Fractal Characteristics of Overburden Rock Fractures and Their Impact on Ground Fissures in Longwall Coal Mining

Abstract

Ground fissures are generated during the coal mining process due to overlying strata migration, which provides gas and water seepage channels and usually contributes to coal mining accidents in shallow buried coal seams with larger mining height working faces. Thus, the evolution features of ground fissures in large mining height working faces and shallow buried coal seams were explored by considering field observation data, similar simulation, and numerical simulations. The results show that the weathered rock layer above the thin bedrock inhibits fracture growth caused by coal mining. Overlying strata fracture expansion can be quantitatively divided into three stages based on fractal dimension: the overburden fracture formation stage, the overburden deformation fracture expansion stage, and the overburden fracture stable development stage. The movement deformation region of the ground fissure can be described by three characteristic zones: the boundary tension zone, the central compression zone, and the central dynamic tension and compression zone. Central dynamic fissures usually have 3–5 fissure counts with 2–5 m intervals between each group of fissures; central fissures develop twice from open to closed widths; the time period for two central fissures to reach their with maximum widths is 11–20 days; and border fissures expand rapidly with maximum values in a time period of 5–6 days.

1. Introduction

Coal is one of the basic energy sources. About 80% of coal mining in China is underground mining [1,2]. However, with the rapid development of the energy economy in China, the demand for coal energy has been increasing in the past 20 years, and the ecological and environmental damage caused by underground coal mining poses a threat to the sustainable development of society in mining areas [3,4]. In western mining areas of China, about 70% of all the raw coal is produced where the depth of the coal seam is generally between 50 and 250 m, the bedrock is relatively thin, the loose layer and coal seam are both thick, and the mining intensity is higher [1,5,6,7,8]. It is difficult to maintain the stability of the main key layer for a long time after the roofs of the coal seam are broken [2,7,9,10,11,12,13]. The uncoordinated movement of the upper strata affects the discontinuous settlement of the ground, which can cause collapse grooves, permanent ground fissures, and boundary ground fissures to appear on the ground. Some ground fissures induced by mining run through to the goafs, which may cause water bursting, sand bursting, and coal spontaneous combustion disasters in the subsequent mining process [1,8,11,14,15,16,17,18].

Underground coal seam mining causes the top plate to break and the overlying strata to subside. Eventually, it causes continuous and discontinuous ground deformation, resulting in ground cracks, step settlement, and collapse pits. At present, the analysis methods used are mainly empirical formula methods, theoretical analysis methods, simulation methods, and field measurements.

At present, the methods used to predict mining subsidence are based on the analysis of ground observation data, which cannot explain the damage caused by overlying strata migration. However, mining subsidence is caused by overlying strata breaking from the coal seam to the ground. The height of the broken roof and backfilling affects the bearing capacity transfer rule of the overlying strata, and finally causes the movement law of ground deformation [1,5,7,12,19,20]. Based on field observation data combined with physical similarity simulation experiments, fractal theory can be applied to explain the movement characteristics and fracture extension of the overlying strata [21,22]. The dynamic evolution of the overlying strata fractures can be analyzed and calculated by numerical simulation software. However, the use of numerical simulations to simply interpret the characteristics in the actual mining process needs to be verified by physical modeling or field engineering measurements [23,24]. The movement of the overlying strata and the damage to and deformation of the strata are discontinuous deformation problems in the longwall high-intensity mining of shallow coal seams. Based on continuous medium finite element numerical simulation analysis, the dynamic development of fractures cannot be accurately described [25,26]. In contrast, the most important advantage of PFC2D is the discrete element particle flow program, which can simulate the overlying strata migration processes of fracture, collapse, accumulation, and compaction [27,28,29].

In summary, this paper studies the evolution law of overlying rock fractures caused by longwall mining, by combining field examples and numerical analysis. Based on the field examples, the monitoring of surface fracture generation and development caused by overlying rock migration in the process of mining is analyzed. Using the PFC2D (Particle Flow code 2D) numerical analysis method, the characteristics of surface fractures and stress change induced by overburden fractures during coal excavation are simulated and analyzed. The research results have theoretical and practical significance for coal mining and environmental and ecological management in coal mining.

2. Geological Conditions

The No. 12401 panel of the No. 1–2 coal seam has a designed advanced length of 5254.8 m, width of 299 m, and height of 8.8 m. The ground elevation varies from 1188 m to 1300 m, with a coal seam floor elevation range of 1043–1066 m. The loose overburden is 0 to 27 m thick and consists mainly of loess and fine sand. The thickness of the overlying bedrock is 120–220 m. The false roof of the 12401 working face is mudstone with a compressive strength of 11.3–13.2 MPa and consolidation coefficient of 1.32. The immediate roof is gray fine sandstone with a compressive strength of 13.3–15.2 MPa and consolidation coefficient of 1.35. The main roof is grayish-white siltstone with a compressive strength of 14.5–36.6 MPa and consolidation coefficient of 2.32. The main roof is silty sandstone with a compressive strength of 14.5–36.6 MPa. As shown in Figure 1, there are three types of ground fissures in the Shendong coal field.

3. Overlying Strata Characteristics of the Working Face

Figure 2 shows the borehole column diagram of the 12401 working face. Ground boreholes R113, b279, and R106 on the outer side of the transport roadway and R110 on the outer side of the return laneway in working face No. 12401 are counted. The lithology statistics based on the surface boreholes around the 12401 working face in the Shangwan Mine are shown in

Table 1. Statistics of borehole lithology around the No. 12401 working face.

No.	Loose Sandy Layer Thickness (m)	Bedrock Thickness (m)	Thickness Ratio of the Loose Layer to Bedrock	Thickness Ratio of Sandstone	Thickness Ratio of Mudstone
R110	19.60	165.90	11.81%	74.98%	14.25%
R113	22.10	219.10	10.09%	68.08%	10.86%
R106	18.20	172.20	10.56%	90.14%	0.29%
b279	9.00	210.00	4.28%	91.78%	4.28%

. The hard rock strata above the main mining seam mainly consists of sandstone (siltstone, medium-grained sandstone, and fine sandstone) and soft rocks (sandy mudstone).

Based on the bedrock lithology analysis of the borehole column diagram near the work area, the bedrock has mudstone at the bottom and top. The rock strength is generally reduced by the oxidation zone. The clay content of the rocks increases relatively, and plasticity generally increases. This inhibits the upward development of overlying strata fractures to a certain extent. Therefore, the upper overlying strata oxide layer has an inhibitory effect on the overlying strata fracture in the shallow bedrock of working face No. 12401.

As shown in Figure 3, Figure 4 and Figure 5, the thicknesses of the bedrock and loose layers were counted by drilling around the working face of the 12401 working face. Contour plots of the bedrock and loose layers and the bedrock thickness ratio were plotted using Surfer 10.0 software. The analysis shows that the thickness of the loose layer above the working face gradually decreases from the air return lane to near the transport lane. The thickness of the bedrock gradually decreases along the working face advance direction. The ratio of the thickness of the loose layer above the working face to that of the bedrock gradually decreases from the air return lane to near the transport lane.

4. Simulation Experimental Study

4.1. Simulation Experimental Analysis of Dynamic Fractures

As shown in Figure 6, the size of the model frame was chosen as 1800 mm × 200 mm × 1200 mm (length × width × height). According to similarity theory [11], the following several types of similarities should be considered.

For geometric similarity,

$$\frac{L_p}{L_m}{=C}_L$$

(1)

where L_p is the size of the on-site prototype, L_m is the size of similar models, and C_L is the size similarity ratio.

For dynamic similarity,

$$\frac{{\gamma }_p}{{\gamma }_m}=Cr$$

(2)

where γ_p is the bulk density of the on-site prototype, γ_m is the bulk density of similar models, and Cγ is the similarity ratio of bulk density.

For time similarity,

$$\frac{T_p}{T_m}{=C}_T$$

(3)

where T_p is the on-site prototype time, T_m is the similarity model time, and C_T is the time similarity ratio.

The geometric similarity ratio is 200:1, the volumetric similarity ratio is 1.5:1, and the model time ratio is 96:1. The simulated materials are river sand as aggregate, calcium carbonate and gypsum as cement, mica as an auxiliary material, and a certain proportion of fly ash that is added to the coal seam.

To analyze the dynamic development law of the overlying strata transport and fractures, the fracture extension height and rock failure area of the overlying strata were determined by similar simulation. Figure 7 shows different advance distances of the rock failure area.

4.2. Simulation of the Caving Process of the 12401 Working Face Based on PFC

In terms of numerical simulation, we simplified the complex geological conditions without too much addition to the temperature field and seepage flow field. Based on the geometry of the Shangwan No. 12401 working face, a two-dimensional model based on PFC2D 5.0 software was established in order to further validate the simulated fracture evolution characteristics and laws of similar simulations, revealing the evolution characteristics of the overlying rock fractures at different mining stages. As shown in Figure 8, the model is 300 m long and 200 m high. The upper boundary is free, the left and right boundaries fix the x-displacement, and the bottom boundary fixes the y-displacement. The particles contact each other through parallel bonding, the particle diameter ranges from 0.3 to 0.5 m, and a total of 102,814 balls are generated. The model is used to simulate the longwall mining process, with advancement from left to right and a mining height of 8.8 m. Compression and tensile tests were carried out using PFC2D 5.0 software. The relationship between rock macroscopic parameters and rock fine-grained parameters was inverted to find the desired fine-grained parameters by inversion of the stratigraphic macroscopic parameters [27,30], as listed in

Table 2. Physical and mechanical parameters of rocks in PFC model.

Lithology	Density (KN/m3)	Tensile Strength (MPa)	Cohesion (MPa)	Friction Angle (°)	Krat	Emod (GPa)	Pb-kn (GPa)	Pb-ks (GPa)
aeolian sand	17	-	-	18	1.0	0.3	7.8	3.9
fine sandstone	24	3.22	1.30	37	1.0	13.3	11.6	10.4
siltstone	25	4.05	2.55	37	1.0	12.7	15.8	9.0
fine sandstone	24	3.22	1.30	36	1.0	13.3	11.6	10.4
siltstone	25	4.05	2.55	37	1.0	10.7	13.8	9.0
fine sandstone	24	3.22	1.30	36	1.0	13.3	11.6	10.4
medium sandstone	24	2.58	4.35	38	1.0	9.1	11.6	9.0
coal	16	1.07	1.21	39	1.0	5.1	5.8	2.6
siltstone	25	4.05	2.55	38	1.0	10.7	13.8	9.0

Strata macroscopic and mesoscopic physic and mechanical parameters. Krat is the normal-to-shear stiffness ratio, Emod the effective modulus, Pb-kn the normal stiffness, Pb-ks the shear stiffness.

.

As the working face advances, the overlying strata collapse and migrate, causing a new fracture extension, which eventually leads to overlying strata step settlement. As shown in Figure 9, the migration laws of the overlying strata from similar simulation and numerical simulations are consistent. From the force chain diagram, the overlying strata fracture extension height was 65 m when the working face advanced to 150 m. When the working face advanced to 200 m, the overlying strata fracture extension height was 160 m. When the working face advanced to 250 m, the overlying strata fracture height extended to the ground surface. The equilibrium structure of the entire overlying strata broke, and the overlying strata broke up into blocks. The settlement of the blocks eventually leads to ground deformation. From the horizontal displacement-x contour, it can be concluded that the horizontal displacement of the ground surface varies unevenly as the working face advances. Eventually, ground tension fissures, compression fissures, and step subsidence fissures form.

5. Results and Discussion

5.1. Overlying Strata Fracture Evolution Characteristics

As shown in Figure 10, a high-speed camera was used to record and photograph the transport characteristics of the overlying strata fracture development characteristics after each advance of the working face. Then, Photoshop and ImageJ image processing software were used to extract the range of fracture development characteristics after each advance of the working face. Finally, the fractal dimensions of the fracture network map were calculated using the box dimension method. First, an image of the main study area is intercepted. Then, the appropriate grayscale and contrast are adjusted to identify the difference between the fracture distribution and nonfracture pixels. The graphics of the study area are imported into ImageJ 1.0 software to derive the fractal dimensions of the fractal network, as shown in

Table 3. Overlying strata failure results of different advance distances.

Mining Length (cm)	Fractal Dimension D	Correlation Coefficient	Overlying Strata Failure Height (cm)	Rock Failure Area (cm2)	Failure Stage of Overlying Strata
60.0	1.325	0.9901	14.4	1485	immediate roof caving
67.5	1.339	0.9901	21.6	3354	first key stratum broken
120.0	1.393	0.9976	68.8	6285	primary key stratum broken
135.0	1.395	0.9975	84.8	7949	overlying strata bending
142.5	1.363	0.9971	110.0	10,169	integral caving

.

The characteristic of fractal dimension is scale invariance, which is universal to all kinds of scales. Fractal dimension can quantitatively describe the complex physical processes in mining engineering and reveal the internal mechanism of these physical processes. Prior research shows that the evolution of overburden fractures is a complex physical and mechanical process, during which many physical and mechanical parameters such as roof stress and deformation will change, and the magnitude and even magnitude of different production geological conditions are different, which make it difficult to use as an accurate prediction index. Therefore, fractal dimension can explain the complex fracture network and quantitatively characterize the evolution law of overcast rock fractures at each stage in the mining process, providing a reference for safe production and ecological restoration and management after mining. As shown in Figure 11, an overlying strata fracture was formed when the working face advanced to 20–60 cm, the fractal dimension was 0–1.325, the extension height of the overlying strata fracture was 20 cm, the rock damage area was 1485 cm², and the height of the overlying strata fracture was 0.9 times the advance distance. When the working face advanced to 60–135 cm, the fractal dimension was 1.325–1.38, the extension height of the crack was 88 cm, the rock damage area was 7949 cm², and the height of the crack in the overlying strata was 0.07 times the advance distance. This is the stage of deformation and fracture extension of the overlying strata. When the working face advanced to 142.5 cm, the rock damage area was 10,169 cm². With the advance of the working face, the three stages of overburden fracture development were divided mainly through the upward–stable–downward trend of the fractal dimension of the overburden fracture. The overlying strata fracture height extension pattern was divided into three stages: the overlying strata fracture formation stage, the overlying strata deformation fracture extension stage, and the overlying strata fracture extension steady-stage. These three stages can better describe the disturbance of the overlying strata and the initial formation of fractures in the early stage of workface advancement. This method can quantitatively explain the evolution law of overburden fractures in the actual mining process of the coal mine.

5.2. Ground Fissure Movement and Deformation Zone

In the early stage of mining, the main roof stratum is bent and sliding, and the ground has no obvious deformation characteristics. With the continuous advance of the working face, the overlying strata will eventually have stepped fault settlement, and the overlying strata fault will penetrate the ground from bottom to bottom [31]. Eventually, boundary fissure zones and central fissure zones form. In the study of ground fissure dynamics, ground fissures begin to crack, expand, contract, stabilize, or close. Ground fissures close due to damage caused by gravity within the soil, resulting in central dynamic ground fissures experiencing a double cycle extension [2,32]. In order to better simulate the morphological changes of surface cracks caused by fracture expansion in the overlying strata, the development and expansion laws of overlying strata cracks in different mining stages were simulated by PFC. As can be seen from the force chain diagram, the entire equilibrium structure of the overlying strata has been disrupted. The settlement of the block ultimately leads to ground deformation. It can be seen from the horizontal displacement-x contour that the horizontal displacement of the surface changes unevenly. Finally, ground cracks, extrusion cracks, and step settlement cracks are formed. As shown in Figure 12, through physical simulation experimental and numerical simulation studies of the overlying strata migration, the main influencing factor is the key strata in the overlying strata. As the working face progressed, key strata were broken, leading to massive settlement displacement of the overlying strata and the development of ground fissures. The rock blocks in the goaf are irregular, the arrangement is also very irregular, and the loose coefficient is relatively large. However, the overlying rock strata are broken and sink again, causing surface cracks to develop again, ultimately forming stable ground fissures. Eventually, from the horizontal displacement-x contour, it can be concluded that the horizontal displacement of the ground surface varies unevenly as the working face advances. The ground fissure compressed zone, tensile zone, compression zone, and central fissure zone form.

5.3. Field Ground Fissure Monitoring Analysis

In previous studies, there were few continuous settlement observations, and the time difference was more than three days. However, the selected ground fissure was continuously observed for monitoring. The Shangwan mine studied in this paper is different from other mines. The characteristics of the Shangwan mine are a large mining height, fast advancing speed, shallow burial depth, and large area of overlying rock caving during mining, so that cracks develop in the overlying rock and penetrate the surface. However, differently from the observed phenomena of fractures in other mining areas, the ground fissures in the middle of the working face are a secondary periodic development in the Shangwan mining area. Due to the complex environment of the field, we could collect only limited data, which provided basic research for this paper. The ground fissure development monitoring data of the working face were counted and listed in

Table 4. Dynamic fissure width.

Measurement Date	Advanced Distance (m)	Central Fissure Width (m)		Boundary Fissure Width (m)
		f08	f14	hf4	hf5	hf2	hf3
4 June	345	—	3.0	0.20	1.00	—	3.0
5 June	360	—	8.0	0.50	1.00	—	17.0
6 June	375	—	10.0	0.60	1.60	—	23.0
7 June	390	—	38.0	1.20	2.70	—	38.0
8 June	395	—	53.0	2.30	3.10	—	41.0
9 June	410	—	51.0	2.70	3.10	—	42.0
10 June	420	—	40.0	2.60	2.00	—	39.0
11 June	435	—	35.0	2.40	2.10	—	38.5
12 June	450	4.0	32.0	2.00	2.00	4.0	36.0
13 June	457	15.0	31.5	1.80	1.80	9.0	35.5
14 June	460	36.0	32.5	1.70	1.90	21.0	27.0
15 June	470	42.0	32.5	1.60	1.85	32.0	25.0
16 June	480	36.0	36.0	1.50	1.80	35.0	24.0
17 June	491	28.0	38.0	1.40	1.80	30.0	23.2
18 June	510	26.0	39.0	1.40	1.70	29.5	23.0
19 June	515	25.0	36.0	1.43	1.80	29.0	23.3
20 June	523	25.5	35.0	1.45	1.85	26.0	23.4
21 June	536	25.0	34.5	1.39	1.90	26.5	23.6
22 June	545	26.0	33.0	1.38	1.80	23.0	23.0
23 June	560	29.0	30.5	1.39	1.80	21.5	23.0
24 June	572	32.0	30.0	1.40	—	20.5	23.0
25 June	581	34.0	29.0	1.40	—	20.0	23.0
26 June	593	33.0	25.0	1.42	—	19.8	23.0
27 June	620	31.0	22.0	1.45	—	19.5	—
28 June	633	29.0	21.5	1.43	—	19.6	—
29 June	645	26.0	22.0	1.42	—	19.5	—
30 June	669	25.0	22.5	1.46	—	19.8	—
1 July	676	22.0	22.0	1.40	—	19.3	—
2 July	681	20.0	22.0	1.38	—	19.0	—
3 July	696	19.5	—	1.37	—	19.5	—
4 July	710	18.0	—	1.38	—	19.0	—
5 July	718	17.5	—	1.40	—	—	—

, as shown in Figure 13a. With the advancement of the working face, the f14 ground fissure forms when the working face advances 360 m, and the f08 ground fissure forms when the working face advances 450 m. From 3 June to 7 June, the f14 ground fissure width expansion is 55 mm, which then decreases to 31 mm. From 13 June to 18 June, the f14 ground fissure width again expands to 39 mm, and then gradually decreases to 20 mm to maintain a stable width after 18 June. From 11 June to 15 June, the f08 ground fissure width expansion is 45 mm, and then the fissure width decreases to 24 mm from 15 June to 19 June. From 19 June to 25 June, the f08 ground fissure width again expands to 35 mm, and then gradually decreases to 18 mm to maintain a stable width after 25 June. As shown in Figure 13b, the hf4 ground fissure forms when the working face advances 360 m, and the hf5 ground fissure forms when the working face advances 375 m. From 3 June to 7 June, the ground fissure width expansion of hf4 is 2.8 mm, which gradually decreases to 1.5 mm from 7 June to 17 June, and maintains a stable width after 18 June. From 5 June to 9 June, the ground fissure width expansion of hf5 is 3.5 mm, which gradually decreases to 1.8 mm from 9 June to 15 June, and a stable width is maintained after 16 June.

As shown in Figure 13c, with the advancement of the working face, the hf3 ground fissure forms when the working face advances 360 m, and the hf2 ground fissure forms when the working face advances 465 m. From 3 June to June, the hf3 ground fissure width expansion is 42 mm, which gradually decreases to 25 mm from 9 June to 15 June, and maintains a stable width after 16 June. From 11 June to 16 June, the ground fissure width expansion of hf2 is 38 mm, which gradually decreases to 22 mm from 16 July to 23 July, and maintains a stable width after 24 June. The available findings indicate that periodic fractures in the overlying strata cause the periodic development of central ground fissures, which is confirmed by observations made under the same geological and mining conditions. With the advancement of the working face, the central ground fissures f14 and f08 are formed by a double cycle development process, while the boundary ground fissures hf2, hf4, hf3, and hf5 are formed by single cycle development processes.

Once the boundary fissure is formed, the opening and drop also expand rapidly, reaching a maximum within 3–4 days and finally close slowly to a certain width. The central ground fissures form in groups of 3–5, and the ground fissures are spaced 2–5 m apart. This indicates that the instability of the main key layer is the direct cause of ground settlement. The central ground fissure developed twice from opening to narrowing its width, and the time interval between when the maximum widths of the two central ground fissures developed was 11–20 days. The width of the central ground fissure that developed first is greater than the width of the second ground fissure. Boundary fissures develop only once, the fissures expand rapidly to the maximum width in 5–6 days, and finally the width of the fissures remains stable. In conclusion, once a boundary fissure forms, the opening and fall also expand rapidly, reaching the maximum value within 3–5 days, and the boundary fissure finally shrinks slowly to a certain width and remains stable. The central ground fissures form in groups of 3–5. The spacing between the ground fissures is 2–5 m. This indicates that the instability of the main key strata is the direct cause of ground settlement.

6. Conclusions

According to the engineering background of the No. 12401 working face of the Shangwan mine, similar simulation, numerical simulation, and fractal theory are used to study the evolution law of overlying rock fractures caused by longwall mining. This analysis and research method can be extended to other mining areas to study the evolution law of overlying rock fractures.

(1)

Laboratory experiments show the overlying strata fracture expansion of the working face is divided into three stages: the overlying strata fracture formation stage, the overlying strata deformation fracture expansion stage, and the overlying strata fracture stable extension stage. The overlying strata are broken into blocks, resulting in ground aeolian sand movement and deformation with the blocks. Finally, ground closure fissures, compression fissures, and open fissures formed;

(2)

Through physical simulation experimental and numerical simulation studies of the overlying strata migration, as the working face progressed, key strata were broken, leading to massive settlement displacement of the overlying strata and the development of ground fissures. From the horizontal displacement-x contour, it can be concluded that the horizontal displacement of the ground surface varies unevenly as the working face advances. Eventually, the ground fissure compression zone, tension zone, compression zone, and central fissure zone formed;

(3)

From the fieldwork, 3–5 central dynamic ground fissures formed in each group, and their spacing is 2–5 m. The central ground fissure developed twice from opening to narrowing its width, and the time interval between when the two central ground fissures developed maximum widths was 11–20 days. The width of the first central ground fissure to develop is greater than the width of the second ground fissure. Boundary fissures develop only once and expand rapidly to the maximum width in 5–6 days, and finally the width of the fissures remains stable. This indicates that in a western shallow buried mine, after mining a working face with a large mining height, the main key stratum cycle fracture leads to two central ground fissure development cycles.