Development and Height Prediction of Fractured Water-Conducting Zone in Weakly Cemented Overburden: A Case Study of Tashidian Erjingtian Mine

Abstract

To clarify the development and height of the fractured water-conducting zone of underground mines with weakly cemented overburden, the W8203 working face of the Tashidian Erjingtian Mine in Xinjiang, China, was selected to carry out a case study. Firstly, a physical analog model test was conducted to investigate the development law of the water-conducting fracture zone, followed by a numerical simulation via the PFC2D program. Afterward, a theoretical analysis based on the key stratum theory was carried out. The results demonstrated that there were one primary key stratum and three sub-key strata upon the W8203 working face. As verified by the physical analog tests, the water-conducting fracture developed to the bottom of the primary key stratum, and the height of the fractured water-conducting zone was 246.38 m. The numerical analysis suggests that the primary key stratum did not completely break and the fracture did not penetrate the stratum. Theoretical calculation indicated that the primary key stratum maintained stability in the structure without any breakage. The height of the fractured water-conducting zone is comprehensively determined to be 246.38 m, which is relatively close to the measured value (229.32 m). Based on the prediction method of key stratum position combined with the characteristics of weak cemented overburden, a method to predict the height of a water-conducting fracture zone suitable for weak cemented overburden was developed. The accuracy of this method was also verified through an in-depth comparison with field test results. Under the background of the “strategic westward shift” of coal resource exploration and development in China, the research results can provide theoretical and technical support for safe production in the Tashidian Mining Area and references for green and safe production in weakly cemented overburden mining areas in western China.

1. Introduction

With the gradual declination of coal resources in eastern China, a “strategic westward shift” was proposed and implemented by the state government. As one of the main coal production areas, western China is featured with its weakly cemented stratum upon the coal seam generated in the Jurassic and Cretaceous eras [1,2,3]. In addition, the mining area in western China is of primarily arid and semi-arid climate. Attributed to its scarce water resources, this area is characteristic with a fragile ecological environment, sparse surface vegetation, and severe desertification. High-intensity underground mining activities have resulted in some ecological and environmental problems such as surface subsidence, groundwater level drop, water and soil loss, as well as land desertification [4,5,6]. Under the condition of weakly cemented coal measure strata, the contradiction between ecological protection and high-intensity development of coal resources has become a significant issue, restricting coal mining in the mining areas in western China [7,8,9,10]. Coal resources with weakly cemented strata are mainly distributed in Xinjiang, Shandong, North Shanxi, East Ningxia, North Shaanxi, Huanglong, East Inner Mongolia, Yunnan, and Guizhou Provinces in China. Among them, Xinjiang is western China’s coal resource emergency reserve and capacity guarantee area, the estimated coal reserve of which accounts for approximately 40% of the total reserve in China. As one of fourteen modern coal production bases of 100 million tons developed in China [1,11], how to achieve environmentally friendly mining is always a critical problem to account for. Previous studies were carried out to investigate the mechanical properties, overburden structures, and models of weakly cemented rock. However, a large amount of research focused on the underground mines in northern Shaanxi and Inner Mongolia rather than Xinjiang, China [12,13,14]. It is thus necessary to analyze the law of motion of weakly cemented overburden and the law of evolution of water-conducting fractures in weakly cemented overburden mining areas.

Meng et al. [15,16] reported that Jurassic Cretaceous extremely weakly cemented rocks were rich in clay minerals (e.g., illite, montmorillonite, and kaolin). Because these mineral components are easy to disintegrate, mudding and rheology, the strata generally exhibit strain softening and volume expansion behaviors. Wang et al. [17] applied a regression analysis to determine the quantitative relationship between clay minerals, quartz, feldspar, and the physical and mechanical parameters of weakly cemented rocks. In addition, the pore structure, physical and mechanical properties, disintegration, and other parameters of the weakly cemented formation rock at different burial depths in the mining area in western China were measured by other scholars [1,18,19,20]. These aforementioned studies indicated the differences between the weakly cemented rock collected from the Middle East Carboniferous and Permian strata. The overlying strata are weakly cemented and mainly characterized by late diagenesis, low strength, poor cementation in the case of cementation, and a low residual crushing expansion coefficient of the rock. Affected by the cement content, the elastic modulus and compressive strength of weakly cemented sandstone are only 1/30–1/10 of those of non-weakly cemented rocks with the same lithology. Coal mining easily causes violent overburden movement, and fractures develop on a large scale due to low strength, weak bearing capacity of weakly cemented strata, and sensitive overburden movement with mining activities [21]. Meng et al. [22] conducted a uniaxial compression test and found that the higher the water content of the weakly cemented soft rock, the easier it was to deform, and 10% was the critical water content of brittle and plastic failures. H Eker et al. found that the long-term strength losses of zeolite-substituted paste backfill mixtures were caused by the reaction of sulfate and hydration products that form secondary gypsum, ettringite, and iron sulfate [23].

Many scholars had studied the rock–water interaction and softening mechanism of weakly cemented rock through various ways and methods [24,25,26,27,28]. It has been well demonstrated that both the temperature and confining pressure for weakly cemented sandstone permeability properties increase with decreasing grain size. Song et al. [29] reported that the rock porosity increased with the number of dry and wet cycles. Meanwhile, the damage degree increased and finally stabilized, suggesting that the disintegration resistance index of weakly cemented rocks is negatively correlated with the disintegration number of cycles. The saturation test showed that the weakly cemented rocks swell with water, which weakens the cohesion between the mineral particles, which in turn leads to a significant reduction in the strength of the rock [20,30,31]. As per the theory proposed by Qian et al. [32,33], some hard strata played a significant controlling role in mining overburden deformation failure and movement evolution in coal measure stratum and established a discriminant overburden method for key stratum location. In accordance with Qian’s theory, Yang et al. [34] analyzed the weakly cemented roof fracture morphology and failure law under fully mechanized caving mining conditions. The overburden damage law and rock pressure characteristics in the mining process were also studied and associated with appropriate control measures.

Wu et al. [35,36,37] used PFC software to simulate the failure process and the law of water and sand inrush. Although the prediction method and research results of the development height of the water-conducting fractured zone under the condition of fully mechanized mining have also made great progress, the research is mostly focused on the Carboniferous and Permian fully cemented overburden in eastern China. There are few studies on the development and evolution of mining-induced fractures in weakly cemented overburden mining areas in China. Methods for investigating the developmental height of a fractured water-conducting zone include the physical experiment method, numerical simulation method, theoretical analysis method, geophysical method, downhole subsection water injection method, borehole flushing fluid loss observation method, and borehole television method [38,39,40,41,42,43,44].

Against the above background, this paper presents a case study as per the geological conditions of the Tashidian Mining Area in Korla, Xinjiang. The combination research, including the physical analog experiment, numerical simulation experiment, and theoretical analysis, was carried out to investigate the deformation and failure laws of weakly cemented overburden and to explore the evolution law of water-conducting fractures. Based on the prediction of the key stratum, an innovative method was developed to predict the height of the water-conducting fracture zone. The research can provide theoretical and technical support for safe production in the Tashidian Mining Area and references for green and safe production in weakly cemented overburden mining areas in western China.

2. Materials and Methods

2.1. Structural Stability Analysis of the Primary Key Stratum

2.1.1. Determination of the Key Stratum Location

Based on years of research and practice on roof stratum, Qian Minggao put forward the “key stratum theory” [33]. As per Qian’s theory, there are one or several layers playing a decisive role in all or part of the rock mass movement, which are determined as the key stratum. The former is generally termed the primary key stratum, and the latter can be called the sub-key stratum. If the overlying load q_n+1 < q_n, the nth layer may become the key stratum. The hard stratum satisfying the conditions may be the key stratum [32];

The load on the stratum can be calculated by the following Equation (1):

$${\left(q_n\right)}_1=\frac{E_1{h}_1^3(r_1{h}_1+r_2{h}_2+\cdots +r_n{h}_n)}{E_1{h}_1^3+E_2{h}_2^3+\cdots +E_n{h}_n^3}$$

(1)

where E₁, E₂, …, E_n denote the elastic moduli of the 1st, 2nd, 3rd, …, nth strata, respectively, MPa; h₁, h₂, …, h_n denote the thicknesses of the 1st, 2nd, 3rd, …, nth strata, respectively, m; γ₁, γ₂, …, γ_n denote the body forces of the 1st, 2nd, 3rd, …, nth strata, respectively, MN/m³.

According to the breaking distance of each hard stratum, the calculation formula of breaking distance was shown in Equation (2). If the breaking distance l_n+1 > l_n, this hard stratum will be determined as the key stratum [32].

$$l=h\sqrt{\frac{{2R}_T}{q}}$$

(2)

where h denote the stratum thickness, m; R_T denote the tensile strength of the stratum, MPa; q denote the load on the stratum, MPa.

2.1.2. Structural Stability of the Key Stratum

As shown in Figure 1, the suspended distance of the overlying strata increases with the working face excavation. Once the ultimate breaking step is reached, the deformation failure will occur. Correspondingly, the fracture will develop into two blocks (e.g., Block 1 and Block 2). Since that the goaf is entirely backfilled by the caved zone fragmentary rock mass, the good support between Block 1 and Block 2 ensures they will not fall into the caved zone. A stabilized articulated structure will be generated between the parent rock and Block 1 and Block 2. The new structure, which is similar to a “masonry beam,” has a limited bearing capacity for the overlying strata.

When a stabilized articulated structure is formed between the broken blocks of the primary key stratum, the primary key stratum will not suffer structural instability. Attributed to the existence of the stabilized support, there may be a buffer zone in the upper part of the primary key stratum. In this case, the water-conducting fracture zone will not be developing upward, and the developmental height of which will be at the bottom of the primary key stratum. If the stabilized articulated structure could not be formed, the primary key stratum would experience structural instability and slip and collapse to the caved zone. The developmental height of the fractured water-conducting zone will even develop into bedrock [45]. As per previous research [46], it is assumed that the primary conditions needed to be satisfied if a stable articulated structure between broken rock blocks should be formed, which are shown in Equations (3)–(5):

$${∆}_{\mathrm{m}\mathrm{a}\mathrm{x}}=h_1-\sqrt{\frac{2q{l}^2}{\sigma }}$$

(3)

$$\mathsf{\Delta }=M+(1-k_p)\sum h$$

(4)

$$\mathsf{\Delta }<{∆}_{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(5)

where Δ_max denotes the maximum gyration threshold that can form a stable articulated structure after the stratum is broken, m; Δ is the overlying strata where the stratum is located and the maximum height left by the overlying stratum for its rotation, m; ∑h is the interlayer distance between the rock mass and the mining coal seam, m; h₁ is the parent rock thickness, m; l is the breaking distance of the parent rock, m; k_p is the residual crushing expansion coefficient of the broken rock mass in the caved zone, which is also termed as the residual crushing expansion coefficient; M is the thickness of the coal seam, m.

2.2. Experimental Background

The target area is W8203 working face of the Tashidian Erjingtian Mine, which is located at Korla, Xinjiang, China, as shown in Figure 2. The average thickness of No. 8 coal seam was approximately 9.6 m and thus the fully mechanized top caving method was adopted. Once the roof is exposed in the water, it will quickly expand and soften, resulting in the potential risks to safe mining. According to the stratigraphic data of the mining area and related exploration test data, the stratum structure of the mining area is dominated by muddy cementation with low strength. More specifically, the uniaxial compressive strength of these weakly cemented overlying stratum is under 30 MPa.

According to the typical borehole histogram of the Tashidian Erjingtian Mine shown in Figure 3, the physical analog experiment and numerical simulation experiment were determined as per the W8203 working face. Both the physical and mechanical parameters of coal–rock masses were shown in

Table 1. Physical and mechanical parameters of the coal–rock mass.

Layer	Lithology	Stratum Thickness (m)	Unit Weight (kN/m3)	Elastic Modulus (GPa)	Poisson’s Ratio	Tensile Strength (MPa)	Cohesion (MPa)	Internal Friction Angle (°)
01	Loose strata	15.90	22.00	0.03	0.25	0.01	0.01	23.00
02	Glutenite	37.63	25.30	1.40	0.19	6.75	2.36	36.60
03	Mudstone	86.66	24.00	1.55	0.15	3.56	4.52	41.85
04	Glutenite	96.85	25.30	1.40	0.19	6.75	2.36	36.60
05	Siltstone	27.00	25.60	1.45	0.23	8.12	5.88	42.10
06	Medium Sandstone	54.00	23.60	1.30	0.18	5.02	3.10	33.65
07	Siltstone	53.97	25.60	1.45	0.23	8.12	5.88	42.10
08	Mudstone	15.69	24.00	1.55	0.15	3.56	4.52	41.85
09	Medium Sandstone	6.92	23.60	1.30	0.18	5.02	3.10	33.65
10	Siltstone	27.00	25.60	1.45	0.23	8.12	5.88	42.10
11	Mudstone	19.80	24.00	1.55	0.15	3.56	4.52	41.85
12	Siltstone	42.00	25.60	1.45	0.23	8.12	5.88	42.10
13	Coal seam	9.60	13.70	1.55	0.27	3.56	4.52	41.85
14	Siltstone	6.00	25.60	1.45	0.23	8.12	5.88	42.10

for reference. The establishment of the physical analog experiment and the numerical simulation experiment, as well as the parameters of the theoretical calculation of the key stratum were based on this parameter in Table 1.

2.3. Physical Analog Experimental Methods

2.3.1. The Basic Principle of Physical Analog

The fully mechanized top coal caving technical has high mining intensity at the full height of one-time mining, which will cause severe damage to overburden and abnormal development of the water-conducting fracture zone [47]. Three similarity theorems were adopted as the theoretical basis to reveal the development characteristics of weakly cemented overburden water-conducting fractures in the western Jurassic coal mining area, as shown in Equations (6)–(8) [48]. According to the geological mining conditions of the W8203 working face, the mine pressure and stratum control laboratory test platform was applied to carry out the physical model experiments at Xinjiang University. The size of the platform was 250 cm × 30 cm × 190 cm (length × width × height). According to the specifications of the test device and the full consideration of the test conditions, the challenges of construction and safety during the whole test process were overcome., the geometric similarity ratio was 1:300, the time similarity ratio was 1:17.3, the bulk density ratio was 1:1.5, and the kinetic similarity ratio was 1:450.

$${\mathsf{\alpha }}_1=\frac{l}{L}$$

(6)

$${\mathsf{\alpha }}_t=\frac{t}{T}=\sqrt{{\alpha }_1}$$

(7)

$${\mathsf{\alpha }}_R={\alpha }_1\times {\alpha }_r$$

(8)

where, α₁ denotes the geometric length similarity ratio (model scale), l denotes the size length of the similar material model, and L denotes the size of the actual coal measure strata; α_t denotes time similarity constant or time ratio, t denotes termed as the movement time of similar material model, T denotes the movement time of actual coal measure strata; α_R denotes the stress similarity ratio, and α_r denotes the bulk density ratio of the similar material model to the actual formation rock mass.

2.3.2. Physical Analog Construction and Monitoring Design

Based on the related experimental results in the Similarity Theory and the Static Model Test [48], the mixing proportions and water mass ratios were determined by the uniaxial compressive strength of the original rock and stress similarity ratio, as shown in

Table 2. Proportions for preparing the materials similar to the overlying strata in Tashidian Erjingtian Mine.

Lithology	Unit Weight of Original Stratum (kN/m3)	Compressive Strength of Original Stratum (MPa)	Unit Weight of the Model (kN/m3)	Compressive Strength of the Model (kPa)	Proportion	Water-to-Mass Ratio
Loose stratum	22	3.23	14.7	7.18	7:0.9:0.1 (791)	1/9
Glutenite	25.3	25.4	16.9	56.44	6:0.7:0.3 (673)	1/9
Mudstone	24	28.4	16	63.11	5:0.7:0.3 (573)	1/9
Siltstone	25.6	37.67	17.1	83.71	4:0.5:0.5 (455)	1/9
Medium sandstone	23.6	20.4	15.7	45.33	7:0.7:0.3 (773)	1/9

.

Before laying the physical simulation model, we cleaned the test platform and applied lubricating oil evenly to the inside of each shield to prevent damage to the physical simulation model when removing the shield. The gap was sealed with tape between the bottom guard plate and the model frame to prevent leakage of test materials. According to previous similar materials, the ratio was determined, and the experimental material in the water was accurately measured by using an electronic scale and a measuring cylinder. We added an appropriate amount of gypsum retarder to delay the consolidation progress of the material, and the electric mixer was used to stir it evenly after laying. The laying model was layered. We used compacted sleepers and hammers to push compaction evenly. After compression was leveling to combine with the level, and the plastering knife was used to smooth. We added a mica sheet between adjacent rock layers to achieve stratification effect. After the physical simulation model was cured under constant temperature and humidity for 7 days, the plate was removed. When the panel was removed, the single guard plate on the front of the model was removed, and the even guard plate on the back was removed. Then, the guard plate alternately was removed periodically until the guard plate was completely removed. To monitor the overlying strata movement and water-conducting fracture during the excavation of coal seam, a 10 cm × 10 cm grid was set with pins and graph paper. As shown in Figure 4, the professional digital cameras were adopted to record the dynamic images before and after the model excavation. To eliminate the boundary effect, 40 cm distances were reserved on both sides of this physical analog model. Considering that the actual propulsion rate of the W8203 working face is approximately 2.4 m/d, the physical analog model was designed to be 10 cm (corresponding to the actual 30 m) per 17 h (corresponding to 12.5 days). Correspondingly, there are 17 excavations in total. In the present research, the excavation direction of the coal seam is set up from left to right.

2.4. Numerical Simulation

2.4.1. Determination of the Numerical Model and Parameter Assignment

Apart from the physical simulation, the discrete element modelling (DEM) simulation with the application of the particle flow simulation (PFC) program was adopted to investigate the dynamic development process of water-conducting fractures and the evolution law of the weakly cemented overburden deformation. The mesoscopic parameters in the PFC model were obtained by repeated debugging of mechanical strength tests (uniaxial compression test and Brazilian splitting test, etc.) [35,36,37]. Through multiple debugging, the mechanical strength parameters of the numerical model were obtained, as shown in

Table 3. Mesoscopic physical and mechanical parameters of strata.

Layer	Lithology	Stratum Thickness (m)	Contact Modulus (GPa)	Friction Factor	Parallel Bond Modulus (GPa)	Parallel Bond Normal Strength (MPa)	Damping Stiffness Ratio
01	Loose strata	15.90	4.20	0.33	4.20	2.50	0.24
02	Glutenite	37.63	6.00	0.50	6.00	3.00	0.30
03	Mudstone	86.66	7.00	0.40	7.00	5.00	0.30
04	Glutenite	96.85	8.00	0.50	8.00	9.00	0.30
05	Siltstone	27.00	7.00	0.50	7.00	4.00	0.30
06	Medium Sandstone	54.00	9.00	0.40	9.00	5.00	0.30
07	Siltstone	53.97	10.00	0.40	10.00	8.00	0.30
08	Mudstone	15.69	8.00	0.30	8.00	3.20	0.30
09	Medium Sandstone	6.92	9.00	0.30	9.00	3.00	0.30
10	Siltstone	27.00	10.00	0.40	10.00	4.50	0.30
11	Mudstone	19.80	8.00	0.30	8.00	3.00	0.30
12	Siltstone	42.00	10.00	0.40	10.00	4.50	0.30
13	Coal seam	9.60	5.90	0.30	5.90	1.00	0.30
14	Siltstone	6.00	15.00	0.80	15.00	10.00	0.30

. Through calculation and analysis, the error between the simulated value and the actual value of each rock mechanical strength mesoscopic parameter is less than 5%, which indicates that the obtained model mechanical strength parameters are scientific and reasonable.

2.4.2. Design of Simulation Based on Numerical Model

A parallel bonding (Pb) model was adopted to generate the numerical model with the length of 750 m and 499.02 m along the X-axis and the Y-axis, which can be seen from Figure 5. Considering the large scale of the numerical model, the particle radius ranges from 1.0 m to1.5 m. To reduce the influence of the boundary effect, a coal seam of 120 m was reserved on both sides of the mining boundary of the numerical model and the total mining width was 510 m. Based on the actual mining situation of the target research objective, the mining direction is also from left to right. The full height of the coal seam was 9.6 m and each mining frequency was 30 m. The range of coal seam excavated in this numerical model was X = 120~630 m, Y = 6~15.60 m, zero particle initial velocity, only influenced by gravity acceleration g = 9.80 m/s².

3. Test Result

3.1. Physical Analog Experimental Result

It can be seen from the physical analog experiment, the mudstone roof exhibited acollapse with the progressive excavation of the working face. When the working face was advanced to 150 m, a large cavity appeared under the roof and the overhanging step of the main roof reached the limit. Correspondingly, the roof suffered from breakage and collapse under self-gravity. Afterwards, these collapsed blocks were filled with crushed rocks and the height of the excavation zone was 41 m, as shown in Figure 6a. When the excavation distance of the working face reached 180 m, the four overlying strata of the main roof were broken, resulting in a large-scale collapse and the broken block formed a stabilized articulated structure. The height of the fractured water-conducting zone rapidly developed to 111.41 m, as shown in Figure 6b. With the continuous excavation, the height of the fractured water-conducting zone remained unchanged at 111.41 m, when the excavation range of the working face was between 180 and 270. Upon advancing to 300 m, the overhanging step distance of siltstone reached the limit and the first fracture occurred. As shown in Figure 6c, the fractured block formed a stabilized articulated structure, and the developmental height of the fractured water-conducting zone rapidly changed to 165.38 m. As the working face moved forward, the two overlying strata on the upper part of the siltstone were also broken, and the developmental height of the fractured water-conducting zone suddenly changed to 246.38 m. When the working face continued to advance to 390 m, the overlying strata broke periodically and the water-conducting fracture zone did not continue to develop upward. In this case, the height remained at 246.38 m, as shown in Figure 6d.

The mining ended after advancing to 510 m, and the goaf-caved rock was compacted. After the overburden became sufficiently stable, the structural stability of the glutenite stratum was of a thickness of 96.85 m. In this situation, the roof fracture was closed and no new tangential fracture was generated. In this case, the development of the water-conducting fracture zone tended to be stable and remained at the height of 246.38 m, and the upper caved stratum of the goaf was arranged in a “saddle shape”, as shown in Figure 7. According to the “upper three-zone theory” [49], the caved zone, the fractured zone, and the continuous deformation zone of the overlying strata were all developed. According to the measured results of the Tashidian Erjingtian Mine, the coal seam roof height of the fractured water-conducting zone on No. 8 was 229.32 m, which was close to the experimental result of the physical analog model. This observation verified the reliability of the developed physical analog model.

3.2. Numerical Simulation Results

According to the numerical simulation results, the deformation characteristics and failure of weakly cemented overburden in the mining process and the evolution of water-conducting fractures were dynamically analyzed. As the distance of the working face excavation increased gradually, the hanging distance of the bottom of the main roof increased and the fracture began to develop upward. As depicted in Figure 8a, the fracture developed to the upper part of the four overlying strata of the main roof, when the excavation distance of the working face was 120 m. With the continuous movement of the working face, the main roof broke after advancing to 150 m (see Figure 8b). When the working face advanced to 180 m, the fracture continued to develop upward and developed to the bottom of the ultrathick glutenite stratum but did not form through the fracture, and the four overlying strata of the main roof also subsided and broke (see Figure 8c). The fracture continued to develop when the working face advanced to 240 m. Nevertheless, it kept developing to the bottom of the ultrathick glutenite stratum with a thickness of 96.85 m, and the first periodic break of the main roof occurred (see Figure 8d). When the working face advanced to 390 m, the ultrathick glutenite stratum with a thickness of 96.85 m broke locally, and its overlying strata tensile fracture gradually increased (see Figure 8e). When the working face advanced to 510 m, the simulation was terminated, the bottom-to-top penetration fracture height remained at the bottom of the glutenite stratum with a thickness of 96.85 m, and the ultrathick glutenite stratum fracture did not penetrate and did not break completely (see Figure 8f).

3.3. Determination of the Working Face Key Stratum

Once the accurate location of the key stratum was determined, both the load and breaking distance of the stratum were calculated layer by layer, which is carried out from the bottom to top and then compared with the adjacent stratum. Both physical and mechanical parameters of overlying strata were shown in

Table 4. Physical and mechanical parameters of the overlying strata.

Serial Number of the Stratum	Lithology	Thickness of Stratum (m)	Body Force (MN/m3)	Tensile Strength (MPa)	Elasticity Modulus (MPa)
1	Mudstone (false roof)	3.00	0.024	3.56	1550
2	Siltstone (main roof)	39.00	0.0256	8.12	1450
3	Mudstone	19.80	0.024	3.56	1550
4	Siltstone	27.00	0.0256	8.12	1450
5	Medium sandstone	6.92	0.0236	5.02	1300
6	Mudstone	15.69	0.024	3.56	1550
7	Siltstone	53.97	0.0256	8.12	1450
8	Medium sandstone	54.00	0.0236	5.02	1300
9	Siltstone	27.00	0.0256	8.12	1450
10	Glutenite	96.85	0.0253	6.75	1400
11	Mudstone	86.66	0.024	3.56	1550
12	Glutenite	37.63	0.0253	6.75	1400
13	Loose stratum	15.90	0.022	0.01	30

. Note that the calculated loads applied on the strata were converted into KPa for ease of comparison.

Due to the limited space of this paper, the calculation processes for many strata were tedious and not repeated here. Based on the theoretical calculation, there were four key strata from bottom to top. Namely, the first layer of mudstone, the second layer of siltstone, the seventh layer of siltstone, and the tenth layer of glutenite. Among them, the tenth layer of glutenite was determined as the primary key stratum and others were all the sub-key strata, the calculation results of which are shown in

Table 5. Calculation results of key strata of working face W8203 of the Tashidian Erjingtian Mine.

Key Stratum	Serial Number of Strata	Lithology	Load on the Stratum (KPa)	Breaking Distance (m)
Sub-key stratum 1	1	Mudstone	75.900	29.056
Sub-key stratum 2	2	Siltstone	1749.111	118.836
Sub-key stratum 3	7	Siltstone	1654.379	169.094
Primary key stratum	10	Glutenite	3149.173	200.525

.

In addition, ∑h is the height of the rock mass from the top of the coal seam, 246.38 m; l is the limit span of the primary key stratum rock mass, 185.421 m; M is the coal seam mining thickness, 9.6 m; k_p is the residual crushing expansion coefficient of the rock in the caved zone. According to previous research results which are shown in

Table 6. Rock swelling coefficient.

Lithology	Swelling Coefficient k
	Initial (after Short-Term Break-Age)	Residual (Compacted)
Clay	<1.20	1.03–1.07
Crushed coal	<1.20	1.5
Argillaceous shale	1.4	1.1
Sandy shale	1.60–1.80	1.10–1.15
Hard sandstone	1.50–1.80	/
Normal soft rock	/	1.02
Normal medium-hard rock	/	1.025
Normal hard rock	/	1.03

[50], the residual crushing expansion coefficient was taken as 1.025. According to Equations (3)–(5), it can be calculated as follows: 3.44 = Δ < Δ_max = 4.52.

If the primary key stratum was stablely attributed to the development of the articulated structure without instability and sliding, the water-conducting fracture would only develop to the bottom of the primary key stratum rather than the higher upward. When the results of the physical analog model and numerical simulation were analyzed together, the height of the fractured water-conducting zone of 246.38 m was determined. This observation is very close to the measured height of the fractured water-conducting zone (i.e., 229.32 m), suggesting the accuracy of the investigation presented in this paper.

4. Discussion

Currently, the most popular method to predict the height of a fractured water-conducting zone is an empirical formula [51], which was established by Liu [49] in the 1990s based on the measured “guide height” of the shallow coal seam of the Permian in north China. This formula only considers the influencing factor of mining height, and the formula makes the single-layer mining thickness 1~3 m. The accumulative mining thickness does not exceed 15 m, limited by the previous coal mining process. When the geological condition of the W8203 working face is further evaluated, the lithology of the No. 8 coal seam roof overlying strata was mainly mudstone and sandstone with a compressive strength of 20.4~37.67 MPa, which belonged to the medium-hard stratum.

According to Equation (9) of the hard stratum in [51], the calculated height of the fractured water-conducting zone ranges from 40.53 m to 56.23 m. As per Equation (10), the height of the fractured water-conducting zone was calculated as 71.97 m. According to the method of predicting the height of the fractured water-conducting zone based on the location of the key stratum [52], the critical height of the fracture penetration was 96 m (i.e., ten times the mining thickness). Note that the height of the primary key stratum location was 246.38 m from the coal seam (i.e., exceeded 96 m). Hence, the roof height of the fractured water-conducting zone can be calculated according to the location of the first key stratum, whose distance from the coal seam height exceeds 96 m. Therefore, the calculated height of the fractured water-conducting zone was 111.41 m.

Table 7. Height of the fractured water-conducting zone obtained by different methods.

Prediction Methods	Predicted Height of Fractured Water-Conducting Zone/m	Measured Height of Fractured Water-Conducting Zone/m	Error Rate/%
Equation (1) in [51]	40.53~56.23	229.32	−80.36~−75.48
Equation (2) in [51]	71.97		−68.62
Predicted value based on key stratum location	111.41		−51.42
Similar test simulation	246.38		+7.44
Numerical simulation and Theoretical analysis	246.38		+7.44

Note: The negative sign in the table indicates that the predicted height of the fractured water-conducting zone is less than the measured height, and the positive sign indicates that the predicted height of the fractured water-conducting zone is greater than the measured height. The results predicted by the method [51] were calculated using the predictive formulas for medium-hard lithology, i.e., Equations (9) and (10).

showed the measured height of the fractured water-conducting zone and the predicted results and the error rate of the above methods:

$$H=\frac{100\sum M}{1.6\sum M+3.6}\pm 5.6$$

(9)

$$H=20\sqrt{\sum M}+10$$

(10)

where H denote predicted height of water-conducting fractured zone, m; ∑M denote the thickness of the coal seam, m.

According to the experimental results of the physical analog model and numerical simulations, the variation curve of the height of the fractured water-conducting zone with the excavation of the working face was drawn in Figure 9. As shown in Figure 9, the developmental height of the water-conducting fracture in the physical analog model and the numerical simulation did not simply increase linearly with the advancing distance of the working face. In addition, there was stagnation and mutation in the development process, and the water-conducting fracture zone had the same development trend. It is apparent that the fracture development process of the numerical simulation was more severe than that of the physical analog model due to the differences in the experimental conditions. When the movement laws of roof strata proposed by Guan et al. [53] is accounted for, the mechanical strength of analog materials was affected by curing humidity, while numerical simulation required no curing. That is, physical analog tests could predict the height of the fractured water-conducting zone and visually and dynamically demonstrate the overlying strata’s collapse, rupture, and fracture development process. On the other hand, PFC program revealed the evolution law of the water-conducting fracture zone during the mining process of the working face, showing the dynamic process of the overlying strata fracture inoculation, the overburden fracture, and the water-conducting fracture development during the mining process. The above discussions can be regarded as an additional demonstration of the physical analog models complementing each other.

With the development of mining technology in China, fully mechanized mining or fully mechanized caving mining technology with high strength, high yield, and high efficiency has been rapidly popularized. A large amount of previous studies have successfully demonstrated [47,54,55,56] that the water-conducting fracture zone abnormally developed in fully mechanized mining or fully mechanized caving mining will not be accurately predicted by a conventional empirical formula [51]. As shown in Table 7, the height of the fractured water-conducting zone was 40.53~56.23 m, and the error rate was from −80.36 to −75.48% when Equation (1) was adopted for the hard stratum [51]. When Equation (2) was applied, the calculated height of the fractured water-conducting zone was 71.97 m with an error rate of −68.62%. Considering that the calculated values were smaller than the measured values proves the above discussions. In the present research, the modified prediction method based on the key stratum was adopted to obtain a height of the fractured water-conducting zone. It is apparent that the calculated height is 111.41 m and the error rate is −51.42%, which were all lower than that of the measured values.

Taking the Yushuling Coal Mine located in Kuqa, Xinjiang, China for example, the measured height of the fractured water-conducting zone was 70~90 m [11], while the prediction values were 42 m, based on the determination of key stratum. The possible reason for this deviation was that the height of the fractured water-conducting zone prediction method based on the key stratum location mainly used the measured data of the eastern mining area. The value of the residual crushing expansion coefficient k_p was 1.1~1.15, and then 7~10 times the mining height was taken as the critical height for the key stratum.

As reported by Sun [14,20], the residual crushing expansion coefficient of weakly cemented overburden was generally between 1.06 and 1.10. Note that the residual crushing expansion coefficient may be equal to 1 under the sufficient pressure. There was a difference in the residual crushing expansion coefficient of the stratum in the east mining area in western China, so that the weakly cemented overburden mining area in the west still used 7~10 times the mining height as the critical height of the key stratum breaking and fracture penetration, which could underestimate the result. Therefore, it is necessary to evolve the prediction method based on the location of key strata to meet the requirements of safe mining in the western weakly cemented overburden mining area.

The simplified formula developed to calculate the critical height of fracture penetration in key strata of overlying strata was shown in Equation (11) [45]:

$$H=\frac{M}{k_p-1}$$

(11)

where H denote the critical distance between the primary key layer that affects the height of the water-conducting fractured zone and the mining coal seam, m; M denote the mining thickness of the coal seam, m; k_p denote the residual expansion coefficient. The value range of residual bulking coefficient k_p of weakly cemented overburden is 1.06~1.1, so the further simplified formula is obtained, as shown in Equation (12):

$$H=(10~16.67)M$$

(12)

According to the above equations, for the convenience of calculation, the calculation results were rounded up. The weakly cemented overburden should be 10~17 times of the mining height with the key layer breaking through the fracture, as shown in Figure 10. To predict the development height of the water-conducting fracture zone, the specific steps of the prediction method are listed below:

(1)

Collect drilling columnar data of the coal face;

(2)

Judge the location of the key strata of the overlying strata;

(3)

Calculate the distance between the key stratum position and the mining coal seam height, and determine whether the key stratum fracture is connected;

(4)

Determine the height of the water-conducting fractured (WCF) zone. When the primary key stratum of overburdened rock is located within the critical height (i.e., 10~17 M), the water-conducting fracture will develop to the top of bedrock, and the height of water-conducting fracture zone is equal to or greater than the thickness of bedrock. When the primary key stratum of overlying strata is located outside the critical height (i.e., 10~17 M), the water-conducting fracture will develop to the bottom of the nearest key stratum above the critical height (i.e., 10~17 M), and the height of the water-conducting fracture zone is equal to the height of the key stratum from the mining coal seam.

To verify the reliability of the prediction method, the calculation results of the consulting literature and engineering cases are shown in

Table 8. Engineering case practice of height prediction of water-conducting fractured zone in weakly cemented overburden rock.

Coal Mine	Coal Thick(M)/m	Key Stratum	Distance from Coal Seam/m	Source
Bayangaole Coal Mine	5.3	Primary key stratum	99	[57]
		Sub-key stratum5	69
		Sub-key stratum4	56
		Sub-key stratum3	23
		Sub-key stratum2	6
		Sub-key stratum1	0
Bulianta Coal Mine	5.92	Primary key stratum	117.27	[58]
		Sub-key stratum2	33.82
		Sub-key stratum1	10.92
Menkeqing Coal Mine	4.35	Primary key stratum	224.3	[12]
		Sub-key stratum3	120.4
		Sub-key stratum2	40.9
		Sub-key stratum1	3
Hulusu Coal Mine	2.5	Primary key stratum	333.02	[59]
		Sub-key stratum6	271.91
		Sub-key stratum5	237.57
		Sub-key stratum4	157.26
		Sub-key stratum3	88.6
		Sub-key stratum2	33.32
		Sub-key stratum1	0
Hongqinghe Coal Mine	7.9	Primary key stratum	571.5	[60]
		Sub-key stratum5	447.5
		Sub-key stratum4	286.2
		Sub-key stratum3	153.9
		Sub-key stratum2	49.7
		Sub-key stratum1	6.3
Tashidian Erjingtian	9.6	Primary key stratum	246.38	[61]
		Sub-key stratum2	111.41
		Sub-key stratum1	3
Yushuling Mine	4	Primary key stratum	78.2	[11]
		Sub-key stratum2	42
		Sub-key stratum1	5.6

. The results obtained by the empirical formula, the results obtained by the 10-times mining height based on the key stratum location prediction method, and the results obtained by the 17-times mining height based on the key stratum location prediction method proposed in this paper were compared with the measured results. The comparison results are shown in

Table 9. Comparison of results of different prediction methods for the height of fractured water-conducting zone.

Coal Mine	Coal Thick (M)/m	Empirical Formula/m		Predicted by Key Stratum/m		Measured Value/m	Empirical Formula Error Rate/%		Predicted by Key Stratum Error Rate/%
		Equation (9)	Equation (10)	10M	17M		Equation (9)	Equation (10)	10M	17M
Bayangaole Coal Mine	5.3	38.27~49.47	56.04	56	99	126	−69.62~−60.73	−55.52	−55.56	−21.43
Bulianta Coal Mine	5.92	39.69~50.89	58.66	117.27	117.27	147.2	−73.04~−65.43	−60.15	−20.33	−20.33
Menkeqing Coal Mine	4.35	35.59~46.79	51.71	120.4	120.4	108	−67.04~−56.67	−52.12	11.48	11.48
Hulusu Coal Mine	2.5	27.29~38.49	41.62	33.32	88.6	62.5	−56.33~−38.41	−33.40	−46.69	41.76
Hongqinghe Coal Mine	7.9	43.05~54.25	66.21	153.9	153.9	120.3	−64.22~−54.91	−44.96	27.93	27.93
Tashidian Erjingtian	9.6	45.03~56.23	71.97	111.41	246.38	229.32	−80.36~−75.48	−68.62	−51.42	7.44
Yushuling Mine	4	34.40~45.60	50	42	78.2	70~90	−61.78~−50.86	−44.44~−28.57	−53.33~−40.00	−13.11~11.71

. The results show that the prediction effect is better in the weakly cemented overburden mining area according to 17 times the mining height as the critical height of the fracture of the key stratum. It is believed that the results obtained from this research can provide meaningful reference for green and safe production in western mining.

Under the background of the “strategic westward shift” of China’s coal resources exploration and development, a prediction formula for the height of water-conducting fracture zone of Jurassic coal seam in west China will be established by collecting the measured height data of water-conducting fracture zone through multiple regression analysis, which provides reference for green and safe production of weakly cemented overburden mining areas in west China.

5. Conclusions

To predict the height of the fractured water-conducting zone for underground mines with weakly cemented overburden, a case study was conducted based on the geological conditions of the W8203 working face in Tashidian Erjingtian Mine. The physical analog model PFC2D numerical simulation as well as the theoretical analysis were carried out. The following conclusions can be drawn based on the discussions:

(1)

The developmental fractured water-conducting zone upon the coal seam does not linearly increase with the advancement of the working face. Nevertheless, it has certain stagnation and sudden changes, and the final developmental height of the fractured water-conducting zone was 246.38 m. The measured height of the fractured water-conducting zone of the No. 8 coal seam was 229.32 m;

(2)

There are one primary key stratum and three sub-key strata among the overlying strata of the W8203 working face, in which the primary key stratum could form a stabilized articulated structure with no sliding;

(3)

The water-conducting fracture developed to the bottom of the primary key stratum;

(4)

These empirical formulas failed to adapt to the current green and safe coal mining needsea because of the difference in the residual crushing expansion coefficient of the stratum in the east mining area in western China;

(5)

The prediction effect is better in the weakly cemented overburden mining area according to 17 times the mining height as the critical height of the fracture of the key stratum.