Comprehensive Analysis of Feasibility by Ascending Mining in Coal Mine

Abstract

In order to study the feasibility of upward mining in a certain coal mine, the mechanical parameters of the coal rock mass were obtained based on on-site investigation and rock mechanics experiments. A numerical model that conforms to the on-site mining layout was established using numerical simulation methods. The stress, displacement, and plastic zone distribution characteristics of the upper coal rock mass at different positions along the X, Y and Z directions after the initial mining of layered coal were analyzed. The critical thickness for tensile failure of the roof during upward mining was calculated using the thick plate theory. A ground penetrating radar was used on site to conduct three-dimensional detection of the fragmentation characteristics of the overlying roof rock. The results show that after the mining of 5# coal, the stress of the overlying roof surrounding rock in the goaf exhibits a dynamic change process of rising peak falling. As the vertical height from the working face increases, the stress in the center of the goaf and around the working face gradually decreases; the displacement distribution extends outwards from the center of the working face, forming a sinking basin with an upward opening in the direction of inclination and direction of the working face. The maximum displacement value is at the bottom of the basin; there is a tensile stress zone above the working face, and the plastic zone has the largest range at the center of the working face direction and inclination. The plastic zone has not evolved to coal 4# and coal 3#; the maximum critical thickness for tensile failure of the roof is 55.4 m, which is much smaller than the actual thickness of 99.82 m on site, and upward mining can be adopted.

1. Introduction

Upward mining in coal mines is not common, and generally, mines do not have such surrounding rock conditions. Upward mining is often adopted to liberate a certain coal seam (such as high concentration gas coal seam), or due to the depletion of mine resources, abandoned coal seams are re-mined to form upward mining [1,2,3,4]. In successful cases of upward mining, a considerable portion of them involve the use of room and pillar mining methods or strip mining methods for lower coal layers [5,6,7]. During the upward mining process, the mining of the coal seam floor rock (coal) layer will also cause certain unloading deformation and damage, resulting in stress redistribution in the surrounding rock of the mining site, forming high stress and low stress zones in the surrounding rock of the mining site. These areas not only form within the coal seam being mined, but also propagate and diffuse upwards and downwards according to certain rules, resulting in attenuation. This depends on the characteristics of the collapse of the lower coal seam roof, as well as the spacing between the two coal seams and the lithology between them. When the distance between two coal seams reaches a certain thickness and the strength of the lithology between them meets certain conditions, the mining of the lower coal seam may not have a significant impact on the mining of the upper coal seam. Domestic and foreign scholars have conducted extensive research on the feasibility of upward mining in coal mines, proposing various discrimination methods such as ratio discrimination, “three zone” judgment, surrounding rock balance, and mathematical statistics [8,9,10,11,12,13,14,15]. Zhang Enqiang et al. determined the feasibility of upward mining by calculating the ratio of the height of the caving zone, fracture zone, and coal seam spacing in the coal mine [16]; Feng Guorui et al. conducted indoor physical similarity simulation experiments to master the stress transfer law of interlayer rock layers in the residual mining area of the collapse method, and revealed the structural mechanism and mechanical properties of the block beam semi-arch structure control layer in the interlayer rock layers of the upward mining area [17]; Cui Feng et al. established a key layer structural mechanics model and proposed an analysis method for the minimum safe distance of coal pillars to address the evolution characteristics and stability issues of overlying rock structure in upward mining of coal seams with strong impact tendency at close range [18].

This article comprehensively analyzes the feasibility of using long-wall caving upward mining in the mine through numerical simulation and thick plate theory, revealing the stress and migration characteristics of the upper coal rock mass after upward mining, in order to provide useful reference for upward mining in coal mines under similar geological conditions.

2. Engineering Background

The mining area has few fault structures and a simple structure. There are three coal seams from top to bottom, namely 3#, 4# and 5#, the average thickness of the 5# coal seam working face is 3 m, the strike length is 300 m, the width is 215 m, and the recoverable reserves are 1.78 million tons. The distance between 3# and 4# coal seams is 30.07 m, and the distance between 4# and 5# coal seams is 99.82 m, all of which are near horizontal coal seams. The basic roof and floor of coal seam 5# are mainly composed of siltstone and fine-grained sandstone, with a large thickness, undeveloped fractures, and good stability. In order to solve the problem of tight funding in the early stage of mine infrastructure construction, an upward mining process using the long-wall caving method was proposed, which first mines the 5# coal seam, and then mines the 3# and 4# coal seams. Therefore, it is crucial to study the degree of damage to the upper coal rock mass after mining the 5# coal seam, in order to determine the feasibility of upward mining. The location of the coal seam and the surrounding lithology and geology are shown in Figure 1.

3. Numerical Simulation Analysis

3.1. Establishment of the Numerical Calculation Model

In order to study the stress and displacement distribution characteristics of the upper coal rock mass after the mining of coal seam 5#, based on the occurrence environment and mining technology conditions of the coal seam, FLAC3 D numerical simulation software was used to construct a three-dimensional numerical calculation model with a model size of 315 m × 280 m × 218.21 m (X × Y × Z). The model is shown in Figure 2a, with 60 m and 70 m coal pillars at the front, back, and left and right boundaries of the model, respectively. The actual mining width and advancing length of the working face are 215 m and 200 m, respectively. The Mohr Coulomb criterion constitutive model was used for model calculation, and the surrounding boundaries are single constraint boundaries. The mining layout framework is shown in Figure 2b. According to the experimental data requirements, corresponding coal and rock samples were taken at the working face. Uniaxial and triaxial rock mechanics parameter experiments were completed at the Key Laboratory of Rock Control at Xi’an University of Science and Technology and the Key Laboratory of Western Mine Advancement and Disaster Prevention of the Ministry of Education, respectively. The quantitative physical and mechanical parameters of coal and rock mass were finally obtained, as shown in

Table 1. Mechanical parameters of coal and rock.

NO.	Lithology	Thickness	Density (kg·m⁻³)	Compressive Strength (MPa)	Tensile Strength (MPa)	Internal Friction angle/°	Elastic Modulus (MPa)	Poisson’s Ratio
1	Loess	30	1786	0.011	0.0018	14	10	0.30
2	Sandy mudstone	19.4	2370	35	1	3.0	33	0.44
3	Coarse-grained sandstone	5.14	2600	50	2	29	41	0.30
4	Fine-grained sandstone	5.25	2320	53.0	2.33	3	38.16	0.33
5	3# Coal	2.95	1320	25	0.61	32	25	0.35
6	Siltstone	25.95	2390	54.1	3.2	8.3	38.16	0.41
7	Mudstone	2.78	2100	23	1.4	28	30	0.36
8	4# Coal	1.25	1320	25	0.61	32	25	0.35
9	Medium-grained sandstone	5.05	2270	47.2	2.2	5.3	35	0.41
10	5# Coal	3.06	1320	25	0.61	32	25	0.35

, which provides reliable quantitative parameters and a basis for three-dimensional numerical calculations.

3.2. Stress Distribution Characteristics

The distribution characteristics of vertical stress at different positions in the Z direction from the bottom plate of the model after coal mining are shown in Figure 3. Figure 3a reflects the vertical stress distribution characteristics at Z = 27–29 m after the mining of 5# coal. It can be seen that the stress around the working face is significantly higher than that at the center above the goaf, and the pressure value is the lowest at all locations in the center of the goaf. Figure 3b reflects the vertical stress distribution characteristics at Z = 61–64 m after the mining of 5# coal. It can be seen that as the height of the Z coordinate increases, the stress values at the center and around the goaf decrease significantly compared to Figure 3a. Figure 3c reflects the vertical stress distribution characteristics at Z = 105–110 m after the mining of 5# coal, where the stress circle in the center of the goaf is most refined. It can be seen that as the height of the Z coordinate increases, the stress in the center of the goaf and around the working face gradually decreases, and the number of stress circles also significantly decreases. This indicates that after the mining of 5# coal, the impact of mining on 4# and coal 3# is relatively small.

The distribution characteristics of vertical stress at different positions along the Y direction from the bottom plate of the model after coal mining are shown in Figure 4. Figure 4a reflects the vertical stress distribution characteristics along the model direction (Y = 40–44 m) after the mining of 5# coal. There is a high stress concentration around the working face, and the stress value at the bottom of the model is relatively high. As the height of the Z coordinate increases, the stress value decreases continuously, the stress value decreases continuously, and the stress distribution above the working face shows a basin shape. Figure 4b reflects the vertical stress distribution characteristics along the model direction (Y = 86–90 m) after the mining of 5# coal. The closer to the center of the working face direction, the larger the area of positive stress above the working face, the higher the height of the stress zone in the center of the working face, and the smaller the area of positive stress at the end. Figure 4c reflects the vertical stress distribution characteristics along the model direction (Y = 105–109 m) after the mining of 5# coal, with the cross-section located in the center of the working face direction. It can be concluded that the height of the basin shaped area with positive stress decreases continuously after the profile position crosses the center of the working face direction.

The distribution characteristics of vertical stress at different positions along the X direction from the bottom plate of the model after coal mining are shown in Figure 5. Through comprehensive analysis, it can be concluded that the area above the working face where the stress is positive has undergone a process of increase peak decrease. The overall stress variation characteristics are similar to the vertical stress characteristics at different positions along the Y direction of the model.

3.3. Displacement Distribution Characteristics

The displacement distribution characteristics at different positions along the Z direction from the bottom plate of the model after coal mining are shown in Figure 6. Figure 6a reflects the displacement distribution characteristics of the 5# coal profile after mining (Z = 27–29 m). After mining, the surrounding rock movement is centered around the center of the working face and extends outward in a circular area. The maximum displacement of the surrounding rock at the center of the working face is −0.09 m. Through comprehensive analysis, it can be concluded that as the height of the Z coordinate increases, the amount and range of rock movement decrease significantly, and the shape of the rock movement area becomes closer to a circle, with a higher degree of refinement of the displacement circle.

The displacement distribution characteristics at different positions along the Y direction from the bottom plate of the model after coal mining are shown in Figure 7. Through comprehensive analysis, it can be concluded that the displacement value of the surrounding rock above the working face has also undergone a process of increase peak decrease. It reaches its maximum at the central position along the working face, while the subsidence value at the opening and stopping line positions is relatively small. As the height of the Z coordinate increases, the range of the surrounding rock affected by mining continues to decrease, and the subsidence value is not sufficient to cause substantial damage to the coal seam above.

The displacement distribution characteristics of the self-model at different positions along the X direction after coal mining are shown in Figure 8. Through comprehensive analysis, it can be concluded that the overall displacement characteristics of the surrounding rock above the working face are similar to the displacement characteristics of the surrounding rock at different positions in the Y direction. As the height of the Z coordinate increases, the range of the surrounding rock affected by mining continuously decreases, and the subsidence value is not sufficient to cause substantial damage to the coal seam above.

3.4. Distribution Characteristics of Plastic Zone

The distribution characteristics of plastic zones at different positions along the Z direction from the bottom plate of the model after coal mining are shown in Figure 9. It can be seen that the surrounding rock at (Z = 61–64 m) and (Z = 105–110 m) is in the original rock stress state and has not undergone plastic deformation, indicating that as the height of the Z coordinate increases, the range of the surrounding rock affected by mining decreases continuously. The mining of 5# coal will not have any mining impact on the subsequent mining of 4# coal.

The distribution characteristics of plastic zones at different positions along the Y direction from the bottom plate of the model after coal mining are shown in Figure 10 and the range of tensile failure in the plastic zone is shown in

Table 2. Tensile failure range of plastic zone along the model direction.

Plastic Zone	The Previous Tension Damage Unit		Current Tension Damage Unit
Position	Quantity	Volume/m3	Quantity	Volume/m3
Y = 40–44 m	69	92.22	166	233.37
Y = 86–90 m	76	97.71	368	515.39
Y = 105–110 m	77	98.35	387	539.55

. The range of the tensile stress zone above the working face increases from (Y = 40–44 m), and the plastic zone area is the largest at (Y = 86–90 m), which is located in the center of the working face direction. Afterwards, the plastic zone area begins to decrease, but the difference is that there is still a large area of tensile stress zone near the stopping line (Y = 105–110 m). Through comprehensive analysis, it can be concluded that there is a tensile stress zone above the working face, and the plastic zone is the largest in the center of the working face. The area of the plastic zone near the stopping line is larger than that near the cutting eye, and the plastic zone has not evolved to 4# coal and 3# coal. It indicates that the mining of 5# coal did not affect the overlying coal seam in the Y-direction profile.

The distribution characteristics of plastic zones at different positions along the X direction from the bottom plate of the model after coal mining are shown in Figure 11 and the range of tensile failure in the plastic zone is shown in

Table 3. Tensile failure range of plastic zone along the model direction.

Plastic Zone	The Previous Tension Damage Unit		Current Tension Damage Unit
Position	Quantity	Volume/m3	Quantity	Volume/m3
X = 40–44 m	68	94.07	276	401.07
X = 86–90 m	85	116.21	302	427.52
X = 105–110 m	87	119.83	305	429.67

. The range of the tensile stress zone above the working face increases from (X = 40–44 m), and this range is in the center of the inclined direction of the working face. The plastic zone area at the left and right ends of the working face is relatively small in the inclined direction, and the difference in plastic zone area between (X = 86–90 m) and (X = 105–110 m) is not significant. Through comprehensive analysis, it can be concluded that the plastic zone has not evolved into 4# coal and 3# coal, which indicates that the mining of 5# coal did not affect the overlying coal seam in the Y—direction profile.

4. Establishment and Analysis of Thick Plate Theory Model

4.1. Establishment of Roof Mechanics Model

The 5# coal adopts the long-wall caving mining process. As the working face advances, the suspended area of the roof will continue to increase, and some surrounding rock will gradually collapse and fill the goaf. In order to analyze the degree of damage to the upper roof surrounding rock after 5# coal mining and determine the feasibility of upward mining, the rock layer between 5# coal and 4# coal can be approximated as a hard composite thick roof. Without considering the support force of the caving gangue on the hard composite thick roof in the goaf, it is only subjected to the force q₀ of the overlying rock layer and its own gravity. The force diagram of the hard composite thick roof is shown in Figure 12a.

Based on the shape and dimensions of the hard composite thick roof in the goaf, it can be assumed to be an elastic rectangular flat plate with a thickness, length, and width of h, 2a, and 2b, respectively. Under the influence of human mining disturbance and roof rock creep, the cracks at the four boundaries of the hard composite thick roof will gradually increase, expanding from the original rock stress zone to the plastic zone. The constraint force of the surrounding rock on the four boundaries of the roof will gradually weaken, and the four boundary constraints will evolve from the original fixed constraints to simply supported constraints [19,20,21,22,23]. The four-sided simply supported constraints are shown in Figure 12b.

According to the ratio of plate thickness to width, plates can be mainly divided into two categories: thin plates and thick plates. The total thickness of the roof rock layer between coal 5# and coal 4# in this mine is 99.82 m, with a working face width of 215 m and a thickness to width ratio of 0.46 greater than 0.2. Therefore, the roof rock layer between coal 5# and coal 4# can be assumed to be a thick plate and was analyzed using the Frasov thick plate theory [19]. When the four sides of the thick plate are simply supported constraints, the equilibrium differential equation is as follows:

$$\begin{gathered} {\displaystyle \frac{2D}{5}}\left[\left(1-\nu \right){\nabla }^2{\psi }_x+\left(1+\nu \right){\displaystyle \frac{\partial \Phi }{\partial x}}+{\displaystyle \frac{1}{2}}{\displaystyle \frac{\partial }{\partial x}}\left({\nabla }^2\omega \right)\right]+{\displaystyle \frac{2}{3}}Gh\left({\displaystyle \frac{\partial \omega }{\partial x}}-{\psi }_x\right)=0 \\ \frac{2D}{5}\left[\left(1-\nu \right){\nabla }^2{\psi }_y+\left(1+\nu \right)\frac{\partial \Phi }{\partial y}+\frac{1}{2}\frac{\partial }{\partial y}\left({\nabla }^2\omega \right)\right]+\frac{2}{3}Gh\left(\frac{\partial \omega }{\partial y}-{\psi }_y\right)=0 \\ \frac{2}{3}Gh\left({\nabla }^2\omega -\Phi \right)+q\left(x,y\right)=0 \end{gathered}$$

(1)

In the formula, $D={\displaystyle \frac{E{h}^3}{12\left(1-{\nu }^2\right)}}$, $\Phi ={\displaystyle \frac{\partial {\psi }_x}{\partial x}}+{\displaystyle \frac{\partial {\psi }_y}{\partial y}}$ and ${\psi }_y$, ${\psi }_x$ are the angles of the two cross-sections $y=\cos s_t$ and $x=\cos s_t$, respectively; ω, ν, G, $h$ and E are the deflection, Poisson’s ratio, shear deformation modulus, thickness, and elastic modulus of the thick plate, respectively.

The expression for the bending moment of thick plates is as follows:

$$\begin{array}{c}{M}_x=-{\displaystyle \frac{D}{5}}\left[4\left({\displaystyle \frac{\partial {\psi }_x}{{\partial }_x}}+\nu {\displaystyle \frac{\partial {\psi }_y}{{\partial }_y}}\right)+\left({\displaystyle \frac{{\partial }^2\omega }{\partial x^2}}+\nu {\displaystyle \frac{{\partial }^2\omega }{\partial y^2}}\right)\right]\\ M_y=-\frac{D}{5}\left[4\left(\frac{\partial {\psi }_y}{{\partial }_y}+\nu \frac{\partial {\psi }_x}{{\partial }_x}\right)+\left(\frac{{\partial }^2\omega }{\partial y^2}+\nu \frac{{\partial }^2\omega }{\partial x^2}\right)\right]\\ M_{xy}=-\frac{D\left(1-\nu \right)}{5}\left[2\left(\frac{\partial {\psi }_x}{{\partial }_y}+\frac{\partial {\psi }_y}{{\partial }_x}\right)+\frac{{\partial }^2\omega }{{\partial }_x\partial y}\right]\end{array}$$

(2)

As shown in Figure 7b, the boundary conditions for a simply supported rectangular plate with four sides are as follows:

$$\begin{array}{l}{\omega |}_{x=0, x=a}=0, {{\psi }_y|}_{x=0, x=a}=0, {M_x|}_{x=0, x=a}=0\\ {\omega |}_{x=0, x=b}=0, {{\psi }_x|}_{x=0, x=b}=0, {M_y|}_{x=0, x=b}=0\end{array}$$

(3)

The displacement functions of rotation angle and deflection can be set as follows:

$$\begin{array}{l}\omega ={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{A}_{mn}\sin \frac{m\pi x}{a}}}\sin {\displaystyle \frac{n\pi y}{b}}\\ {\psi }_x={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{B}_{mn}\cos \frac{m\pi x}{a}\sin \frac{n\pi y}{b}}}\\ {\psi }_y={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{C}_{mn}\sin \frac{m\pi x}{a}\cos \frac{n\pi y}{b}}}\end{array}$$

(4)

Therefore, the force q0 acting on the overlying rock layer of the hard composite thick roof and its own gravity can be expanded as follows:

$$q\left(x,y\right)={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{q}_{mn}\sin \frac{m\pi x}{a}\sin \frac{n\pi y}{b}}}$$

(5)

By substituting Equations (4) and (5) into Equation (1), respectively, we can obtain the following expressions:

$$\begin{array}{l}{A}_{mn}=\left\{1+{\displaystyle \frac{6D{\pi }^2}{5Gh}}\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]\right\}\times {\displaystyle \frac{q_{mn}}{D{\pi }^4{\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]}^2}}\\ B_{mn}=\left\{1-{\displaystyle \frac{3D{\pi }^2}{10Gh}}\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]\right\}\times {\displaystyle \frac{m{q}_{mn}}{aD{\pi }^3{\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]}^2}}\\ C_{mn}=\left\{1-{\displaystyle \frac{3D{\pi }^2}{10Gh}}\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]\right\}\times {\displaystyle \frac{n{q}_{mn}}{aD{\pi }^3{\left[{\left(m/a\right)}^2+{\left(n/b\right)}^2\right]}^2}}\end{array}$$

(6)

In order to simplify the calculation and ensure a certain degree of accuracy, we approximate $m=n=1$. By substituting Equations (4)–(6) into Equation (2), we can obtain the following expressions:

$$\begin{array}{l}{M}_x={\displaystyle \frac{D}{5}}\left[{\displaystyle \frac{q_{11}\left(\frac{5}{a^2}+\frac{4\nu }{ab}+\frac{\nu }{b^2}\right)}{D{\pi }^2{\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}^2}}+{\displaystyle \frac{6q_{11}\nu \left(\frac{1}{b^2}-\frac{1}{ab}\right)}{5Gh\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}}\right]\times \sin {\displaystyle \frac{\pi x}{a}}\sin {\displaystyle \frac{\pi y}{b}}\\ M_y={\displaystyle \frac{D}{5}}\left[{\displaystyle \frac{q_{11}\left(\frac{5}{a^2}+\frac{4\nu }{ab}+\frac{\nu }{b^2}\right)}{D{\pi }^2{\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}^2}}+{\displaystyle \frac{6q_{11}\nu \left(\frac{1}{a^2}-\frac{1}{ab}\right)}{5Gh\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}}\right]\times \sin {\displaystyle \frac{\pi x}{a}}\sin {\displaystyle \frac{\pi y}{b}}\end{array}$$

(7)

The bending moment is the maximum value at the lower surface of the center position of the rectangular thick plate, that is, at $x=a/2$ and $y=b/2$. Moreover, the rectangular thick plate has symmetry, so only the bending moment in the x direction needs to be analyzed. Therefore,

$$M_{x\max }={\displaystyle \frac{D}{5}}\left[{\displaystyle \frac{q_{11}\left(\frac{5}{a^2}+\frac{4\nu }{ab}+\frac{\nu }{b^2}\right)}{D{\pi }^2{\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}^2}}+{\displaystyle \frac{6q_{11}\nu \left(\frac{1}{b^2}-\frac{1}{ab}\right)}{5Gh\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}}\right]$$

(8)

The maximum tensile stress in the x direction is as follows:

$${\sigma }_{x\max }={\displaystyle \frac{12M_{x\max }}{h^3}}z={\displaystyle \frac{12M_{x\max }}{h^3}}\cdot {\displaystyle \frac{h}{2}}$$

(9)

By substituting Equation (8) into Equation (9), the maximum tensile stress in the x-direction of the thick plate can be obtained as follows:

$${\sigma }_{x\max }={\displaystyle \frac{6q_{11}\left(\frac{5}{a^2}+\frac{4\nu }{ab}+\frac{\nu }{b^2}\right)}{5{\pi }^2{\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}^2{h}^2}}+{\displaystyle \frac{6q_{11}\nu \left(\frac{1}{b^2}-\frac{1}{ab}\right)}{25\left(1-\nu \right)\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}}$$

(10)

In the formula $q_{11}=q_0+\rho gh$, where $q_0$ is the load exerted by the overlying rock layer on the thick plate, $\rho$ is the average density of the thick plate, and $g$ is the acceleration due to gravity.

After the mining of 5# coal, the thick plate changed from the original triaxial stress state to a biaxial stress state. The strength of the thick plate rock mass is compressive but not tensile, so the main failure mode of the thick plate is bending and tensile. When the maximum tensile stress ${\sigma }_{max}$ of a thick plate is greater than or equal to its ultimate tensile strength ${\sigma }_t$, the thick plate will undergo failure.

4.2. Engineering Examples

According to the mechanical parameters and occurrence conditions of the coal rock mass in the mine, the length, width, thickness, and average density of the thick plate are $2a=215 \mathrm{m}$, $2b=200 \mathrm{m}$, $h=99.82 \mathrm{m}$, and $\rho =2252.2 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$, respectively. The average density and thickness of the overlying rock layer on the thick plate are ${\rho }_0=2112.6 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$, $h_0=95.33 \mathrm{m}$, $\pi =3.14$, gravity acceleration $g=9.8 \mathrm{m}/{\mathrm{s}}^2$, and Poisson’s ratio $\nu =0.41$. If $q_0={\rho }_{0}g{h}_0=1.97 \mathrm{M}\mathrm{P}\mathrm{a}$, $\rho gh=2.2 \mathrm{M}\mathrm{P}\mathrm{a}$, and the thick plate is composed of multiple layers of rock such as siltstone and fine-grained sandstone, then the minimum tensile strength of a single rock layer in the thick plate can be taken as ${\sigma }_{t1}=2 \mathrm{M}\mathrm{P}\mathrm{a}$, and the maximum cumulative tensile strength of multiple rock layers can be taken as ${\sigma }_{t2}=21.77 \mathrm{M}\mathrm{P}\mathrm{a}$. When the maximum tensile stress ${\sigma }_{max}={\sigma }_t$ in Equation (10), the critical thickness for tensile failure of thick plates can be obtained. By substituting the above parameters into Equation (10), it can be concluded that when ${\sigma }_{t1}=2 \mathrm{M}\mathrm{P}\mathrm{a}$, the critical thickness $h_1=55.4 \mathrm{m}$, and when ${\sigma }_{t2}=21.7 \mathrm{M}\mathrm{P}\mathrm{a}$, the critical thickness $h_2=15.4 \mathrm{m}$. However, the actual total thickness of the roof rock layer between coal 5# and coal 4# in this mine is 99.82 m. Therefore, upward mining of the mine is feasible.

5. On-Site Testing

In order to further determine the distribution characteristics of the plastic zone of the overlying surrounding rock after the mining of coal seam 5#, the SIR-20 of the American Laurey Company professional geological radar imported from the United States was used for comprehensive three-dimensional detection of the overlying surrounding rock of coal seam 5#. The effective depth of this geological radar is less than 35 m, and the accuracy decreases when it exceeds 35 m. When the surrounding rock is relatively intact, the color of the geological radar detection result graph appears as a single color, and when the surrounding rock is relatively fragmented, the color of the geological radar detection result graph may become disordered. Starting from the track roadway near the working face, the detection angle was 60 degrees, and the distance measurement along the working face was 100 m. The inclination depth measurement was 45 m. The detection scheme is shown in Figure 13a, and the detection result is shown in Figure 13b. It can be seen that within the range of 0–100 m in the direction of the working face and 0–7 m in the inclined depth measurement, yellow and blue-green colors are mainly present, mixed with red spots. The radar electromagnetic wave speed is high and the wavelength is long, and the medium undergoes significant changes. The strip-like characteristics are obvious, indicating that the coal rock mass is loose and relatively fragmented within this range. This fragmented area is mainly caused by the excavation construction of the track roadway. Within the range of 0–38 m for distance measurement and 20–40 m for inclined depth measurement, there is a slight change in color, indicating that the degree of rock fragmentation in this range is not significant. Within the range of 38–100 m for distance measurement and 7–40 m for inclined depth measurement, the color is mainly red and there is no obvious change, indicating that the overall integrity of the surrounding rock in this range is good and there is no fragmentation. Based on comprehensive analysis, it can be concluded that the mining of 5# coal is not sufficient to have an impact on the mining of 4# coal, and it is feasible to choose upward mining for this mine.

6. Conclusions

(1)

After the mining of 5# coal, the stress of the overlying roof surrounding rock in the goaf shows a dynamic change process of rising peak falling. With the increase in height, the stress in the center of the goaf and around the working face gradually decreases.

(2)

From the displacement distribution characteristics, it can be seen that the movement of the surrounding rock is centered around the center of the working face and extends outward in a circular area. The maximum displacement of the surrounding rock at the center of the working face is −0.09 m. As the height increases, both the amount and range of rock movement decrease significantly.

(3)

From the distribution characteristics of the plastic zone, it can be seen that the surrounding rock at (Z = 61–44 m) and (Z = 105–110 m) is in the original rock stress state and has not undergone plastic deformation, indicating that the range of influence of mining on the surrounding rock continues to decrease with increasing height, and the mining of 5# coal is not sufficient to affect the mining of 4# coal.

(4)

A mechanical model of a hard composite thick roof was established based on the theory of thick plates. The critical thickness for tensile failure of the roof was determined using the mechanical parameters and occurrence conditions of the coal rock mass in the mine. It was found that the critical thickness for tensile failure of the roof was much smaller than the actual thickness on site. It is believed that the mine can adopt the method of upward long-wall collapse mining.

(5)

This article studies the feasibility of upward mining of the mine under existing technological conditions, which is targeted and limited. There may be certain differences in geological conditions and mining techniques among different mining areas. Subsequent research should fully utilize multiple methods for comparative study and use multiple methods in combination to achieve ideal results.