As shown in Figures 15 and 16, the upper surface of the elastic foundation-supported zone near the coal wall is in the biaxial compressive-tensile stress state. e shear fracture is easy to occur. Since the end and center of the lower surface of the unsupported zone are in the uniaxial tensile state, the tensile fracture is easy to occur. In order to distinguish different forms of fracture, green is used to represent shear fracture, and blue is used to represent tensile fracture. e KS first fracture characteristics are shown in Figure 15. In section I-I, the shear slip line of the upper surface of the elastic foundation-supported zone extends obliquely below the coal wall. e tensile fracture line of the middle of the lower surface of the unsupported zone extends vertically upward. After the KS's fracture, the boundary conditions of KS change, and the stress will transfer, increasing the tensile stress near the coal wall in the unsupported zone. e tensile fracture line expands obliquely along the tensile-compressive transition line. e above fracture characteristics have been confirmed in two-dimensional numerical simulation and similar simulation or field measurement [27,[34][35][36][37][38]. In section II-II, the maximum tensile stress of the lower surface of the unsupported zone is symmetrically distributed along the centerline. With the bending and sinking of KS, the tensile fracture line extends obliquely upward.
According to the stress distribution law, we can distinguish the first fracture sequence of KS according to the stress distribution characteristics. e first fracture position of the KS is the upper surface of the elastic foundationsupported zone parallel to both sides of the longwall panel and the center of the lower surface of the unsupported zone. Shock and Vibration e crack expansion direction is parallel to the longwall panel. en, the elastic foundation-supported zone is parallel to the excavation direction fracture. e crack expansion direction is parallel to the excavation direction. When the fractures around the elastic foundation-supported zone are connected in the corner, an "O" shaped interconnected fracture will form. When the crack in the middle of the lower surface of the unsupported zone expands to the coal wall on both sides, the crack expansion direction deflects at the corner. It forms an "X" shaped fracture. In the end, the oblique tensile interconnected fracture occurs around the unsupported zone near the coal wall, forming an "O" shaped interconnected fracture. Finally, the KS forms a double "O-X" shaped interconnected fracture zone after the first fracture, as shown in Figure 15. e internal "O-X" shaped fracture characteristics have been confirmed in The thickness of key stratum (m) Figure 13: Major principal stress on xz section of periodic fracture model. three-dimensional simulation experiments [6,39,40]. However, the similarity ratio of the three-dimensional simulation is relatively large, and it is difficult to observe the tiny shear fractures of the rock strata above the coal pillar [34]. e KS periodic fracture characteristics are shown in Figure 16. In section I-I, the shear slip line of the upper surface of the elastic foundation-supported zone extends obliquely below the coal wall. After the KS's fracture, the boundary conditions of KS change, and the stress will transfer, increasing the tensile stress near the coal wall in the unsupported zone. e tensile fracture line expands obliquely along the tensile-compressive transition line. e above fracture characteristics have also been confirmed in two-dimensional numerical simulation and similar simulation or field measurement [27,[34][35][36][37][38]. e fracture characteristics in section II-II are the same as those in the KS first fracture. According to the stress distribution law, we can distinguish the periodic fracture sequence of KS according to the stress distribution characteristics. e first fracture position of the KS is the upper surface of the elastic foundation-supported zone in front of the longwall panel and the corner regions of the free boundary. e crack expansion direction of the elastic foundation-supported zone is parallel to the longwall panel.
e crack in the corner regions of the free boundary extends obliquely to the inside of the coal wall. It is connected with the crack in the elastic foundation-supported zone to form a "C" shaped interconnected fracture. en, the cracks in the two edges' tensile stress concentration area of the free boundary deflect to the two corner regions of the longwall panel,   Shock and Vibration forming a "K" shaped fracture. In the end, the oblique tensile interconnected fracture occurs around the unsupported zone near the coal wall, forming a "C" shaped interconnected fracture. Finally, the KS forms a double "C-K" shaped interconnected fracture zone after periodic fracture, as shown in Figure 16. e internal "C-K" shaped fracture characteristics have been confirmed in three-dimensional simulation experiments [6].

Zoning Model of Overburden.
According to the KS's fracture mechanism, the KS can be divided into three zones: compressive shear fracture zone, tensile fracture zone, and original rock zone. e shear fracture zone is distributed in the elastic foundation-supported zone near the goaf. Due to the clamping of the upper and lower strata, the large-scale movement generally does not occur, and the rock mass remains continuous. e tensile fracture zone is distributed in the unsupported zone. Due to the lack of effective support, large-scale movement will be formed in the process of strata movement, and the integrity of rock mass cannot be maintained. Both sides of the shear fracture zone are original rock zones.
Strata movement is the whole movement behavior from overburden to surface above goaf after coal mining. Taking three groups of KS in the overburden as an example, we analyzed the zoning characteristics of mining-induced overburden movement. After the lower IKS's fracture, the plastic displacement occurs in the compression-shear fracture zone. As the elastic foundation of the upper IKS, its supporting capacity is weakened. e elastic foundation thickness of the upper IKS increases, the foundation modulus decreases, and the supporting capacity decreases. As a result, the compressive shear fracture zone of the upper IKS increases, and the fracture range expands to the outside. e oblique tensile fracture near the coal wall of the lower IKS causes the support range of the upper IKS to increase and the tensile fracture range to decrease. e tensile fracture trace of the overburden shows an inverted step shape from bottom to top.
During longwall mining, the zoning characteristics of overburden above the goaf are shown in Figure 17. In the direction vertical to the goaf, according to the degree of overburden fracture, it is divided into three zones: caving zone, mining fracture zone, and continuous deformation zone. In the direction parallel to the goaf, the overburden is divided into three zones: original rock zone, compressive shear fracture zone, and tensile fracture zone. e strata movement boundary bounds the original rock zone and compressive shear fracture zone. e tensile fracture line of rock strata bounds the compressive shear fracture zone and tensile fracture zone. e compressive shear fracture zone is approximately inverted triangle distribution. e tensile fracture zone is approximately trapezoidal, with inclined interconnected fractures and horizontal cracks [22,41]. e rock strata in the fracture zone form a trapezoidal block fracture. A biting relationship exists between rock blocks, forming a "voussoir beam" balanced structure [15]. When the rock beam structure is unstable, the fracture zone will be transformed into the caving zone. When the coal seam is buried shallowly, the PKS's fracture will lead to surface step subsidence [42].

Conclusions
(1) Considering the elastic supporting effect of coal and rock mass, we established a KS's mining-induced mechanics model. Before the KS's first fracture, the upper surface of the elastic foundation-supported zone was in a compressive-tensile stress state. e middle of the lower surface of the unsupported zone was in a tensile stress state. Before the KS's periodic fracture, the upper surface of the elastic foundationsupported zone was in a compressive-tensile stress state. e free boundary of the KS's lower surface was in a tensile stress state. (2) According to the stress distribution of the KS, we obtained the KS's fracture shape. After the KS's first fracture, the elastic foundation-supported zone formed an "O" shaped interconnected shear fracture.  e unsupported zone formed an "O-X" shaped interconnected tensile fracture. After the KS's periodic fracture, the elastic foundation-supported zone formed a "C" shaped interconnected shear fracture. e unsupported zone formed a "C-K" shaped interconnected tensile fracture.
(3) According to the KS's fracture mechanism, we established an overburden zoning model. e overburden above goaf was divided into three zones along the horizontal direction: the original rock area, the compressive shear fracture zone, and the tensile fracture zone. e overburden's zoning model reveals the tensile fracture mechanism of the inverted step shape in the mining fracture zone and explains the shear fracture mechanism of the inverted triangle in the coal pillar supporting zone.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.