Experimental Study on the Fracture Distribution Characteristics of the Overlying Strata in an Abandoned Gob

: A lot of gas resources remain in the abandoned gob. The overlying strata of the abandoned gob are the main places for gas storage and flow. The fracture distribution characteristics of the overlying strata have a significant impact on the gas migration. The mining similarity simulation test device of a plane stress was used to study the deformation and failure characteristics of overlying strata in an abandoned gob. The caved strata of the abandoned gob formed a trapezoidal distribution, and the caving range decreased gradually with an increase in distance from the coal seam. The strata collapsed in the caved zone, whereas the strata collapsed mainly on the bending subsidence in fractured zone. The subsidence curves of caved strata showed a lower concave shape, and the maximum subsidence existed in the middle of the abandoned gob. The caved strata subsidence decreased with an increase in distance from the coal seam. The horizontal fractures were dominant in the fractured zone. The abscission rate of the end mining position was greater than that of the start mining position. Large numbers of vertical fractures existed in the caved zone. The development degree of vertical fractures near the end mining position were larger than that of the start mining position, and the width of the gas-conducting fracture was more than three times that of the start mining position. The development degree, quantity and connectivity of the fracture in the end mining position were better than those in the start mining position.


Introduction
China has had abundant coal resources and coal mining operations for more than 100 years. A large area of coal mine gob has formed during long-term coal mining, in which the movement of overlying strata tends to stabilize. This area is termed the abandoned gob after the mining panel closes (Xu, 2011). For the abandoned gob, approximately 50% of the coal remains underground.
Gas has not desorbed completely from the residual coal, coal pillar and stress relief coal seam. A certain amount of gas resources remain and accumulate in the abandoned gob (Karacan, 2015;Qin et al., 2015;Meng et al., 2016). The fracture distribution characteristics of the overlying strata in the abandoned gob affect gas storage and flow directly.
During coal seam mining, the overlying gob strata will yield deformation and failure to different degrees. Most researchers have divided the failure characteristics of the overlying strata in the gob into three zones: the caved, fractured and bending zones (Booth and Spande, 1992;Palchik, 2003;Yavuz 2004;Zhang et al. 2019). The surface soil layer has been divided into the soil zone, which is on top of the bending zone, so the overlying strata of the gob were divided into four zones (Peng and Chiang, 1984;Gao 1996). For longwall mining with shallow coal seams, the overlying strata of the gob were divided into two zones: the caved zone and the fractured zone (Wang et al., 2015). For the above three classification methods, the caved zone and the fractured zones appear in the overlying strata of the gob. Large amounts of vertical and horizontal fractures exist in the caved and fractured zone, in which the vertical fractures are several times higher than the mining height, and the horizontal fractures develop within a certain height range (Palchik, 2005;Islam et al., 2009;Sang et al., 2010;Zhang et al., 2011;Majdi et al., 2012;Wei et al., 2016).
The fracture of the overlying strata in the gob is a significant factor that affects gas storage and flow (Karacan, 2007;Palchik 2014;Yang et al., 2014;Fan and Liu, 2017). Vertical fractures are the main channel for gas flow, whereas the horizontal fractures are the main channel for gas storage (Liu, 2011;Li et al., 2014;Qu et al., 2015). After the mining panel was closed, an "O"-shaped circle resulted with mining-induced fractures around the gob. This area is the main channel and space for gas flow (Qian et al., 1998). However, the "O"-shaped circle around the abandoned gob has a widely distributed range, and obvious differences exist in different locations. Therefore, it is necessary to study the fracture distribution characteristics of the overlying strata in the abandoned gob to determine the space of gas flow and storage.
We studied the deformation and failure characteristics of overlying strata in the abandoned gob by a similar simulation experiment. Firstly, we analyzed failure characteristics of overlying strata in the abandoned gob. The collapse law of rock strata was obtained in the caved and fractured zones. Secondly, we analyzed deformation law of the overlying strata in the abandoned gob. The subsidence curve of overlying strata was obtained. Finally, we analyzed fracture distribution of overlying strata in the abandoned gob. The optimal location of gas flow and storage was determined in the overlying strata of the abandoned gob.

Scheme of similar simulation experiment
The research object was panel 3305 in No.5 coal mine, Hebi, Henan Province, China. The mining depth ranged from 502.5 to 552 m. Panel 3305, was 102.8 m wide, 442.05 m long and approximately 527.25 m deep. The average coal seam thickness was 8.26 m with a dipping angle of 8°. The mining method was longwall mining on strike.

Similarity coefficient
We studied the fracture distribution characteristics of rock strata in the caved and fractured zones of the abandoned gob. According to the similarity criterion, the parameters of the similarity ratio were determined as follows: Time similarity 10 : where CL is the geometric similarity; Lm is the model length, cm; Lp is the prototype length, m; Cμ is the Poisson ratio similarity; μm is the Poisson ratio of similar materials; μp is the Poisson ratio of rock; Cρ is the density similarity; ρm is the density of similar materials, kg/m 3 ; ρp is the rock density, kg/m 3 ; CE is the stiffness similarity; Em is the stiffness of similar materials, N/m; Ep is the rock stiffness, N/m; Cσ is the stress similarity; σm is the stress of the overlying strata in the model, kPa; σp is the stress of the overlying strata in the prototype, MPa; Ct is the time similarity; tm is the excavation time of the model, h; and tp is the panel mining time, h.

Proportion of similar materials
The dimensions of the model frame were a 2500 mm length, 200 mm width and 1300 mm height in the similar simulation experiment. The experiment materials included mainly sand, gypsum, calcium carbonate and borax (Li, 1988). Sand was the main material with a diameter less than 0.5 mm. Gypsum was used as a cementing material to increase the strength. The calcium carbonate strength was lower and could be used to adjust the strength and deformation properties of the similar materials. Borax was the retarder and prevented similar materials from coagulating into blocks. The proportion of similar materials was determined by the rock mechanical properties.
The proportions and strengths of the similar materials are listed in

Layout of displacement monitoring points
To analyze the displacement and deformation law of caved strata in the gob, the displacement monitoring points were laid in the overlying strata of the coal seam. Figure 1 shows the layout of the displacement monitoring points for overlying strata. Seven-layer monitoring points were present and the interval between layers was 10 cm. The interval of adjacent points was 10 cm in each layer. From the bottom to the top of the model, the monitoring line numbers were D1, D2, D3, D4, D5, D6 and D7. The circular monitoring points were noncoding markers, and the square monitoring points were coding markers. The change of displacement monitoring points can reflect caved strata subsidence. A XJTUDP optical close-range photogrammetric system was used to monitor the caved strata movement. The XJTUDP optical close-range photogrammetric system components are references by Wu et al (2015). After coal seam excavation, the displacement monitoring points were captured by a high-resolution digital camera at different angles and locations when the movement of the caved strata stabilized. The captured photos were read by data analysis software. The software recognized and calculated the three-dimensional coordinates of the target points automatically.

Model excavation
The protective coal pillar was 30 cm on both sides of the model. The excavation sequence of the model was from left to right, and the excavation step was 10 cm. The excavation time was 30 minutes to ensure that the movement of the caved strata became stable in the gob. A digital camera was used to capture the caving characteristics of the rock strata.

Caving characteristics of the overlying strata in the gob
The variation characteristics of caved strata in the gob that occur during the mining process are shown in Fig.2. As shown in Fig. 2d, no obvious deformation and failure in the overlying strata of the gob resulted after the coal seam was excavated to 50 cm. When the coal seam was excavated to 60 cm, the immediate roof collapsed as bending subsidence (Fig. 2e). When the coal seam was excavated to 70 cm, the immediate roof collapsed directly (Fig. 2f). When the coal seam was excavated to 90 cm, the D1 line collapsed as bending subsidence. A concave-shaped abscission layer formed between the D1 and D2 lines. The other displacement monitoring lines do not show an apparent collapse (Fig. 2h). When the coal seam was excavated to 100 cm, the caving range of the overlying strata increased visibly and extended to the D3 line. A concave-shaped abscission layer formed between the D3 and D4 lines, and horizontal fractures began to appear at the D4, D5 and D6 lines (Fig. 2i). When the coal seam was excavated to 120 cm, the caving range of the overlying strata extended to the D5 line. A concave-shaped abscission layer formed between the D5 and D6 lines. A distinct horizontal fracture resulted at the D6 line (Fig. 2k). When the coal seam was excavated to 130 cm, the abscission layer increased between the D5 and D6 lines, and a distinct horizontal fracture existed between the D6 and D7 lines (Fig. 2l). When the coal seam was excavated to 140 cm, the caving range of the overlying strata extended to the D6 line and the abscission layer increased between the D6 and D7 lines (Fig. 2m). When the coal seam was excavated to 160 cm, a concave-shaped abscission layer formed near the D7 line (Fig.   2o). When the coal seam was excavated to 180 cm, the caving range of the overlying strata extended to the top of the model. The amount of abscission layer decreased visibly between the D6 and D7 lines because of gravity action of the caved rock strata (Fig. 2q). When the coal seam was excavated to 190 cm, the caving range of the overlying strata continued to increase, and the caved rock strata formed a trapezoidal shape. The overlying strata collapsed as bending subsidence above the D2 line, whereas the overlying strata collapsed directly below the D2 line.
Obvious horizontal fractures existed on both sides of the gob, whereas the abscission layer between the caved strata was compacted in the middle of the gob (Fig. 2r).
Therefore, a concave-shaped abscission layer will appear when an overlying strata collapses.
In the middle of the gob, the abscission layer will be compacted as the mining panel continues to advance and the deformation and failure state of the overlying strata have a transition process, which is from the formation of fractures to the compacted state.

Subsidence
The subsidence is a variation of caved strata in the vertical direction. It is expressed by the elevation difference between the first and m times the observation of one point in the overlying strata. The formula is as follows: where wn is the subsidence of the n-point in the overlying strata, mm; hn0 is the elevation of the n-point at the first observation, mm; and hnm is the elevation of the n-point at the m-times observation, mm.

Abscission rate
The abscission rate represents the development height of a fracture in unit thickness strata.
The calculation method is the ratio of the subsidence difference between the lower and upper strata to the distance between the upper and lower strata. The formula is as follows: where F is the abscission rate, mm·m -1 ; Sd is the subsidence of the lower strata, mm; Su is the subsidence of the upper strata, mm; and h is the distance between the upper and lower strata, m.
As shown in Fig. 5, the abscission rate of the right is significantly higher than that on the left side for D1-D2, D2-D3, D3-D4 and D4-D5. That is, the abscission rate near the end mining position is greater than that near the start mining position. The main reason is that the caved strata near the start mining position are affected significantly by periodic weighting of the roof during mining. In contrast, the abscission rate on the left is significantly higher than that on the right for D5-D6 and D6-D7. The main reason is that the upper strata of the model are less affected by the gravity of the caved strata, which experiences a process of gradual expansion.

Horizontal movement
The horizontal movement is the displacement of the caved strata in a horizontal direction. It is represented by the horizontal distance difference between the m-times and the first observation of one point. The formula is as follows: where un is the horizontal movement of the n-point, mm; ln0 is the horizontal distance between the n-point and the observation line at the first time observation, mm; and lnm is the horizontal distance between the n-point and the observation line at the m times observation, mm. Figure 6 shows the variation curves of the horizontal movement for the caved strata in the abandoned gob. The caved strata move to the right, and the horizontal movement is positive. The caved strata move to the left, and the horizontal movement is negative. From the start to the end mining position, the horizontal movement shows an increasing-decreasing-increasing trend. The maximum horizontal movement is on both sides of the gob, whereas the minimum horizontal movement is in the middle of the abandoned gob. In the start mining position, the peak points shift gradually to the right with an increase in distance from the coal seam. In the end mining position, the peak valley points shift gradually to the left with an increase in the distance from the coal seam.
The main reason is that the range of caved strata decreases with an increase in the distance from the coal seam.

Inclination
The inclination is the ratio of the subsidence difference between the two adjacent points to the horizontal distance. It reflects the slope of the movement for caved strata along one direction.
The formula is as follows: where im-n is the inclination between m and n points, mm/m; lm-n is the horizontal distance between m and n points, m; and wn , wm is the subsidence of m and n points, mm.

Horizontal deformation
The horizontal deformation is the ratio of the horizontal movement difference between two adjacent points to the horizontal distance. It reflects the stretching or compression of unit length.
The formula is as follows: where εm-n is the horizontal deformation between m and n points, mm/m; um and un are the horizontal movement of m and n points, respectively, mm; and lm-n is the horizontal distance between m and n points, m.

Curvature
The curvature is the ratio of the inclination difference between two adjacent line segments to the horizontal distance between the middle points of two adjacent line segments. It can reflect the bending degree of the observation section. The formula is as follows: where km-n-p is the mean curvature of line segments m-n and n-p, mm/m 2 ; im-n is the inclination between m and n points, mm/m; in-p is the inclination between n and p points, mm/m; lm-n is the horizontal distance between m and n points, m; and ln-p is the horizontal distance between n and p points, m. Figure 9 shows the variation curves of curvature for caved strata in the abandoned gob. The curvature is positive on both sides of the abandoned gob, and negative in the middle of the abandoned gob. From the start to the end mining position, the curvature shows an increasing-decreasing-increasing-decreasing trend. The curve presents an upper convex-lower concave-upper convex shape. The variation curve is consistent with the horizontal deformation.
With an increase in distance from the coal seam, the curvature decreases gradually, and the peak points move toward the middle of the abandoned gob. The location of the peak valley points remains unchanged in the middle of the abandoned gob.

Fracture distribution characteristics of the caved strata in the abandoned gob
To analyze the fracture distribution characteristics of caved strata in the abandoned gob, Fig.3(c) was processed by binarization. Figure 10 show that the horizontal fractures are dominant on both sides of the abandoned gob. In the bottom of the model, the horizontal abscissions of the end mining position are larger than that of the start mining position according to the calculation results of the abscission rate, and the development degree of vertical fractures near the end mining position is greater than that near the start mining position. The length of the blue line represents the range of gas-conducting fractures in the horizontal direction. The width of gas-conducting fractures is 108.71 cm near the end mining position. The width of the gas-conducting fractures is 35.56 cm near the start mining position. The width of the gas-conducting fractures near the end mining position is more than three times that near the start mining position. Therefore, the development degree, quantity and connectivity of fractures near the end mining position are larger than those near the start mining position. The end mining position is more conducive to gas flow in the abandoned gob.

Conclusions
(1) The caved strata present a trapezoidal distribution, and the caving range decreases gradually with an increase in distance from the coal seam. The strata collapse in the caved zone, whereas the strata collapse mainly on bending subsidence in the fractured zone.
(2) From the start to the end mining position, the subsidence curves of caved strata show a lower concave shape, and the maximum subsidence exists in the middle of the abandoned gob.
The subsidence decreases with an increase in distance from the coal seam. The abscission rate near the end mining position is greater than that near the start mining position.
(3) The horizontal fractures are dominant in the fractured zone. Large numbers of vertical fractures in the caved zone. The development degree , quantity and connectivity of fractures near the end mining position is larger than that of the start mining position, and the width of the gas-conducting fracture is more than three times that of the end mining position.