*Article* **A Study on the Development and Evolution of Fractures in the Coal Pillar Dams of Underground Reservoirs in Coal Mines and Their Optimum Size**

**Bao Zhang 1,2,\*, Wei Ni 2, Xiuqiang Hao 2, Huiqiang Li <sup>2</sup> and Yupeng Shen 1,\***


**Abstract:** The western mining areas of China, which are rich in coal resources, lack water resources. Large-scale and high-intensity coal mining in China's western mining areas has led to the loss of groundwater resources. Underground reservoirs in coal mines are an effective means of achieving the protection and utilization of water resources in these western mining areas. One of the important standards for the safety of an underground reservoir in a coal mine involves checking whether the development of cracks in the coal pillar dam body, under the dual stress conditions of overlying strata and lateral water pressure, passes through the coal pillar dam body or its top and bottom plates, forming a seepage channel for mine water. This article focuses on the safety issues associated with coal pillar dams in the underground reservoirs of coal mines. From the perspectives of overlying rock pressure and lateral water pressure on coal pillar dams, mechanical models, numerical calculations, and similar simulation methods were used to analyze macroscopic deformation, displacement, and crack development in coal pillar dams of different sizes under vertical and horizontal stress and to study the optimum width of coal pillar dams. Our research results indicated that the optimal width of the coal pillar dam body can be determined via numerical simulation based on the deformation and stress state in a given dam. When the horizontal stress increases, the smaller the coal pillar width is, the greater the increment of syy and sxx becomes, and the more likely the coal pillar is to be damaged. Similar simulations showed that the smaller the size of the coal pillar is, the easier it is to generate stress concentration, and the more likely this stress is to "eat away" the coal pillar dam body. There is a certain relationship between the size of the coal pillar dam and the range of crack development. The larger the coal pillar size is, the less obvious the stress concentration effect becomes, and the less likely the crack is to penetrate the internal and external parts of the reservoir. Taking the Shangwan mine as an example, it was determined that the maximum water head height that could be carried by the 15-m coal pillar dam body was 50 m. A comprehensive study of the development and evolution of cracks in the coal pillar dam of an underground reservoir in a coal mine, and the characteristics of sliding instability, was conducted to determine the optimal size and maximum water storage height of a coal pillar that does not penetrate the inner and outer parts of the reservoir. The development and evolution of cracks are important factors affecting the stability of coal pillar dams. This study can expand and improve the basic theory of underground reservoirs in coal mines, provide a scientific basis for determining the optimum size of a coal pillar dam, guarantee the long-term safe and stable operation of the coal pillar dams of underground reservoirs in coal mines, and continuously save mine water resources and increase the economic benefits of coal mines. These implications are of great significance for the long-term stable operation of underground reservoirs in coal mines under similar geological conditions.

**Keywords:** coal mine underground reservoir; coal pillar dam; fissure development and evolution law; optimum size of coal pillar; maximum water level

**Citation:** Zhang, B.; Ni, W.; Hao, X.; Li, H.; Shen, Y. A Study on the Development and Evolution of Fractures in the Coal Pillar Dams of Underground Reservoirs in Coal Mines and Their Optimum Size. *Processes* **2023**, *11*, 1677. https:// doi.org/10.3390/pr11061677

Academic Editor: Ján Pitel'

Received: 5 April 2023 Revised: 21 May 2023 Accepted: 26 May 2023 Published: 31 May 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/).

#### **1. Introduction**

Coal currently has the most stable energy supply and the highest independent guaranteed supply rate, and is the most economic basic energy, in China, and has always guaranteed the energy security of China [1–3]. The overall distribution pattern of coal resources in China is "more in the north and less in the south, more in the west and less in the east, deep in the east and dry in the west" [4,5]. Following years of high-intensity mining, the coal resources in the east and central regions have tended to be exhausted, and coal production has been transferred to the western provinces, which contributed 81% of China's coal production in 2022. However, the water resources in the western mining area are extremely short, accounting for only 3.9% of the country's water resources, and the ecological environment in the western area is fragile. According to the relevant statistics, every 1 ton of coal mined in China produces approximately 2 tons of mine water; however, to date, the rate of mine water utilization has only been approximately 25% [6]. Most of the produced mine water is discharged to the ground, not only causing the waste of water resources due to evaporation but also polluting the environment [7,8]. The Shendong mining area is the world's only 200-million-ton mining area, with seven mines producing an annual output of more than 10 million tons. The Shendong mining area is located on the edge of the arid and water-scarce Maowusu Desert, where the ecological environment is extremely fragile and water resources are extremely scarce [9]. Coal mining causes the destruction of water resources, accelerates the loss of surface water, and leads to more and more prominent problems of water use in mining areas. After years of exploration and practice, more than 30 underground reservoirs of coal mines have been successfully built in the Shendong Mining area, and this has largely solved the problem of water resource protection and utilization in the mining area and protected the area's ecological environment. With the continuous popularization and application of underground reservoir technology in coal mines, more and more attention has been paid to the long-term operational safety of underground reservoirs in coal mines—especially the safety of coal pillar dams—and this has become key to ensuring the long-term safe operation of underground reservoirs in coal mines.

Based on the 20 years of technical exploration and engineering practice in the Shendong mining area, academician Gu Dazhao [10] put forward the theoretical framework and technical system of underground reservoirs for coal mines with "transport, storage and use" as the core themes. The idea of using the goaf as an underground water storage space was thus conceived, creating a new way to protect and utilize mine water resources in the process of coal mining. A large number of engineering practices have since been carried out and good results have been achieved [11,12]. Based on theoretical analysis and numerical simulation, Pang Yihui [13] comprehensively analyzed the feasibility of building an underground reservoir in a coal mine under the condition of large mining height. In their study of coal mining stress fields, B. Unver and Zhang Guojun [14,15] established a three-dimensional calculation model to analyze the movement law of overlying strata and its mining response mechanism in thick coal seam mining. Rajendra Singh [16] studied the variation law of mining stress and the movement law of overlying strata in thick coal seam mining through field testing. Zhang Nong [17] analyzed the failure characteristics and the stability of roof roadways in relief mining. Kong Xiangsong and Shan Renliang [18] established the theoretical expression of stress waves and the dynamic constitutive model of coal, and studied the classification of surrounding rock and the theory of dynamic pressure resistance. In a study on coal pillar dams, Ashok Jaiswal and B.K. Shrivastva [19] established a numerical calculation model and used the strain softening constitutive model to study the strengths of coal pillars. Robert Bertuzzi et al. [20] collated coal pillar detection data from Australia, South Africa, the United States, and other countries and analyzed the strengths of coal pillars under different conditions by using various methods. Petr Waclawik et al. [21] studied the stability of coal pillars by monitoring and analyzing the stress states of coal pillars. Academician Gu Dazhao [22] analyzed the stability of coal pillars in underground reservoirs of coal mines. Song Yimin and Zhang Jie et al. [23,24] analyzed

the deformation field and energy evolution characteristics of coal pillar instability failure and studied the instability characteristics of coal pillars and their overlying rocks. Zhang Cun [25] analyzed the stability of residual coal pillars in underground reservoirs of mines under mining-induced water flooding. Chen Dongdong and Zhao Hongbao et al. [26–28] studied the distribution characteristics of the lateral stress field in coal pillar goaf under different conditions. Tu Min and Wu Baoyang [29,30] used a variety of research methods to study the rational arrangement of coal pillar dams in distributed underground reservoirs of coal mines. In a study on fracture detection, Cao Zhiguo [31] analyzed the distribution model and water flow characteristics of the main channels of water-conducting fractures in mining-induced overlying rocks. Xie Hongxin [32] studied the damage characteristics of water-bearing coal samples under cyclic loading–unloading. Wu Baoyang and Wang Fangtian et al. [33,34] studied the damage and failure law in coal pillar dams under various conditions. Wang Zhenwei [35] numerically analyzed the stress wave propagation law and its influencing factors on coal rock mass. Reed Guy et al. [36] studied the stability of the coal pillar system based on an evaluation method that accounted for the interaction between the coal pillar and the overlying strata. Based on a large number of experimental studies, Yilmaz found that decrease in the friction angle under water infiltration was the main reason for the strength weakening of water-soaked coal rock mass, and that compared with what was found in dry water-soaked coal rock mass, Poisson's ratio increased while Young's modulus decreased [37]. Through component analysis and mechanical tests, Verstrynge et al. found that the transition from metastable creep failure to accelerated failure in water-soaked sandstone was related to the reaction between water and mineral components [38]. E. Ozdemir et al. found that increase in water content significantly reduced the tensile and compressive strengths of rocks [39].

In the past, the domestic methods of water conservation coal mining were limited height mining, strip mining, and filling mining, all of which affected mining efficiency. For Shendong, with its shallow buried working face with a large mining height, limited mining and strip mining would lead to the waste of coal resources. Large-mining-height filling mining has the disadvantages of high cost and poor effectiveness, while water-preserved coal mining, or the large discharge of mine water, will cause a large amount of evaporation and high loss of water resources, and so underground reservoir technology is the best choice to solve the problem of mine water protection and utilization. With the popularization and application of underground reservoir technology, increasing attention has been paid to the safety of coal pillar dams. Increasing numbers of scholars are studying the coal pillar dams in underground reservoirs of coal mines, but at present, there are few studies on the development and the evolution law of cracks in coal pillar dams and the critical conditions of instability and slip. These factors are key to the safety of coal pillar dams and can determine the optimum size of a coal pillar and the height of water storage while being of great significance to the long-term stable operation of underground reservoirs in coal mines.

Underground reservoirs in coal mines are extremely valuable for the mining industry. They offer an effective way to protect mine water and can reduce the pumping of mine water, save electricity and energy, purify mine water, and realize the green mining of coal. The construction of underground reservoirs in coal mines could reduce global carbon dioxide emissions and the pollution caused by mine water in the environment, effectively contributing to addressing the global climate problem.

The main purpose of this paper is to determine the optimum width of coal pillar dams in the underground reservoir of the Shangwan coal mine so as to reduce and prevent the seepage from the coal pillar dam and improve the safety of underground reservoirs in coal mines.

The research plan of this paper is to analyze the mechanical conditions of crack propagation inside the coal pillar dam under different stress conditions from the perspective of overlying rock pressure and lateral water pressure and study the crack development law and safety of coal pillar dams with different widths, using numerical simulation and similar simulation, so as to obtain the optimum width of the coal pillar dam in the Shangwan coal mine.

## **2. The Mechanical Mechanism of Fracture Development and Evolution in the Coal Pillar Dam**

The coal rock mass is a complex porous solid, and the primary fractures are formed in the coal rock body due to geological tectonic action; the overlying rock layer on the working face is in equilibrium when mining is not carried out, and the primary fractures exist in isolation. With the remining of the working face, the original stress balance is broken, and a stress increase zone and stress reduction zones are formed in the coal pillar dam and in the top and bottom plate, respectively, as shown in Figure 1. Stress changes cause primary fractures to propagate and create secondary fractures. As the overlying rock layer on the working face continues to separate, fracture, and balance, the stress is transmitted to the coal pillar dam and to the top and bottom plate so that the stress field also changes. The repeated stress changes make the secondary fractures continue to increase and form a network through each other and then form macroscopic mining cracks [40–42]. If a macroscopic mining fracture has a high degree of development, resulting in the formation of a seepage fracture channel between the underground reservoir of the coal mine and the adjacent roadway outside, the phenomenon of water seepage will result. Therefore, the degree of fracture development in the coal pillar dam is a key factor affecting the safety of underground reservoirs in coal mines, and the fracture development characteristics of the coal pillar dam are inseparable from the stress state in which it is located.

**Figure 1.** Stress distribution of the coal pillar dam.

In the coal pillar dam's stress increase zone, as the stress increases from the original rock stress to the peak of lateral support pressure, the coal rock mass is subjected to compressive stress. According to the Griffith strength theory, the cracks in the coal rock body propagate due to tensile stress, which is measured by uniaxial tensile strength, Rt, and the strength criterion of fracture propagation is as follows:

$$\begin{cases} \frac{\left(\sigma\_{1}-\sigma\_{3}\right)^{2}}{8\left(\sigma\_{1}+\sigma\_{3}\right)} \geq R\_{\text{t}} & \text{if } \frac{\sigma\_{3}}{\sigma\_{1}} \geq -\frac{1}{3} \\\ \sigma\_{3} = -R\_{\text{t}} & \text{if } \frac{\sigma\_{3}}{\sigma\_{1}} < -\frac{1}{3} \end{cases} \tag{1}$$

The angle between the propagation direction of the secondary crack and the long axis of the crack is 2*β* when *<sup>σ</sup>*<sup>3</sup> *<sup>σ</sup>*<sup>1</sup> ≥ −<sup>1</sup> <sup>3</sup> , *<sup>β</sup>* <sup>=</sup> <sup>1</sup> <sup>2</sup> arccos *<sup>σ</sup>*1−*σ*<sup>3</sup> <sup>2</sup>(*σ*1+*σ*3), and the propagation direction of the secondary crack is parallel to the direction of the long axis of the crack when *<sup>σ</sup>*<sup>3</sup> *<sup>σ</sup>*<sup>1</sup> ≥ −<sup>1</sup> 3 (Figure 2).

**Figure 2.** Expansion direction diagram of secondary crack tensile fracture.

In the coal pillar dam's stress increase zone, when the stress is reduced from the peak of the lateral support pressure to the original rock stress, the lateral pressure change is not obvious, and the vertical stress decreases significantly (this is the pressure relief process; Figure 3. The main form of crack expansion is reverse slip [43], and its critical stress is derived thus:

$$\sigma\_1 = \frac{\frac{\sigma\_2 \sin 2\theta}{2} - \mu \left(\sigma\_3 - \frac{8\mathbf{C}\_0 \mathbf{a}}{k+1}\right) \cos^2 \theta - 2 \left(\mathbf{r}\_c + \mu \sigma\_{1m} \sin^2 \theta\right)}{\cos \theta \sin \theta + \mu \cos^2 \theta} \tag{2}$$

where *μ* is the friction coefficient of coal rock, *τ<sup>c</sup>* is cohesion, *σ*1m is the axial lateral stress at the starting point of unloading, *θ* is the angle between crack and principal stress direction, and *G0* is the shear modulus of coal rock.

**Figure 3.** Expansion direction diagram of secondary crack reverse slip.

In the stress reduction zone of the coal pillar dam, the stress is significantly reduced, a large number of secondary fractures are generated by the development of primary fractures, and the secondary fractures of the coal rock mass penetrate due to the tensileshear composite failure. As shown in Figure 4, the propagations of any two fractures AB and CD produce secondary fractures AF and CE, and the secondary fractures penetrate with tension crack EF to form a fracture network. The penetration strength between fractures is depicted below [44,45]:

$$\sigma\_1 = \frac{h\sigma\_l(\sin\alpha + f\_r\cos\alpha) - 4lc\_r + B\sigma\_3}{A} \tag{3}$$

where *h* is the vertical distance between fractures, *σ<sup>t</sup>* is the uniaxial tensile strength of the rock, *α* is the inclination angle of the tensile crack, *fr* is the friction coefficient of the rock, *cr* is the rock cohesion, *l* is the length of the secondary fracture, and *A* and *B* are the penetration functions.

**Figure 4.** Diagram of transfixion between secondary cracks.

#### **3. Numerical Simulation of Coal Pillar Dam Width in the Shangwan Mine**

The special ecological environment of the Shendong area has created the diversity and complexity of the ecological system of the region, and the problem that needs to be solved urgently at this stage is the lack of water resources. However, the coal seam in the Shendong mining area has good storage conditions, large reserves, and a high output, and there is a high loss of surface water and groundwater resources due to the transportation of surrounding rock as a consequence of coal mining, exacerbating the water shortage in the region. Therefore, the utilization of the underground reservoir in the coal mine is an important measure to achieve a win–win situation of energy development and water resource protection and utilization.

The typical underground reservoir of a Shendong coal mine is exemplified in the Shangwan coal mine. The Shangwan coal mine is located in Ejin Horo Banner, Ordos City, Inner Mongolia Autonomous Region, China, and was completed and put into operation in 2000. It covers an area of 61.8 square kilometers and has nine coal seams that can be mined, geological reserves of 1.23 billion tons, recoverable reserves of 830 million tons, an approved production capacity of 16 million tons/year, and a service life of 53 years. The coal is long-flame coal and non-bonded coal, and is a source of high-quality power, coal-to-oil, and chemical and metallurgical coal. The geological structure is simple, and the hydrogeological type is classified as medium. The rock mass of the top and floor of the coal seam in the mining area is of good quality and is relatively complete, but its mechanical strength is low, as it contains mainly weak rocks, and the stability of the top and floor rocks of the coal seam is poor.

#### *3.1. Numerical Simulation Construction and Research Scheme Design of the Underground Reservoir Dam in the Coal Mine*

In a study of underground reservoirs, understanding the size and stability of coal pillar dams is the top priority. The general stratigraphic column of the Shangwan coal mine engineering is shown in Figure 5, and the width of the coal pillar dam in the mining process of the UDEC discrete element and the internal stress field, displacement field, and fracture development and change characteristics of the coal pillar dam under the action of lateral water pressure in the goaf area have been constructed by using UDEC discrete elements. This construction has obtained the optimum size of the coal column dam body, providing a theoretical basis for the retention of the coal pillar dam in the Shangwan coal mine.

Based on the general stratigraphic column of the Shangwan coal mine, the numerical simulation is as shown in Figure 6. The model size is defined as length (working face layout direction) × height (vertical direction) = 236 m × 280 m, with a 2-2 coal roof plate of 74 m, 2-2 coal seam and 3-1 coal seam spacing 100 m, and 3-1 coal floor of 50 m. The boundary impact area on both sides of the model is of 40 m, the excavation area studied in the middle is of 200 m, and the model contains two layers of coal in the form of 2-2 coal and 3-1 coal. The upper coal seam of 2-2 coal simulates the excavation face in the central area and its two side roadways and the lower coal seam, 3-1 coal, simulates the excavation of two roadways and one working face on the left and right sides of the central area. The two layers of coal are arranged with 30-m and 15-m coal column dam bodies, respectively, and the spatial relationship between the excavation areas of the upper and lower coal seams is shown in Figure 6.


**Figure 5.** General stratigraphic column of the Shangwan coal mine working face.

**Figure 6.** Spatial distribution characteristics of the simulated excavation area.

In order to study the internal variation characteristics of the coal pillar dam, a measuring line with an interval of 1 m is arranged in the middle of the studied coal pillar dam

to monitor its deformation and stress. The objective of the simulation is to excavate 2-2 coal first and then excavate 3-1 coal. Horizontal stress is applied to the 3-1 coal pillar dam to effectively replace the influence of goaf water pressure. During this process, the width and roadway height of the coal pillar dam on the same side of 2-2 coal and 3-1 coal are consistent, and the difference is only limited to the coal pillar dam. There is no lateral horizontal stress. Due to limited space, it is assumed that the optimum coal pillar width for 2-2 coal excavation is equivalent to that for 3-1 coal excavation without lateral horizontal stress. Therefore, the main focus of the simulation study is on the changes of the coal pillar dam body under the conditions of 3-1 coal excavation with horizontal stresses of 0 MPa and 10 MPa.

#### *3.2. Analysis of Simulation Results*

(1) Variation characteristics of coal pillar dam body without lateral horizontal stress

From a longitudinal comparison of the distribution of internal stress and deformation under the condition of changing the width of the coal pillar, the vertical stress distribution characteristics and horizontal deformation amount of the coal pillar dam body under only the roof load are obtained using the FISH language as shown in Figures 7 and 8. Figure 7 shows that the widths of the left coal pillar are 15 m, 20 m, and 25 m, respectively, from top to bottom, and the widths of the right coal pillar are 30 m, 35 m, and 40 m, respectively. From the horizontal deformation amount of the coal pillar, it can be concluded that as the size of the coal pillar decreases, the deformation amount on both sides of the coal pillar shows an increasing trend, with a large increment on the free side of the coal pillar and a small increment on the roadway side of the coal pillar. The internal deformation amount of the 15–25-m coal pillar increases approximately linearly, while the internal deformation amount of the 30–40-m coal pillar is basically consistent and small. By dividing the deformation amount by using a color scale and analyzing the range of coal pillar deformation using color scale area of displacement of less than 0.1 m as a reference, it can be concluded that the corresponding areas of coal pillars that are of 15 m, 20 m, 25 m, 30 m, 35 m, and 40 m are 0 m, 5 m, 10 m, 17 m, 22 m, and 29 m, respectively, accounting for 0%, 25%, 40%, 57%, 62%, and 72% of coal pillar width, respectively. The proportion of this area increases with the increase in coal pillar width, with increments of 25%, 15%, 17%, 5%, and 10%, respectively. From these results, it can be concluded that the stable area inside the coal pillar under the condition of 30 m has a larger increment compared to under the conditions of 25 m and 35 m. From the perspective of the distribution characteristics of vertical stress inside the coal pillar, it can be seen that the vertical stress on the left and right sides of the coal pillar increases as the size of the coal pillar decreases. Between them, the vertical stress peak value of the 30-m coal pillar is the highest and the bearing stress is the largest. Considering that the internal deformation of the coal pillar is small, it can be concluded that the 30-m coal pillar has the optimal size of the coal pillar dam.

**Figure 7.** Cloud Chart of Horizontal Displacement of Coal Pillar Dam/m.

**Figure 8.** Change characteristics of a coal pillar dam body without lateral horizontal stress.

(2) Variation characteristics of coal pillar dam considering lateral horizontal stress

Based on the above pressure variation characteristics of coal pillar dams without horizontal lateral pressure, it is necessary to supplement the variation characteristics of coal pillar dam stability under goaf water filling conditions in order to further study the stability of coal pillar dams in underground reservoirs. Due to the large amount of data from multiple groups of comparative analysis, when analyzing only 15 m and 30-m coal pillars, horizontal stress is applied to both sides of the 3-1 coal seam, and the variation rules of sxx and syy stresses under the conditions of 0 MPa, 5 MPa, and 10 MPa are shown in Figure 9.

**Figure 9.** *Cont*.

**Figure 9.** The influence of the change in the width of the coal pillar dam on its stress variation characteristics.

As shown in Figure 9, under the action of horizontal stress applied to the goaf side of the coal pillar dam, the stress of syy and sxx on the goaf side of the coal pillar dam, which is positively correlated with the horizontal stress, increases. The smaller the size of the coal pillar is, the greater the increment of stress in syy and sxx is. After comparing and analyzing the differences in the changes of coal pillar syy and sxx under the action of horizontal stress, it can be concluded that horizontal force has an impact on the stability of coal pillars. With the increase in coal pillar width, the influence range of horizontal force on the goaf side of the coal pillar dam becomes smaller and smaller. When the coal pillar width is 15 m or 20 m, the application of horizontal stress causes changes in sxx and syy in all areas inside the coal pillar, thus indicating that horizontal force is transmitted from the goaf side to the roadway side. Horizontal force has a significant impact on the stress state of the coal pillar, indicating that the stability and bearing capacity of the coal pillar decrease under the action of horizontal force. When the width of the coal pillar is 25–40 m, the variation areas of the syy of the coal pillar after the horizontal force is applied are 12 m, 8 m, 8 m, and 7 m, and for those values, the sxx variation areas are 16 m, 10 m, 8 m, and 7 m, respectively. Considering the influence range of the horizontal force on the

coal pillar stress in the goaf side when the width of the coal pillar is 30–40 m, it can be found that the influence range of the horizontal force on the coal pillar is basically the same. When the width of the coal pillar is 30 m, the influence of the horizontal force on the coal pillar on the goaf side no longer changes significantly. From the comparison of the bearing capacity and stress state of the coal pillar, it can be concluded that a coal pillar of 30 m is the optimum width.

As shown in Figure 10, by comparing the internal stress variation characteristics of 15–25 m and 30–40-m coal pillars under the same horizontal force conditions, when there is no horizontal stress on the coal pillar dam body, the fluctuation range of syy and sxx stress in the middle area of both coal pillars and the side of the goaf is relatively large. When a 5-MPa horizontal stress is applied to the goaf side of the coal pillar dam, the fluctuation range of syy and sxx stress in the middle area of the 15–25 m and 30–40-m coal pillars and the side of the goaf is significantly reduced. When a 10-MPa horizontal stress is applied to the goaf side of the coal pillar dam, the syy and sxx stresses in the middle areas of the 15–25 m and 30–40-m coal pillars and the side of the goaf are similar. The coal pillar width of 15–25 m is significantly larger than the area affected by the horizontal force of 30–40-m coal pillars. Therefore, when the horizontal stress on the side of the gob of the coal pillar dam increases, the smaller the coal pillar width is, the greater the stress change on syy and sxx on the side of the gob of the coal pillar dam becomes. Therefore, as the horizontal stress increases, the size of the coal pillar decreases, and the stress increment of syy and sxx becomes more significant. The goaf side of the coal pillar is the starting point for the stress increment of syy and sxx. The larger the stress increment is, the more easily the coal pillar is damaged, indicating that small coal pillars are more sensitive to horizontal pressure.

**Figure 10.** Stress variation characteristics of a coal pillar dam body under lateral horizontal stress conditions.

#### **4. Experimental Study on Crack Development in a Coal Pillar Dam**

Based on the numerical simulation results for crack development in a coal pillar dam body of different sizes in the Shangwan mine, the coal pillar dam is of the best size when the width of the coal pillar is 30 m. In this section, similar simulation experiments that were used to study coal pillar dams with two widths—30 m and 15 m—are described.

### *4.1. Similar Simulation Experiment Research Scheme*

This simulation experiment, which is similar to the previous one, analyzed the macroscopic fracture development in and slip instability characteristics of a coal pillar dam under different stress conditions and used the "Multi-seam Mining Coal Mine Underground Reservoir Simulation Test Platform" to carry out the relevant experiments. Above this platform are seven servo motors, which can load vertical force, that can simulate the self-weight of the overlying strata and achieve local loading, and two servo motors, which can load horizontal force, that can simulate the lateral water pressure of underground reservoirs of coal mines. The simulation test platform can be laid on a simulation test platform with dimensions of 2100 mm × 1800 mm × 300 mm. The similarity ratio of this experiment was 1:150, and the physical and mechanical parameters of each rock layer were consistent with the numerical simulation parameters. In this simulation, the process of mining a 2-2 coal face and a 3-1 coal face in Shangwan coal mine and forming an underground reservoir was simulated. The two layers of coal were arranged with coal pillar dams of 30 m and 15 m, respectively. As shown in Figure 11, the 2-2 coal layout had a 178-m-wide working face and a 15 m and a 30-m coal pillar dam body were arranged on both sides. The 3-1 coal layout had two 132-m working faces, and the two adjacent coal pillar dam bodies, which were of 15 m and 30 m, were arranged in the middle.

In order to monitor the stress change characteristics inside the coal column dam, a coordinate system was established, with X in the transverse direction and Y in the longitudinal direction, and the stress measurement points were arranged. The scheme, as shown in Figure 12, indicated that one stress measuring point in the Y direction was uniformly arranged inside the two coal pillars of 2-2 coal seam along the X direction, and two stress measuring points in the Y direction were uniformly arranged at the upper boundary along the X direction (Figure 12a,b). One stress measuring point in the X direction was uniformly arranged inside the two coal pillars of 3-1 coal along the Y direction, and one stress measuring point in the Y direction was arranged at the upper boundary (Figure 12c,d).

**Figure 11.** Similar simulation experiment scheme.

**Figure 12.** Arrangement of stress monitoring points of a coal pillar dam.
