Study on the Co-Evolution Mechanism of Key Strata and Mining Fissure in Shallow Coal Seam Mining

Abstract

Shallow coal seam mining makes the evolution form of mining fissures in rock and soil layers diversified, which leads to the easy penetration of mining fissures as the main channel of water, sand inrush, and air leakage. In order to reveal the co-evolution mechanism of broken rock beam structure and mining fissures in key strata, taking Hanjiawan Coal Mine as the research background, the relationship between mining fissures and rock beam structure, fissure activation period, propagation characteristics, and connectivity of working face was studied by means of field observation, physical similarity simulation, and theoretical derivation. The research shows that the fracture structure of key strata in shallow coal seam mining mainly includes hinged rock beam and step rock beam structures. Through the analysis of the rock beam structure, we found that the types of mining fissures in the overlying strata of key strata were up and down I-I and I-II mining fissures, and the heights of fissure development were 44.38 m and 98.35 m, respectively. The key block rotation made the mining fissures undergo five dynamic activation processes. The calculation formula of the fissure activation cycle was established, and the rock breaking angle, mining fracture lag distance, and fissure penetration discriminant were obtained and verified by field measurement results.

1. Introduction

Mining fissures are an unavoidable problem in the process of coal mining. At the same time, as the dominant factor of wind leakage, water intrusion, and sand intrusion disasters, it has become a precursor to the occurrence of complex mine disasters [1,2,3]. Mining operations cause the fracturing of the key bearing layer, which in turn weakens the control capacity of the overlying load layer and accelerates the complete development of mining fissures [4,5,6]. On the one hand, the formation of mining fissures is affected by mining parameters; on the other hand, it is controlled by the occurrence conditions of key strata [7,8]. The fracture characteristics of the key stratum and the bearing structure formed to determine the shape of mining fissures [9]. The mining fissure is the embodiment of the fractured form of the key strata, and the fracture of the key strata is the prerequisite for the formation of the mining fissure; moreover, there is a strong causal relationship between the two [10,11,12]. It can be seen that the research on mining fissures should be a process of the comprehensive analysis of key strata fracture structures and mining fissures. Therefore, this study started from the fracture of the key strata in the mining face and led to the mining fissure, forming a research system of the key strata-mining fissure co-evolution.

According to fissure mechanics, there are three types of fractures formed by objects, which are opening type (type I), sliding type (type II), and tearing type (type III). There are dynamic fissures and shearing mining fissures, and the tearing type is less likely to appear during the mining process [13]. The fracture characteristics of overlying rock in the mining face can be divided into a caving zone, fissure zone, and curved subsidence zone, and there is no curved subsidence zone in the mining of typical shallow coal seams [14]. For the distribution of fissures, after the mining of the working face, the overall fracture shape formed on the surface or its profile is defined, and related theories such as O rings, high-level annular fissures, and elliptical belts are proposed [15,16,17]. On the basis of the above studies, many scholars have formed different research directions to study the evolution characteristics of fissures and formed the empirical formula prediction method and the key strata theoretical discrimination method mentioned in the three regulations to study the development height of fractures [18,19,20,21,22]. At the same time, in order to more comprehensively develop the influence of mining parameters on fissure evolution characteristics, the main influential factors of fissure evolution characteristics were obtained through corresponding research on mining height, mining depth, and working face length [23,24,25]. In the field production process, the mining fissure is not completely a disadvantage factor. For the gas drainage, the accurate determination of the fissure height and distribution range can reasonably arrange the location of the drainage hole, effectively extract the gas, and ensure the safety of the mine recovery [26,27,28,29]. The formation of mining fissures on the surface is inseparable from the characteristics of the soil. Due to the characteristics of compressive but not tensile properties of the soil layer, the soil layer is prone to tensile failure after mining. When the overlying rock is mined in shallow coal seams to produce a stepped rock beam structure, the soil layer will be sheared and damaged, prompting the formation of mixed mining fissures in the soil layer [30,31,32]. Taking the vertical section of the working face as the dividing line, the mining fissures can be divided into advanced mining fissures and co-located mining fissures. The advanced mining fissures basically coincide with the surface subsidence movement angle position, and the horizontal deformation value of the rock and soil mass is greater than its limit tension. When the elongation deformation value is higher, mining fissures are formed [33,34,35,36]. From the above analysis, it can be seen that mining fissures play a vital role in the mining process, and an accurate grasp of the failure form of mining fissures has a positive effect on coal mining operations and surface damage mining [37,38,39,40]. The formation of mining fissures is difficult to avoid. Changing the fracture morphology of rock strata from the control method is one of the solutions to weaken the evolution characteristics of mining-induced fractures [41,42]. Therefore, for the study of mining fissures in shallow coal seams, there are often limitations in only studying the distribution of mining fissures, and the evolution characteristics of mining fissures cannot be obtained. In order to study the formation mechanism of mining fissures, a comprehensive study should be carried out, combining the fracture patterns of key strata and mining fissures.

This article takes shallow coal seam mining as the research premise and uses on-site research and physical similarity simulation tests to study the fracture structure of key strata and the evolution characteristics of mining fissures. On the basis of on-site measurement and simulation experiments, the synergistic evolution relationship between the fracture morphology of key strata and mining fissures was presented, and a mechanical calculation model for key strata mining fractures was established, providing a certain theoretical basis for studying mining fissures in shallow coal seams.

2. Evolution Law of Surface Mining Fissures

2.1. Engineering Background

The Hanjiawan Coal Mine in northern Shaanxi mainly mines No.2-2, No.3-1, and No.4-2 coal seams. This time, the No.2-2 coal working face was used as the research background. The surface of the study area was covered with 4.55 m of aeolian sand and 18.13 m of laterite. The coal seam had an average buried depth of 79 m and a mining height of 4.3 m. There was a 16 m medium-grained sandstone key strata above the coal seam. The working face had an inclined length of 278 m and a strike length of 1828 m. Comprehensive mechanized mining was adopted, and the roof was managed by the full caving method, which is typical shallow buried near horizontal coal seam mining, as shown in Figure 1.

2.2. Development Law of Surface Mining Fissures

(1)

Static development law of surface mining fissures

In order to obtain the development law of surface mining fissures, the evolution characteristics of surface mining fissures in the No.2-2 coal working face of Hanjiawan Coal Mine were investigated. Since the buried depth of the working face in this research was 79 m, according to the sufficient mining conditions proposed in the literature [43], it can be known that full mining can be achieved when the pushing length of the working face is 110.6 m. Through the analysis of on-site production conditions and surface characteristics, a working face with a strike length of 500 m was selected as the research area for surface mining fissures.

According to the space–time relationship between mining fissures on the surface and the mining push in the working face, the mining fissures are divided into two types: permanent fissures and periodic fissures. A total of 31 periodic fissures and 11 permanent fissures were found in the study area. The outermost permanent fissure of the cut hole was 38.5 m away from the coal wall, and the width of the fissure was 29 cm. The maximum distance between the two ends of the face was 19.4 m, and the fissure drop was 0~52 cm. Periodic fissures appeared periodically as the working face advanced, and the distance between the two fissures was 13.2~19.7 m. The fissures produced step sinking, the drop was 0~25 cm, and the fissure width was 0~20 cm, as shown in Figure 2. According to the distribution characteristics of surface mining fissures, the fissures with large drops were mainly distributed in the cut hole and both ends of the working face, and were less distributed in the normal mining area. Moreover, the drop was small. The periodic fissures were distributed approximately in parallel, and the boundary fissures at both ends of the working face were discontinuously distributed.

In the process of working face mining, periodic mining fissures are more frequent than permanent fissures. Combined with the research content of this paper, the evolution characteristics of periodic mining fissures were statistically analyzed. The periodic mining fissure drop of 0 cm accounted for about 25% of the total, the fissure drop of 0~5 cm accounted for 21.9% of the total, the fissure drop in 5~10 cm accounted for 21.8%, the fissure drop of 10~15 cm accounted for 15.6%, the fissure drops of 15~20 cm accounted for 9.4%, and the fissure drop of more than 20 cm accounted for 6.3%, as shown in Figure 3a. The fissure width of 0~5 cm accounted for 68.7% of the total, the fissure width of 5~10 cm accounted for 21.9% of the total, the fissure width of 10~15 cm accounted for 6.2% of the total, and the fissure width of 15~20 cm accounted for 3.2% of the total, as shown in Figure 3b. According to the evolution characteristics of surface mining fissures, it can be seen that the gap of periodic fissures was relatively small, and there were a large number of fissures with no gap or a small gap. The fissure width was mainly concentrated in the range of 0~5 cm, and only a small part of the fissure width was large. This shows that the periodic fissures had a strong healing ability, which can be closed during the mining process of the working face and can reduce the surface damage to a certain extent.

(2)

Temporal and spatial evolution characteristics of surface mining fissures

The formation of surface mining fissures is the result of working face mining, so it is the key to determine the relationship between working face advancing distance and mining fissures. Periodic mining fissures span across the working face and become the main fissure channel for mine air leakage, water inrush, and sand inrush during the mining process of the working face, which poses an unpredictable threat to the working face. Through the coordinate control system of the upper and lower wells, the progress table of the working face, and the advancing position of the working face, the statistical analysis was carried out on the position relationship of the maximum mining fissure lagging behind the working face within the range of 200~350 m from the cutting hole, and the surface mining fissure was obtained. The spatiotemporal location characteristics of the working face are shown in

Table 1. Space–time relationship between surface mining fissures and working surfaces.

Observed Time (d)	Working Face Position (m)	Maximum Mining Fissure Location (m)	Daily Footage (m)	Lag Distance (m)	Lag Angle (°)
1.3	204.3	167.48	11.4	36.8	65.0
1.5	219.5	187.59	9.7	31.91	68.9
1.3	236.6	203.05	12.4	33.5	66.9
1.4	252.4	221.84	11.2	30.5	68.8
1.5	271.2	241.37	12.2	29.8	69.2
2.0	285.9	254.48	7.2	31.4	68.2
1.9	302.3	270.12	8.4	32.1	67.7
1.0	314.5	285.59	12.1	28.9	69.8
1.3	331.7	299.86	13.1	31.8	68.0
2.2	350.4	321.0	8.4	29.4	69.5
Average value			10.63	31.61	68.2

.

According to Table 1, there were 10 surface fissures distributed in the monitoring range, and the distance between the fissures and the working face was 29.4~36.8 m, with an average lag distance of 31.61 m. The lag angle of the fissure was in the range of 65.0°~69.8°, and the average lag angle was 68.2°. It was found from the monitoring of mining fissures that the position of the maximum mining fissures was usually the same as that of the advanced mining fissures in the working face, and they both had high coincidence, which is the embodiment of mining fissures relative to the working face during different mining periods.

3. Fracture Structure of Key Strata and Evolution Characteristics of Mining Fissures

3.1. Physical Similarity Simulation Experiment Design

The experimental prototype is based on the geological data of the No.2-2 coal seam working face of the Hanjiawan Coal Mine in northern Shaanxi to build a near-horizontal physical model. In the experiment, a 3 m plane model frame made by Xi’an University of Science and Technology was selected. The thickness of the coal seam was 4.3 m, and the thickness of the coal seam was 4.5 m. It is known that the bearing capacity of the loose soil layer is insufficient, and it breaks simultaneously with the key strata and the bedrock layer. Therefore, this study focused on the bedrock layer. The bedrock layer was built to 41 m, and the equivalent load was applied to the unbuilt part.

According to the research content, the geometric similarity constant was selected as 1:100, and the model construction size was 300 cm (length) × 20 cm (width) × 44 cm (height). Based on the similarity law, the bulk density similarity constant was selected as 1.56; the stress similarity constant was selected as 156; and the time similarity constant was selected as 10. River sand, fly ash, gypsum, and large white powder were used as similar model building materials, among which river sand and fly ash were used as model aggregates, gypsum and large white powder were used as cement, and mica powder was used as joint division material. The test process was recorded by a total station and a digital camera, and the relevant mechanical properties of similar simulated test materials are shown in

Table 2. The main mechanical properties of each material in the model.

Number	Lithology	Thickness (m)	Model Thickness (m)	Tensile Strength (MPa)	Cohesion (MPa)	Bulk Modulus (MPa)	Shear Modulus (MPa)	Volumetric Weight (kN·m−3)
13	Loading layer	\	\	\	\	\	\	\
12	Fine-grained sandstone	3.7	4	1.77	1.72	1124	512	24.1
11	Mudstone	2.8	3	1.04	1.38	752	435	25.3
10	Fine-grained sandstone	0.8	1	2.02	1.50	998	488	22.7
9	Sandy mudstone	1.69	2	2.12	1.34	715	472	22.4
8	Fine-grained sandstone	4.8	5	1.78	1.90	1180	641	23.4
7	Sandy mudstone	2.6	3	2.12	1.32	780	467	24.1
6	Mudstone	2.8	3	1.25	1.24	731	412	27.4
5	Medium-grained sandstone	16.04	16	2.32	0.8	1269	620	21.6
4	Fine-grained sandstone	2.8	3	1.94	2.50	1531	832	23.0
3	Sandy mudstone	0.97	1	2.35	1.22	750	450	25.6
2	No.2-2 coal seam	4.3	4.5	0.35	1.18	612	333	13.4
1	Siltst one	2.78	3	1.53	0.15	141	510	23.4

.

3.2. Analysis of the Fracture Structure and Bearing Characteristics of the Key Strata

(1)

Analysis of key strata fracture structure characteristics

In this study, the overlying rock was a single key strata geological condition, and the relationship between the fracture structure of the key strata and the evolution of mining fissures was explored. According to field measurements and similar simulation experiments, when the working face was pressed for the first time, the lower layer of the key strata was broken, and the upper part of the key strata did not break. When the working face advanced to 84 m, the overlying bedrock of the key strata broke synchronously. During the mining process of the working face, the key strata were mainly composed of a hinged rock beam structure, supplemented by a stepped rock beam structure, forming the supporting system of the working face. The broken structure of the key strata led to differences in the shape of the mining fissures. When the key strata were a hinged rock beam structure, the mining fissures were similar, and the fissures had a small or no drop, as shown in Figure 4. When the key strata were broken to form a stepped rock beam structure, there was a large drop on both sides of the mining fissure, as shown in Figure 5.

(2)

Hinged rock beam structure-(I-I) type mining fissure

When the key strata form a hinged rock beam structure, the mechanical characteristics of the key block can be simplified, as shown in Figure 6. The key block B was subjected to the mining action to carry the upper overlying rock and loose soil layer to produce counterclockwise rotation movement, and the key blocks A and B generated upward tensile fissures at point F1. At this time, the overlying rock located on the upper part of the key block was subjected to tensile stress acting on both sides, and the stress characteristic of the mining fissure was the opening type (type I) in fracture mechanics [13], resulting in upward tensile fissures in the overlying rock. When the cumulative tensile strength of the overlying rock and loose soil layer is less than the tensile stress generated by the rotation of the key block, the fissures will penetrate and develop to the surface. If the cumulative tensile strength is equal to the tensile stress generated by the rotation of the key block, the fissures will stop growing to the cumulative height of the overlying rock development. When the two are equal, the development of mining fissures in the rock formation will have stopped, so there will be no greater situation. At the same time, due to the rotation of the key block B, the overlying rock and soil layer produce a subsidence space, forming a certain deflection. According to the principle of curvature calculation, the curvature w is positively correlated with the radius of curvature r, so the surface curvature is the largest, and it is easy to be damaged to produce downward type I mining fissures, which are collectively referred to as type I-I mining fissures. The depth of the descending type I mining fissures generated from the surface is affected by the geological occurrence conditions and the opening degree of the fractures [44].

For the relationship between fissure opening degree and fissure depth, Formula (1) can be used for calculations.

$$h_f=\mathrm{F}\sqrt{d}$$

(1)

where h_f is the fissure depth, m; d is the fissure opening, m; F is the correlation coefficient, which is 8 for the loose soil layer and 15 for the bedrock layer.

(3)

Stepped rock beam structure-(I-II) type mining fissure

When the key strata form a stepped rock beam structure, the stress characteristics of the key block and the migration characteristics of the overlying rock can be simplified, as shown in Figure 7. Due to the breakage of the key block, the rock and soil layer formed a relative up-and-down movement and rotary subsidence based on the key block D and E, which prompted the downward cutting and turning of the overlying rock and loose soil layer. At this time, the overlying rock and soil layer is subjected to the shear stress acting up and down at a certain angle and the tensile stress of reverse rotation, forming opening type (type I) and sliding type (type II) mining fissures, which are collectively referred to as type I-II mining fissures. According to the S-R standard and deflection principle, with the increase of the radius of curvature r based on the F₁ point, the type I mining fissures caused by the tensile stress gradually dominate. Similarly, for mining fissures near the F₁ point, shear stress is the main action. Under the action of shear stress, the upper overlying rock produces shear failure to form type II mining fissures that develop upward from the key strata. When the shear strength of overlying rock $\left[{\sigma }_{\mathrm{t}}\right]$ ≥ the maximum shear stress ${\sigma }_{\mathrm{tmax}}$ or the lower broken rock mass is full of free movement space, type II mining fissures stop developing upwards. The type I mining fissures produced by rock formation rotation are similar to the downward mining fissures formed by the hinged rock beam structure, so no further details are given.

Regarding the development height of mining fissures, it can be divided into two cases. One is that the key strata do not break. At this time, the height of fracture development is the distance between the coal seam and the key strata. It is the sum of the depth of the developed down-going production fissures and the height of the up-going production fissures developed upward from the key strata. If the depth of the mining fissure exceeds the buried depth of the key strata, it indicates that the mining fissure on the surface is connected to the working face, and it is easy to cause the water-bearing body or aeolian sand in the surface and the overlying rock and soil layer to collapse into the underground, accompanied by air leakage, which is harmful to the mine. Mining is hazardous. On the contrary, if the mining fissures are not penetrated, the working face mining will not be affected by the above factors.

The above analysis is the situation when the broken structure of the key strata is in a stable state. The stability of the hinged rock beam structure or stepped rock beam structure generated by the key strata can be calculated by using the S-R stability theory [14]. The broken structure of the key strata has strong self-stability and bearing capacity, but there is still the possibility of instability, so a certain supporting force needs to be provided for it.

For the hinged rock beam structure to maintain stability, the required supporting force R_J is

$$R_{\mathrm{J}}=\frac{4i_{\mathrm{J}}(1-\sin {\theta }_{\mathrm{J}})-3\sin {\theta }_{\mathrm{J}}-2\cos {\theta }_{\mathrm{J}}}{4i_{\mathrm{J}}+2i_{\mathrm{J}}\sin {\theta }_{\mathrm{J}}(\cos {\theta }_{\mathrm{J}}-2)}\times (P_{\mathrm{SJ}}+P_{\mathrm{J}})+P_{\mathrm{n}}$$

(2)

where i_J is the degree of the key block B of the hinged rock beam; P_SJ is the upper load of the hinged rock beam, MPa; P_J is the self-weight load of the hinged rock beam, MPa; and P_n is the rock load of the lower part of the key strata, MPa.

The supporting force R_T required for the stability of the stepped rock beam structure is

$$R_{\mathrm{T}}=\frac{i_{\mathrm{T}}-\sin {\theta }_{\max }+\sin {\theta }_{\mathrm{T}}-\tan {\varphi }_{\mathrm{T}}}{i_{\mathrm{T}}-2i_{\mathrm{T}}\sin {\theta }_{\mathrm{T}}+}\times (P_{\mathrm{ST}}+P_{\mathrm{T}})+P_{\mathrm{n}}$$

(3)

where i_T is the block degree of the key block E of the stepped rock beam; ${\theta }_{\max }$ is the maximum rotation angle of the key block E of the stepped rock beam, generally 8°~12°; $\tan {\varphi }_{\mathrm{T}}$ is the friction coefficient between rock blocks, which is 0.5; P_ST is the step rock beam upper load, MPa; and P_T is the self-weight load of the stepped rock beam, MPa.

When the load-bearing structure becomes unstable, the overlying load layer will impact the working face, which is prone to sudden disasters. Therefore, the stability of the rock beam structure at the key strata should be ensured.

3.3. Analysis of Mining FISSURE Activation Period

(1)

Activation characteristics of type I-I mining fissures

When the key strata are broken into a hinged rock beam structure, the key block C is in a stable state, and the lower broken caving rock blocks are compacted. The key block A has no obvious change, and the key block B turns counterclockwise, articulating with key blocks A and C, playing a bearing role in the upper rock layer. During the process of pushing the working surface to the key block A, the key block A has the same movement characteristics as the key block B, and the key block B rotates clockwise at the F₁ point until it is in the state of the key block C. When the key block B rotates counterclockwise, it carries the overlying rock and soil layer to produce similar coaxial rotation and subsidence, and the up and down type I-I mining fissures between the key blocks A and B are generated and expanded to form a fissure, as shown in Figure 6, displaying the mining fissure morphology. When the key block B rotates clockwise, the mining fissure between the key blocks A and B gradually closes, and the mining fissure between the key blocks B and C that tends to close is reactivated and expanded, with the level generated during the continuous advancement of the working face closing again under the action of extrusion stress.

(2)

Activation characteristics of type I-II mining fissures

Mining of shallow coal seams is easy in terms of forming a stepped rock beam structure, and under the action of this structure, type I-II mining fissures are produced in the rock and soil layer. The broken block of the stepped rock beam structure formed by the key strata is divided into four parts, namely, D, E, F, and G. The key block G is in a stable state and only forms horizontal extrusion stress with the key block F. The key blocks E and F are the support blocks of the stepped rock beam. When the key blocks D and E form a relative cutting displacement, the rock and soil layer above them will form a synchronous migration phenomenon and form II mining fissures under the action of shear stress. At the same time, the surface produces step subsidence. Since the rock mass below the key block D has collapsed to form a free movement space, the key block D is prompted to rotate counterclockwise around the F₁ point and carry the rock and soil layer above it to rotate. Tensile stress occurs between rock and soil layers, and when the ultimate tensile strength is reached, type I mining fissures develop along a certain angle on the surface. With the mining of the working face, the key block D breaks to form a migration feature similar to that of the key block E, and the evolution process of mining fissures is almost the same. At this time, the key block E turns clockwise and moves downward, the mining fissure between the key blocks D and E gradually closes, with the mining fissure between the key blocks E and F expanding. When the stepped rock beam structure formed by the key block E is not unstable, the surface mining fissures still evolve cyclically based on the step drop.

From the above analysis, it can be seen that under the action of mining rotation on the key blocks, the mining fissures located in the advancing direction of the working face experience five dynamic activation processes, namely, generation, expansion, closure, regeneration, and reclosure.

(3)

Analysis of mining fissure activation time

The evolution process of mining fissures is periodic. In order to better study the relationship between mining fissures and the advancing distance of the working face, the research was carried out by combining the development position of mining fissures and the pushing distance of the working face during the field measurement and similar simulation tests. In order to obtain a single mining fissure evolution process, the statistical analysis of the advancing position and time of the working face during the five fissure evolution processes can be approximated as the calculation model of the mining fissure period and recovery distance shown in Figure 8. Point O in the figure is the position where mining fissures appear when the working face is recovered to point O₁, and the lagging distance of mining fissures is L₁. When the working face is recovered to point O₂, the mining fissure at point O is close to closing for the first time, and the advancing length of the working face at this time is L₂. During the mining process from O₂ point to O₃ point in the working face, the key blocks rotate clockwise, and the mining fissures are activated. As the working face advances, the key blocks and mining fissures are closed again by horizontal extrusion, after which the mining fissures are no longer activated. In Figure 8, ${\beta }_{\mathrm{h}}$ is the hysteresis angle of the mining fissure, °; $\phi$ is the first closure angle of the mining fissure, °; ${\beta }_{\mathrm{h}1}$ is the activation angle of the mining fissure, °; ${\phi }_1$ is the second closure angle of the mining fissure, °; v is the average advancing speed of the working face, m/d; O is the first generation position of the mining fissure; L₁ is the hysteresis distance of the mining fissure, m; L₂ is the first closing distance of the mining fissure, m; L₃ is the mining fissure activation expansion distance, m; L₄ is the second closing distance of the mining fissure, m; H is the buried depth of the working face, m; and T is the evolution time of the mining fissure, d.

According to the evolution characteristics of mining fissures [44], the fissure evolution time can be obtained as

$$T=\left(L-L_1\right)/v$$

(4)

where L and L₁ can be expressed as

$$\{\begin{array}{l}L=H/\tan {\phi }_1\\ L_1=H/\tan {\beta }_{\mathrm{h}}\end{array}$$

(5)

Substituting Formula (5) into Formula (4) can obtain

$$T=\frac{H\left(\tan {\beta }_{\mathrm{h}}-\tan {\phi }_1\right)}{v\cdot \tan {\phi }_1\tan {\beta }_{\mathrm{h}}}$$

(6)

To predict whether mining fissures can heal on their own, it is necessary to calculate the horizontal force between key blocks in the mining process. Assuming that the breaking length of the mining key block and the uniform load on the upper part of the working face remain unchanged, and the rock beam structure is not unstable, then when the mining fissure is closed for the second time, it is necessary to satisfy

$$F_{\mathrm{S}}\ge \frac{L_{{}_{\mathrm{G}}}^2\gamma H\zeta }{n-1}$$

(7)

where F_S is the horizontal thrust of the key block, kN; $L_{\mathrm{G}}$ is the average breaking length of the key block, m; n is the number of breaking times of the key block from the secondary activation mining fissure to counterclockwise rotation; $\gamma$ is the average bulk density of the rock and soil layer, kN/m³; and $\zeta$ is the friction coefficient between the key block and its underlying rock formation.

From the above analysis, it can be seen that the time T₄ required for the second closure of mining fissures at this time is

$$T_4=\frac{\left(n-1\right)L_{\mathrm{G}}}{v}$$

(8)

At this time, the mining fissure evolution time can be expressed as

$$T=\frac{\left(n+1\right)L_{\mathrm{G}}}{v}$$

(9)

4. Analysis of Mining Fissure Propagation Characteristics and Evolution Parameters

4.1. Analysis of Mining Fissure Propagation Characteristics

According to rock and soil mechanics [30] and Griffith’s criterion [45], a certain amount of microcracks or weak structural planes exist in rock and soil mass, assuming that there is only one fissure in a unit rock and soil mass. Under the action of force, the unit rock and soil mass are subjected to unidirectional tensile stress, compressive stress, or confining pressure, and stress concentration will occur at the end of the fissure, with the tensile stress at the tip of the fissure being many several times the principal stress.

The relationship between the tensile stress and the principal stress at the fissure tip is

$$\{\begin{array}{l}\frac{{\left({\sigma }_1-{\sigma }_3\right)}^2}{{\sigma }_1+{\sigma }_3}=8{\sigma }_{\mathrm{t}},{\sigma }_1+3{\sigma }_3\ge 0\\ {\sigma }_3-{\sigma }_{\mathrm{t}}=0,{\sigma }_1+3{\sigma }_3\le 0\end{array}$$

(10)

where σ₁ and σ₃ are, respectively, the maximum principal stress and the minimum principal stress in the fissure area of the weak plane, MPa, and σ_t is the tensile stress at the fissure tip, MPa.

The type I and type II mining fissures formed by the breaking of the key strata are all caused by the failure and expansion of the fissure tip. According to the stress relationship in the direction of mining fissure propagation, the fissure propagation characteristics of rock and soil can be obtained, as shown in Figure 9.

According to the composite fissure propagation criterion of linear elastic fracture mechanics [46], the expressions of ${\beta }_1$ and ${\beta }_2$ can be obtained as

$$\{\begin{array}{l}{\beta }_1\\ {\beta }_2\end{array}=\arctan \left(\frac{\left({\sigma }_1+{\sigma }_3\right)\mp \sqrt{{\left({\sigma }_1+{\sigma }_3\right)}^2+4\left(\tan \varphi {\sigma }_3+\mathsf{\Omega }{\sigma }_{\mathrm{t}}\right)\left(\tan \varphi {\sigma }_1+\mathsf{\Omega }{\sigma }_{\mathrm{t}}\right)}}{\tan \varphi \left({\sigma }_3-{\sigma }_1\right)+2\mathsf{\Omega }}\right)$$

(11)

where $\mathsf{\Omega }$ is the mining fissure damage coefficient.

It can be seen from Figure 9 that if mining fissures expand, they must develop along the action lines of horizontal principal stress and vertical principal stress. At this time, the mining fissure propagation angle ${\varphi }_0$ has the following relationship:

$$\tan {\varphi }_0=\tan \left({\beta }_2-{\beta }_1\right)$$

(12)

According to the relation of an inverse trigonometric function, parallel vertical Formulas (11) and (12) can give ${\varphi }_0$ as

$${\varphi }_0=\arctan \left(\frac{\sqrt{{\left({\sigma }_1+{\sigma }_3\right)}^2+4\left(\tan \varphi {\sigma }_3+\mathsf{\Omega }{\sigma }_{\mathrm{t}}\right)\left(\tan \varphi {\sigma }_1+\mathsf{\Omega }{\sigma }_{\mathrm{t}}\right)}}{\tan \varphi \left({\sigma }_3-{\sigma }_1\right)+2\mathsf{\Omega }}\right)$$

(13)

According to the relationship between the fissure propagation angle and the arc length, the opening degree d of the mining fissure can be calculated as follows:

$$d=2r_0\sin \frac{{\varphi }_0}{2}$$

(14)

Under the assumption of unit rock and soil mass, the fissure azimuth ${\beta }_0$ satisfies the following formula:

$$\tan 2{\beta }_0=\tan \left({\beta }_2+{\beta }_1\right)$$

(15)

Then, the expression of fissure azimuth ${\beta }_0$ is

$${\beta }_0=\frac{1}{2}\arctan \left(\frac{\tan {\beta }_2+\tan {\beta }_1}{1-\tan {\beta }_1\tan {\beta }_2}\right)$$

(16)

If the directions of horizontal stress, vertical stress, maximum principal stress, and minimum principal stress are the same, then the fissure azimuth is the rock-soil fracture angle. If there is an included angle ${\theta }_0$, the fracture angle of the unit rock and soil mass fissure is

$${{\beta }^{\prime }}_0=\frac{1}{2}\arctan \left(\frac{\tan {\beta }_2+\tan {\beta }_1}{1-\tan {\beta }_1\tan {\beta }_2}\right)+{\theta }_0$$

(17)

Since rock formation fracture is mainly affected by rock-soil load and rock formation breaking distance [47], according to the Mohr–Coulomb criterion, the mining fissure angle of different rock formations can be calculated by the following formula:

$${\beta }_i={{\beta }^{\prime }}_i+\frac{1}{2}\arctan l\sqrt{\frac{{\mathrm{R}}_{\mathrm{T}}}{q_i}}$$

(18)

where ${{\beta }^{\prime }}_i$ is the breaking angle of fissures in the ith layer of rock and soil, °; l is the fracture distance of the rock layer, where $\sqrt{4.5}$ is taken for the initial break, and $\sqrt{3}$ is taken for periodic breaks; R_T is the ultimate tensile strength of the ith layer of rock, MPa; and q_i is the rock formation load, which can be uniformly distributed load or calculated load for key strata.

Based on the control of the key strata on the overlying strata, the key strata and the strata they control can be considered as a whole, and the breaking angle of the overlying strata can be approximated as the breaking angle of the key strata. Since the immediate roof is located below the key strata, it needs to be calculated layer by layer. According to the layered characteristics of sedimentary rocks, the breaking angle of each rock layer determines the overall breaking angle of the rock layer. There are differences in the occurrence properties of rock formations in different mines, so the correction coefficient A of the breaking angle is taken, and the overall breaking angle B of the rock formation is

$${\beta }_Z=\delta \arctan \frac{{\displaystyle \sum _{j=1}^m{h}_j\cot {\beta }_j+}{\displaystyle \sum _{k=1}^n{h}_k\cot {\beta }_k}}{{\displaystyle \sum _{j=1}^m{h}_j+{\displaystyle \sum _{k=1}^n{h}_k}}}$$

(19)

where m is the number of strata on the j_th layer on the immediate roof; h_j is the thickness of the j_th layer on the immediate roof, m; β_j is the breaking angle of the j_th layer on the immediate roof, °; n is the number of key strata of overlying strata; h_k is the thickness of the key strata of the k_th layer of overlying rock, m; β_k is the overall breaking angle of the key strata of the k_th layer of overlying rock, °.

The fracture angle of the rock formation determines the development position of the mining fissure, so the lag distance L_Z of the mining fissure can be obtained as

$$L_{\mathrm{Z}}={\displaystyle \sum _{j=1}^m{h}_j\cot {\beta }_j+}{\displaystyle \sum _{k=1}^{n+s}{h}_k\cot {\beta }_k}$$

(20)

where s is the number of layers of the sth layer of the overlying rock and soil layer on the key strata.

4.2. Analysis of Mining Fissure Evolution Parameters

(1)

Evolution depth of type I mining fissures in the downward direction

The mining action of the mine promotes the counterclockwise rotation of the key strata and the overlying rock and soil layer. When the tensile deformation ${\epsilon }_{x\mathsf{c}}\left(x,y,{\theta }_{\mathrm{r}}\right)$ and the ultimate tensile deformation $\left[\epsilon \right]$ caused by the rotation and subsidence satisfy Formula (21), the surface forms a downward type I mine moving fissures.

$${\epsilon }_{x\mathsf{c}}\left(x,y,{\theta }_{\mathrm{r}}\right)\ge \left[\epsilon \right]$$

(21)

In order to obtain an effective formula for calculating the development depth of type I mining fissures, the unit body in the fissure was studied and analyzed, and a calculation model for the development depth of type I mining fissures under mining action was established, as shown in Figure 10 and Figure 11.

First, it is assumed that the unit body has the following characteristics. The unit body is small enough to ignore its own load. The elevation of rock and soil layers at the same elevation is consistent, there is no undulating shape, and the influence of terrain can be ignored. At this time, the force acting on the top and bottom surfaces of the unit body is σ_Z, and the forces acting on the left, right, and front surfaces are σ_x and σ_y. Because it is mainly affected by tension, the shear stress effect is neglected in the study of the downward mining fissure. According to the theory of advanced soil mechanics [30], the calculation formulas can be obtained as

$$\{\begin{array}{l}{\sigma }_Z=\gamma H_{\mathrm{d}}\\ {\sigma }_x={\sigma }_y=\frac{\mu }{1-\mu }{\sigma }_Z=\frac{\mu }{1-\mu }\gamma H_{\mathrm{d}}\end{array}$$

(22)

where σ_Z is the vertical principal stress of the unit body at the depth H_d, MPa; σ_x and σ_y are the horizontal principal stresses of the unit body at the depth H_d, MPa; and μ is Poisson’s ratio.

According to the generalized Hooke’s law and the Mohr–Coulomb criterion, the following stress–strain relationship can be obtained [48,49]:

$$\{\begin{array}{l}{\epsilon }_x=\frac{1}{E}\left[{\sigma }_x-\mu \left({\sigma }_Z+{\sigma }_y\right)\right]\\ {\epsilon }_y=\frac{1}{E}\left[{\sigma }_y-\mu \left({\sigma }_Z+{\sigma }_x\right)\right]\\ {\epsilon }_Z=\frac{1}{E}\left[{\sigma }_Z-\mu \left({\sigma }_x+{\sigma }_y\right)\right]\\ {\sigma }_x={\sigma }_y={\sigma }_Z{\tan }^2\left(45+\varphi /2\right)-2\mathsf{c}\tan \left(45+\varphi /2\right)\end{array}$$

(23)

where E is the elastic modulus of the soil layer, MPa.

Under the condition of the same depth and direction of advancing tensile deformation, the additional stress $\mathsf{\Delta }{\sigma }_Z=\mathsf{\Delta }{\sigma }_y=0$ is applied in the vertical and inclined directions of the working face, and the additional stress $\mathsf{\Delta }{\sigma }_x$ is applied in the direction of the working face as follows:

$$\mathsf{\Delta }{\sigma }_x=\frac{E{\epsilon }_{\mathsf{c}}}{1-\mu }$$

(24)

where ${\epsilon }_{\mathsf{c}}$ is the critical tensile deformation of the surface, which is 2~3 mm/m. At this time, the deformation ${\epsilon }_{x\mathsf{c}}$ and stress ${\sigma }_{x\mathsf{c}}$ under the mining disturbance in the strike direction of the working face are

$$\{\begin{array}{l}{\epsilon }_{x\mathsf{c}}=\frac{1}{E}\left[\left({\sigma }_x-\mathsf{\Delta }{\sigma }_x\right)-\mu \left({\sigma }_Z+{\sigma }_y\right)\right]\\ {\sigma }_{x\mathsf{c}}={\sigma }_Z{\tan }^2\left(45+\varphi /2\right)-2\mathsf{c}\tan \left(45+\varphi /2\right)-\mathsf{\Delta }{\sigma }_x\end{array}$$

(25)

Substituting simultaneous Formulas (22)–(24) into Formula (25), the deformation ${\epsilon }_{x\mathsf{c}}$ of type I mining fissures under mining action can be obtained as

$${\epsilon }_{x\mathsf{c}}=\frac{\left(1+{\mu }^2\right)\gamma H-E{\epsilon }_{\mathsf{c}}}{E\left(1-\mu \right)}$$

(26)

When the amount of deformation generated under mining satisfies Formula (27), type I mining fissures are formed downward from the surface.

$${\epsilon }_{x\mathsf{c}}=\frac{\left(1+{\mu }^2\right)\gamma H-E{\epsilon }_{\mathsf{c}}}{E\left(1-\mu \right)}\ge \left[\epsilon \right]$$

(27)

Similarly, the Mohr–Coulomb criterion applicable to the downward type I mining fissure can be obtained by combining the above formulas:

$$\frac{\mu }{1-\mu }{\sigma }_Z-\frac{E{\epsilon }_{\mathsf{c}}}{1-\mu }={\sigma }_Z{\tan }^2\left(45+\varphi /2\right)-2\mathsf{c}\tan \left(45+\varphi /2\right)$$

(28)

Substituting Formulas (22) and (26) into Formula (28), the depth H_c of the descending type I mining fissure can be obtained as

$$H_{\mathrm{c}}=\frac{\frac{E{\epsilon }_{\mathsf{c}}}{1-\mu }-2\mathsf{c}\tan \left(45+\varphi /2\right)}{\gamma \left(\frac{\mu }{1-\mu }-{\tan }^2\left(45+\varphi /2\right)\right)}$$

(29)

(2)

Evolution height of upward type I mining fissures

During the mining process of the working face, under the action of tensile stress, upward and downward type I mining fissures are formed. Compared with the soil layer, the rock layer has greater cohesion. When studying the rock layer fracture, it is not easy to continue to use the method of calculating fissures in down mining. According to the nature of the rock formation, the research methods related to fracture mechanics are used for the research on upward mining fissures. From the formation process of fissures in fracture mechanics, it can be seen that the angle at which fissures are generated in the rock formation at this time is the fracture angle of the rock formation. Therefore, combining the fracture angle β_c of the rock formation with the unit body at the tip of the fracture can obtain the mechanical calculation model of the upward type I mining fissure, as shown in Figure 12.

According to the force characteristics of type I mining fissures in the working face [13], in the advancing direction of the working face, the stress field expression of the type I fissure tip in fracture mechanics can be obtained:

$$\{\begin{array}{l}{\sigma }_x+\mathsf{\Delta }{\sigma }_x=\frac{K_{\mathsf{I}}}{\sqrt{2\pi r_{\mathsf{I}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(1-\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\right)\\ {\sigma }_z+\mathsf{\Delta }{\sigma }_z=\frac{K_{\mathsf{I}}}{\sqrt{2\pi r_{\mathsf{I}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(1+\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\right)\\ {\tau }_{xz}=\frac{K_{\mathsf{I}}}{\sqrt{2\pi r_{\mathsf{I}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\end{array}$$

(30)

where $r_{\mathsf{I}}$ is the distance between the type I fissure and the fissure tip in polar coordinates, m, and $K_{\mathsf{I}}$ is the stress intensity factor of the type I fissure tip.

When it is known that fissures are formed in the rock formation, the fissures tend to pinch out gradually due to the inhibition of the force of the rock formation. At the same time, the occurrence of type I mining fissures needs to reach the critical value of stress intensity $K_{\mathrm{IC}}$, so the judgment condition for determining whether fissures are generated in the rock formation satisfies the following formula:

K_I ≤ K_IC

(31)

From the previous analysis, it can be seen that at the same depth of the unit body, there is only an additional stress $\mathsf{\Delta }{\sigma }_x$ in the strike direction of the working face, and at the same time, type I fissures are formed under the action of tensile stress and the effect of shear stress is small. Therefore, Formula (30) can be abbreviated as for

$$\{\begin{array}{l}{\sigma }_x+\mathsf{\Delta }{\sigma }_x=\frac{K_{\mathsf{I}}}{\sqrt{2\pi r_{\mathsf{I}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(1-\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\right)\\ {\sigma }_z=\frac{K_{\mathsf{I}}}{\sqrt{2\pi r_{\mathsf{I}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(1+\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\right)\end{array}$$

(32)

According to the small-scale yield theory in fracture mechanics, when $r_{\mathsf{I}}\to 0$, ${\sigma }_x\to \infty$, ${\sigma }_z\to \infty$. It is obviously inconsistent with the reality under mining conditions. When the above situation occurs in the rock formation, it shows that the rock formation has undergone plastic deformation, that is, plastic failure.

According to the Mises criterion, the force on the unit body satisfies the following formula:

$${\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_3-{\sigma }_1\right)}^2=2{\sigma }_s{}^2$$

(33)

According to the stress relation of Formula (22), we can obtain

$${\sigma }_s{}^2={\left({\sigma }_x+\mathsf{\Delta }{\sigma }_x\right)}^2+{\sigma }_y{}^2+{\sigma }_z{}^2$$

(34)

Substituting the stress at the tip of the type I fissure, under the plane stress, $r_{\mathsf{I}}$ can be obtained as

$$r_{\mathsf{I}}=\frac{1}{2\pi }{\left(\frac{K_{\mathsf{I}}}{{\sigma }_s}\right)}^2\left[{\cos }^2\frac{{\beta }_{\mathsf{c}}}{2}\left(1+3{\sin }^2\frac{{\beta }_{\mathsf{c}}}{2}\right)\right]$$

(35)

It can be seen from Formula (35) that the value of $r_{\mathsf{I}}$ is related to the stress intensity response at the tip of the type I fissure, the stress of the unit body, and the fracture angle of the rock formation. The unit body stress and rock formation failure angle can be calculated by Formulas (19) and (22), respectively. Therefore, only the stress intensity at the tip of the fissure should be an unknown parameter.

Plastic failure occurs at the tip of the fissure under the mining action of the rock formation, and the $K_{\mathsf{I}}$ plastic zone can be corrected to obtain

$$K_{\mathsf{I}}=\frac{\sigma \sqrt{\pi a}}{\sqrt{1-\frac{1}{2}{\left(\frac{\sigma }{{\sigma }_s}\right)}^2}}$$

(36)

where $\sigma$ is the stress without fissures, MPa, and a is the length of 1/2 of the major axis of the fissure, m.

It can be seen from Formula (36) that when $\sigma ={\sigma }_s$ is the largest, $K_{\mathsf{I}}$ is the largest, that is, the mining fissure is the longest, and the probability of sudden disasters in the mining process of the working face is the largest. Substituting $\sigma ={\sigma }_s$ into Formula (36) can obtain

$$K_{\mathsf{I}}={\sigma }_s\sqrt{2\pi a}$$

(37)

Due to different geological conditions and different mining thicknesses, there are differences in the rotation of key strata. According to the relationship between mining thickness and hinged rock beam rotation and subsidence, we can obtain

$$\frac{a}{b}=\frac{h\sin {\beta }_{\mathrm{c}}}{h\cos {\beta }_{\mathrm{c}}/2}=\lambda$$

(38)

where b is the length of 1/2 of the minor axis of the fissure, m.

By substituting Formulas (37) and (38) into Formula (35), the evolution height of upward type I mining fissures under polar coordinate conditions can be obtained. By transforming it into rectangular coordinates, the evolution height H_st of upward mining fissures can be obtained as

$$H_{\mathrm{st}}=\lambda a\left[{\cos }^2\frac{{\beta }_{\mathsf{c}}}{2}\left(1+3{\sin }^2\frac{{\beta }_{\mathsf{c}}}{2}\right)\right]\cdot \cos {\beta }_{\mathsf{c}}$$

(39)

(3)

Upward II type mining fissure evolution height

The analysis of the migration characteristics of the fractured overlying strata shows that when the key strata produce a stepped rock beam structure, the overlying strata will undergo shear failure and form upward type II mining fissures. At the same time, for the surface soil layer, the tensile stress generated by the turning action of the key strata causes the downward type I mining fissures to occur in the loose soil layer at the turning point of the key strata F₄, as shown in Figure 13.

Since type I mining fissures are tensile fissures, according to the previous analysis, the rotation phenomenon is similar under the hinged rock beam and stepped rock beam structures, so the fissure evolution characteristics are similar, and thus this section will not explore it. The force characteristics of the unit body at the tip of the upward type II mining fissure can be simplified, as shown in Figure 14.

According to the force characteristics of type II mining fissures in the working face [13], it can be known that in the advancing direction of the working face, the stress field expression of the type II fissure tip in fracture mechanics can be obtained:

$$\{\begin{array}{l}{\sigma }_x+\mathsf{\Delta }{\sigma }_x=\frac{K_{\mathrm{II}}}{\sqrt{2\pi r_{\mathrm{II}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(-\sin \frac{{\beta }_{\mathrm{c}}}{2}\left(2+\cos \frac{{\beta }_{\mathrm{c}}}{2}\cos \frac{3{\beta }_{\mathrm{c}}}{2}\right)\right)\\ {\sigma }_z+\mathsf{\Delta }{\sigma }_z=\frac{K_{\mathrm{II}}}{\sqrt{2\pi r_{\mathrm{II}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(\sin \frac{{\beta }_{\mathrm{c}}}{2}\cos \frac{{\beta }_{\mathrm{c}}}{2}\cos \frac{3{\beta }_{\mathrm{c}}}{2}\right)\\ {\tau }_{xz}=\frac{K_{\mathrm{II}}}{\sqrt{2\pi r_{\mathrm{II}}}}\cos \frac{{\beta }_{\mathrm{c}}}{2}\left(1-\sin \frac{{\beta }_{\mathrm{c}}}{2}\sin \frac{3{\beta }_{\mathrm{c}}}{2}\right)\end{array}$$

(40)

where $K_{\mathrm{II}}$ is the stress intensity factor at the tip of the type II mining fissure.

In the process of coal seam mining, the key strata break to form a stepped rock beam structure, accompanied by a large displacement of the overlying rock, which leads to the penetration of the upward and downward mining fissures, forming the mining fissures connecting the working face to the surface. Not all mining fissures will be connected, and type II mining fissures are gradually pinched out by the inhibition of rock strata. Similarly, the occurrence of type II mining fissures needs to reach the critical value of stress intensity $K_{\mathrm{II}\mathrm{C}}$, so the judgment condition for determining whether type II mining fissures are generated in rock formations is

K_II ≤ K_IIC

(41)

Since the shear stress is one of the main factors for producing type II mining fissures in rock formations, according to the shear strength formula of the Coulomb criterion, we can obtain

$${\tau }_f=\mathsf{c}+\sigma \tan \varphi$$

(42)

where τ_f is the shear strength of the rock formation, MPa; c is the cohesion of the rock formation, MPa; and $\sigma \tan \varphi$ is the friction strength, MPa.

Here, τ_f is the resultant force of τ_xy and τ_yx, which can be expressed as

$${\tau }_f=\sqrt{2}{\tau }_{xy}$$

(43)

From the principal stress relationship in Coulomb’s criterion, it can be obtained that

$$\sigma =\frac{{\sigma }_1+{\sigma }_3}{2}+\frac{{\sigma }_1-{\sigma }_3}{2}\cos 2{\beta }_{\mathrm{c}}$$

(44)

From the force characteristics of the fissure tip unit body and the expression of Formula (44) at the same depth, we can obtain

$$\sigma =\frac{\left({\sigma }_x+\mathsf{\Delta }{\sigma }_x\right)+{\sigma }_z}{2}+\frac{\left({\sigma }_x+\mathsf{\Delta }{\sigma }_x\right)-{\sigma }_z}{2}\cos 2{\beta }_{\mathrm{c}}$$

(45)

Simultaneous Formulas (40), (42), and (45) can obtain the distance r_II of the type II fissure tip unit as

$$r_{\mathrm{II}}=\frac{K_{\mathrm{II}}^2{\left[\sqrt{2}\cos \frac{{\beta }_{\mathsf{c}}}{2}\left(1-\sin \frac{{\beta }_{\mathsf{c}}}{2}\sin \frac{3{\beta }_{\mathsf{c}}}{2}\right)+\cos \frac{{\beta }_{\mathsf{c}}}{2}\sin \frac{{\beta }_{\mathsf{c}}}{2}\left(1+\left(1+\cos \frac{{\beta }_{\mathsf{c}}}{2}\cos \frac{3{\beta }_{\mathsf{c}}}{2}\right)\cos 2{\beta }_{\mathsf{c}}\right)\right]}^2}{2\pi {\mathsf{c}}^2}$$

(46)

From Formula (46), it can be seen that this formula is the relational formula between the stress intensity factor K_II of the fissure tip of the unit body and the fracture angle ${\beta }_{\mathrm{c}}$ of the rock formation. Similarly, the unit body stress and rock formation failure angle can be calculated using Formulas (19) and (22), respectively. Therefore, only the stress intensity at the tip of the fissure should be an unknown parameter.

The type II mining fissures formed by the mining of the working face are the result of mutual dislocation between the strata in the same layer. According to the continuous distribution theory of dislocation in fracture mechanics, the calculation expression of the stress intensity factor K_II at the fissures tip of the unit body is

$$K_{\mathrm{II}}={\tau }_f\sqrt{\pi a}$$

(47)

Substituting Formula (47) into Formula (46), we can obtain the evolution height of the upward type II mining fissure under the condition of polar coordinates and transform it into Cartesian coordinates to obtain the evolution height H_sr of the upward mining fissure as

$$H_{\mathrm{sr}}=\frac{{\tau }_{{}_f}^2\pi a{\left[\sqrt{2}\cos \frac{{\beta }_{\mathsf{c}}}{2}\left(1-\sin \frac{{\beta }_{\mathsf{c}}}{2}\sin \frac{3{\beta }_{\mathsf{c}}}{2}\right)+\cos \frac{{\beta }_{\mathsf{c}}}{2}\sin \frac{{\beta }_{\mathsf{c}}}{2}\left(1+\left(1+\cos \frac{{\beta }_{\mathsf{c}}}{2}\cos \frac{3{\beta }_{\mathsf{c}}}{2}\right)\cos 2{\beta }_{\mathsf{c}}\right)\right]}^2}{2\pi {\mathsf{c}}^2}\cos {\beta }_{\mathsf{c}}$$

(48)

To predetermine the evolution characteristics of mining fissures, the penetration of upward and downward mining fissures has become one of the evaluation criteria. From the depth of the downward type I mining fissures and the development height of the upward type I and type II mining fissures, the determination formula of mining fissure penetration can be obtained as

$$\{\begin{array}{l}{H}_{\mathrm{c}}+H_{\mathrm{st}}\ge H_{\mathrm{gd}}\\ H_{\mathrm{c}}+H_{\mathrm{sr}}\ge H_{\mathrm{gd}}\end{array}$$

(49)

where H_gd is the buried depth of the key strata, m.

It can be seen from the above formula that when the sum of the up and down mining fissures exceeds the burial depth of the key strata, it indicates that the mining fissures have penetrated the surface and are prone to water inrush, sand inrush, and air leakage. On the contrary, the working face will not produce the above disaster phenomenon.

5. Verification of Mining Fissure Evolution Parameters

The upward mining fissure is caused by the fracture of the key strata, which causes the tensile stress or shear stress of the overlying rock to reach the ultimate bearing capacity of the overlying rock, thereby generating fissures. At the same time, the strength of the key strata is much greater than that of the overlying strata, so the minimum fissure length of the overlying strata must exceed the breaking height of the key strata, that is, a ≥ 16 m, which is taken as 16 m in this paper. The specific parameters of the occurrence characteristics of rock and soil layers in Hanjiawan Coal Mine are shown in

Table 3. The occurrence characteristic parameters of rock and soil layers in Hanjiawan Coal Mine.

Soil Layer Related Parameters	Average Bulk Density (kN/m3)	Poisson Ratio	Cohesion (MPa)	Angle of Internal Friction (°)	Elastic Modulus (MPa)	Critical Tensile Deformation of Ground Surface (mm/m)
	23	0.35	0.077	36	32.45	−0.003
Related parameters of rock strata	Average Bulk Density (kN/m3)	Fracture Angle of Rock Stratum (°)	Cohesion (MPa)	Angle of Internal Friction (°)	Buried Depth of Key Strata (m)	/
	26	68	1.2	37	54.89	/

.

(1)

In order to simplify the calculation process, the given data in the paper are selected for calculation, and the mining fissure lag distance L_Z can be obtained as

$$L_{\mathrm{Z}}={\displaystyle \sum _{j=1}^m{h}_j\cot {\beta }_j+}{\displaystyle \sum _{k=1}^{n+s}{h}_k\cot {\beta }_k}=36.84 \mathrm{m}$$

From Formulas (22) to (48), the fissure evolution parameters of the mining face up and down mining can be obtained as

(2)

The depth H_c of the downward type I mining fissure is

$$H_{\mathrm{c}}=\frac{\frac{E{\epsilon }_{\mathsf{c}}}{1-\mu }-2\mathsf{c}\tan \left(45+\varphi /2\right)}{\gamma \left(\frac{\mu }{1-\mu }-{\tan }^2\left(45+\varphi /2\right)\right)}=6.03 \mathrm{m}$$

(3)

The height H_st of the upward type I mining fissure is

$$H_{\mathrm{st}}=\lambda a\left[{\cos }^2\frac{{\beta }_{\mathsf{c}}}{2}\left(1+3{\sin }^2\frac{{\beta }_{\mathsf{c}}}{2}\right)\right]\cdot \cos {\beta }_{\mathsf{c}}=38.35 \mathrm{m}$$

(4)

The height H_sr of the upward type II mining fissure is

$$H_{\mathrm{sr}}\ge 5.77a=92.32 \mathrm{m}$$

Therefore, according to the sum of the depth of down-going type I mining fissures and the height of up-going type I and type II mining fissures, the relationship with the buried depth of key strata is as follows:

$$\{\begin{array}{l}{H}_{\mathrm{c}}+H_{\mathrm{st}}=44.38 \mathrm{m}\le H_{\mathrm{gd}}\\ H_{\mathrm{c}}+H_{\mathrm{sr}}=98.35 \mathrm{m}\ge H_{\mathrm{gd}}\end{array}$$

It can be seen that when the mining height of the No.2-2 coal seam in Hanjiawan Coal Mine is 4.3 m, the downward type I mining fissures and the upward type I mining fissures are not connected, and it is not easy to produce water inrush, sand inrush, and air leakage in the process of working face mining. The downward type I mining fissures and the upward type II mining fissures are connected, and sudden disasters are prone to occur in the working face. The results are similar to those measured by field drilling, which verifies the rationality of this study.

6. Conclusions

(1)

Through the monitoring of the development characteristics of surface mining fissures during the mining process, it was found that the periodic fissures in the mining face of the shallow coal seam were in the shape of “C”, and the boundary fissures were in the shape of “(”. The maximum mining fissure position was the same as the advanced mining fissure position of the working face, with a high degree of overlap, being a reflection of mining fissures during different mining periods.

(2)

Based on the fracture characteristics of the key strata and the stress distribution pattern, it can be concluded that the overlying rock and soil layer on the key strata of the working face formed up and down type I-I mining fissures and type I-II mining fissures, and the rotation of the key blocks resulted in mining fissures. The dynamic fissures experienced five dynamic activation processes, namely, generation, expansion, closure, generation, and re-closure, and the calculation formula for the dynamic periodic evolution of the mining fissures was obtained.

(3)

Through the study of the fissure propagation characteristics, the calculation expression of the influence of the rock-soil layer load and the fracture distance of the rock formation on the mining fissure propagation was obtained. According to the control function of the key strata on the overlying strata and the geological occurrence characteristics, the overall fracture angle ${\beta }_Z$ of the strata and the lagging distance L_Z of the mining fissures were 36.84 m.

(4)

According to the stress distribution characteristics of mining up and down type I-I and type I-II mining fissures in the working face, the formula for calculating the dynamic evolution depth of mining fissures was obtained, and the discriminant formula for the penetration of up and down mining fissures was proposed.

(5)

According to theoretical calculations and on-site drilling measurements, it was found that the up-and-down type I-I mining fissures in Hanjiawan Coal Mine No.2-2 coal mining did not penetrate, and the type I-II mining fissures penetrated. The heights of fissure development were 44.38 m and 98.35 m, and the penetrated fissures easily formed sudden disasters such as water inrush, sand inrush, and air leakage.

7. Shortcomings and Innovations of Manuscripts

(1)

This paper mainly studied the co-evolution of key strata and mining fissures in the working face, and the research on the control method of rock fracture is still insufficient, with no targeted weakening mining fissure evolution method having been proposed. According to the research, the control of mining fissures should effectively reduce the free movement space of the overlying strata, so as to realize the overall control of the overlying strata, and relevant research will be carried out continuously in the follow-up work.

(2)

In this paper, the pole measurement system was used to make a useful connection between the geometric parameters of the surface mining fissures and the mining position of the mine working face. Based on the mining position of the mine working face and the surface coordinate points, the field measured parameters such as the lag distance of the mining fissures and the breaking angle of the rock strata were obtained, providing an effective measurement method for the prediction of the surface mining fissures position in the subsequent working face.

(3)

In this paper, the field mining fissure development position and physical similarity simulation experiment were combined to realize the purpose of the field verification similarity simulation experiment and similarity simulation experiment to predict the field. At the same time, according to the evolution characteristics of the two, five dynamic activation processes of mining fissures were obtained. Based on the monitoring data, the formulas for calculating the lag distance of mining fissures, the breaking distance of rock strata, and the evolution time of mining fissures were obtained.

(4)

Based on geotechnical mechanics and Griffith’s criterion, the propagation characteristics of mining fissures were obtained by combining the micro-fissures in rock and soil with the macro-fissures in the working face. At the same time, considering that the coal mine strata were sedimentary rocks, and the evolution characteristics of mining fissures in rock mass were different, the calculation formula of the overall breaking angle of rock strata was obtained based on the control effect of key strata.

(5)

According to the evolution characteristics of mining fissures in the field and similar simulation experiments, and according to the fracture characteristics of rock strata, the idea of upward and downward (I-I) and (I-II) mining fissures was proposed. Based on fracture mechanics and generalized Hooke’s law, the mechanical calculation model of mining fissure evolution height was established. Based on the mechanical model, the calculation formula of mining fissure evolution value and the discriminant of mining fissure penetration were obtained.