Research on the Characteristics and Patterns of Roof Movement in Large-Height Mining Extraction of Shallow Coal Seams

Abstract

This paper focuses on the issues of roof movement and ground pressure behavior in large-height mining extraction of shallow coal seams. By adopting a combined method of theoretical analysis and physical simulation experiments, it establishes a mechanical model for the rotational subsidence of key blocks and a physical simulation test model to conduct stability analysis on the rotational subsidence of key blocks, thereby revealing the characteristics and laws of roof movement. The findings indicate that the horizontal thrust during the rotational subsidence of key blocks increases non-linearly with the rotation angle, exhibiting a higher growth rate when the block size coefficient is less than 0.5. Two modes of instability—sliding and deformation—are observed for key blocks. To prevent sliding instability, the block size coefficient should be maintained below 0.75; however, sliding instability is likely to occur when the rotation angle exceeds 10°. Conversely, smaller rotation angles and larger block size coefficients reduce the likelihood of deformation instability. The reasonable working resistance of the support decreases with the increase in the rotation angle (it decreases sharply when the rotation angle exceeds 10°) and increases with the increase in the block size coefficient. Physical simulation indicates that roof movement is divided into three stages: immediate roof collapse, stratified fracturing and instability of the basic roof, and periodic fracturing of the basic roof. An increase in mining height accelerates the instability of the immediate roof, enlarges the opening of through-layer fissures, shortens the step distance of mining pressure, and heightens the risk of sudden pressure. The research results provide theoretical guidance for the safe and efficient mining with large mining height in shallow coal seams.

1. Introduction

In China, the extraction and utilization of coal resources are critical for supporting economic development and ensuring energy security [1]. According to the Norms for Classification of Hydrogeological Conditions of Coal Mines, all coal seams located below the local erosion base level and with a burial depth of less than 500 m are defined as shallow coal seams [2]. Statistics indicate that the majority of the recoverable coal resource reserves in the Shendong mining area are concentrated at depths of 100 to 150 m and consist of thick coal seams [3]. Research shows that shallow mining is significantly affected by factors such as shallow burial, thin bedrock, and thick loose layers. These factors may lead to intense roof movement and surface deformation, including large-scale fractures, step-like collapse pits, and extensive subsidence, resulting in both continuous and dis-continuous surface deformation characteristics [4,5]. Additionally, with the advancement of large-height mining technology and equipment, the recovery rate of thick coal seams has significantly increased. Large-height mining refers to coal extraction heights in working faces that reach between 4.5 and 7.5 m, achieved through the implementation of longwall mechanization techniques for the efficient extraction of thick coal seams [6]. To minimize resource waste and maximize recovery, attempts have been made to employ large-height mining techniques for the extraction of shallow thick coal seams [7]. However, understanding the characteristics and patterns of roof movement during mining operations—including roof fractures, step distance of mining pressure, and support resistance—is essential for evaluating the feasibility of safe large-height mining and preventing roof-related accidents, highlighting its significant research importance.

Significant research has been conducted on the issue of roof movement in shallow coal mining. Huang [3] defined shallow-buried coal seams by summarizing the characteristics of mining pressure manifestation in shallow extraction. Xu et al. [8] proposed a method for calculating the range of roof movement and surface subsidence based on key layer theory. He et al. [4] employed a combination of field measurements, physical similarity simulations, numerical calculations, and theoretical analyses to investigate the characteristics and patterns of mining pressure in shallow coal seam extraction, discovering that hydraulic fracturing can alter the roof structure of interbedded strata, effectively reducing dynamic pressure hazards in working faces. Zhang et al. [9] through engineering examples, studied the stress transmission and dynamic variation in shield loads during the extraction of shallow coal seams, determining the mechanisms of mining pressure generation and calculating maximum support resistance. Sun et al. [5] proposed a new method for constant-resistance support that enhances the stability of deep mining roadways by combining deep and shallow cutting techniques. Liang et al. [10] designed physical similarity simulation experiments to explore the distribution characteristics and influencing factors of roof fractures in shallow coal seam mining, concluding that the development of roof fractures is a primary cause of air leakage in mining areas. Han [11] systematically studied the stability of old mined-out areas under multi-coal seam extraction and proposed corresponding grouting filling technologies. Zhang et al. [12] utilized a combination of theoretical analysis, laboratory experiments, and field measurements to design tailings paste filling in shallow mining and analyze surface subsidence effects, establishing a subsidence model for filling in roadway extraction. These studies provide valuable guidance for enhancing the understanding of roof pressure patterns in shallow mining and for the prevention and control of mining pressure-related disasters.

To adapt to the application of large-height mining technology in underground coal mining, researchers have conducted studies on the multifield responses of surrounding rock and support structures under large-height mining conditions [13,14,15]. Based on an analysis of the current state of research on ultra-high extraction technology and equipment in China, Kang et al. [16] proposed key technologies and equipment specifically for the extraction of the 10 m-thick coal seams at the Caojiatan Coal Mine, addressing the geological conditions of ultra-high extraction. Xue et al. [6] employed a combination of theoretical analysis, physical experiments, numerical simulations, and statistical methods to conduct a quantitative sensitivity study on various factors affecting the coal wall instability during large-height mining through the design of orthogonal experiments. Li et al. [17] investigated three typical forms of the basic roof movement using the Dongliang Coal Mine as a case study, proposing corresponding critical failure conditions and revealing the interaction mechanisms between the roof strata and the coal above. Liu et al. [18] researched the mechanism of coal wall spalling at large-height mining working faces through theoretical analysis, numerical simulation, and field tests, developing a new type of grouting material and grouting reinforcement technology to enhance the stability of the coal wall. Zhang et al. [19,20] utilized numerical simulation methods to study the movement of the roof and the patterns of mining pressure during large-height mining, analyzing the influence of key layer positioning and support resistance, and suggested that in situ weakening of the key layer using hydraulic fracturing could mitigate the impacts of severe mining pressure on the working face. Li et al. [21] systematically studied six movement modes of the key layers in the roof during large-height mining, establishing support resistance calculation formulas for each mode through a combination of theoretical analysis, numerical simulations, and field observations. While large-height mining technology is a reliable method for improving resource recovery rates, its application in certain specific coal seam extractions or complex geological conditions remains to be further researched [22,23,24,25], such as in shallow coal seams, steeply inclined seams, and coal seams with complex geological structures [26,27,28].

To maximize the recovery of shallow coal resources, large-height mining technology has been progressively applied to the extraction of thick shallow coal seams. Practical experience has demonstrated that both shallow mining and large-height mining can induce significant manifestations of mining pressure. Although some research achievements have been made regarding the movement patterns of the roof in both shallow and large-height mining, there remains a lack of in-depth studies specifically addressing the roof movement characteristics, failure conditions, mining pressure manifestations, and appropriate support resistance under large-height conditions in shallow coal seams. To address this gap, this paper investigates the issues of roof movement and mining pressure manifestation in large-height mining of shallow coal seams. By establishing a mechanical model for the rotational subsidence of key blocks applicable to large-height mining and developing a physical simulation model based on similarity theory, we conduct a mechanical analysis of the stability of rotational subsidence of key blocks. This study reveals the characteristics and patterns of roof movement in shallow large-height mining, providing valuable guidance for the safe and efficient extraction of shallow coal seams.

2. Analysis of Rotational Instability of Key Block Structures in Shallow Large-Height Mining

2.1. Establishment of the Mechanical Model

Since its introduction, the theory of key layers has been widely applied in the analysis of overburden movement and roof pressure [29,30]. According to the definition of a key layer, it refers to relatively hard and thick rock strata within the overburden that primarily control the movement of the overburden and the pressure exerted on the mining face [31]. In shallow coal seams, due to the thin bedrock and thick loose layers, it is often the case that only a single key layer exists within the overburden. The failure and instability of this single key layer directly affect the patterns and characteristics of mining pressure manifestations in the mining face. In general, it can be assumed that the key layer consists of strata with uniform lithology, exhibiting consistent deformation and strength parameters. Consequently, the key layer can be simplified as a “beam” or “plate” for the purpose of calculating the limit collapse step distance of the key layer [32]. Upon initial failure, the key layer will form two key blocks, and the rotational subsidence deformation of these key blocks, along with the horizontal forces they experience, is crucial for maintaining the structural stability of the mining face and the normal operation of the support system. This also serves as an important basis for calculating the support resistance in the working face.

Under the conditions of large-height mining technology applied to thick coal seams, after the initial failure of the key layer, the subsidence of the roof increases with the increasing rotation and subsidence angle of the key block. On one hand, due to the constraints of the rotational movement space of the key block, the deformation contact area and strain of the key block continuously expand. On the other hand, because of the significant mining height, the immediate roof collapse is insufficient to fully occupy the mined-out area, resulting in a substantial space for the key block’s rotational subsidence. Therefore, when establishing a mechanical model for the rotational instability of key blocks during large-height mining, it is essential to consider the effects of block deformation. The following will present a mechanical model for analyzing the horizontal forces affecting the subsidence of key blocks, taking into account block deformation under large-height mining conditions.

The fundamental assumptions and conditions for establishing the mechanical model are as follows:

(1)

The subsidence motion of the key block occurs within a constrained space, specifically limited to L = 2l, where L represents the advancing distance of the working face and l denotes the length of the key block.

(2)

Considering the initial pressure exerted on the mining face, the key layer fractures into two blocks that are symmetrically positioned, with the two blocks undergoing opposing rotational movements.

(3)

It is assumed that the left and right hinge points of the two key blocks remain fixed, while vertical subsidence occurs at the center.

(4)

The deformation of the blocks is symmetrical, with horizontal stress generated by the deformation, and the stiffness of the surrounding rock mass constraining the block movement is sufficiently large.

(5)

For the sake of simplification in the analysis, the effects of geological structures and inclined strata are temporarily disregarded. It is considered that vertical failure occurs in the key layer, and the roof strata are horizontal.

(6)

The rock strata of the key blocks are homogeneous and isotropic.

Thus, a horizontal force analysis model for the subsidence process of the key block is established, as shown in Figure 1a. In the figure, h represents the thickness of the key block, α denotes the rotation angle of the key block, and P represents the load borne by the key block, including its own weight and that of the overlying strata. Here, let h₁ be the equivalent thickness of the rock column exerted on the key block by the overlying strata; therefore, P can be expressed as:

$$P=\rho \mathrm{g}\left(h+h_1\right)l$$

(1)

In the equation, ρ represents the average unit weight of the overburden, and g denotes the acceleration due to gravity.

2.2. Solution and Analysis of the Mechanical Model

In Figure 1, due to the symmetry in the shape, stress state, boundary conditions, and subsidence motion of the key block, the left key block ABCD can be separated for individual analysis, as shown in Figure 1b. Considering the compressive deformation resulting from the rotational subsidence of the block, point B moves to point B′, and point D moves to point D′. Under the compressive forces, it is assumed that the left side of the block is in surface contact with the surrounding rock (FB′), while the right side is in surface contact with the adjacent block (ED′). Given that the adjacent block structures and loads are symmetric, and that equilibrium must be maintained in the horizontal direction, the block experiences equal and opposite horizontal forces T at the contact surfaces FB′ and ED′. Additionally, at the contact surface ED′, the friction between adjacent blocks generates an upward shear force Q, which opposes the rotational subsidence of the block. When neglecting support resistance, and assuming that the key block structure is in a state of self-equilibrium, an upward shear force Q will similarly act at the contact surface FB′.

$$Q=T\tan \phi$$

(2)

In the equation, φ represents the friction angle at the contact surface. Through field experiments, it has been determined that tanφ can be considered as 0.5 [33].

A horizontal line is drawn through point A, intersecting the contact boundary lines FB′ and ED′ at points H and G, respectively, as shown in Figure 1b. Here, the lengths of the different segments are denoted as l_AC, l_CD, l_FG, and so forth. When the rotation angle of the block reaches α, the maximum deformation in the length direction of the block is given by l_BB′ = l_DD′ = δ. Assuming that the initial failure of the key layer occurs as a vertical fracture, the shape of the key block can be approximated as rectangular. Based on the geometric relationships following the rotational deformation of the key block, the subsidence amount w can be calculated as:

$$w=\left(l_{\mathrm{AD}}-l_{{\mathrm{DD}}^{\prime }}\right)\sin \alpha =\left(l-\delta \right)\sin \alpha$$

(3)

In triangle EDD′, the following relationship holds:

$$\delta =l_{{\mathrm{DD}}^{\prime }}=l_{\mathrm{DE}}\tan \alpha$$

(4)

Assuming the key block behaves as an ideal elastic body, after the rotational compressive deformation, triangles EDD′ and BB′F are congruent, leading to the relationships l_DE = l_BF and l_ED′ = l_FB′. In triangles AFH and AD′G, geometric analysis yields:

$$\left\{\begin{array}{l}{l}_{\mathrm{AH}}=l_{\mathrm{AF}}\sin \alpha =\left(h-l_{\mathrm{BF}}\right)\sin \alpha \\ l_{\mathrm{AG}}=l_{{\mathrm{AD}}^{\prime }}\cos \alpha =\left(l-\delta \right)\cos \alpha \\ l_{\mathrm{HG}}=l=l_{\mathrm{AH}}+l_{\mathrm{AG}}\end{array}\right.$$

(5)

By simultaneously solving Equations (2)–(5), the expression for the deformation amount δ along the length direction of the key block and the subsidence amount w of the block can be derived as:

$$\left\{\begin{array}{l}\delta ={\displaystyle \frac{1}{2\cos \alpha }}\left[h\sin \alpha +l\left(\cos \alpha -1\right)\right]\\ w={\displaystyle \frac{l\left(\cos \alpha +1\right)-h\sin \alpha }{2\mathrm{ctg}\alpha }}\end{array}\right.$$

(6)

Based on the deformation behavior of the key block, assumed to be an ideal elastic body during the rotational subsidence process, the distance from the point of action of the horizontal thrust T on the contact surfaces FB′ or ED′ to points B′ or D′is given by:

$$l_T={\displaystyle \frac{1}{3}}{l}_{{\mathrm{FB}}^{\prime }}={\displaystyle \frac{\delta }{3\sin \alpha }}={\displaystyle \frac{h\sin \alpha +l\left(\cos \alpha -1\right)}{3\sin 2\alpha }}$$

(7)

where l_T represents the distance from the point of application of the horizontal thrust T on the contact surface FB′ to point B′.

Based on the established mechanical model of the key block (Figure 1b), the moment equilibrium equation for point A of the key block can be expressed as:

$$T\left(l_{\mathrm{FH}}+{\displaystyle \frac{2}{3}}{l}_{{\mathrm{FB}}^{\prime }}\right)-P\left({\displaystyle \frac{l}{2}}-l_{\mathrm{AH}}\right)-P{l}_{\mathrm{AH}}-T\left(w+{\displaystyle \frac{l_{{\mathrm{FB}}^{\prime }}}{3}}\right)=0$$

(8)

Thus, the expression for the horizontal thrust T can be derived as:

$$T={\displaystyle \frac{Pl}{2h\cos \alpha -2l\sin \alpha +\left(1-\frac{3{\cos }^2\alpha +1}{3\sin \alpha }\right)\frac{h\sin \alpha +l\left(\cos \alpha -1\right)}{\cos \alpha }}}$$

(9)

Here, the block size coefficient of the key block is introduced as i = h/l, which allows the horizontal thrust T to be simplified as follows:

$$T={\displaystyle \frac{P}{2i\cos \alpha -2\sin \alpha +\left(1-\frac{3{\cos }^2\alpha +1}{3\sin \alpha }\right)\frac{i\sin \alpha +\left(\cos \alpha -1\right)}{\cos \alpha }}}$$

(10)

From Equation (10), it can be observed that, when considering the compressive deformation conditions during the rotational subsidence process of the key block in large-height mining, the horizontal thrust generated is primarily related to the rotational angle α of the key block, the block size coefficient i, and the load P acting on the key block. In the following sections, an analysis will be conducted on the stability, equilibrium range, and influencing factors of the key block based on the derived expression for the horizontal thrust (10), leading to the determination of the reasonable support resistance that the hydraulic supports in the working face need to provide.

2.3. Pattern of Horizontal Thrust Variation

To elucidate the variation in horizontal thrust during the rotational subsidence process of the key block, based on Equation (10), a constant load P is assumed to act on the key block. The ratio of horizontal thrust T to load P, denoted as T/P, is examined for block size coefficients i = 0.1, 0.3, 0.5, 0.7, 0.9, and 1, as well as for rotational angles α ranging from 0.10° to 30°. The resulting variation curve of T/P with respect to the rotational angle α is illustrated in Figure 2.

As shown in Figure 2, the horizontal thrust generally exhibits a non-linear increasing trend with the increase in the rotational angle α during the rotational subsidence process of the key block. Notably, when the block size coefficient i < 0.5, the rate of increase in horizontal thrust T with respect to the rotational angle α is significantly higher than that when the block size coefficient i ≥ 0.5.

2.4. Analysis of the Balance Conditions of Key Blocks

Practical experience indicates that there are primarily two modes of instability for the key block during large-height mining of shallow coal seams: sliding instability and deformation instability [33], as illustrated in Figure 3. Sliding instability (Figure 3a) occurs when the frictional force at the contact surfaces of the two key blocks is less than the shear force between them. Conversely, deformation instability (Figure 3b) arises when the stress concentration generated by the horizontal thrust at the contact surfaces exceeds the strength limit of the key block in the localized area, resulting in compressive failure in that region and causing the key block to accelerate its rotation.

According to the equilibrium conditions of the key block, to ensure that sliding instability does not occur, the following condition must be satisfied: Q ≥ 0.5P. By combining Equations (2) and (10), the criterion conditions for the block size coefficient i and the rotational angle α to prevent sliding instability of the key block are obtained as follows:

$$i\le {\displaystyle \frac{0.75\sin 2\alpha +3\sin 2\alpha \sin \alpha +\left(3\sin \alpha -3{\cos }^2\alpha -1\right)\left(1-\cos \alpha \right)}{3\sin 2\alpha \sin \alpha +\left(3\sin \alpha -3{\cos }^2\alpha -1\right)\sin \alpha }}$$

(11)

According to Equation (11), the relationship curve between the block size coefficient i and the rotational angle α under the critical conditions for sliding instability of the key block is illustrated in Figure 4a. It is evident that to prevent sliding instability of the key block, the block size coefficient should be less than 0.75. This also indicates that under the conditions of large-height mining in shallow coal seams, a larger block size coefficient following the failure of the key layer is a primary cause of sliding instability. As the rotational angle increases, the block size coefficient corresponding to the limit equilibrium of the key block also increases. Based on extensive field measurements, the block size coefficient of the key block typically remains below 1 at the initial pressure on the roof [34]. Consequently, once the rotational angle of the key block exceeds 10°, sliding instability becomes more likely.

Let l represent half of the step distance of the initial pressure on the basic roof [33], then we have:

$$l={\displaystyle \frac{1}{2}}h\sqrt{{\displaystyle \frac{2{\sigma }_{\mathrm{t}}}{\rho \mathrm{g}\left(h+h_1\right)}}}={\displaystyle \frac{1}{2}}h\sqrt{{\displaystyle \frac{0.2{\sigma }_{\mathrm{c}}}{\rho \mathrm{g}\left(h+h_1\right)}}}$$

(12)

where σ_c represents the compressive strength of the rock mass, and σ_t denotes the tensile strength of the rock mass, typically expressed as σ_t = 0.1σ_c. By relating Equations (11) and (12), the following equation can be obtained:

$$h+h_1\le {\displaystyle \frac{{\sigma }_{\mathrm{c}}}{20\rho \mathrm{g}}}{\left[{\displaystyle \frac{0.75\sin 2\alpha +3\sin 2\alpha \sin \alpha +\left(3\sin \alpha -3{\cos }^2\alpha -1\right)\left(1-\cos \alpha \right)}{3\sin 2\alpha \sin \alpha +\left(3\sin \alpha -3{\cos }^2\alpha -1\right)\sin \alpha }}\right]}^2$$

(13)

Here, we take σ_c = 40 MPa and ρg = 25 kN/m³. Based on Equation (13), the relationship curve between h + h₁ and α under the critical conditions for sliding instability of the key block was plotted, as shown in Figure 4b. It is evident that the area below the curve represents the equilibrium zone of the key block, and as the rotational angle increases, its bearing capacity exhibits a non-linear increasing trend.

According to the equilibrium conditions of the key block, to ensure that deformation instability does not occur, the following condition must be satisfied:

$${\displaystyle \frac{T}{a}}\le \eta \left[{\sigma }_{\mathrm{c}}\right]$$

(14)

where η[σ_c] represents the compressive strength at the edge of the key block, and a denotes the height of the compressive contact surface at the edge of the key block. According to the geometric relationships of the rotational deformation of the key block (as illustrated in Figure 1), the following equation can be obtained:

$$a=l_{{\mathrm{ED}}^{\prime }}={\displaystyle \frac{\delta }{\sin \alpha }}$$

(15)

By simultaneously considering Equations (6), (10), (14) and (15), the following equation can be obtained:

$$h+h_1\le {\displaystyle \frac{\eta \left[{\sigma }_{\mathrm{c}}\right]}{\rho \mathrm{g}}}\left[{\displaystyle \frac{3i\sin 2\alpha \cos \alpha -3\sin \alpha \sin 2\alpha +\left(3\sin \alpha -3{\cos }^2\alpha -1\right)\left(i\sin \alpha +\cos \alpha -1\right)}{1.5{\sin }^{2}2\alpha }}\right]\left(i\sin \alpha +\cos \alpha -1\right)$$

(16)

Figure 5 illustrates the relationship curve between h + h₁ and the rotational angle α under the critical conditions of deformation instability for the key block at different block size coefficients i. It is evident that, for a constant block size coefficient i, as the rotational angle increases, the bearing capacity of the key block gradually weakens, making it more susceptible to deformation instability. Additionally, for a fixed rotational angle α, an increase in the block size coefficient enhances the bearing capacity of the key block, thereby reducing the likelihood of deformation instability.

During the large-height mining of shallow coal seams, to ensure that the key block structure formed by the fracture of the roof remains in a balanced and stable state, it is essential to simultaneously satisfy the conditions for preventing both sliding instability and deformation instability of the key block, which requires compliance with both Equations (13) and (16). Therefore, based on Figure 4 and Figure 5, the stable equilibrium regions for the key block structure, as a function of the rotational angle α at different block size coefficients i, are illustrated in Figure 6.

In Figure 6, the maximum load for the key block in a critical stability condition during the rotational subsidence process at different block size coefficients i is presented, as shown in

Table 1. The ultimate bearing thickness of the key block structure in the roof under varying block size coefficients during large-height mining.

Block size coefficient (i)	0.1	0.2	0.3	0.4	0.5	0.6
Ultimate bearing thickness (h + h1)/(m)	37.6	100	135	175	209	274

. Through a regression analysis of the data in Table 1, a regression equation relating the block size coefficient to the limiting bearing thickness is derived, as indicated in Equation (17). It is evident that the limiting bearing capacity of the key block increases linearly with an increase in the block size coefficient.

$$h+h_1=441.37i+0.4867$$

(17)

2.5. Supporting Structure Working Resistance

By analyzing the two modes of instability that are prone to occur in the key block structure of the roof under the conditions of large-height mining in shallow coal seams, corresponding criteria for stability have been established. In practice, sliding instability is often a primary cause of severe roof pressure and the occurrence of step subsidence at the working face [35]. Therefore, the fundamental task of mining pressure control in shallow large-height mining is to ensure that the support provides sufficient bearing capacity to prevent sliding instability of the basic roof. According to the mechanical analysis, the condition for preventing sliding instability of the basic roof is given by Q + R ≥ 0.5P:

$$R\ge \left[1-{\displaystyle \frac{1}{4i\cos \alpha -4\sin \alpha +2\left(1-\frac{3{\cos }^2\alpha +1}{3\sin \alpha }\right)\frac{i\sin \alpha +\left(\cos \alpha -1\right)}{\cos \alpha }}}\right]P$$

(18)

To further determine the support resistance required to prevent sliding instability of the key block during the rotational subsidence process at different block size coefficients i, the load P on the key block is considered a constant value. The ratio of support resistance R to load P is defined as R/P. The block size coefficients selected for the immediate roof are i = 0.1, 0.3, 0.5, 0.7, 0.9, and 1, along with rotational angles α = 0.1°, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, 3.0°, 3.5°, 4°, 4.5°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, 15°, 16°, 17°, 18°, 19°, 20°, 22°, 24°, 26°, 28°, 30°. Using Equation (18), the support resistance curves controlling sliding instability of the key block at various block size coefficients and rotational angles are calculated and illustrated in Figure 7.

As observed in Figure 7, during the rotational subsidence of the key block, the support resistance gradually decreases with the increase in the rotational angle α. Specifically, when the rotational angle of the key block is less than 10°, the rate of decrease in support resistance is relatively slow. However, when the rotational angle exceeds 10°, the support resistance decreases rapidly with increasing rotational angle. Furthermore, as the block size coefficient i increases, the support resistance required to control the sliding instability of the key block also increases correspondingly.

3. Analysis of the Roof Movement Patterns During Large-Height Mining of Shallow Coal Seams

3.1. Establish a Physical Simulation Model

Physical simulation experiments are an effective method for studying the movement of overburden during coal seam extraction, offering good intuitiveness, controllability, and repeatability. To further investigate the movement characteristics and patterns of the roof during large-height mining of shallow coal seams, a physical simulation model using similar materials was established, set against the backdrop of a coal mine in the Shendong mining area of China. This was conducted using a large-scale plane strain simulation test platform (dimensions: 3000 mm × 3000 mm × 200 mm), as illustrated in Figure 8.

The Shendong mining area is characterized by several distinct features: shallow burial depth, thin bedrock, a thick layer of alluvial sand cover, and abundant groundwater. The coal seam being mined has a thickness ranging from 4.75 to 7.65 m, with an average burial depth of 122.05 m. The mining method employed is large-height mining with full thickness extraction. The average thickness of the alluvial sand above the coal seam is 10.03 m, while the average thickness of the bedrock is 112.02 m. The immediate roof is predominantly siltstone or fine sandstone, averaging 5.8 m in thickness, and the basic roof consists of medium sandstone or fine sandstone, cemented with calcium carbonate, averaging 5.3 m in thickness. Based on the engineering geological conditions of the mine and the experimental setup, and according to similarity theory [36], the geometric similarity ratio was determined to be C_l = 1/50; the specific weight similarity ratio C_γ = 0.68; the stress similarity ratio C_σ = 0.0136; and the time similarity ratio C_t = 0.0136. The dimensions of the physical model are 3000 mm × 2723.8 mm × 200 mm (as shown in Figure 8a). The model is constrained around its perimeter and bottom by 20# channel steel and 25 mm thick acrylic panels, with the top of the model being a free end. The entire model is subjected to self-weight stress. Due to the displacement constraints applied at the boundaries of the model, a state of horizontal stress can be established under static conditions as a result of gravitational forces. Based on rock mechanics parameters and considering a fissure influence coefficient of 0.8, the physical and mechanical parameters of the model materials, along with their proportions and quantities, were derived using similarity theory [37], as detailed in

Table 2. Main parameters and material proportions of the surrounding rock for simulated coal seam.

Layer	Lithology	Thickness (m)	Density (kg/m3)	Compressive Strength (MPa)	Elastic Modulus (GPa)	Similarity Ratio	Sand (kg)	Cement (kg)	Calcium Carbonate (kg)	Gypsum (kg)	Water (kg)	Borax (g)
1	Windblown sand	11.70	1700				238.7
2	Siltstone	8.60	2460	40.6	35	655	152.9		12.3	12.3	33.6	336
3	Sandy mudstone	5.10	2240	22.8	23	346	74.6	(9.3)		14	9.3	186
4	Coarse sandstone	10.28	2430	36.6	35	855	185.7		11.3	11.3	20.4	204
5	Fine sandstone	7.03	2500	44.6	32	955	131.9	7.2		7.2	14.3	143
6	Sandy mudstone	9.8	2240	22.8	23	337	143.3		(13.4)	31.4	25.6	512
7	Coarse sandstone	11.24	2430	36.6	35	855	203.1		12.4	12.4	22.3	223
8	Sandy mudstone	27.52	2240	22.8	23	337	402.4		(37.7)	88.0	71.9	1437
9	Coarse sandstone	9.89	2430	36.6	35	855	178.7		10.9	10.9	19.6	196
10	Sandy mudstone	6.17	2240	22.8	23	337	90.2		(8.5)	19.7	16.1	322
11	Fine sandstone	7.27	2500	44.6	32	955	136.4	7.4		7.4	14.8	148
12	Sandy mudstone	4.16	2240	22.8	23	337	60.8		(5.7)	13.3	10.9	217
13	Coal seam	5.5 (7.0)	1480	10.5	15	373	53.1	(11.6)		5	6.6	133
14	Siltstone	1.48	2460	40.6	35	655	26.3		2.1	2.1	4.2	42
15	Sandy mudstone	3.25	2240	22.8	23	337	47.5		(4.5)	10.4	8.5	170
16	Fine sandstone	5.70	2500	44.6	32	955	107	5.8		5.8	11.6	116

. The materials and proportions used to characterize the rock layers with different mechanical parameters in the physical model were derived from extensive orthogonal proportion experiments and mechanical parameter testing conducted by previous researchers [38].

Additionally, displacement measurement points were arranged at various heights of the coal seam roof within the physical model, as illustrated in Figure 8b. In the horizontal direction, 12 rows of measurement points were established, with an inter-row distance of 20 cm. In the vertical direction, horizontal measurement lines were initiated 5 cm above the coal seam, with the first four rows spaced at 10 cm apart and the subsequent three rows spaced at 15 cm. A total of 105 displacement measurement points were installed. During the physical simulation test of coal seam excavation, a Nikon DTM-531E total station (Hangzhou Dongxin Instrument and Equipment Co., Ltd., Hangzhou, China) was utilized to measure the coordinates of the established points on the immediate roof, basic roof, and overburden, in order to determine the displacement of the measurement point locations. Concurrently, a digital camera was employed to document the roof movement throughout the extraction process.

To elucidate the impact of mining height on roof movement during large-height mining of shallow coal seams, physical experimental models were established with coal seam thicknesses of 5.5 m and 7.0 m, based on the thickness and geological conditions of the Shendong mining area. The two models share identical lithological conditions, forming a control group, with the only difference being the mining height. Taking the 5.5 m high mining model as an example, the process of the physical simulation experiment is as follows:

(1)

After the model was completed and dried for 5 days, the glass panels were removed to arrange the displacement measurement points (as shown in Figure 8b). Reference points for total station measurements were selected, and initial readings for each measurement point were recorded.

(2)

To minimize boundary effects, a cut was excavated 10 m from one edge of the model, with a width of 8 m and a mining height of 5.5 m. A four-column hydraulic support was placed within the cut to simulate the actual mining environment.

(3)

In accordance with the mining operation schedule, and based on time and geometric similarity ratios, each coal cut was allocated 11 min, with an advance of 0.8 m, resulting in a total daily advancement of 12 m to simulate the real mining process. The cumulative advancement of the working face reached 130 m. Throughout the simulation, the total station and digital camera were utilized in conjunction to monitor and record the roof movement in real-time.

3.2. Analysis of the Roof Collapse Process

Figure 9 illustrates the roof collapse and movement process under the conditions of 5.5 m of mining height. It is evident that the characteristics of roof movement can be broadly divided into three stages: (1) immediate roof collapse (Figure 9a,b), (2) stratified fracturing and instability of the basic roof (Figure 9c–f), and (3) periodic fracturing of the basic roof (Figure 9g–i).

During the immediate roof collapse stage, the various layers of the immediate roof exhibit an alternating movement characteristic of “delamination-collapse,” progressing from near to far as the working face advances. When the working face reaches 15.2 m, delamination first occurs in the first and second layers of the immediate roof (Figure 9a). As the working face continues to advance, the first layer collapses while the third layer experiences delamination. By the time the working face advances to 20 m, complete collapse of the immediate roof occurs, resulting in the formation of a triangular overhanging space at the roof (Figure 9b). Following the total collapse of the immediate roof, the overhanging length of the basic roof is measured at 10 m, with a collapse angle of 52°.

During the stage of stratified fracturing and instability of the basic roof, the various layers of the basic roof exhibit a movement characteristic of “low-level fracturing—sliding instability—high-level fracturing” as the working face advances. When the working face reaches 29.6 m, fracturing occurs in the lower layers of the basic roof, forming two interconnected key blocks that divide the triangular overhanging space into upper and lower sections (Figure 9c). As the working face advances to 35.2 m, the left key block experiences sliding instability, resting approximately flat on the fallen rock mass below (Figure 9d), while the collapsed zone gradually becomes compacted, and the right key block maintains a more stable connection with the rock wall. With further advancement of the working face to 40 m, the lower-level basic roof becomes unstable, and cracking occurs in the upper-level basic roof, resulting in the formation of a new key block hinge structure at a higher position (Figure 9e). When the working face advances to 50.4 m, the entire basic roof undergoes fracturing and instability, causing the overburden to subside, while the collapsed zone is compacted, marking the initial loading of the working face (Figure 9f).

During the stage of periodic fracturing of the basic roof, the basic roof and several overlying strata it controls exhibit a movement characteristic of “composite cantilever beam periodic cracking” as the working face advances. As the advancement distance increases, the area behind the worked out section gradually becomes compacted, resulting in an increase in the overhanging length of the basic roof above the coal wall of the working face, thereby forming a cantilever beam. When the working face reaches 69.6 m, the span of the cantilever beam reaches its limit, and under the load of the overburden, the basic roof fractures. This triggers cooperative cracking of several overlying strata, leading to the first periodic loading of the working face (Figure 9g). At this point, a through-layer fissure measuring 12.5 m in length forms 15 m in front of the working face. As the working face continues to advance, the cantilever beam structure formed by the basic roof undergoes periodic cracking upon reaching its span limit, resulting in periodic loading of the working face (Figure 9g–i).

Figure 10 illustrates the roof collapse and movement process under the conditions of 7.0 m of mining height. Due to the influence of environmental weather conditions and the degree of air dryness, the colors of the obtained photographs exhibit certain discrepancies compared to those in Figure 9. A comparative analysis with Figure 9 reveals that when the mining height increases from 5.5 m to 7.0 m, during the immediate roof collapse stage, the immediate roof collapses into the mined-out area as the working face advances, resulting in a more fragmented rock mass after collapse (Figure 10a). Once the immediate roof has fully collapsed, the roof movement transitions into the stage of stratified fracturing and instability of the basic roof (Figure 10b–d). It is evident that with an increase in mining height to 7.0 m, the basic roof exhibits instability immediately following cracking, lying flat on the already collapsed rock layers, and failing to form an effective key block hinge structure. This phenomenon can be attributed to two main factors. Firstly, with a constant thickness of the immediate roof, an increase in mining height results in the inability of the fully collapsed immediate roof to fill the delamination space created by the increased height, despite the expansion effect after the fragmentation of rock masses. Secondly, the distance between the basic roof and the coal seam remains constant, meaning that an increase in mining height enlarges the rotational subsidence space of the basic roof after fracturing, accompanied by an increase in the rotation angle of the key blocks. According to previous mechanical analysis results, a larger rotation angle weakens the load-bearing capacity of the key blocks, making them more susceptible to deformation and instability. Additionally, when the rotation angle exceeds 10°, the key blocks are prone to sliding instability. During the stage of periodic fracturing of the basic roof, when the mining height is increased to 7.0 m, the combined cantilever beam structure formed by the basic roof experiences fracturing, leading to a significant increase in the opening of the through-layer fissure in front of the working face (Figure 10e,f). This is attributed to the increased mining height providing greater rotational space for the fractured combined cantilever beam.

3.3. Analysis of the Characteristics of Roof Movement

Based on the results of physical simulation experiments, key indicators were extracted at various stages of roof movement under different mining heights, including working face advancement distance, loading step distance of mining pressure, basic roof collapse angle, and the distance from the fracture position of the basic roof to the coal wall. These indicators further elucidate the characteristics of roof movement during large-height mining of shallow coal seams, as shown in Figure 11. From the perspective of working face advancement distance during different stages of roof movement, when the mining height increases from 5.5 m to 7.0 m, the initial working face advancement distance at the time of immediate roof collapse is similar, measuring 20 m and 20.8 m, respectively (Figure 11a). Overall, the initial fracture and periodic fracture advancement distances of the basic roof at a mining height of 7.0 m are 5.6 to 17.6 m shorter than those at a height of 5.0 m. This indicates that increasing the mining height has minimal impact on the collapse of the immediate roof but does reduce the working face advancement distance associated with basic roof fracturing. Regarding loading step distances of mining pressure, with the exception of the second periodic loading step distance at 7.0 m being nearly twice that of the 5.0 m height, the overall loading step distance at 7.0 m is less than that at 5.0 m (Figure 11b). This suggests that increasing the mining height effectively shortens the loading step distance of the working face. This phenomenon can be attributed to the instability that occurs after fracturing of the basic roof at greater heights, which prevents the formation of an effective key block hinge structure capable of bearing part of the overburden load, resulting in the majority of the overburden load being supported by the combined cantilever beam of the basic roof above the coal wall.

Figure 11c presents the collapse angles of the basic roof during loading at mining heights of 5.5 m and 7.0 m. It is evident that during the initial loading from the basic roof, the collapse angle at a height of 5.5 m is significantly greater than that at 7.0 m, measuring 82° and 37°, respectively. During the periodic loading from the basic roof, the collapse angle at 7.0 m is generally greater than that at 5.0 m. In the context of large-height mining of shallow coal seams, the average collapse angle of the basic roof exceeds 61°. In large-height mining operations, an increase in the collapse angle may lead to an expansion of the fracture zone in the roof strata and exacerbate non-uniform damage, resulting in uneven loading on the supports, which could cause support failure or collapse. This also increases the risk of roof falls in front of the supports and the potential for coal wall spalling. Furthermore, significant collapse angles may lead to unstable accumulation of waste rock, resulting in the formation of overhanging or cutting roof phenomena, necessitating enhanced support or pre-treatment measures.

Figure 11d illustrates the distance from the fracture position of the basic roof to the coal wall under mining heights of 5.5 m and 7.0 m. It is apparent that during the initial loading from the basic roof, the fracture positions for both high mining scenarios are directly above the coal wall. In the periodic loading phase, the differences in the distance from the fracture positions to the coal wall at both mining heights are minimal, ranging approximately from 0.67 to 2.2 m. However, with the increase in mining height, the rotational subsidence space following the periodic fracturing of the basic roof enlarges, resulting in a significant increase in the opening of through-layer fissures, which can even extend to the surface, as shown in Figure 10f.

3.4. Analysis of Roof Subsidence Displacement

Figure 12 presents the subsidence curves for displacement measurement points 1 to 3 located on the immediate roof during the collapse phase under mining heights of 5.5 m and 7.0 m, as the working face advances. A comparison reveals that under the 5.5 m mining height, the displacement of the immediate roof undergoes a process characterized by slow subsidence, followed by delamination, and ultimately culminates in a sudden collapse. The final subsidence at measurement point 1 is approximately 3.4 m, while measurement points 2 and 3 exhibit an average final subsidence of about 4.9 m. In contrast, when the mining height is increased to 7.0 m, the slow subsidence of the immediate roof is not significantly observable as the advancement distance increases, with subsidence values remaining close to 0 m. Once the working face reaches a certain distance, the immediate roof experiences a sudden collapse. The average final subsidence at the three measurement points is approximately 5.8 m. Therefore, as the mining height increases, the displacement associated with the immediate roof collapse also increases, leading to a heightened risk of sudden collapse.

Figure 13 illustrates the subsidence curves for displacement measurement points 13 to 15 located on the lower basic roof as the working face advances under mining heights of 5.5 m and 7.0 m. It is evident that under the 5.5 m mining height, the displacement of the lower basic roof generally exhibits a “stair-step” increase (with more than two steps), ultimately stabilizing. Measurement point 13 experiences a final subsidence of approximately 3.3 m, while measurement points 14 and 15 show an average final subsidence of about 5.1 m. Further comparative analysis indicates that when the mining height is increased to 7.0 m, the movement of the lower basic roof displays three distinct phases. The first phase is characterized by zero displacement during the static cantilever phase. The second phase involves a sudden increase in displacement during the fracture instability phase. The third phase is marked by stable displacement during the post-instability static phase. This behavior can be attributed to the increased mining height providing sufficient space for the rotational subsidence of the key blocks following the fracturing of the basic roof, which prevents the formation of a stable key block hinge structure, resulting in immediate instability and collapse of the basic roof.

Figure 14 presents the subsidence curves for displacement measurement points 25 to 27 located on the upper basic roof as the working face advances under mining heights of 5.5 m and 7.0 m. A comparative analysis reveals that under the 5.5 m mining height, as the working face advances, the upper basic roof initially experiences slow subsidence, stabilizing at approximately 1 m during the delamination phase. When the advancement distance reaches about 40 m, the upper basic roof fractures, resulting in a rapid increase in subsidence, which ultimately stabilizes. In contrast, when the mining height is increased to 7.0 m, there is no significant subsidence observed prior to the fracture of the upper basic roof as the working face advances. This indicates that increasing the mining height in shallow coal seam extraction raises the risk of sudden fracturing of the basic roof, leading to unexpected loading on the working face, which can cause support failures, large-scale coal wall spalling, and even dynamic pressure disasters. During the mining process, it is essential to implement timely protective measures, such as roof watering and manual cutting of the roof, to mitigate these risks.

4. Conclusions

To address the issues of roof movement and mining pressure manifestation associated with large-height mining techniques in shallow coal seams, a combined approach of theoretical analysis and physical simulation experiments was employed. This study focused on the characteristics and patterns of key block rotational instability and roof movement under large-height mining conditions in shallow coal seams. The findings are of significant practical importance for support design or pre-fracturing techniques in large-height extraction of shallow coal seams, leading to the following conclusions:

(1)

A mechanical model was established to calculate the horizontal thrust during the rotational instability of key blocks, considering the deformation of the block as it undergoes rotational subsidence under large-height mining conditions. The horizontal thrust increases non-linearly with the rising rotation angle. When the block’s dimension ratio is less than 0.5, the rate of increase in horizontal thrust with respect to the rotation angle is higher.

(2)

Two modes of instability are prone to occur in key blocks during large-height mining of shallow coal seams: sliding instability and deformation instability. The equilibrium conditions of the key block were analyzed, leading to a regression equation relating the dimension ratio to the limit bearing thickness during rotational subsidence. To prevent sliding instability, the dimension ratio of the key block should be less than 0.75. As the rotation angle increases, the corresponding dimension ratio for maintaining limit equilibrium also increases. Practically, once the rotation angle of the key block exceeds 10°, sliding instability becomes likely. A smaller rotation angle allows for a larger dimension ratio, enhancing the bearing capacity of the key block and reducing the likelihood of deformation instability.

(3)

Reasonable support working resistance necessary to prevent sliding instability of the basic roof during large-height mining operations was determined. During the rotational subsidence of the key block, the support resistance gradually decreases as the rotation angle increases. Beyond a rotation angle of 10°, the support resistance declines rapidly with increasing rotation angle. Additionally, as the dimension ratio increases, the support resistance required to control sliding instability of the key block also increases.

(4)

Based on physical simulation experiments, the characteristics of roof movement can be generally categorized into three stages: immediate roof collapse, stratified fracturing and instability of the basic roof, and periodic fracturing of the basic roof. As mining height increases, instability immediately follows the fracturing of the basic roof, failing to form an effective key block hinge structure. The increased rotational space significantly enlarges the opening of through-layer fissures formed in front of the working face. Moreover, higher mining heights effectively shorten the loading step distance of mining pressure, increase the collapse angle of the basic roof, and elevate the risk of sudden collapse, leading to unexpected loading on the working face.