## 1 Introduction  
With the large-scale exploitation of coal resources, under the traditional mining mode of leaving coal pillars, the cost of roadway excavation has been increasing significantly. In order to respond to the development concept of green mining and reduce the waste of coal resources, pillarless mining technology has begun to be widely applied in the coal industry. The application of gob-side entry retaining technology avoids the resource waste caused by the traditional method of leaving coal pillars and also reduces the amount of roadway excavation [1, 2, 3]. There are some technical problems in the application of pillarless gob-side entry retaining technology, such as large deformation and damage to the surrounding rock of the roadway caused by mining influence and problems with the support structure. However, based on the synergistic effect of mine pressure driving and the theory of rock swelling and self-stabilization, this technology achieves the dynamic balance of the surrounding rock stress in the stope through in situ solidification and filling of the goat, effectively controlling the deformation of the overlying strata [4; 5; 6]. When implementing gob-side entry retaining in the fully mechanized mining face of shallow-buried \"three-soft\" coal seams, due to its unique geological characteristics, the fully mechanized mining face still faces severe challenges in implementing gob-side entry retaining. Therefore, it is necessary to study the fracture characteristic laws of the overlying roof in the fully mechanized mining face to determine whether the conditions for gob-side entry retaining are met. According to relevant mechanical theories, such as the thin-plate theory, after the working face has mined a certain distance forward from the cut-off position, the main roof reaches its strength limit and fractures in the goat to form key rock blocks A, B, and C. Among them, the fracture position and movement form of key rock block B play a very important role in the stability of the surrounding rock of the gob-side roadway [7; 8; 9; 10; 11]. In recent years, many researchers have carried out a large number of studies on the fracture characteristics of the overlying roof. [PERSON], [PERSON] et al. [12] addressed the problem of surrounding rock deformation and instability in gob-side coal and rock roadways of inclined coal seams. Based on the influence of different main roof fracture locations on surrounding rock stress and displacement, they revealed the intrinsic relationship between fracture types and roadway stability. [PERSON], [PERSON] et al. [13] focused on the deformation and instability of gob-side entry retaining with soft rock composite roofs, constructing a mechanical model of a key block structure. By predicting the main roof fracture line position, analyzing the roof subsidence law on the backfill side, and combining numerical simulations, they revealed the plastic zone expansion and stress distribution characteristics induced by the main roof fracture rotation, providing a basis for roadway stability control. [PERSON], [PERSON] et al. [14] tackled the issues of main roof fracture and roadway instability caused by narrow coal pillars in gob-side entry driving. Using the block beam theory, they established an elastic foundation beam model, derived expressions for roof bending moment and displacement to determine fracture locations, and analyzed the impact of different fracture scenarios on surrounding rock stability through numerical simulations, solving the problems of main roof fracture and roadway instability induced by narrow coal pillars in gob-side entry driving. [PERSON], [PERSON] et al. [15] studied the disturbance height of the overlying strata and the fracture characteristics of the hard roof in the mining of extra-thick coal seams through on-site measurement and three-dimensional physical similar simulation methods, and explained the large and small cycles and the strong mine pressure manifestations in the large-space stope. [PERSON], [PERSON] et al.