The Development Law of Mining-Induced Surface Cracks in Shallow Coal Seam Through Double Gullies Terrain: A Case Study in a Mine

: Mining - induced surface cracks in gullies in shallow seams seriously threaten the development of ecological stability and the safety of mine production. The development law of surface cracks in shallow coal seam mining through double gullies terrain was studied, by taking the Cao Jiatan coal mine in the Yushen Mining Area as a project example. The function T and its discriminant were first put forward to describe the relative position both the surface cracks and working face advanced in shallow coal seam mining through double gullies terrain. The relationship between valley parameters of double gullies terrain and the relative position of surface cracks development was discussed through numerical simulation experiment, similar material simulation experiment and theoretical analysis. The results showed that when the working face passed through the G1 gully, the development of surface cracks led the working face. There were four surface cracks with a maximum width of 23 cm, and the maximum vertical displacement was 11 cm; while passing through the G2 gully, the development of surface cracks lagged the working face. There were seven surface cracks with a maximum width of 79 cm, and the maximum vertical displacement was 45 cm. It can be concluded that the relative position of crack development is greatly affected by geological conditions, gully depth, slope angle, span and other factors of the gully, among of which the gully slope angle is the main influencing factor. T and | T | value has a certain correlation with the lagging distance, crack width, vertical displacement and the total number of cracks in a single gully.


Introduction
Mining-induced surface cracks is a frequent cause of damage to building features, surface and underground water resources, and other environmental features [1][2][3][4][5]. In northwest China, the majority of mining areas are located within or on the edges of deserts, which often have shallow coal seam reserves for mining and vertical and horizontal gullies on the surface. However, these areas also have arid and semi-arid climates with fragile ecological environments and significant water shortages [6][7][8].
Yushen Coalfield is located in the transition zone between the Loess Plateau and the Mu Us Sandy Land with rugged topography, and a gullied surface [9], under gullies topography, mining-induced surface cracks is a severe threat to the local fragile ecological environment [10][11][12][13]. Researchers have studied the influence of valley topography on mining-induced surface cracks using numerical simulation [14][15][16][17], physical simulation [18][19][20][21][22][23][24], theoretical analysis [25][26][27][28] and field survey [19,21,29,30]. The research shows that a single slope and different slopes angle, the overburden strata load increases with the increase of the gully slope angle; and with the continuous increase of the gully depth, the dynamic pressure behaviour of the working face in the upper slope section of the gully behaves stronger [20,31,32]. The strenuous degree of pressure behaviour in shallow coal seam mining under the gully shows the characteristics of "back gully section > toward gully section > bottom gully section > normal mining section" [33]. Under the assumption that the slope in the gully is single and the slope angle is constant, the mechanical model of "non-uniform load beam" [34] can fully characterize the dynamic load process of the working face through the gully terrain [22,35].
Remote sensing technology and field survey can effectively reveal the plane distribution law and dynamic development law of mining-induced surface cracks and their relationship with the generation progress of the working face [36].
The above studies show that the gully geomorphology has a significant influence on the mining surface cracks, especially in the shallow coal seams where loess and blown-sand exist in the topsoil.
However, the studies above are mostly based on a single gully landform. At present, there is little research on the development characteristics of surface cracks in shallow coal seam mining through double gullies terrain, which needs to be studied urgently.
In this paper, FLAC3D numerical simulation, similar material simulation and theoretical analysis were used to study the development law of surface cracks caused by mining through double gullies terrain in the shallow coal seam, and the effects of gully depth, slope and span on the relative position of surface cracks were also analyzed.   Table 1.      Table 3. The establishment of the physical model was carried out using similar materials, and the process can be divided into five steps: weighing materials, mixing materials, adding water and uniformly mixing, placing and tamping, and natural air drying. Finally, the total height was 600 mm, as shown in Figure 5.   Table 1. During the experiment, the VIC-3D digital speckle method was used to monitor the overburden displacement of the working face while mining through G1 and G2

Tab. 3 Material selection and matching
gullies.

The development law of surface cracks
The results of similar material simulation experiment showed that the surface crack was a dynamic process from development to stability.
In the process of mining through the G1 gully in the working face, the surface crack was a tensile crack

Discussion
The Based on multilateral block structure [37][38][39]and mining slope theory [27], when the shallow coal seam is mined through double gullies terrain, the structure and force of the broken block of the gully are shown in Figure 8. With the integral contact between K1 and K2 blocks as the research object, the stress can be analyzed as follows: Where N is the extrusion stress in the horizontal direction along the multilateral block fracture surface; G is the gravity stress of the multilateral block; A is the multilateral block volume per thickness; r is the volume weight; β is the mean fracture angle of the multilateral block.
h H   (8) Where ξ is the gully depth influence coefficient, H is the depth of gully, h is the mean mining thickness.

sin
Where λ is the slope gradient influence coefficient, H is the depth of gully, L is the dip length of gully, α is the mean gully angle. G N f  (11) The formula (7) and (10) are brought into formula (11) to obtain the following: Intermediate parameter ω: The formula (13) is brought into formula (12) to obtain the following: From the formula (7)～(14) and the experimental simulation results, the results of Table 4  Note: α∈(0, 2/π); in the bottom-gully section α=0, sinα is unmeaning.
According to the comparison between results in Table 4  The tanα is a monotone increasing function, and its value is positive (α∈(0, 2/π)), so the gully slope is the main controlling factor affecting the relative position of surface cracks.
The basic parameters of double gullies terrain as listed in Table 1 can be calculated by the formula (15) Table   5.
Tab. 5 The development law of surface cracks and the result of the relative position function

Conclusions
The numerical simulation of the working face passing through the double gullies terrain was

Data Availability
The data used to support the findings of this study are included within the article.

Conflicts of Interest:
The authors declare no conflict of interest. Figure 1 Plan view of the local panel layout and drill column The numerical simulation model