Theoretical Discrimination Method of Water-Flowing Fractured Zone Development Height Based on Thin Plate Theory

Abstract

The water-flowing fractured zone development height (WFZDH) is of great importance for water prevention and control in coal mines. The purpose of this research is to obtain a WFZDH prediction method of the first mining face based on thin plate theory, considering the rock stratum as a thin plate. By analyzing the thin plate, we expect to derive formulas for deflection, thus further analyzing the deformation of the rock formation. Existing methods tend to analyze the rock stratum as if they were beams, and their results are errors from reality. The proposed method is more realistic in analyzing the rock stratum as a plate. The theoretical discrimination method for the WFZDH based on thin-plate theory was investigated using theoretical analysis, numerical simulation, and field measurements. A mechanical model of the key stratum (a hard and thick rock stratum that controls the activity of all rock formations overlying a mining site, either locally or up to the surface) as a thin plate was established. The formulae for the deflection of the key stratum and the critical span for fracture were obtained from this model. The failure of the key stratum must meet two conditions: the key stratum’s suspended span exceeds the critical span at which key strata first fracture, and the free space height below the key stratum is greater than its maximum deflection. Based on the above demarcation basis and key stratum failure conditions, the method of discriminating the WFZDH and its applicable conditions are proposed. In accordance with Yeping Coal Mine’s geological background, the method was applied to discriminate the WFZDH, and the WFZDH was calculated to be 54 m. The results of the numerical simulation show that WFZDH is 55 m, and the measured results using the double-end water plugging device observation method and the Borehole TV method are 55.3 m~58.9 m. By comparing and analyzing the results obtained via various methods, the results show that the WFZDH analyzed using thin-plate theory is similar to those measured in the field and obtained through numerical simulation, verifying the appropriateness and practicability of the WFZDH discrimination method based on thin-plate theory. This research obtained the WFZDH of Yeping Coal Mine, which ensured its safe mining and provided guidance for the estimation of WFZDH in other mines with similar conditions.

1. Introduction

China has diversified coal resources with abundant reserves, but the hydrogeological conditions are complex and diverse. Most mining areas are plagued by mine water hazards, and there is a constant occurrence of water intrusion accidents [1,2,3]. Pang Mingkun [4] studied the flow state of the groundwater system and analyzed the mechanism of water emergencies in coal mines. The existence of bed separations above the coal seam can gather a large amount of water or act as a channel to direct water to the working face, leading to water ingress accidents. The study of the generation and distribution of bed separations is essential for preventing water inrush accidents in mines [5,6,7]. In the western part of China, there are more aquifers, and the problem of large water surges in mines can occur at any time. Also, due to the thicker coal seams in the western mine, the fissures and bed separations above them are more fully developed, which is more likely to lead to sudden water accidents [8,9,10]. The roof bed separations act as possible water storage spaces and water conduits, with a high probability of triggering water damage in mines [11,12]. The water-flowing fractured zone development height (WFZDH) is closely related to coal mine water control work. It is of great significance to understand the WFZDH under various geological environments in order to achieve safe, economical, and environmentally sustainable mine development [13,14].

In light of the findings on the deformation and failure of rock formation above the working face, Chinese scholars have conducted extensive research in this field. In 1981, Qian Minggao made a creative proposal for the “masonry beam” mechanical model for the overlying strata [15]. Since then, Qian Minggao has enriched and developed this theory and proposed the “key stratum” theory [16,17]. This theory posits that the position of the main key stratum exerts a significant influence on the WFZDH. Once this critical height is reached, the main key stratum will begin to fracture. These fractures will then propagate, or spread and extend, through the entire thickness of the main key stratum. The fractures do not remain confined within the stratum but rather continue to grow and expand upwards towards the surface. When the main key stratum has not yet exceeded its critical height, the fracture is impeded at the base of the sub-key stratum in proximity to its critical height. Xu Jialin [18], Gong Peilin [19], Yu Bin [20], and others conducted studies into the fracturing and movement laws of overlying strata under conditions of large mining depths and the presence of a competent, rigid roof layer. They supplemented and improved the key stratum theory. Gong Peilin [19] and Yi Yongjie [21] applied the key stratum theory in analyzing the WFZDH and verified the key stratum theory with field measurements. In studying the overlying layer fracture mechanism in mining faces, the thin plate theory has been applied to a certain extent. Chen Zhonghui, Xie Heping [22], Zhong Yang, Yin Jianhua [23], and Song Yanqi [24] established the mechanical model of thin plates and analyzed roof deformation using the corresponding numerical calculation method. Yu Hui [25], Huang Changguo [26], and Liu Zhengchun et al. [27] established corresponding thin plate mechanical models for different working face conditions and obtained the calculation formula for roof fracture distance. For roof load calculation, Liu Xiaobo [28], Zhang Yidong [29], Lin Haifei [30], WU Fengfeng [31], and others conducted corresponding research work and obtained the critical load for roof strata failure through different methods. In addition to the research on the calculation of roof deformation, roof load, and roof step distance, Wang Xinfeng [32] used thin plate bending theory to establish roof mechanical models at different mining stages and revealed the roof ‘O-X’-type breaking mechanism; Tu Hongsheng [33] established the steep-face roof panel model and studied the deflection deformation characteristics of the steeply inclined working face. Yang Shengli [34] analyzed the key stratum-breaking forms under different thickness conditions. Chang Xikun [35] studied the characteristics of WFZDH in shallow, thick coal seam underwater. He Xiang [36] used multiple regression analysis to establish a non-linear model for predicting the WFZDH by combining factors such as mining height, percentage of hard rock, mining depth, and extraction rate. Guo Wenbing [37] studied the damage transfer process of upper rock under intensive mining and proposed a new theoretical method based on the overburden failure transfer process to predict the WFZDH. Xu [38] developed a trapezoidal fracture model to explain water intrusion during coal mining based on overburden strata movement induced by coal mining.

Currently, there are more studies on the failure characteristics of mine roofs based on elastic thin plate theory. However, there is relatively less research on WFZDH using the thin plate theory. Therefore, this paper analyzes the deflection and the key stratum span in the process of bending and deformation to breakage by establishing a thin-plate mechanical model. It studies the links between key stratum failure and the WFZDH, proposes a method for discriminating the WFZDH based on thin plate theory and applicable conditions, and verifies the reasonableness of this method by combining it with the actual geological conditions of the 1301 face in Yeping Coal Mine.

2. Mechanical Modeling of Key Stratum and Its Fracture Analysis

2.1. Mechanical Modeling of Key Stratum Sheet

In elastic mechanics, a geometric object surrounded by two horizontal planes and four vertical planes is called a plate. The distance between the two horizontal planes, denoted as h, is referred to as the plate thickness. If h is less than one-fifth of the shorter side, the plate is considered a thin plate [39]. The elastic thin plate model is illustrated in Figure 1.

The key stratum can be regarded as a continuous elastomer, and the load borne by the thin plate can be decomposed into vertical load and horizontal load, while the vertical load causes the plate to undergo bending deformation. Since the 1301 working face is the first face mined in this area, it can be considered that the key stratum is surrounded by solid support conditions, and the effect of horizontal load on the thin plate is ignored.

The small deflection bending theory postulates that the deflection is significantly less than its thickness, owing to its certain bending stiffness. Based on Kirchhoff’s plate theory, the following basic assumptions are made for the overlying strata: ① The vertical strain caused by vertical stress ε_z = 0; ② The vertical strain components ε_z, γ_zx, and γ_zy can be ignored; ③ The horizontal displacement is zero.

2.2. Key Stratum Breakage Analysis

In the case where the collapsed zone with loose and fragmented rocks is unable to fully fill the goaf, the key stratum determines the division of the WFZ [40]. The WFZDH is affected by the key stratum; whether the key stratum experiences fracturing determines if the overlying rock fissures can continue to propagate upwards. When the key strata remain intact, the fissures are impeded at its bottom. As the working face continues to advance, if the key stratum remains unbroken, it can be considered that the WFZ has developed to the bottom of the key strata at this point.

The relationship between the maximum subsidence deformation and the height of free space underneath determines whether the rock strata will be damaged [41]. Meanwhile, it is only when the working face has advanced a sufficient distance, causing the rock strata below the key strata to fracture, that the suspended span of the key strata reaches its fracturing distance, at which point the key strata will fracture. Therefore, the key stratum fracture needs to meet two conditions: (1). In the direction of advancement, the suspended span of the key strata is greater than the critical span at which the key strata first fracture. (2). The free space height below the key stratum is greater than its maximum deflection, and the expression is shown in Equation (1):

$$\left\{\begin{array}{l}{a}_j>a_{jT}\\ w_{\max }<\Delta =M-{\displaystyle \sum _{i=1}^{j-1}{h}_i(k_i-1),}\end{array}\right.$$

(1)

where a_j is the suspended span of key strata, m; a_jT is the critical span at which the key strata first fracture, m; ∆ is the free space height below the key strata, m; M is the coal seam thickness, m; k_i is the residual bulking coefficient of the jth stratum, the average coefficient of the caved strata is related to the distance from the coal seam [37].

The deflection differential equation of the thin plate is as follows:

$$D{\nabla }^{4}w=q$$

(2)

$$D={\displaystyle \frac{E{h}^3}{12\left(1-{\mu }^2\right)}},$$

(3)

where D is the bending stiffness, N/m; $\nabla$ is the Laplacian operator; q is the vertical load on the thin plate. MPa; μ is the Poisson ratio; h is the thin plate thickness, m; E is the elastic modulus of the thin plate, MPa.

3. Theoretical Method for Determining the WFZDH

Based on the previous analysis, the key factors in determining WFZDH are the working face advancement distance and whether the key strata experience fracturing. Therefore, this section will analyze the key strata as a thin plate and specifically examine the conditions for key strata fracturing. Theoretical analyses of this issue can help to understand the essence and inner mechanism of things in depth and provide guidance and predictions for practical applications. In addition, theoretical analysis provides the basic assumptions and model construction for numerical simulation.

3.1. Key Stratum Fracture Analysis

For the first mining face, the surrounding area is unmined solid coal. Before the initial fracturing of the key stratum, it can be regarded as a thin plate with four edges fixed, subjected to a uniformly distributed vertical load q. Assume that the suspended span of the key stratum at the moment of initial fracturing is 2a × 2b. The coordinate axes are taken as shown in Figure 2, and the boundary conditions are as shown in Equation (4):

$$\left\{\begin{array}{l}{\left(w\right)}_{x=\pm a}=0\\ {\left(w\right)}_{y=\pm b}=0\\ {\left({\displaystyle \frac{\partial w}{\partial x}}\right)}_{x=\pm a}=0\\ {\left({\displaystyle \frac{\partial w}{\partial y}}\right)}_{y=\pm b}=0.\end{array}\right.$$

(4)

The Galerkin method is used to solve the small deflection problem of thin plates. The Galerkin variational equation is expressed as Equation (5), and the deflection expression of the thin plate is given using Equation (6):

$$\left\{\begin{array}{l}{\displaystyle {\int }_V\left(\frac{\partial {\sigma }_z}{\partial z}+\frac{\partial {\tau }_{zx}}{\partial x}+\frac{{\partial }_{zy}}{\partial y}+f_z\right)w_{m}dV=0}\\ {\displaystyle \int {\displaystyle {\int }_{A}D\left({\nabla }^{4}w\right)w_{m}dxdy={\displaystyle \int {\displaystyle {\int }_{A}q{w}_{m}dxdy}}}}\end{array}\right.$$

(5)

$$w={\displaystyle \sum _m{C}_m{w}_m}={\left(x^2-a^2\right)}^2{\left(y^2-b^2\right)}^2\left(C_1+C_2{x}^2+C_3{y}^2+\dots \right),$$

(6)

where C_m are m undetermined coefficients that are independent of each other, and w_m is the setting function that satisfies the displacement boundary condition.

Suppose that only one coefficient is considered in Equation (6):

$$w_1=C_1{w}_1=C_1{\left(x^2-a^2\right)}^2{\left(y^2-b^2\right)}^2.$$

(7)

So we get

$$w_m=w_1={\left(x^2-a^2\right)}^2{\left(y^2-b^2\right)}^2$$

(8)

$$\begin{array}{l}{\nabla }^{4}w={\displaystyle \frac{{\partial }^{4}w}{\partial x^4}}+{\displaystyle \frac{{\partial }^{4}w}{\partial y^4}}+2{\displaystyle \frac{{\partial }^{4}w}{\partial x^2\partial y^2}}\\ =8C_1\left[3{\left(y^2-b^2\right)}^2+3{\left(x^2-a^2\right)}^2+4\left(3x^2-a^2\right)\left(3y^2-b^2\right)\right]\end{array}.$$

(9)

By substituting Equation (5), we get

$$4D{\displaystyle {\int }_0^a{\displaystyle {\int }_0^b{\nabla }^{4}w{\left(x^2-a^2\right)}^2}}{\left(y^2-b^2\right)}^{2}dxdy=4q{\displaystyle {\int }_0^a{\displaystyle {\int }_0^b{\left(x^2-a^2\right)}^2}}{\left(y^2-b^2\right)}^{2}dxdy.$$

(10)

After the integration of Equation (10), C₁ is solved and then substituted into Equation (6), resulting in the deflection expression of the key stratum thin plate:

$$w={\displaystyle \frac{128q{\left(x^2-a^2\right)}^2{\left(y^2-b^2\right)}^2}{\left(a^4+b^4+0.57a^2{b}^2\right)D}}.$$

(11)

In Equation (11), it can be seen that when x = 0 and y = 0, the thin plate is allowed to deflect to its maximum as follows:

$$w_{\max }={\left(w\right)}_{x=y=0}={\displaystyle \frac{128q{a}^4{b}^4}{D\left(a^4+b^4+0.57a^2{b}^2\right)}}.$$

(12)

Especially when the thin plate is square, with b = a, the deflection of the key stratum thin plate is as follows:

$$w={\displaystyle \frac{128q{\left(x^2-a^2\right)}^2{\left(y^2-b^2\right)}^2}{2.57a^{4}D}}.$$

(13)

The maximum deflection is

$$w_{\max }={\left(w\right)}_{x=y=0}={\displaystyle \frac{128q{a}^4}{2.57D}}.$$

(14)

3.2. Analysis of Key Stratum Thin Plate Collapse Distance

After coal extraction, the layers above the goaf lose support and become suspended. The suspended span increases as the working face progresses. The relationship between the suspended span a_j and the working face advance distance l_j is shown in Figure 3.

In the case where all four edges are fixed, Figure 4 shows the bending moment distribution of the key stratum thin plate [15]. The maximum principal bending moment M_a is at the center of the long side, forming a positive bending moment zone in the center. According to the Marcus modified solution shown below

$$\left.\left|M_{\mathrm{a}}\right.\right|={\displaystyle \frac{(1-{\mu }^2)(1+\mu {\lambda }^2)}{12(1+{\lambda }^4)}}\cdot q{a}^2,$$

(15)

where $\mu$ is the Poisson‘s ratio of the key stratum; q is the load carried by the key stratum, MPa; $\lambda$ is the geometric shape coefficient of the key stratum, where ${\lambda }_1$ = a/b; a is the distance from the key stratum to the dew, m; b is the suspended span, m.

Consider the relation between stress and bending moment:

$$M_a={\displaystyle \frac{h^2{\sigma }_t}{6}},$$

(16)

where h is the key stratum thickness, m; σ_t is the tensile strength of the key stratum, MPa.

Substituting Equation (16) into Equation (15), the suspended span in the strike direction of the key stratum at the time of its initial fracture under four-edge fixed boundary condition is obtained as follows:

$$a_{jT}={\displaystyle \frac{h}{1-{\mu }^2}}\sqrt{{\displaystyle \frac{2{\sigma }_t}{q}}\cdot {\displaystyle \frac{1+{\lambda }^4}{1+\mu {\lambda }^2}}}.$$

(17)

When the key stratum undergoes initial fracture, a_j = a_jT. The connection between the suspended span of the key stratum at the initial fracture and the working face advance distance can be derived from Figure 4, as shown in Equation (18).

$$a_{jT}=l_j-2H_j\cot \beta$$

(18)

where H_j is the distance from the coal seam to the bottom of the key stratum, and β is the overburden fracture angle, which is generally 60°.

Substituting Equation (18) into Equation (17), the expression for the working face advance distance when the key stratum’s initial fracture is obtained, as shown in Equation (19):

$$l_{jT}={\displaystyle \frac{h_j}{1-{{\mu }_j}^2}}\sqrt{{\displaystyle \frac{2{\sigma }_{tj}}{q_j}}\cdot {\displaystyle \frac{1+{\lambda }_j^4}{1+{\mu }_j{\lambda }_j^2}}}+2H_j\cot \beta .$$

(19)

As mining continues, the corresponding jth key stratum also has a sufficient suspended span to fracture. Due to the fracturing of the fractured rock mass, the free space height below the overlying key stratum decreases continuously as the fractured rock mass caves. When the free space height becomes less than the maximum deflection of the key stratum, the free space height below the key stratum will be insufficient for it to fracture, and the overlying strata fracturing will be obstructed by this key stratum. Thereafter, even if the working face advancement distance continues to increase, the rock stratum above this key stratum will no longer fracture [42].

3.3. Method for Determining the WFZDH

By analyzing the maximum bending subsidence deformation within the key stratum mechanical model and the critical span at the initial fracture of the key stratum, a WFZDH determination method is proposed:

Step 1: According to the rock stratum assignment conditions, combined with the key stratum discrimination method [15], the key strata positions above the coal seam can be obtained. Meanwhile, the load borne by each key stratum and their respective stratigraphic positions were also calculated. The key strata were then sequentially numbered from bottom to top as key stratum j (j = 1, 2, …).

Step 2: By considering the information on the working face dimensions and advance distance, in combination with the parameters of the key stratum, such as tensile strength, thickness, and the load it bears, the relationship between the suspended span and its initial fracture distance was determined. If the suspended span of a key stratum exceeds its initial fracture distance, the key stratum can undergo fracturing, enabling the next step of the evaluation to proceed.

Step 3: By sequentially substituting the bearing load, thickness, and Poisson’s ratio of each key stratum into Equation (14), the maximum bending subsidence deformation of each key stratum was calculated. Meanwhile, the height of the free space below each key stratum was calculated using Equation (1). If the free space height below a key stratum is greater than its maximum deformation, it indicates that the key stratum has not fractured, and the WFZ will continue to develop upwards. Conversely, if the free space height is less than the maximum deformation, the key stratum will not fracture, and the WFZDH will be at the bottom of that key stratum.

There are two applicable conditions for the application of this discriminative method: Firstly, this method is primarily intended for determining the WFZDH in the working face with boundary conditions of four-sided fixed support. Secondly, it requires a comprehensive understanding of the thickness, lithology, and mechanical parameters of the strata. The WFZDH determination procedure is shown in Figure 5.

4. Example Analysis Validation

4.1. Overview

The 3# coal seam of Yeping Mine is a near-horizontal coal seam with a thickness of about 0~4 m and an average thickness of 3 m. It is buried at a depth of around 600 m. The 1301 working face is the initial mining face within this mining area. The inclined length is 180 m, and the mineable length is 1321 m. The overlying strata above the 3# coal seam contain a relatively large number of aquifers. Notably, the aquifer of the Luohe Formation, located approximately 120 m above the 3# coal seam, exhibits strong water abundance. The working face layout and the lithological characteristics of the overlying rocks are shown in Figure 6.

4.2. Theoretical Calculation of the WFZDH

Using the key stratum theory [15], there are three inferior key strata between the aquifer and the 3# coal seam, which are the second stratum of siltstone, the seventh stratum of medium sandstone, and the tenth stratum of siltstone. Distances from the 3# coal seam are 9 m, 31 m, and 54 m, respectively. The thin plate theory was used to analyze the WFZDH.

Table 1. Analysis and calculation results (a_j is the suspended span; a_jT is the ultimate span at the initial failure of key strata; w_max is the maximum deflection of key strata.).

Lithology	Thickness /m	Distance to Coal Seam/m	aj /m	ajT /m	wmax /m	△ /m	Break or Not
siltstone	10	9	34	45.23	2.47	3.82	Yes
medium sandstone	10	31	72	108.45	1.73	3.38	Yes
siltstone	15	54	94	156.78	5.5	2.92	No

shows the specific calculation results.

From the results in Table 1, the maximum deflection of the inferior key stratum 3 is 5.5 m, which exceeds the free space height of 2.92 m underneath it. At this point, the void below inferior key stratum 3 has been filled, and no further bending deformation of inferior key stratum 3 is allowed. Therefore, inferior key stratum 3 will not be damaged, and the water-conducting fissures will be impeded by inferior key stratum 3. Consequently, inferior key stratum 3 is the lower boundary layer of the bending subsidence zone, indicating that the WFZDH in the 1301 working face is 54 m.

4.3. Numerical Simulation Analysis of WFZDH

4.3.1. Modeling

For extending the UDEC two-dimensional discrete medium description to three dimensions, the 3DEC (v.7.0) procedure is used. It can describe the basic constituent objects of a rock body, i.e., rock masses and structural surfaces. Also, it has a rich library of structural material models for geotechnical bodies, which is especially suitable for studying the motion, deformation, and damage characteristics of discrete media. To study the destruction of overburdened rock and the development of fractures as the working face advances, we used 3DEC to carry out simulation and analysis. The numerical simulation method is more complex and comprehensive, providing richer information and better visualization of results, as well as allowing for comparison between theoretical analysis and field measurement parts of this study.

In order to facilitate numerical model calculations based on the geological conditions of the Yeping Coal Mine, thinner rock layers were merged and simplified. Using 3DEC simulation software, a calculation model of 400 × 280 × 120 m (strike × tendency × height) was established, in which the working face size was 300 × 180 × 4 m (strike × tendency × height), as shown in Figure 7. The numerical model selected was a Mohr–Coulomb model for the block and the contact Coulomb slip model for the joint. Based on field drilling data and indoor test results, physical and mechanical parameters were determined, as shown in

Table 2. Coal rock mechanics parameter table. D is the density; K is the bulk modulus; G is the shear modulus; C_m is the cohesion; σ_tm is the tensile strength; φ_m is the friction angle.

Lithology	Thickness/m	D/(kg·m−3)	K/GPa	G/GPa	φm/(°)	Cm/MPa	σtm/MPa
Medium sandstone	5	2.4	26.7	7	35	3	4
Mudstone	9	2.5	18.9	5	25	1.5	3
Medium sandstone	5	2.4	26.7	7	35	3	4
Mudstone	8	2.5	18.9	5	25	1.5	3
inferior key stratum 3	14	2.5	26.7	7	35	3	4
Mudstone	12	2.5	18	5	25	1.5	3
inferior key stratum 2	12	2.4	26.7	7	35	3	4
Mudstone	12	2.5	18	5	25	1.5	3
inferior key stratum 1	10	2.6	26.7	7	15	4	4
Mudstone	9	2.5	20	5	25	1.5	3
3#coal seam	4	1.5	13.2	10	20	1.2	2.6
Medium sandstone	20	2.5	18.9	7	35	3	4

.

To minimize boundary effects, 50 m coal pillars were left around each side of the 1301 working face. Each step of excavation was 5 m, with a mining height of 4 m, for a total of 60 steps of excavation. When the rock formation in the model breaks and gradually moves to a steady state, the model can be considered to have converged at this point.

Horizontal displacement constraints were applied around the perimeter boundary of the numerical model while constraining vertical displacements at the bottom boundary. The upper boundary was an unconstrained boundary. The numerical model height is only 120 m, while the depth of cover is 600 m, so it is necessary to apply vertical stress. The stress calculation expression is given in Equation (20):

$$P=\gamma H,$$

(20)

where γ is the average bulk density of the overlying rock layers, and H is the overlying rock thickness (m).

The result calculated according to Equation (20) is 12.96 MPa.

4.3.2. Simulation Result Analysis

The development of the overlying fissures under different advancing distances is shown in Figure 8.

According to Figure 8, when advancing to 40 m, inferior key stratum 1 reaches the first weighting distance and experiences its first weighting. The fractures continue to propagate upwards. As the working face advances to 60 m, inferior key stratum 1 undergoes periodic weighting. When the working face reaches 110 m, inferior key stratum 2 starts to experience its first weighting, and the overlying strata controlled by inferior key stratum 2 move synchronously. As advancing, inferior key stratum 2 undergoes periodic weighting, causing the fractures in the overlying soft rock to continuously expand. Until the working face reaches 300 m, inferior key stratum 3 does not experience weighting. At this point, it can be assumed that the fractures in the overlying strata no longer propagate upwards. The WFZ has developed up to the bottom of inferior key stratum 3, with an estimated height of 55 m.

4.4. Field Measurements

4.4.1. Observation Program Design

This field measurement adopts the double-end water plugging device observation method and the Borehole TV method. The principles of these field detection methods are shown in Figure 9, and the detection equipment is shown in Figure 10. Field measurements can directly reflect the actual situation, and the data are highly credible, which is conducive to an in-depth understanding of the complexity of the problem. The measured data can be used to verify the accuracy of other methods. The observation locations were selected 200 m ahead of the 1302 rail crossheading. Three monitoring stations were set up, with each station having a 90 mm diameter, 75 m-deep observation borehole drilled using a drilling rig. To facilitate the movement of the drilling rig, the spacing between the three monitoring stations was set at 10 m. The borehole design parameters are shown in

Table 3. Borehole design parameter table.

Borehole	Aperture/mm	Hole Length/m	Vertical Height/m	Angle of Elevation (°)	Axial Relationship with Roadway
1	90	75	60	55	It is perpendicular to the axial direction of the roadway and faces the goaf of 1301 working face.
2	90	75	60	60
3	90	75	60	65

, and the drilling design diagram is shown in Figure 11.

In addition to the quantitative analysis of overburden deformation using the double-ended plugger, direct observation and photographic documentation of overburden fracture development were conducted using borehole TV detection equipment (Zhongkuang Huatai Technology Development Co., LTD, Xuzhou, China).

4.4.2. Results and Analyses of Observations

The specific measurement process is shown in Figure 12.

The observation results of the boreholes are shown in Figure 13. The variation in leakage across the three boreholes exhibits similar trends. Therefore, this analysis will focus on the variation in leakage and the reasons in Borehole 1 as a representative case. In the borehole section with a depth of 18~38 m, the overall leakage was slightly small, generally not exceeding 10 L/min, indicating that secondary fissures were not well-developed within this zone and that the strata were less affected by mining activities, maintaining relatively high integrity. The predominant fractures in this interval were the original, inherent fractures in the rock mass. However, in the borehole interval of 40–68 m in depth, the leakage during drilling increased sharply to 13–15.8 L/min. This significant increase in leakage suggests that this zone had been heavily impacted by the mining-induced deformation. The enhanced interconnectivity of these secondary fractures led to the formation of a highly permeable fracture network within this interval of the overburden strata. Therefore, the drilling data indicates that this deeper zone had been penetrated by the borehole, entering the WFZ.

After 68 m, the leakage was 5.2~7.4 L/min, indicating that the overall permeability of the strata in this zone was relatively low. This suggests that the fractures were reduced in this interval compared to the zone above. Therefore, it can be considered that the boundary of the WFZ was at a depth of 68 m in the drill hole, making the WFZDH 58.9 m. The leakage in Borehole 2 and Borehole 3 is similar to that of Borehole 1, and the WFZDHs can be obtained from the analysis as 55.3 m and 57.4 m.

Figure 14 shows observations of the mining overburden fissures through Borehole 1. According to the pictures from the field observations, no fissures were present in the overburden until the hole depth was 30 m, and slight fissures started to appear at 30 m. At 36 m and 45 m, the rock stratum was seriously damaged. From 63 m onwards, the damage to the rock layer began to weaken, and the fissures decreased until 72 m when no obvious fissures appeared in the rock mass. It can be assumed that the WFZ develops to a depth of 63 m in the borehole, at which the WFZDH is 54.5 m.

4.5. Comprehensive Analysis

The WFZDH was simulated using 3DEC at 55 m. Through the field measurement, the WFZDH of the 1301 working face is 55.3 m~58.9 m. It can be found that the results of theoretical analysis (54 m) and numerical simulation (55 m) are close to the measured results (55.3 m~58.9 m), which verifies the reasonableness and practicability of the analysis method of the WFZDH based on thin plate theory.

Through further analysis, it can be found that the result of theoretical analysis is smaller than the measured result. However, we found that in the literature [28,29,30], the results obtained from the theoretical analysis are greater than field measurement results. There are two main reasons for this: First, in conducting the theoretical analysis, we considered the boundary conditions at the working face to be four-sided fixed support. Under this condition, the theoretical analysis results may be underestimated. Second, field measurements were taken two months after the working face had passed through that location, by which time the WFZDH had already reached its maximum value. Therefore, the results from the theoretical calculations would be smaller than the field measurement results.

5. Conclusions

A theoretical discrimination method for the WFZDH based on thin-plate theory was proposed following a study of the 1301 working face at Yeping Coal Mine. The following conclusions were drawn:

(1)

Key stratum failure needs to satisfy two conditions: the suspended span of the key stratum must be greater than the critical span at which the key strata first fracture, and the free space height below the key stratum must be greater than its maximum deflection. The deflection variation of the key stratum before its initial failure was analyzed, as well as the relationship between the suspended span of the key stratum and the advancement distance of the working face. Based on thin-plate theory, the theoretical discrimination method for the WFZDH was proposed.

(2)

According to the geological information at Yeping Coal Mine, the proposed theoretical discrimination method was applied to calculate the WFZDH development in the 1301 working face. The field measurement results are similar to theoretical discrimination method, which verifies the reasonableness and practicability of the discrimination method.

(3)

The method only requires knowledge of the geological information above the working face and a simple calculation can be used to obtain the WFZDH. However, this method does not consider the influence of factors such as possible pre-existing fissures in the overlying rock layers on the WFZDH, and there will be a certain degree of error between its calculation results and the actual values. At the same time, this research has some limitations, and it is mainly for the first mining or a single working face. Further research is needed on the WFZDHs for subsequent working faces and after multiple working faces have been mined.