Abstract
After mining, upward fractures develop from bottom to top, and they are key channel for groundwater and gas flow and also sand burst; therefore, it is important to study the development mechanism and criterion of upward fractures. Combining with physical simulation and theoretical analysis, the development law of mining-induced upward fractures was revealed, and the mechanism and criterion of fracture propagation was studied. The results show that the development of mining-induced upward fractures can be divided into the following three stages: with the face advances from the open cut, the vertical fractures are generated at the mining boundary, and the roof is flexural but not caved; it is “Fractures generate stage.” After roof caves, the upward fractures extend and develop upward along the caving angle with continue advances; it is “Fractures develop and extend stage.” When the face reaches critical mining, the development height of the upward fractures is at its maximum and is basically invariable; it is “Fractures stabilization stage.” Mining-induced fractures can be analyzed as mixed-type fractures in fracture mechanics; when the combined stress exceeds the critical strength of stratum, it will extend downward until penetrate through the stratum, and the upward fracture develops and extends upwards. The parameter controlling the fracture of the rock stratum is the maximum hoop tensile stress σ(θ)max, at the fracture end, the theoretical model of fracture propagation was established, and the criterion of upward fractures was proposed.
1. Introduction
The upward fractures are the key channel of water and gas conduction. In order to realize water conservation mining and mine disaster prevention, it is important to study the criterion of upward fractures. The development essence of upward fracture is that the concentrated stress reaches the tensile strength, it develops continuously with the face advances, and it finally reaches a stable stage.
Lots of research studies relating to the development law of upward fractures by field measurement have been published. Zhu and Teng [1] concluded that the development height of the upward fracture is directly proportional to the total mining thickness. Zhang and Zhang [2] analyzed the overburden of thick coal seam mining fracture propagation mechanics and principle based on the related theories of elastic-plastic and fracture mechanics. Bai and Tu [3] summarized the mining-induced fracture characteristics in shallow coal seam. Through engineering tests, Tan et al. [4] obtained the height of water-conducting fracturing zone. Huang et al. [5] studied the height of upward fracture by transient electromagnetic and drilling in Wanli mining area.
Besides, physical simulation, numerical calculation, and theoretical model were applied to study the development law of upward fractures. Wen et al. [6] established a fracture expansion model. By using the elasticity and Winkler foundation theory, Li et al. [7] established the numerical calculation model of fracture and the evolution of overburden strata under the condition of seepage-stress coupling and analyzed the dynamic change process of overburden strata fracture development height. By using physical simulation experiment, Bai et al. [8] revealed the failure mechanism of water-conducting fracture zone. Xu et al. [9, 10] revealed that the position of main key strata of overlying strata will affect the upward crack development height of coal seam roof. Based on partial filling mining in shallow coal seams, Zhang and Huang [11] found that different backfilling parameters directly affect the development height of upward fractures. Zhao et al. [12] established the development height of upward fractures with the subsidence of key strata and analyzed the dynamic development process of upward fractures with the longwall face advances. Cao and Huang [13] obtained the development characteristics of fractures in shallow single seam mining and repeated mining, and the relationship between pillar staggered distance and fractures is revealed. Besides, fractal theory was used to quantitatively study the development process of fractures [14–28].
Above all, at present, based on various research methods, there are lots of studies on the upward fractures development in single seam and multiseams mining. Fractures development is a macroscopic phenomenon, which contains fracture generation and expansion fracture mechanics is an effective method to analyze the development of upward fracture; however, there are few studies in this area. Therefore, based on fracture propagation theory in fracture mechanics and physical simulation, the development law of mining-induced upward fractures was revealed in this paper, and mechanism and criterion of fracture propagation were studied.
2. Development Law of Mining-Induced Upward Fractures
2.1. Fractures Development Based on Physical Simulation Experiment
2.1.1. Fractures Development of No. 1-2 Coal Seam Mining in Daliuta Coal Mine
(1) Physical Simulation Experiment Model. Physical simulation experiment was established to reveal the development stage of mining-induced upward fractures. Based on the mining condition of the No. 1-2 coal seam in Daliuta Coal Mine, the average thickness of the coal seam is 4 m, and its buried depth is about 73 m. The experiment model is 1.5 m long × 1.3 m wide × 0.16 m height (Figure 1). Sand was adopted as the aggregates, cementitious materials are gypsum and calcium carbonate, and the material ratio is shown in Table 1.
(2) Fractures Development with Longwall Face Advances. The coal seam was excavated from left to right. When the longwall face advances to 15 m, the immediate roof caves. There is no fracture development in the overburden, and the roof caving height is 1.4 m, as shown in Figure 2.
When it advances to 46 m, the overlying strata above immediate roof suddenly cave, and it is the first caving of main roof. The roof caving angle is about 55°, as shown in Figure 3.
When it advances to 54 m, the main roof produces the first periodic caving, the development height of fracture reaches 20.5 m, the separation height of fracture is 3.2 m, and its separation width is 31.8 m. As the longwall face advances, when the longwall face advances to 64 m, 76 m, …, 120 m, the main roof produces the 2nd, 3rd, …, 7th periodic roof caving, respectively, and simultaneously, the fractures develop upwards, as shown in Figure 4. When it advances to 120 m, it reaches critical mining, and the mining-induced fractures have developed to the ground surface (Figure 4(d)). The relationship between fracture development height and face advances distance is shown in Figure 5.
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(3) The Relationship between Fractal Dimension and Face Advances Distance. The two-dimensional slice image is obtained from 3DEC numerical calculation, the image obtained is often RGB color image, and it is converted into gray image, the processed gray image is imported into MATLAB, and the image is binarized by using the threshold segmentation method. The gray transformation discriminant function of binary processing is as follows:
FracLab toolbox is used to calculate the fractal dimension of the processed digital image, and the fractal dimensions of fractures with different advance distances are shown in Figure 6.
Figure 6 shows that in normal mining stage, the fractal dimension increases gradually while the longwall face advances, and when it reaches critical mining, the development height of fractures does not change significantly while the longwall face advances.
2.1.2. Fractures Development of No. 4-2 Coal Seam Mining in Hongliulin Coal Mine
(1) Physical Simulation Experiment Model. Taking the No. 4-2 coal seam mining in Hongliulin Coal Mine as the background, the average thickness of the coal seam is 2.1 m, and its buried depth is about 115.7 m. The experiment model is 2.0 m long × 1.5 m wide × 0.2 m height (Figure 7), the geometric similarity ratio is 1 : 200, and the material ratio is shown in Table 2.
(2) Fractures Development with Longwall Face Advances. The coal seam was excavated from left to right. When it advances to 22 m, the immediate roof caves and roof of longwall face is deflected, as shown in Figure 8. When it advances to 50 m, the overlying strata above the immediate roof suddenly cave, and it is the first caving of main roof; the roof caving angle is about 60°, as shown in Figure 9. When it advances to 50 m, the roof caving and fracture development are shown in Figure 10; when the longwall face reaches critical mining, the roof caving and fracture development are shown in Figure 11. It can be known that the fracture development height increases when the longwall face advances.
2.2. Development Stage of Mining-Induced Upward Fractures
With the longwall face advance, under the force of the concentrated tensile stress and gravity, the overlying strata gradually become flexural and then cave. At the same time, the upward fractures continue to develop upward along a certain caving angle, which is usually about 60. According to the development characteristics, the development of mining-induced upward fractures can be divided into the following three stages, and it is shown in Figure 12.(1)Fractures generate stage: With the longwall face advances from the open cut, the vertical fractures are generated at the mining boundary, and the roof is flexural but not caved, as shown in Figure 12(a).(2)Fractures develop and extend stage: After the roof caves, the upward fracture develops upward along the caving angle of the roof. With the longwall face advances and the roof caves from bottom to top, the upward fracture extends upward along the caving angle of the roof, and the development height of the fracture increases with it, as shown in Figures 12(b) and 12(c).(3)Fractures stabilization stage: When the advance of the longwall face reaches critical mining, the development height of the upward fractures basically reaches the maximum value. Therefore, the longwall face continues to advance, and the upward fractures on the open cut side no longer developed, while the fractures on the longwall face side represent periodic development process of “fractures generation—fractures development and propagation—fractures stabilization—fractures closure-new fractures generation,” but its development height is basically invariable, as shown in Figure 12(d).
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3. Development Mechanism of Upward Fractures Based on Fracture Growth Theory
3.1. Stress Analysis of Fracture End
The development of upward fractures is the result of the vertical force (weight of overlying strata) and concentrated tensile stress induced by roof caving. When the comprehensive stress reaches the ultimate tensile strength of rock, the rock strata will be damaged and generate fracture. Fracture mechanics can correlate the fracture strength of rock with the stress and is an effective method to analyze the development mechanism of upward fractures; therefore, fracture mechanics were used to analyze the stress and growth process of the fracture (Figure 13).
When the gravity G of the rock layer and the overburden load q act on the vertical direction of the fracture end, it can lead to in-plane shear fractures (Fracture type I in Figure 14(a)). When the boundary concentrated tensile stress σθ acts on the direction which is perpendicular to the upward fracture propagation direction, it can lead to tensile fractures (Fracture type II in Figure 14(b)).
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The propagation of mining-induced fractures is the combined action of the previous two types of fractures. Therefore, it should be analyzed as mixed-type fractures (Fracture type I and II) in fracture mechanics, as shown in Figure 15.
3.2. Development Mechanism of Upward Fractures
It is known that after longwall face mining, there are three zones along the vertical section of the rock strata. In caving zone, the caving roof represents disorder caving state, fractured zone is above caving zone, its roof shows as orderly caving, and broken roof shows that the upper part is stretched and the lower part is squeezed. In continuous deformation zone, there are no fractures that exist.
Due to the fact that the roof represents layered caving with mining, in order to analyze the development mechanism of the upward fracture in the fractured zone and determine its development height, the strata in the fractured zone were numbered from bottom to top (1, 2, …, n), as shown in Figure 16.
The broken propagation of strata in fractured zone is calculated layer by layer from bottom to top. When the tensile stress and the vertical stress exceed its critical strength, fracture is first generated at the top of the rock layer, and then, under the effect of combined stress, the fracture will extend downward. If it penetrates through the rock layer, it will be broken and become a channel for water or gas conduction, and at the same time, the upward fracture develops and extends upward.
3.3. Determination Method for the Development Height of Upward Fractures
According to the development mechanism of upward fractures, with the increase of the calculated layer in fractured zone, when the fracture of No. n − 1 layer can penetrate through the layer’s free surface, this rock layer is completely broken, and the upward fracture can develop upwards. When the No. n layer is calculated, if the resultant stress is not large enough and cannot result in fracture propagation, the No. n layer is not broken completely; therefore, the upward fractures cannot develop upwards.
Based on the critical mining conditions, the method for the development height of upward fractures can be determined. Its development height is from the top of the coal seam to the bottom of the No. n rock layer, as shown in Figure 17.
4. Theoretical Model and Criterion of Fracture Propagation
4.1. σ(θ)max Theoretical Model of Fracture Propagation
According to the σ(θ)max theory proposed by Li et al. [29], the parameter controlling the fracture of the rock stratum is the maximum hoop tensile stress σ(θ)max at the fracture end. Based on this, the theoretical model of fracture propagation is established (Figure 18).
The stress state at the fracture end is given aswhere θ is the fracture propagation angle, °. r is the distance from infinitesimal to fracture end, m. KI is the strength factor of fracture type I, . KII is the strength factor of fracture type II, . KI and KII can be calculated by the equations (3) and (4).where σθ is the tensile stress at point A, MPa. τ is the shear stress at point A, MPa. c is the half-length of the fracture, m, take c = 1, r/c ≪ 1.
4.2. Establishment of Fracture Propagation Criterion
The fracture extends in the radial direction at its end. When σ(θ)max reaches the critical strength factor of the rock formation, the fracture starts to extends. According to equation (2), it can be expressed as equations (5) and (6) mathematically:where KIc is the critical stress strength factor of fracture type I (material constant), . KIIc is the critical stress strength factor of fracture type II (material constant), and . θ0 is the fracture propagation initiation angle, °. According to equations (5) and (6), the fracture initiation trace of the σ(θ)max theory is obtained as shown in Figure 19.
The criterion for fracture propagation is as follows:(1)According to equations (3), (4), and (6), the fracture propagation initiation angle θ0 can be obtained.(2)According to equations (3)–(5) and the value θ0 calculated above, combining with Figure 19, it can be judged whether the fracture extends (whether the upward fractures develop).
If the coordinate (KI/KIc,KII/KIIc) is inside the fracture initiation trace, the fractures do not extend, and the mining-induced upward fractures do not develop upwards. On the contrary, if it is outside the fracture initiation trace, the fracture extends until it reaches the free surface, and the upward fracture continues to develop upwards.
5. Conclusions
The development of upward fractures can be divided into the following three stages: with the face advances from the open cut, the vertical fractures are generated at the mining boundary, and the roof is flexural but not caved; it is “Fractures generate stage.” After roof caves, the upward fractures extend and develop upward along the caving angle with continue advances; it is “Fractures develop and extend stage.” When the face reaches critical mining, the development height of the upward fractures is at its maximum and is basically invariable; it is “Fractures stabilization stage.”
Mining-induced fractures can be analyzed as mixed-type fractures (in-plane shear fractures and tensile fractures) in fracture mechanics; when the combined stress exceeds the critical strength of stratum, it will extend downward until penetrate through the stratum, and the upward fracture develops and extends upwards.
The parameter controlling the fracture of the rock stratum is the maximum hoop tensile stress σ(θ)max at the fracture end, the theoretical model of fracture propagation was established, and the criterion of upward fractures was proposed. If the coordinate (KI/KIc,KII/KIIc) is inside the fracture initiation trace, the upward fractures do not develop upwards; on the contrary, the upward fracture continues to develop upwards.
Data Availability
The experimental data are all included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors thank the Natural Science Foundation of Inner Mongolia of China (grant number no. 2022QN05007) for its support in this study. This research was funded by the Natural Science Foundation of Inner Mongolia of China, grant number no. 2022QN05007, and Introduce Excellent Talents Support Project of Inner Mongolia, grant number no. 0701012101.