Research on the Control of Mining Instability and Disaster in Crisscross Roadways

Abstract

In order to solve the disaster caused by the instability of spatial crisscross roadways under the action of leading abutment pressure in the coal mine face, combined with a specific engineering example, the methods of theoretical analysis, numerical simulation and field measurement are adopted to simulate and analyze the stress mutual disturbance intensity and influence range of spatial crisscross roadways. The evolution law of the plastic zone in spatial crisscross roadways under the influence of mining is explored, and the key to mining instability control is made clear. The roof of the return air roadway, the shoulder angle of the two sides and the coal wall are the key parts of surrounding rock stability control. On this basis, the cooperative control scheme of changing the roadway section shape (straight wall semicircular arch), supporting (anchor cable and “U” section steel) and modifying (grouting) is put forward. Through the field measurement, within the influence range of the return air roadway, the displacement deformation of the top and bottom is less than 200 mm, which achieves the goal of roadway safety and stability. Furthermore, based on the theory of “butterfly plastic zone”, the mechanical mechanism of the overall instability of the spatial crisscross roadway is revealed; that is, during the advance of the working face, the advance mining stress is superimposed with the surrounding rock stress of the crisscross roadway, and the peak value of the partial stress of the surrounding rock mass of the crisscross roadway is increased. The expansion of the plastic zone is intensified, and beyond 7 m from the crisscross position, the shoulder angle of the two sides and the leading plastic zone of the coal wall of the working face are connected with each other, which leads to the overall failure and instability of the surrounding rock between the roadways at the intersection.

1. Introduction

Crisscross roadways are commonly seen in coal mines due to usage demands and design conditions. In contrast to single roadways, the load-bearing structure and stress damage characteristics of the surrounding rock are also affected by the superimposed interference and dynamic pressure of the working surface [1,2,3,4]. This could induce a perforation crack in the surrounding rock, alongside accidents such as roof falling and slicing, thus posing a seriously threat to production safety in the coal mine.

Given the unique rock pressure characteristics of crisscross roadways, scholars have conducted substantial research on the stability control of the complex surrounding rocks. Bu Qing et al. [5] studied the crisscross roadway between the main factors influencing the stability of surrounding rock, their conclusion was that the destruction and instability of the surrounding rock is mainly caused by distance and angle; Yan Xiaodong et al. [6] proposed a surrounding rock stability control technology of crisscross roadways by studying the surrounding rock stability under different influencing factors. Chen Shanchang [7] stated that crisscross roadways can effectively reduce the roof pressure of the underlying roadway by reducing the span of the upper roadway. Zheng Bingliang [8] analyzed the deformation and failure mechanism, as well as the characteristics, of the surrounding rock and proposed the shoring method of rock bolt with grouting. Cao Hongri et al. [9,10] conducted a study on the stability of crossing sections in underground sites and believed that the smaller the crossing angle, the greater the deformation of the roadway. Lu Xingli et al. [11] discussed the deformation and crack characteristics of the surrounding rocks and the shoring structure of roadways, then put forward a collaborative control scheme of a prestressed composite rock bolt -U-shaped steel support and step-by-step grouting.

The difficulty in controlling the deformation of the surrounding rocks as a result of advanced mining in the working face has also attracted great attention among experts and scholars. Yang Renshu et al. [12] proposed support technologies based on plastic zone reinforcement, the elastic zone bearing capacity, broken zone repair and floor partition differentiation for the asymmetric failure of roadways in the process of mining. Wu Xiangye et al. [13] revealed the space-time evolution pattern and extension mechanism of the plastic zone in repeated mining, and proposed the reinforcement support method by degrees. Lv Kun et al. [14] studied the deformation and failure characteristics of the surrounding rocks and the malignant expansion failure mechanism of the plastic zone; they came up with the bolt-mesh-cable combined support technology and stress regulation technology. Wang En et al. [15] analyzed the influence of the surrounding rock stability of roadways on adjacent working faces of the coal seam, as well as the concentrated stress of the remaining coal pillar in the upper coal seam and mining at the working face; they put forward the asymmetric control technology, combining the high-prestressed rock bolt (cable) and truss rock bolt. Małkowski, P. et al. [16] have carried out long-term stability monitoring of three roadways with different support schemes, and in this study, it is clear that the selection of support, roof separation and rock stratum strength are the key factors affecting roof displacement. Iordanov, I. et al. [17] derived the function expression of surrounding rock displacement increment of transportation roadways in inclined coal seams under the influence of mining and put forward the control method to change the deformation characteristics of the supporting structure above the roadway.

At present, there are many theoretical and technical research achievements concerning the surrounding rock control of crisscross roadways and advanced mining roadways [18,19]. However, most of the research on the surrounding rock stability control of spatial crisscross roadways caused by strong mining is only based on experience, and lacks reliable scientific basis. Research concerning the failure characteristics and mechanical mechanisms of roadways’ surrounding rocks under such conditions is relatively scarce, and the existing research results cannot meet the needs of surrounding rock stability control.

Therefore, this paper takes the Laoshidan Coal Mine of Wuhai Energy as the research background, and the research area location is shown in Figure 1. Through numerical simulation, the evolution law of the surrounding rock plastic zone of the spatial crisscross roadway is analyzed, and its instability catastrophe process is shown. The disaster mechanisms of mining instability in spatial crisscross roadways is revealed, the key to mining instability control is clarified, and the surrounding rock stability control scheme and concrete measures are put forward. The purpose of this paper is to provide a valuable research basis and reference for solving the problem of surrounding rock control of spatial crisscross roadways caused by this kind of strong mining.

2. Case Analysis on the Mining Influence of Crisscross Roadway

2.1. Project Overview

The 16# coal seam in Laoshidan Coal Mine of Wuhai Energy is the main part of the mine; its average thickness is 8.8 m with a dip angle of 1–4° and buried depth of approximately 400 m. The working face adopts the full-mechanized caving coal mining method with long wall backward mining. The 031604 working face spans across the 16# roadway, downward. Its return aircourse and 16# track downward space is in a vertical direction. The distance between the roadways is approximately 3 m, which the return aircourse presents as a rectangular shape, with width × height = 4100 mm × 3750 mm. The descending section of 16# and the transportation section is also rectangular, with width × height = 4000 mm × 3500 mm, the distance between the two descending sections is 40 m. The spatial position of the roadways is shown in Figure 2.

Before the tunneling of the 031604 return aircourse, the drilling hole peeping method is adopted on the spot, and three boreholes, with a depth of 15 m and a diameter of 32 mm, are arranged in front of the working face of the side 031601 transport roadway. The roof strata structure and the failure form of the mining surrounding rock are analyzed, representative screenshots are selected to express and combined with geological data, and the comprehensive column is obtained, as shown in Figure 3. There is solid coal in the range of 0–5.3 m from the roadway roof, and the cracks crisscross in the range of 0–2 m from the roof, which is seriously broken. The coal body is cut into a large number of pieces, and the fragments are of different sizes, accumulated on both sides of the top coal drilling wall, and local voids and hole collapses occur, as shown in Figure 3a,b. The distance from the roadway roof is approximately 5–6.9 m, which is composed of solid coal, sand shale and carbon shale interbedding. In this range, the coal (rock) body is relatively complete, with one or more horizontal, vertical and inclined fissures, with a large scale and wide extension. The fissures contain a small number of small fragments, with a width of approximately 0–15 mm, as shown in Figure 3c,d. Within 7–15 m from the roof of the roadway is fine sandstone; the rock mass is complete, only a small number of small cracks exist locally, and the hole wall is relatively flat, as shown in Figure 3e. There are a small amount of coal lines in the 14.0–14.3 m position, there is a phenomenon of separation, the integrity is good, and the development of cracks is rare, as shown in Figure 3f.

2.2. The Influence of Crisscross Roadway on Engineering Safety

According to analysis of the stability and safety of the surrounding rock in the intersection of the return aircourse in the 031604 working face: (1) the abandoned roadway with crisscross layout exists above the return aircourse, which forms the near-distance crisscross roadway, causing the obviously superimposed and complicated surrounding rock stress interference; (2) in the intersection position of the roadway and its vicinity, the bearing burden of the surrounding rock at the side of the return aircourse is significantly increased, and the stress state of its roof is not conducive to bearing stability, and there are hidden dangers of perforation failure instability; (3) with the mining of the working face, the influence of advanced mining worsens the stress failure degree of the surrounding rock and the instability of the surrounding rock between the roadways; (4) The layout of the crisscross roadway changes the load-bearing characteristics of the surrounding rock. As the single support design is unable to meet the demands of stability, it is necessary to study the surrounding rock stability control method in the mining.

3. Research Process and Methods

In order to explore the evolution pattern of the plastic zone in the surrounding rock at the intersection in the mining, identify the interference degree and influence range in the crisscross roadways, and find out the changes of the plastic zone of the surrounding rock in the working surface, numerical simulation analysis was carried out on the roadway mining situation based on the field situation, in order to reveal the mechanism of instability and disaster.

3.1. Numerical Modeling

According to the geological conditions, a FLAC^3D numerical model was established, with the model size of 3000 m × 900 m × 230 m (length × width × height), as shown in Figure 4. The model takes the intersection position of the roadway as the center and the vertical range as 40 m. The local grid is encrypted as 0.5 m for the direction and inclination range of 100 m, and the grid size of the rest is set as 2 m to meet the stress transfer in the process of numerical calculation. With the Mohr-Coulomb constitutive relation, the thickness of the overburden layer of the model is 260 m; therefore, the vertical load applied on the upper part of the model is 6.5 MPa, the lateral pressure coefficient is set to 1.5, and the surrounding and bottom of the model are fixed constraints. The physical and mechanical parameters of the rock are shown in

Table 1. Mechanical parameters of the rock model.

Rock Stratum	Bulk Modulus/GPa	Shear Modulus/GPa	Density/m−3	Cohesion/MPa	Internal Friction Angle/(°)	Tensile Strength/MPa
Fine sandstone	5.4	3.1	3270	9.0	34	2.67
sandy shale	2.5	2.0	3180	3.5	28	1.51
Coal	2.2	1.5	2800	2.5	26	1.22
Marlstone	4.3	2.0	3270	4.0	30	1.40
Siltstone	4.5	3.2	3570	12.0	32	2.32

.

Considering the engineering situation and the extraction rate of the 031604 working face, the model adopts the internal excavation method. The simulated working face distance is 10 m along the coal seam, and the mining distance is 5 m at a time. The top coal is put in the rear of the working face and the caving zone of the mined-out area is filled in; that is, 5 m is pushed into the working face and 5 m is filled into the mined-out area, until balance is reached. The simulation method of “excavation and filling” is adopted until the working face is near the crisscross roadway to achieve the actual effect.

3.2. The Characteristics of Surrounding Rock Interference in Crisscross Roadway

When not affected by mining superposition, the stress nephogram and plastic zone distribution of the roadway’s surrounding rock in the single and crisscross layout are captured, as shown in Figure 5. In order to clarify the interference effect of shoring stress and the failure degree of the crisscross roadway, the foundation is provided for obtaining the evolution pattern of the surrounding rock plastic zone of the crisscross roadway under the influence of mining stress superposition.

As for a single roadway, the deviatoric stress of the surrounding rock shows a “line-shaped” distribution, with a peak value of approximately 12 MPa. The depth of the plastic zone is 0.5 m, the bottom plate is 2 m, and both sides are 1.5 m. When designing the crisscross roadway, the distribution of the deviatoric stress in the surrounding rock presents a “cross” shape, and the peak value of the deviatoric stress is near the crossing section, reaching approximately 17 MPa; 1.41 times of that in single roadway arrangement. Under the influence of the lower roadway, the depths of the plastic zone and the two sides of the upper roadway are extended by 0.5 m, while the depths of the plastic zone of the two sides of the lower roadway and the bottom plate are 1.5 m. The roof plate is connected with the plastic zone of the bottom plate in the upper roadway, which can potentially cause bearing instability in the surrounding rock between the roadways.

In order to further analyze the influence range of the upper roadway stress on the lower roadway, the principal stress of the surrounding rock in the roadway position is extracted under the condition that the roadway of the 031604 working face is not excavated, and the generated curve graph is shown in Figure 6.

As can be seen from Figure 6, within 50 m in front of the intersection, the maximum principal stress and deviatoric stress values increase with the rise in the distance from the intersection, due to the side effect of 031601 goaf, while the minimum principal stress is on the contrary. The maximum principal stress slowly shifts counterclockwise and then sharply shifts clockwise to 42.9°. The variation range of the principal stress within 10 m before and after the intersection of the two roadways is large, and the deviatoric stress presents a single peak distribution of approximately 2.9 MPa. The maximum principal stress sharply swings to the minimum in the vertical direction counterclockwise, which is 12.8°. Hence, it can be concluded that the local stress variation in the lower roadway caused by the two crisscross roadways is within 10 m before and after the intersection.

3.3. The Evolution Pattern of Plastic Zone in Crisscross Roadway

Based on the clarified influence degree of the shoring stress superposition and mutual interference of the crisscross roadway, the mining process of the working face was simulated. When the working face is 50 m, 30 m, 15 m, 10 m, 5 m and 3 m away from the intersection, respectively, the evolution process of the surrounding rock plastic zone within 10 m before and after the crisscross roadways is shown in Figure 7.

As shown in Figure 7a, when the working face is 50 m away from the crisscross center, the surrounding rock within the influence range of the crisscross roadway is affected by the advanced mining of the working face, and the scope of the upper roadway roof and the plastic zone on both sides increases significantly, while the shoulder angle of the plastic zone on both sides of the lower roadway rises by 2 m. The comparative analysis of Figure 7a,b shows that in the 50–30 m process from the intersection center of the working face, the plastic zone slightly ascends, the plastic zone depth in the upper roadway increases, and the lower roadway almost remains the same. According to Figure 7c, when the working face advances to 15 m from the crisscross center, the depth of the plastic zone in the upper roadway roof at the intersection is 1.5 m, and the depth of the plastic zone in the two sides of the roadway at the intersection is 3 m, which increases by 0.5 m. The depth of the plastic zone in the two sides of the roadway at the lower roadway extends to 2.5 m, and the edge position is only 5 m away from the working face. The coal wall is connected with the plastic zone, formed by advanced mining of the working face, and the damage of the shoulder angle is evident. It can be preliminarily concluded that the plastic zone in front of the working face near the end is 7 m. In Figure 7d, when the working face is pushed 10 m away from the crisscross center, the lower roadway edge is completely connected with the parallel coal wall of the working face and the advanced mining plastic zone of the working face. The plastic zone of the roof reaches 5.5 m, and the plastic zone at the shoulder angle of the coal pillar expands significantly to the roof. As shown in Figure 7e, when the advanced distance of the working face is 5 m from the crisscross center position, the influence of advanced mining in the working face is severe, and the plastic zone range of the roof in the upper roadway increases significantly. The depth of the plastic zone of the coal wall and floor increases to 3 m and 2 m, respectively. Meanwhile, the plastic zone of the coal wall and the advanced plastic zone of the working face show a trend of perforation. Figure 7f demonstrates that, when the working face is advanced to 3 m away from the crisscross center, the plastic zone in the lower roadway continues to deteriorate and is connected with the advanced plastic zone in the working face.

Overall, the intense expansion range of the plastic zone of the return aircourse is approximately 7 m ahead of the working face, and the plastic zone of the shoulder angle is particularly evident. The coal wall is connected with the plastic zone of the working face with the advance of the working face. Hence, the roof of the return aircourse, the shoulder angles of the two sides and the coal wall are the key to maintaining the stability of the surrounding rock.

4. Results

4.1. The Key of Mining Instability Control in Crisscross Roadway

Based on the analysis of the surrounding rock stress interference and the evolution pattern of the surrounding rock’s plastic zone in the process of mining, the surrounding rock stress of the crisscross roadway presents the superposition interference effect. The failure of the surrounding rock in the roadway leads to the instability of the surrounding rock, and the plastic zone expansion of the shoulder angles of the two sides is particularly obvious. The roof, the shoulder angles of the two sides, and the coal wall are the key parts of the stability control of the surrounding rock. The rectangular section is not conducive to the bearing capacity of the surrounding rock of the roof, while the semicircular arch section of the straight wall can apply the mechanical properties of “stress resistance” in the surrounding rock of the roof [20]. Combined with the grouting reinforcement method of the roadway’s surrounding rock, the integrity and strength loss of the destroyed surrounding rock can be effectively improved [21,22] by grouting the roof and coal wall of the intersection of the return aircourse, meaning the overall strength and integrity of the roof and coal wall can be increased.

In the crisscross arrangement of the roadway, the size of the surrounding rock mass is limited, and it is difficult to realize the support function of the surrounding rock in the intersection. At this time, passive shoring is particularly important to support the stability of the surrounding rock in the crisscross roadway; thus, the joint control scheme of “U” steel metal support passive shoring and rock bolt net active shoring is adopted [23,24] and achieves the bearing function of the roadway’s surrounding rock and shoring structure, reduces the partial stress and stress gradient changes in the shallow part of the surrounding rock, and forms the prestressed bearing structure in the surrounding rock mass of the roadway [25]. In this way, the potential dangers of roof failure caused by the continuous advance of the working face can be controlled.

The collaborative control scheme of “changing the section shape of roadway (straight wall in semicircular arch)—shoring (rock bolt and “U” shaped steel)—modification (grouting)” is proposed, which gives full play to the bearing advantage of the joint structure of the surrounding rock and the shoring of the crisscross roadway, and ensures the smooth operation of the return aircourse.

4.2. The Collaborative Control Scheme Design of Space Crisscross Roadway

Within 10 m before and after the crisscross part of the return aircourse, the layout construction is altered to a straight wall and semicircle arch roadway, with a section width of 4500 mm, wall height of 1450 mm and arch height of 2650 mm. The roadway is supported by U29 steel, and the shed spacing is 0.8 m, with a total of 25 frames. The length of the shed beam is 4187 mm, the length of the shed leg is 3522 mm, and the height of the straight leg is 1450 mm. The beam and the leg are overlapped for 400 mm. The upper part of the shed beam is arranged every 700 mm with a pine-made brake rod, and tightened with wooden wedge, so that the brake rod is closely connected with the roof and covered with metal mesh. Both ends of the shed beam and the two sides of the shed leg are set up with a pull rod, the position of the shed leg is 0.5 m from the bottom plate. Nine Φ20 mm × 2400 mm left-screwing threaded steel bolt s are arranged in the roof of the roadway with a row spacing of 800 mm × 800 mm, and two Φ18 mm × 1800 mm left-screwing threaded steel bolts with a row spacing of 800 mm × 800 mm are selected for each side. The shoring section is shown in Figure 8. For the coal wall at the end of the return aircourse, 10 m away from the downhill track of 16#, and 1 m away from the roof of the working face, at an elevation angle of 60°, hole depth of 3.5 m and hole spacing of 4 m, four grouting holes are arranged and approximately 1 ton of reinforcement material is injected into each hole. Every time the working face pushes forward one cycle, the hole is drilled, and grouting is performed once, which plays a grouting modification effect on the coal wall at the end of return aircourse and the surrounding rock between the crisscross roadways. On this basis, when the working face is 7 m from the intersection, the working face is adjusted to 10 m in the way of “two ends and one head”, in order to reduce the stress gradient of the crisscross roadway affected by the advanced mining of the working face.

4.3. The Control Effect Analysis of Crisscross Roadway

Regarding the mining influence of the crisscross roadway in front of the 031604 fully-mechanized caving face in the Laoshidan Coal Mine, the numerical simulation method was adopted to analyze the change in the plastic zone of the surrounding rock at the intersection in advancing the working face based on the scheme of “changing the section shape of roadway (straight wall in semicircular arch), as shown in Figure 9.

According to the comparative analysis of Figure 7 and Figure 9, the depth of the plastic zone of the surrounding rock of the return aircourse below the intersection is significantly reduced, while the failure degree of the surrounding rock of the crisscross roadway is improved. When the working face is 15 m and 10 m away from the intersection, the depth of the plastic zones, on both sides of the return aircourse, decreases to 1.0 m before and after the optimization of the roadway section, and the plastic zone on the floor is basically the same, with the depth of 1.5 m. When the working face is 5 m away from the intersection, the depth of the plastic zone on both sides of the return aircourse is 1.5 m, the plastic zone range on both sides of the shoulders decreases significantly, and the depth of the plastic zone on the floor is 2 m. When the working face is advanced to 3 m from the interleaving position, the left side of the return aircourse is connected with the plastic zone, the depth of the plastic zone on the right side is 1.9 m, and the plastic zone of the floor shows no expansion. After the optimization of the roadway section, the arch structure of the lower roadway roof fully exerts the bearing advantage of the surrounding rock, has an obvious gain effect on the structural bearing capacity of the surrounding rock between the roadways, and finally achieves the goal of surrounding rock stability within the influence range.

The proposed joint control scheme was implemented for the crisscross roadway in front of the 031604 fully-mechanized caving face of the Laoshidan Coal Mine, and the deformation of the surrounding rock was monitored for the return aircourse at the intersection, on site. The layout of the measuring points of the roadway below the intersection is shown in (Figure 10). The deformation of the observation points on the roadway surrounding the rock surface is recorded in the process of the working face advancing 200 m away from the roadway monitoring surface, and the monitoring results are shown in Figure 11.

As can be seen from the monitoring results in Figure 11, with the advance of the coal seam working face, slow deformation appears before the working face is 60 m away from the roadway monitoring surface, and the deformation of the surrounding rock of the roadway shows a trend of slow increase. When it is 60 m away from the roadway monitoring surface, the deformation at each measuring point of the monitoring section is 101, 97, 94, 18, 28 and 40 mm, respectively. During the process in which the working face is 60~30 m away from the monitoring section of the roadway, the influence of advanced mining approaches to the crisscross roadway ahead, and the rock pressure of the crisscross roadway gradually becomes explicit. The deformation of the surrounding rock of the roadway is more severe, and the deformation increases significantly. When it reaches 30 m away from the monitoring surface of the roadway, the deformation of each measuring point in the monitoring section is 158, 161, 152, 61, 35 and 47 mm, respectively. In the process of the working face advancing to the last 30 m from the monitoring section, the curve shape shows an obvious tendency of decelerating deformation, the surrounding rock deformation tends to be stable, and the roadway enters the stable state, influenced by advanced mining. The maximum deformation at each monitoring point is 168, 171, 162, 70, 39 and 51 mm, respectively. On the whole, the monitoring results are obtained from the collaborative control scheme of “changing the section shape of roadway (straight wall in semicircular arch)—shoring (rock bolt and” “U” shaped steel)—modification (grouting)”, which gives full play to the bearing capacity of the joint structure of the surrounding rock and shoring, thus effectively controlling the failure deformation of the surrounding rock of the crisscross roadway. In general, the displacement and deformation of the top and bottom sides of the return aircourse under the intersection are all less than 200 mm, and there is no appearance of roof fall, wall collapse, roof crushed shoring, rock bolt support failure, etc. In the process of on-site mining, there appears to have been no roof accident in the whole service period of the return aircourse, which ensures the production safety of the coal mine.

5. Discussion

5.1. Study on Morphological Law of Plastic Zone of Surrounding Rock of Roadway

The failure problem of the surrounding rock of the roadway is essentially a mechanical elastic-plastic problem. In practice, the buried depth of the roadway is greater than the radius of the roadway, so the stress field around the roadway can be regarded as a uniformly distributed load, and it is assumed that the surrounding rock of the roadway is an isotropic homogeneous medium. The problem can be simplified to a plane strain circular hole problem, in which the load and structure are axisymmetric in the elastoplastic mechanics. The stress model of the circular roadway is established, as shown in Figure 12, in which r is the radius of the roadway, R₀ and θ are polar coordinates, σ₁ and σ₃ are the maximum and minimum principal stress. To define the η main stress ratio (confining pressure ratio), that is the ratio of maximum to minimum principal stress, the expression is as follows:

$$\eta ={\sigma }_1/{\sigma }_3\ge 1$$

(1)

According to the established mechanical model, the reference [26,27] is based on the Mohr-Coulomb failure criterion and makes use of the two-dimensional stress distribution solution around the circular hole in the elastic plate of elastics. The hidden equation of the plastic zone boundary of the circular roadway in the non-isobaric stress field under polar coordinates is derived.

$$\begin{array}{l}\hspace{1em}9{\left(1-\eta \right)}^2{\left(\frac{r}{R_0}\right)}^8-\left[12{\left(1-\eta \right)}^2+6\left(1-{\eta }^2\right)\cos 2\left(\theta -\alpha \right)\right]{\left(\frac{r}{R_0}\right)}^6\\ +\left\{2{\left(1-\eta \right)}^2\left[{\cos }^{2}2\left(\theta -\alpha \right)\left(5-2{\sin }^2\phi \right)-{\sin }^{2}2\left(\theta -\alpha \right)\right]+{\left(1+\eta \right)}^2+4\left(1-{\eta }^2\right)\cos 2\left(\theta -\alpha \right)\right\}{\left(\frac{r}{R_0}\right)}^4\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\left[4{\left(1-\eta \right)}^2\cos 4\left(\theta -\alpha \right)+2\left(1-{\eta }^2\right)\cos 2\left(\theta -\alpha \right)\left(1-2{\sin }^2\phi \right)-\frac{4}{P_3}\left(1-\eta \right)\cos 2\left(\theta -\alpha \right)\sin 2\phi C\right]{\left(\frac{r}{R_0}\right)}^2\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left[{\left(1-\eta \right)}^2-{\sin }^2\phi {\left(1+\eta +\frac{2C}{P_3}\frac{\cos \phi }{\sin \phi }\right)}^2\right]=0\end{array}$$

(2)

In the equation, r is the roadway radius; θ is the polar coordinates of any point on the boundary of the plastic zone; R₀ is the boundary of the radial plastic zone; α is the angle between the maximum principal stress and the vertical direction (positive clockwise); C is the rock cohesion; φ is the internal friction angle of the rock.

The equation analysis shows that under different stress conditions, the plastic zone of the surrounding rock of the circular roadway has three basic shapes, namely, round, oval, and butterfly [28,29,30]. The morphological distribution of the plastic zone of the roadway’s surrounding rock, affected by the mining stress field, will have an important influence on the stability of the roadway’s surrounding rock, in order to study the distribution characteristics of roadway plastic zone of mining stress field. By using the boundary equation formula of the plastic zone of the surrounding rock of the circular roadway under the condition of the non-uniform stress field, fixed σ₃ and other parameters are unchanged (γ = 25 KN/m³, r = 2 m, C = 3 MPa, φ = 25°). By changing σ₁, the ratio of principal stress η is 1.5, 2, 2.5 and 3, respectively. The size of the butterfly plastic zone in different positions of the circular roadway in the mining stress field (different ratio of mining principal stress). Draw the shape diagram of the butterfly plastic zone of the surrounding rock of the circular roadway, as shown in Figure 13.

It can be seen from the diagram that the maximum size of the plastic zone of the roadway increases with the increase in the principal stress ratio, from 1.5 to 3. Under the condition of the mining stress field, the shape of the plastic zone of the roadway’s surrounding rock will gradually expand from oval to butterfly. When the parameters of the surrounding rock are fixed, σ₁ and σ₃ fix one of the forces and change the ratio of principal stress by changing the other force, which can show that with the increase in the ratio of principal stress, the maximum size of the plastic zone is larger, the shape of the plastic zone is more irregular, the more disadvantageous to the stability of the roadway’s surrounding rock, and the failure depth of the butterfly plastic zone is obviously larger and more unstable than the other shapes. When the plastic zone develops to the butterfly shape, the size of the four butterfly leaves in the plastic zone is highly sensitive to the increase in the principal stress ratio.

Combined with the mutual disturbance characteristics of the crisscross roadway, it can be known that when the stress of the surrounding rock of the roadway changes, the direction of the principal stress also changes. According to the Equation (2), α is the angle between the maximum principal stress and the vertical direction, which is positive clockwise. The change law of the plastic zone when changing the angle of principal stress is obtained, as shown in Figure 14.

The results show that when the principal stress direction of the surrounding rock is deflected, the distribution shape of the plastic zone of the surrounding rock will change accordingly, which is an important mechanical mechanism for the non-uniform failure of the roadway.

5.2. The Mining Instability and Disaster Mechanism in Crisscross Roadway

The deviatoric stress nephogram and vertical stress curve of the surrounding rock in the roadway at 50 m, 30 m, 15 m, 10 m, 5 m and 3 m intersections were obtained, respectively, as shown in Figure 15 and Figure 16.

It can be seen from Figure 15a that the stress concentration is formed in front of the working face, and the peak value of deviatoric stress at the end of the roadway is 22 MPa. At the crisscross center, the upper roadway roof is connected with the plastic zone of the lower roadway roof to enter into the state of stress relaxation. The deviated stress value of the surrounding rock between the roadways is low, with the deviated stress concentration area of approximately 19 MPa around. The surrounding rock of the crisscross roadway is not significantly affected by the working face mining. In Figure 15b,c, in the process of advancing the working face, the concentration degree of lateral deviatoric stress in the working face and goaf evidently increases, which has gradually formed the superimposed influence of mining with the stress of the surrounding rock between the crisscross roadways. The degree of deviatoric stress concentration at the “upper left corner” of the intersection increases at approximately 25 MPa; the surrounding rock of the coal pillar wall in the lower roadway gradually carries more load, while the degree of partial stress concentration at the “lower left corner” of the intersection shows a rise at approximately 26 MPa. According to Figure 15d–f, when the working face gradually advances to the intersection, the yield failure of the coal wall in front of the working face is connected with the failure of the surrounding rock in the upper roadway, and the deviated stress is concentrated and transferred to the right side of the upward roadway. The surrounding rock at the “upper left corner” of the intersection is relieved, then the deviated stress concentration at the “upper right corner” of the intersection increases to approximately 22 MPa. The degree of lateral deviatoric stress concentration in the goaf and the surrounding rock of the crisscross roadway continues to increase. The deviatoric stress of the surrounding rock at the “lower left corner” of the intersection reaches 27 MPa, in which the deviatoric stress concentration of the surrounding rock at the “lower right corner” of the interleaved position increases remarkably.

Figure 16 indicates that with the advance of the working face, the vertical stress curves of the surrounding rock on both sides of the roadway present a single peak distribution. In the process of 50 m to 15 m from the advance distance of the working face to the intersection, the peak value of vertical stress on the left side of the intersection gradually increases from 31.45 MPa to 37.18 MPa, and the peak value is approximately 10 m in front of the working face. In the process of advancing the working face to 10 m–3 m away from the intersection, the peak value of vertical stress in front of the working face gradually decreases to 4.35 MPa. During the process from 50 m to 3 m, the right side of the intersection gradually augments with the vertical stress peak value of the working face, and when it comes to 3 m from the intersection, the peak value reaches 34.29 MPa.

In expanding the working face, the advanced mining stress is gradually superimposed with the surrounding rock stress of the crisscross roadway, and the concentration peak of deviatoric stress in the surrounding rock near the crisscross roadway is increased bit by bit, which leads to the expansion of the plastic zone. Until it reaches 7 m away from the intersection, the advanced plastic zone of the working face coal wall is connected with that of the return aircourse, and the shoulder angles of the two sides are also connected, which causes the overall destruction of the surrounding rock between the roadways at the intersection point, and then leads to the overall instability of the crisscross roadway.

6. Conclusions

(1) The influence range of stress mutual disturbance of the spatial crisscross roadway is 10 m around the crisscross position, and the partial stress concentration factor of the surrounding rock mass between the roadways is 1.4, resulting in crack penetration of the surrounding rock mass between the roadways.

(2) During the mining process of the working face, the leading mining stress and the surrounding rock stress of the crisscross roadway are superimposed, the peak value of the partial stress of the surrounding rock mass of the crisscross roadway increases, and the plastic zone expands; after 7 m from the crisscross position, the shoulder angle of the two sides and the leading plastic zone of the coal wall of the working face are connected with each other, which induces the overall failure and instability of the surrounding rock between the intersection roadway, thus revealing the overall instability mechanism of the spatial crisscross roadway.

(3) The roof of the return air roadway, the shoulder angle of the two sides and the coal wall are the key to control. A cooperative control scheme of changing the roadway section shape, (straight wall semicircle arch)-support (anchor cable and “U” section steel)-modified (grouting), is put forward. Within the influence range of the crisscross return air roadway, the displacement deformation of the top and bottom is less than 200 mm, which ensures the safety of coal mine production.