## 1 Introduction  
Coal seam mining destroys the overlying strata's original stress balance. The overlying strata produce tensile damage, shear damage, bending, collapse, and other damage and deformations, thus forming goal voids and separation gaps in the strata [1, 2, 3]. These voids are widely distributed in collapse zones and fracture zones. Due to residual voids in the stope, water and gas gather, leading to water and gas outburst accidents [4, 5, 6]. In addition, these voids also lead to the secondary settlement of the goat, which leads to the settlement of ground buildings, local cracks, tilt, and other damages [7, 8, 9]. However, using space as an underground space resource is an environmental protection idea [10, 11, 12]. With coal mining, a large amount of solid waste, i.e., gangue, is also produced. The emissions from gangue account for approximately 10-15% of those from coal resources. A large amount of waste rock is directly discharged and piled up on the surface to form a waste rock hill. While polluting and occupying land, air, and water resources, coal mining also seriously threatens the mining area's ecological security and the coal industry's sustainable development. According to China's policy requirements for the construction of safe and efficient green coal mines, the safe mining of deep coal resources and the large-scale treatment of solid coal gangue waste have become important tasks for developing coal enterprises. Many scholars have analyzed the structure and shape of the overburden in the goat, the distribution of residual voids in the goat, and the related residual settlement and stability. Some scholars [13; 14; 15] believe that the overburden structure of the goaf is mainly divided into a caving zone, a fracture zone, and a bending subsidence zone. The rock structure in the caving zone is loose, and the mining structural plane mainly exists in the form of voids, cracks, and some large cavities. Some scholars [16; 17; 18] and other researchers have adopted similar material simulation and numerical simulation methods to simulate the existence of \"O\"-type separation fracture zones around the goaf and put forward the distribution law of fractured rock. They believe that the fracture expansion coefficient of a fractured rock mass is inversely proportional to its distance from the coal seam. Scholars [19; 20; 21] have considered the influence of time and goaf span factors, and they have carried out residual settlement predictions for old goaf. At the same time, some scholars [22; 23; 24] have also analyzed the void ratios of slopes using field data. [PERSON] [25] and other scholars have analyzed the void seepage characteristics within the fracture range of a goaf based on the actual measurements, and this provided the equivalent area of the separation fractures after the initial fracture of the key layer. They also analyzed the void permeability coefficients of different fracture development areas. [PERSON] [26] studied a drilling double-plug plugging subsection water injection test device and a drilling television observation system, which were used to detect the overlying rock saving in a fully mechanized mining face, and a digital analysis of the fracture dip distribution characteristics was carried out [27; 28; 29]. The authors also used a CMS three-dimensional laser scanning instrument to monitor goaf, and they detected that the goaf within 10 m of the working face had a void with a diameter of 1 to 10 m, as shown in Figure 1. However, only some of the above results could intuitively obtain the distribution forms of goaf voids. Based on the current research results, this article defines a void fraction as the ratio of a void's volume in goaf to its mining volume. The authors have put forward a concept of the overall distribution of a goaf void, deduced the theoretical formula, and calculated the distribution of the stope gap boundary and the central void ratio.