Determination of Water-Proof Coal (Rock) Pillar Height in Mining Coal Seam Group under Water-Bearing Rock Stratum

In order to determine the reasonable height of water-proof coal (rock) pillar when mining multiple coal seams under aquifer, this paper analyzes the expansion height of water-conducting fracture zone when coal seams mining. Considering the expansion law of water-conducting fracture zone in coal seams mining, two schemes of coal seams mining in upper and lower groups and one-time mining of all coal seams are designed for comparative analysis, and the height of water-proof coal (rock) pillar is determined based on the expansion height of water-conducting fracture zone. The results show that the height of water-proof coal (rock) pillar is calculated as 91.08m when mining upper and lower groups and 105.46m when mining all coal seams at the same time. According to UDEC numerical simulation results, the height of water-proof coal (rock) pillar is 56.08m when mining upper and lower groups and 86.36 m when mining all coal seams at the same time. Comparing the results of theoretical calculation and numerical analysis, the maximum value is selected as the ﬁnal result, and the reasonable water-proof coal (rock) pillar height is determined to be 105.46m.


Introduction
After underground coal seam mining, the migration and destruction of overlying strata will form a hydraulic connection channel between stope and surrounding waterbearing rock stratum, which threatens the safety of mine production. By studying the height of water-conducting fracture zone in overlying strata, preventive measures can be taken to avoid mine water disasters. In recent years, methods for determining the height of water-conducting fracture zone, such as geophysical prospecting, high-density resistivity method, transient electromagnetic method, and borehole peeping method, have been developed [1][2][3][4][5], and many researchers have done a lot of research and obtained very fruitful results [6][7][8][9][10][11][12][13]. Jiang [14] established the "rock quality index" method for water-conducting fracture zone prediction. Zhao et al. [15] analyzed the height of waterconducting fracture zone under special conditions such as full-mechanized caving mining and full-seam mining based on the theory of internal and external stress fields. Xu [16] put forward the concept of "effective water-proof thickness." Gao [17] established the "four zones" model of strata movement. Zhang et al. [18] established the physical model of "mining-bursting" and the relationship between mining kinetic energy and strain energy and determined the relationship between the safe distance of rock blasting and the height of water-conducting fracture zone. Jia et al. [19] analyzed the distribution range of mining fault zone in steep working face and determined the reasonable width of waterproof coal (rock) pillar. Huang et al. [20] proposed a new method for predicting the height of water-conducting fracture zone based on the calculation of overburden composite structure and rock tensile deformation. Yu et al. [21] analyzed the maximum caving height and effective water guide height of overlying strata under different mining-caving ratios. Many researchers used numerical simulation to verify theoretical results. Tang et al. [22] used RFPA system to simulate the dynamic development process of water-conducting fractured zone. Yin [23] simulated and analyzed the stress evolution of surrounding rock in advancing of different mining faces based on FLAC3D numerical method. Li et al. [24] used FLAC to study the height of water-conducting fracture zone in coal mining face under water-rich extra-thick glutenite. Xu et al. [25,26] quantitatively analyzed the model of mining fracture propagation based on FIMAGE. Yang et al. [27] used UDEC to study the influence of mining sequence of multiple coal seams under rivers on the development height of water-conducting fracture zone in overlying strata.
Reasonable height of water-proof coal (rock) pillar can effectively inhibit the development of water-conducting fracture zone of overlying strata in mining field and ensure that the working face is not threatened by water disasters during mining. However, because of the complex geological conditions in coal mines, there is no consistent standard for determining the size of water-proof coal (rock) pillar. For example, the formula of water-proof coal (rock) pillar applied in Europe earlier [28] only considers the influence of water pressure and coal seam thickness on coal pillar, but ignores the determination of coal pillar by coal strength and buried depth. Based on the pressure arch, the formula [29] for determining water-proof coal (rock) pillar is only applicable to coal seams with a buried depth of 400-2800 feet. e early formula of water-proof coal (rock) pillar applied in the United States [30] ignores the influence of water pressure and caving zone, and the calculated water-proof coal (rock) pillar size is too small. Wang gives the observation equation of water-proof coal (rock) pillar according to the abovementioned problems [31]. In recent years, some achievements have been made in the research on the height of water-proof coal (rock) pillar in coal mines in China. e representative ones are Shi et al. [32], who deduced the formula of waterproof coal (rock) pillar in stope fault based on the comprehensive factors of mine pressure. Peng et al. [29], aiming at different fault dip angles, obtained the formulas of waterproof coal (rock) pillar with different widths by using fluid mechanics, elastoplastic limit equilibrium theory, and soil mechanics theory.
Analysis of the development law of water-conducting fractured zone under multiple coal seams is of great significance for multiseam mining under aquifer. From the foregoing analysis, it can be seen that there is a lack of relevant research on the development law of water-conducting fracture zone in multiseam mining under waterbearing stratum. In view of the potential danger of waterbearing stratum in multiseam mining, this paper analyzes the development height of water-conducting fracture zone in multiseam mining by theoretical analysis and UDEC numerical simulation and further designs reasonable waterproof coal (rock) pillar height to provide basis for on-site safety production.

Background of the Project
e length of a coal mine from east to west is about 9.3 km, 1.3∼3.1 km wide from north to south, covering an area of 22.41 km 2 , with a designed production capacity of 1.2 Mt/a and a service life of 60.5 a. e whole mine field is monoclinic structure, with 11 faults in the whole mine field, only one fault with a fall greater than 30 m, and the dip angle is 4°∼24°, so the stratigraphic structure is relatively simple. ere are 7 layers of minable coal seams in the whole area, most parts and parts of the mine field, which are numbered as nos. 13,12,10,9,, and 8-1 from bottom to top. e total thickness of minable coal seams is 21.92 m, and the dip angle of coal seams is between 4°and 24°, which belongs to nearly horizontal coal seams. According to the field hydrogeology survey, the pore fissure water-bearing rock stratum overlying 8-1 coal has a pressure head of 0.44 MPa, and its thickness is 64.91∼158.00 m, with an average thickness of 116.48 m revealed by 44 boreholes. e unit water inflow in the water-bearing rock stratum mine field is 0.1 l/ s.m < q < 1.00 l/s.m, and the permeability coefficient is 0.0469∼0.2288 m/d, which belongs to medium water-rich property and is the main water filling source for coal mining. At the bottom boundary of tertiary system, variegated mudstone was formed after weathering of middle and lower Jurassic strata, with an average thickness of 10.3 m, which is a good natural water-proof strata.
e above stratum structure features have both advantaged and disadvantaged factors for mining coal seam group under water-bearing rock stratum. e advantaged factor is that there is no hydraulic connection between the effective water-bearing rock strata of bedrock, the relative waterproof strata, and the weak water-bearing rock stratum in the area, because there are thick multilayer argillaceous waterproof strata. e disadvantaged factor is that the roof and floor of minable seam are extremely unstable and soften strongly when meeting water, so it is necessary to analyze the height of water-conducting fracture zone and determine the water-proof coal (rock) pillar.

Determination of Height of Water-
Conducting Fracture Zone e water-conducting fracture zone refers to the sum of caving zone and fracture zone of overlying strata in goaf. e saturated uniaxial compressive strength of roof and floor strata of the coal mine is within 40 MPa, and the roof and floor strata in this area are medium hard strata. When there are extremely hard strata in the overlying strata of coal seam roof, the suspended roof can be formed after mining, and the formula of caving zone is where H m is the maximum caving zone height; M is the thickness of coal seam mining; K is the crushing expansion coefficient of caving rock, and α is the dip angle of coal seam. At present, when determining the water-conducting fracture zones with different overlying strata lithology in gently inclined and inclined thick coal seams in China, the calculation is mainly based on the formula in Regulations for Coal Pillar Retention and Coal Mining in buildings, water bodies, railways, and main roadways [33]. Determine the formula of water-conducting fracture zone in minable seam of this coal mine as follows: where H li is the height of water-conducting fracture zone and M is the thickness of coal seam mining.
In water-conducting fracture zone calculation, the smaller the coal seam thickness, the smaller the expansion height of water-conducting fracture zone, and the greater the coal seam thickness, the greater the expansion height of water-conducting fracture zone. According to the coal seam occurrence conditions in the preliminary design of the mine, the following two schemes are designed when determining the height of water-conducting fracture zone.
Grouping mining: calculate the expansion height of waterconducting fracture zone according to the mining of upper and lower coal groups. e upper coal group includes 8-1 coal seam, 8-2 coal seam, 8-3 coal seam, 9 coal seam, and 10 coal seam, and the lower coal group includes 12 coal seam and 13 coal seam. In the calculation process of the lower coal group, firstly calculate the height of the caving zone, determine whether the caving zone affects the overlying coal seam, and then calculate the expansion height of water-conducting fracture zone according to the relevant formula.
Simultaneous mining of all coal seams: calculate the expansion height of water-conducting fracture zone according to one-time mining of all coal seams.

Determination of Height of Water-Conducting Fracture Zone by Grouping Mining.
e total thickness of the lower group coal is 5.6 m, the dip angle of coal seam is 14°, and the crushing expansion coefficient is taken as 1.3. According to formula (1), the height of water-conducting fracture zone in the lower group coal mining is 19.2 m, and the distance between the lower group coal 12 and the upper group coal 10 is about 124.6 m, so the caving zone in the lower group coal mining cannot reach the upper group coal range. According to formula (2), the height of water-conducting fracture zone of lower group coal is calculated to be 50.2 m, and formula (3) is calculated to be 57.2 m. e maximum value of calculation results is selected, and the height of water-conducting fracture zone is determined to be 57.2 m when the lower group coal is produced. e total thickness of the upper group coal is 12.6 m, and the height of water-conducting fracture zone of the upper group coal is calculated as 58.6 m according to formula (2) and 81 m according to formula (3). e maximum value of calculation results is selected, and it is determined that the height of water-conducting fracture zone is 81 m, when the upper group coal is produced. Figure 1 shows the schematic diagram of the height of water-conducting fractured zone in grouping mining.

Determination of Height of Water-Conducting Fracture
Zone by Simultaneous Mining of All Coal Seams. Total height of recoverable thickness of 7 layers of coal is 18.1 m.
According to formula (2), the height of water-conducting fracture zone is calculated as 61.2 m and that of waterconducting fracture zone is calculated as 95.1 m according to formula (3). Figure 2 shows the schematic diagram of height of water-conducting fracture zone in simultaneous mining of all coal seams.

Determination of Height of Water-Proof Coal (Rock)
Pillar. According to the article [33], it is stipulated that when the outcrop of coal seam is covered by a loose waterbearing rock stratum with strong water-rich property (as shown in Figure 3), water-proof coal (rock) pillar should be retained to prevent the water-conducting fracture zone from penetrating through the water body, so the thickness of the water-proof coal (rock) pillar should be greater than or equal to the sum of the height of the water-conducting fracture zone and the thickness of the water-proof protective rock stratum, that is, where H f is the water-proof coal (rock) pillar; H L is the water-conducting fracture zone; H b is the water-proof protective rock stratum; and α is the coal seam dip angle. e accumulated mining thickness of 7 layers of coal is 18.1 m, and the average thickness of mudstone waterresisting strata is 10.3 m. According to [33], the height of water-proof protective rock stratum of medium hard overlying strata should be taken as 4A according to the formula e formula M is the accumulated mining thickness; n is the number of layered layers. e calculated A � 2.59. According to formula (5), the thickness of water-proof protective rock stratum of grouping mining is 10.08 m, and the thickness of water-proof protective rock stratum of simultaneous mining of all coal seams is 10.36 m.
According to formula (4), it is determined that the height of water-proof coal (rock) pillar of grouping mining is 91.36 m, and the height of water-proof coal pillar of simultaneous mining of all coal seams is 105.46 m.

UDEC Simulation Analysis
Considering that the roof and floor of coal seam are mainly unstable sandstone-like strata, after being affected by mining, cracks develop upward along the weak surface of fault, which poses a great threat to mine water filling. At present, there is little research on the evolution law of caving zone of coal seam group under water-bearing strata. In view of the fact that discrete element software can vividly simulate the phenomena of separation and caving between strata, typical discrete element software UDEC is used to simulate and analyze the development height of water-conducting fracture zone.

Establishment of Numerical Model.
Based on the occurrence state of coal seams, it is considered that when all coal seams are built in the same model in the simulation results, because the whole thickness of the model is large and the thickness of a single coal seam is small, the simulation results cannot effectively display the range of water-conducting fracture zone. erefore, in the establishment of the model, the range of model will be narrowed, the specific range of overlying strata caving in coal seam mining will be highlighted, and the models of two mining methods will be established. e mechanical parameters of coal and rock used in modeling are shown in Table 1.

Numerical Model of Simultaneous Mining of All Coal
Seams. According to the occurrence conditions of coal seams, all minable coal seams are taken as a group of coal for mining design. In the model, the total thickness of coal seam is 18.1 m, and the model range includes 15 m siltstone in the lower part of coal seam, covered with 40 m fine sandstone, 50 m siltstone, and 8 m mudstone, and the above mudstone is the water-bearing rock stratum range. e rock layer 457 m above the model is applied to the upper surface of the model in the form of vertical stress. e average bulk density of overlying strata is 23 kN/m 3 , and the applied vertical stress is 10.5 MPa. e strike length of the model is 400 m, and the mining design model is shown in Figure 6.
After the model is established, the coal seam excavation test is carried out. During coal seam excavation, 50 m boundary coal pillars are set on the left and right sides of the model, and the advancing length of coal seam is 300 m along the strike direction. e specific excavation model is shown in Figure 7. When the coal seams are mined in groups, the excavation of the lower group of coal seam is carried out   first, and the extension height of the water-conducting fracture zone of the overlying strata is analyzed. If the waterconducting fracture zone has no influence on the upper group coal during the mining of the lower group coal, the excavation of the upper group coal is carried out, and the expansion height of the water-conducting fracture zone during the mining of all coal seams is taken as the expansion height of the water-conducting fracture zone. When all coal seams are mined at the same time, all coal seams are regarded as a layer of coal for excavation, and the expansion height of water-conducting fracture zone during all mining is determined.       Figure 8 shows the evolution trend of movement and displacement of overlying strata in group coal mining under group coal mining simulation. It can be seen that, after the mining of the lower group of coal, the boundary line of 0displacement of overlying strata moves to 21.2 m above the coal seam. If there is no movement of rock above 0-displacement boundary line, the range from 0-displacement to goaf can be regarded as the extension height of caving zone and water-conducting fracture zone, that is, the waterconducting fracture zone extends to 21.2 m above the lower group of coal seam during mining. Figure 9 shows the evolution trend of movement and displacement of overlying strata in grouping simulation

46.0m
Water-bearing rock strata -  mining of upper group coal. It can be seen that the 0-displacement boundary line of overlying strata movement after the upper group coal mining extends to 46 m above the coal seam, that is, the water-conducting fracture zone of the upper group coal mining extends to 46 m above the 8-1 coal. Figure 10 shows the evolution trend of displacement during simultaneous mining of all coal seams. It can be seen that after coal seam mining, the 0-displacement boundary line of overlying strata extends to 76 m above coal seam, that is, the water-conducting fracture zone extends to 76 m above 8-1 coal.

Results
Analysis. According to formula (4), the height of water-proof coal (rock) pillar in numerical simulation of grouping mining is determined to be 56.08 m (calculated as 91.36 m), and the height of water-proof coal (rock) pillar in simulation results of simultaneous mining of all coal seams is determined to be 86.36 m (calculated as 105.46 m). e two simulation results are smaller than the height of waterconducting fractured zone calculated one. For safety production, the height of the water-proof coal (rock) pillar is finally determined as 105.46 m, which provides a basis for the design of the field working face.

Conclusions
(1) Establishing two schemes: grouping mining and simultaneous mining of all coal seams. rough theoretical analysis, it is concluded that the height of water-proof coal (rock) pillar in grouping mining is 91.08 m and that in simultaneous mining of all coal seams is 105.46 m.
(2) UDEC numerical simulation software is used to design two models: grouping mining and simultaneous mining of all coal seams. It is determined that the height of water-proof coal (rock) pillar in grouping mining is 56.08 m and that in simultaneous mining of all coal seams is 86.36 m. (3) For safety production, the height of the water-proof coal (rock) pillar is finally determined as 105.46 m, which provides a basis for the design of the field working face.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.