**1. Introduction**

With the development of automation and intelligence in coal mine production, more and more large sections and super-large section cavern groups are required for large-scale mining and the transportation of machinery and equipment. The cavern group of the mine is relatively densely distributed. In deep geology, the rock mass is in a high-confining pressure state. It greatly increases the difficulty of the maintenance of the cavern group, and the serious deformation of the surrounding rock makes it easy to induce the instability of the surrounding rock [1–3]. In particular, the failure of one of the cavern groups can induce the linkage instability of the surrounding cavern, which will seriously affect the safety and stability of deep, large section caverns [4,5]. A large deformation disaster occurs in soft rock roadways and is usually characterized by high stress, large deformation, strong

**Citation:** Chen, L.; Wang, Z.; Wang, W.; Zhang, J. Study on the Deformation Mechanisms of the Surrounding Rock and Its Supporting Technology for Large Section Whole Coal Cavern Groups. *Processes* **2023**, *11*, 891. https://doi.org/10.3390/ pr11030891

Academic Editor: Zhongyang Luo

Received: 12 February 2023 Revised: 4 March 2023 Accepted: 13 March 2023 Published: 16 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

rheology, low strength, and difficult support. The deformation of soft rock often shows obvious nonlinear large deformation characteristics, and it is difficult to support. Therefore, the deformation mechanism and support technology of soft rock roadways with deep high stress in the large section whole coal cavern groups have become a hot topic in the research field of roadway support all over the world [6–8].

At present, many scholars have focused on these aspects of the research, including classification methods, surrounding rock instability mechanisms, and reinforcement control technology. In terms of classification methods, the cavern is divided on the basis of section area and span in the field of coal mining. According to the section area, it can be divided into small sections (<8 m2), medium sections (8–12 m2), large sections (12–20 m2), and extra-large sections (≥20 m2) [9]. According to the span, it can be divided into a small section (≤3 m), a medium section (3.1–4.0 m), a large section (4.1–5.0 m), and a super section (≥5.1 m) [10]. The stability of the surrounding rock is also affected by the depth, excavation disturbance, and distance between the caverns. In terms of the failure and instability mechanisms of the cavern, the deep surrounding rock presents rheological instability and dynamic instability. He et al. [11] and Sun et al. [12] pointed out that interbedded shear slip deformation mechanisms and high stress dilatation deformation mechanisms are the main manifestations of asymmetric rock deformation and failure mechanisms. Numerical methods have been used to evaluate the safety of cavern groups and optimize the allowable pillar width [13–15]. Kang et al. [16,17] analyzed the rock rheological properties from the perspective of time and space scales and believed that the dynamic instability of deep surrounding rock was more frequent. Pan et al. [18] carried out a similar simulation test of explosion loading and obtained the dynamic failure process of the cavern under the action of an explosion load using digital speckle technology. Wang et al. [19] used a large-scale geomechanical model test system to study the deformation and failure response law of surrounding rock under the combined action of dynamic and static loads. By evaluating the stress and strain distribution, the stress and strain concentration can be easily determined [20]. The plastic zone can be assessed to determine whether elements yield [21]. Wu et al. used the true triaxial simulation technique to establish a model of the inclined strata and carry out high stress triaxial loading experiments. The deformation mechanism of high stress inclined rock masses is discussed in detail [22]. Zhao et al. [23] aimed to propose a dual-medium model, including equivalent continuous and discrete fracture media, to study the coupled seepage damage effect in fractured rock masses. However, it is difficult and counterintuitive to quantify the stability degree of the surrounding rock for large section whole coal cavern groups using these indices. The linkage impact between large section whole coal cavern groups is rarely studied.

Meanwhile, many scholars have made in-depth explorations into the reinforcement control technology of the surrounding rock. Wang et al. [23–26] proposed the asymmetric phased control method for large section caverns and verified the rationality of the method through field monitoring. Hou et al. [27,28] proposed methods of improving the stress state and mechanical properties of roadways surrounding rock and rationally selecting the support form of the roadway. New combined supporting system for weak floor reinforcement in deep underground coal mines is proposed by Yang and Kang et al. [29,30]. Jiao et al. [31] modified the traditional U-section steel group to effectively support and stabilize the loose and thick coal seam roadway. Li and Yao [32] proposed the key technologies of segmented roadway support after considering the time effect, local breakdown characteristics, and fracture development. Li et al. [33] developed a high-strength anchorage grouting support technology with a new type of high-strength hollow grouting bolt as the core. The problems, such as the serious weak crushing of surrounding rock and the frequent destruction of large section cavern supporting components, are solved. Singh et al. [34] studied the causes of the failure of two wire ropes used at high stress levels in two different coal mines in India. Rama et al. [35] conducted a detailed parameterized study of a roof bolt breaking line support (RBBLS) and proposed an empirical formula for the design of a RBBLS. An analytical solution for surrounding rock that took influences of water

seepage, strain softening, dilatancy, and intermediate principals into account was given and a grouting measure was provided to improve roadway stability by Yuan et al. [36]. The deformation mechanical characteristics of weakly consolidated siltstone surrounding rock are described and control techniques are proposed [37]. The above scholars have achieved considerable achievements in the control of the surrounding rock in the cavern group. However, the failure mechanism and stability control theory of the surrounding rock in the whole coal cavern group need to be further perfected. With the increase of mining depth and cavern section, it is more urgent to study the deformation law and control technology under linkage impacts between large section whole coal cavern groups.

This paper aims for the stability of whole coal cavern groups with large sections and provides technical support for the stability of similar large section cave groups. From the background of practical engineering, the stress and deformation law of the surrounding rock of the WCCG under different section sizes and side pressure coefficients are studied by a numerical calculation method, and the deformation failure mechanism of the WCCG is obtained under linkage impact between large section whole coal cavern groups. The stratified reinforcement ring concept of LBG was proposed based on the obtained deformation mechanism under linkage impact between large section whole coal cavern groups. The surrounding rock control theory proposed can not only put forward a new control solution for rock cavern stability but also improve the technical aspects of the WCCG. It has important theoretical significance and practical value for the safe and stable production of working faces.

#### **2. Study Area**

The coal mine is located in the southeast region of Shanxi Province and northwest of Changzhi City. It is 8 km away from Tunliu County. The actual production capacity of the mine has reached 7.1 million tons. Coal seam No. 3 is mainly mined. The inclined angle of the No. 3 coal seam is from 0◦ to 7◦ in the east-west direction and from 0◦ to 22◦ in the north-south direction. The roof and floor are basically stable, and the geological structure is simple. According to the exploration data, the Taiyuan Formation, Shanxi Formation, and Xiashihezi Formation are weakly water-bearing. The hydrogeological conditions of the #3 coal seam are mainly simple type, and the local and regional geological conditions are intermediate type to complex type.

The gas pump station is located in the No. 91 mining area, which belongs to the whole coal cavern, including high- and low-negative pressure caverns. The relative positions of the two caverns are shown in Figure 1. A large gas extraction pump and pipeline need to be installed in the underground gas pumping station, which requires a large cavern size. The cavern area reached 50 m2, and its support difficulty greatly increased. The section of the connection roadway is a rectangular section with a size of 6.4 × 6.15 m2. The highnegative-pressure cavern is a rectangular chamber divided into two sections. The length of the roadway in the western section is 69.5 m, and the section size is 6.0 × 6.15 m2. The eastern section of the cavern (small section roadway) is 25 m in length and 5.0 × 4.55 m<sup>2</sup> in size. The low-negative pressure cavern is a rectangular chamber divided into two sections. The length of the roadway in the western section is 60 m, and the section size is 7.4 × 6.75 m2. The eastern section of the cavern (small section roadway) is 20 m in length and 6.0 × 4.55 m2 in size. According to the exposure of surrounding rock in the cavern, the lithologic characteristics of the roof and floor of the cavern are shown in Table 1.

**Figure 1.** The relative positions of cavern groups.



### **3. Method and Material**

#### *3.1. Solve the Loose Circle of the Rectangular Roadway Based on the Equivalent Circular Method*

Due to roadway excavation, surrounding rock stress will be redistributed. The original stress state is destroyed, and the stress is transferred to the depth. Failure occurs when the stress reaches or exceeds the strength of the surrounding rock. It is prone to roof collapses and slough accidents. Especially in the excavation of large section whole coal cavern group, each cavern group and intersection influence each other during excavation. Stress superposition leads to a high local stress concentration coefficient in large section caverns, which is more prone to deformation and failure.

The methods to solve the loose zone of a rectangular roadway mainly include the equivalent circle method, the complex function method, and the pressure arch method. In order to quantitatively solve the plastic range of the surrounding rock during excavation of a rectangular cavern, the equivalent circle method is adopted to theoretically calculate the influence range of the surrounding rock's loose circle caused by the excavation of a large section cavern [38]. Based on the loose circle of the circular roadway, the loose circle of the rectangular roadway is determined, and the plastic zone range of the rectangular roadway is finally determined:

(1) Construction of the mechanical model of the equivalent circle method expression

In order to calculate the stress state of the roadway, the circular roadway is taken as the theoretical analysis object, and the vertical stress is set as *σ*<sup>v</sup> and the horizontal stress as *σ*h. We can obtain:

$$
\sigma\_{\mathbf{h}} = \lambda \sigma\_{\mathbf{v}} \tag{1}
$$

where *λ* is the lateral pressure coefficient of the rock mass;

(2) Calculate the stress in the loose zone of the roadway surrounding the rock

For a circular roadway, the radial stress at any point is

$$\sigma\_{\mathbf{r}} = \sigma\_{\mathbf{v}} [\frac{1+\lambda}{2}(1-m) - \frac{1-\lambda}{2}(1+3m^2 - 4m)\cos(2\theta)].\tag{2}$$

The circumferential stress at any point is

$$
\sigma\_0 = \sigma\_\mathrm{v} \left[ \frac{1+\lambda}{2} (1+m) + \frac{1-\lambda}{2} (1+3m^2) \cos(2\theta) \right], \tag{3}
$$

The shear stress at any point is

$$
\pi\_{\rm r0} = \sigma\_{\rm v} \cdot \frac{1-\lambda}{2} (1 - 3m^2 + 2m) \sin(2\theta),
\tag{4}
$$

where *m* = *r*<sup>0</sup> 2/*r*<sup>1</sup> 2

*r*<sup>0</sup> is the radius of the circular roadway, m;

*r*<sup>1</sup> is the radius of the loose ring, m;

*θ* is the polar angle of any point in the plastic zone of the surrounding rock, ◦;

#### (3) Determine the expression based on the equivalent circle method

The surrounding rock conforms to the Mohr–Coulom (M–C) constitutive by analyzing the physical and mechanical strength parameters of the surrounding rock. When the Mohr– Coulomb criterion is used to calculate the loosening range of the surrounding rock, its plastic condition is:

$$\sin \varphi\_{\rm m} = \frac{\sqrt{\left(\sigma\_{\rm 0} - \sigma\_{\rm r}\right)^{2} + \left(2\tau\_{\rm r0}\right)^{2}}}{\sigma\_{\rm 0} + \sigma\_{\rm r} + 2\mathcal{C}\_{\rm m} \cot \varphi\_{\rm m}} (2\theta) \tag{5}$$

where *C*<sup>m</sup> and *ϕ*<sup>m</sup> are the cohesion and internal friction angles of the surrounding rock mass, respectively. σ<sup>θ</sup> and τ<sup>r</sup> are the circumferential stress and radial shear stress, respectively.

By substituting Equations (2–4) into Equation (5), we can obtain:

$$f\_{\mathbf{m}} = k\_1 \mathbf{m}^4 + k\_2 \mathbf{m}^3 + k\_3 \mathbf{m}^2 + k\_4 \mathbf{m} + k\_5 \tag{6}$$

where *k*<sup>1</sup> = 9(1 − *λ*)

$$\begin{aligned} k\_2 &= 6(1 - \lambda)(1 + \lambda)\cos(2\theta) + 2(1 - \lambda) \\ k\_3 &= 4(\sin^2\varphi\_{\rm m} - 3)(1 - \lambda)^2\cos^2 2\theta + (1 - \lambda)^2\cos(2\theta) + (1 - 6\lambda + \lambda^2) \\ k\_4 &= 4(1 - \lambda)^2\cos(4\theta) + 2(1 - \lambda)[(1 + \lambda) - (1 + \lambda + \frac{2C\_{\rm m}\cot\varphi\_{\rm m}}{\sigma\_{\rm v}})\cdot\sin^2\varphi\_{\rm m}]\cos(2\theta) \\ k\_5 &= (1 + \lambda + \frac{2C\_{\rm m}\cot\varphi\_{\rm m}}{\sigma\_{\rm v}})^2\sin^2\varphi\_{\rm m} - (1 - \lambda)^2. \end{aligned}$$

When *θ* is given, the relationship between the radius of the plastic loosening circle and the coefficient of lateral pressure of the roadway surrounding the rock can be obtained by Equation (6). Then the radius of the loose circle in the surrounding rock is calculated to provide the theoretical conditions for roadway support. When *λ* = 1 and *σ*<sup>h</sup> = *σ*v, we can substitute into Equation (6):

$$f\_{\rm m} = 4m^2 + \left(2 + \frac{2C\_{\rm m} \cot \varphi\_{\rm m}}{\varphi\_{\rm V}}\right)^2 \sin^2 \varphi\_{\rm m} = 0\tag{7}$$

Additionally the radius of the loosening ring can be obtained by Equation (7).

$$r\_1 = r\_0 \sqrt{\frac{\sigma\_\text{V}}{(\sigma\_\text{V} + \text{C}\_\text{m} \cot \varphi\_\text{m}) \sin \varphi\_\text{m}}} \tag{8}$$

where *r*<sup>0</sup> is the radius of the circular roadway.

The stress change of the circular roadway can be obtained, as shown in Figure 2.

**Figure 2.** Stress distribution of the circular roadway.

At the interface of the elastic zone and the plastic zone, tangential stress *σ*<sup>θ</sup> reaches its maximum value, and the stress at the interface gradually diffuses to the depth of the roadway (see Figure 1). When the elastic zone is exceeded, the surrounding rock stress gradually returns to its initial stress state.

According to the plastic zone of the circular roadway, the plastic zone range of rectangular roadway after excavation is also solved. Assuming that the width and height of the rectangular roadway are 2c and 2d, the radius of the circular roadway is solved,

$$r\_0 = \sqrt{c^2 + d^2}.\tag{9}$$

The equivalent circular radius is substituted into *r*<sup>0</sup> to solve the radius range of the loose circle of the roof and two sides of the rectangular roadway. It provides the reliability basis for the design of roadway supporting parameters.

Therefore, the range of the loose circle is on the roof of the rectangular roadway:

$$l\_{\mathbb{A}} = r\_1 - d \tag{10}$$

The range of loose rings on both sides:

$$l\_{\mathfrak{c}} = r\_1 - \mathfrak{c} \tag{11}$$

where *d* is half the height of the rectangular roadway, and *c* is half the width of the rectangular roadway.

Taking the cavern of the gas pump station as a case, the mechanical parameters of the roadway are *r*<sup>0</sup> = 4.84 m, *ϕ*<sup>m</sup> = 30◦, *C*<sup>m</sup> = 1 MPa, and *σ*<sup>v</sup> = *p*<sup>0</sup> = 10 MPa. By substituting into Equation (8), we obtain, *r*<sup>1</sup> = 6.34 m.

By substituting *r*<sup>1</sup> into Equations (9) and (10), we get the height of the roof loose ring, *l*<sup>s</sup> = 3.34 m, and the loose ring of the two sides, *l*<sup>e</sup> = 2.54 m. The range of loose circles provides a theoretical basis for future roadway support technology.

#### *3.2. Numerical Calculation*

According to the geological conditions, the direction of extension of the large destressing hole was in the *x*-axis (120 m), the axial direction of the cavern was in the *y*-axis (50 m), and the vertical direction of the coal and rock mass was in the *z*-axis (40 m), forming a numerical calculation model as shown in Figure 3. The M-C constitutive model was used in the calculation. The boundary conditions of the model are as follows: the upper boundary is free; the horizontal displacement of the boundary around the model is constrained; and the bottom boundary is fixed. By excavating the model, the influence law of stress distribution and plastic zone distribution of the surrounding rock is simulated. The mechanical parameters of rock strata are shown in Table 2.

**Figure 3.** Numerical model diagram.



The cavern of the gas pump station studied in this paper includes a low- and highnegative pressure cavern. The numerical calculation model systematically studied the deformation and failure laws of the surrounding rock for the whole coal cavern group. The high- and low-pressure caverns are simulated according to the excavation sequence of the practical project. The excavation process is divided into five stages: the first stage is to excavate the connection roadway; the second stage is to excavate the western section of the high-negative pressure system cavern, and the length is 69.5 m; the third stage is to excavate the east section of the western section, and the length is 25 m; the fourth stage is to excavate the western section of the low-negative pressure system cavern, and the length is 60 m; and the fifth stage is to excavate the east section of the low-negative pressure system chamber, and the length is 20 m. It provides guidance for determining the supporting parameters of the whole coal cavern group.

#### **4. Results and Discussion**

#### *4.1. Deformation Law of Surrounding Rock with Different Lateral Pressure Coefficients*

The horizontal tectonic stress in the stratum has a great influence on the stability of the surrounding rock after excavation of the cavern. In this study, a low-negative pressure cavern was selected as the research object, and the influence of different lateral pressure coefficients (γ = 0.5, 1, 1.5, and 2) on the stability of the surrounding rock in the cavern was analyzed. The nephogram of maximum principal stress and the figure of the plastic zone were shown in Figures 4 and 5.

**Figure 4.** A cloud diagram of the maximum principal stress with different lateral pressure coefficients. (**a**) γ = 0.5; (**b**) γ = 1.0; (**c**) γ = 1.5; and (**d**) γ = 2.0.

The peak value of the maximum principal stress in the cavern gradually increases from 5.09 MPa to 6.71 MPa as the lateral pressure coefficient γ increases (see Figures 4 and 5). The stress concentration area on both sides of the cavern increases laterally and then changes to longitudinal diffusion. When the lateral pressure coefficient γ = 2.0, the stress concentration area appears in the roof. The stress distribution of the vertical stress relative to the maximum principal stress changes little with the lateral pressure coefficient. The area of stress concentration near the cavern gradually increases, but the peak value of vertical stress gradually decreases. With the increasing lateral pressure coefficient, the plastic zone area of the cavern decreases. Additionally, under the influence of horizontal stress, the scope of the plastic zone gradually decreases in the two sides of the cavern, so as to gradually extend to the top and floor, and the distribution of the plastic zone changes from a chunky distribution to a thin distribution.
