## 1 Introduction
[PERSON] [16] conducts comparative tests on the load capacity of three-point and four-point criteria, as well as their respective loading capacities under the condition of filling gauge. It is found that filling the three-point and four-point crib with gauge increases its maximal load several times compared to the empty ribs. The bonding characteristics of the TSL material formed a composite layer with the rock skin, thus increasing the specimen's ability to resist rock skin failure, which can provide a method for reinforcing the surrounding rock of the roadway [17]. [PERSON] et al. [18] find in their study that shearing strands at pillar corners near the roof and floor are critical for failure initiation. Therefore, in roadway support, attention should be paid to the control at the pillar corners near the roof and floor of the roadway. [PERSON] et al. [19] propose the concept of equal-strength beam support for the roof of deep rectangular roadways, which means designing different support lengths of anchors for the same roadway section to achieve the uniform distribution of local stresses on the roof. [PERSON] et al. [20] analyze the deformation mechanism of deep high-stress roadway-surrounding rock and propose a directional tensile blasting roof-cutting and  
Figure 1: The schematic diagram of GERRC. pressure-relieving surrounding rock control technology for deep roadways. The technique actively controls the collapse position of the overburden structure to optimize the stress environment of the roadway. [PERSON] et al. [21] analyze the manifestation characteristics of mine pressure in the surrounding rock of thick hard roof direct overburden gob-side entry retaining in kilometer-deep mines and propose a comprehensive control technology for surrounding rock structure optimization that combines the optimization of roof caving in the advanced working face and the structural breaking and pressure relief of the roof on the gob side. [PERSON] et al. [22] addressed the challenge of surrounding rock control in deep high-stress mining roadways, using the Sun Village Coal Mine as an engineering background. They analyzed and proposed a deep high-strength anchoring and grouting gob-side entry retaining method. This method uses high-strength anchoring and grouting to improve the integrity of the roadway roof and uses roof pre-splitting to cut off the stress transfer between the gob area and the roadway roof, placing the roadway in a stress-reduction zone. In summary, GERRC uses advanced pre-splitting to cut off the physical and mechanical connection between the roadway roof and the working face roof, transforming the roadway roof from a long cantilever to a short cantilever beam structure during the retaining period. This reduces the supporting pressure of the roof and optimizes the stress environment of the retaining roadway roof. As the mining depth increases, the control of the roadway roof requires both pressure relief and improved coordination between the roadway internal support and roof subsidence deformation. This manuscript focuses on the roof deformation law of the GERRC and establishes the relationship between the roof and support stiffness, providing a theoretical basis for the calculation of gob-side entry retaining by roof cutting roof deformation and roof support.