## 1 Introduction  
As the depth of coal mining rises, an increasing number of coal mining areas are faced with the technical problem of short-distance multi-seam mining [1, 2, 3, 4]. During the mining of short-distance coal seams, the gob and coal pillars left from the upper coal seams greatly affect the selection and control of the roadway location in the lower coal seams [5, 6, 7]. An unreasonable roadway location in the lower coal seams often causes extreme roadway deformation, which greatly affects normal recovery of the working face [8, 9, 10]. Therefore, gob-side entry driving in lower coal seams should not only consider factors influencing lower-coal-seam mining, but also avoid the influence of the high stress concentration of residual coal pillars in the upper coal seams, which is of great significance for safe and efficient coal mining [11].  
Experts have conducted extensive research on the stress distribution characteristics of short-distance coal seams, the reasonable coal pillar width in gob-side entry driving, and the surrounding rock control [12, 13, 14]. [PERSON] [15] analyzed the correlation between the deformation failure of bottom coal in the gob-side entry and coal pillar width by theoretical analysis, numerical calculation, and similar simulation experiments. [PERSON]. [16] studied the mechanical behavior of coal pillar load on the floor rock strata in multi-seam downward mining and discovered that stress was highly concentrated in the floor rock strata near coal pillars, with the stress concentration degree in floor rock strata positively correlated with the distance between the surrounding rock and coal pillars. [PERSON] et al. (2020) [17] adopted numerical simulation software and determined a reasonable design for roadway supporting pillars. [PERSON] (2004) [18] used the method of similarity simulation experiments to study the laws of roof activity. [PERSON] et al. (2014) [19] applied fuzzy logic to predict sate pillar sizing in room and pillar coal mines. [PERSON] et al. (2012) [20] summarized the main factors causing roadway damage in adjacent gobs and found that roadway deformation can be effectively controlled using high-preload and dense-bolt (cable) support systems. With respect to problems such as serious asymmetric deformation and support failure of gob-side roadways, [PERSON] et al. (2020) [21] proposed a hydraulic fracture technique to pre-fracture the two hard roofs, and the validity of the above roof treatment was verified via field application. Meanwhile, some experts have improved the geological and mechanical conditions of the coal mining process through backfilling technology [22; 23].  
Based on the engineering background of the 4602 head roadway in the Honghui Coal Mine, this study establishes a theoretical model for floor failure in short-distance coal seams and analyzed the floor failure range of the residual coal pillars. In addition, it establishes a mechanical model of inclined gob-side roadways and deduces an expression for the influence range of low stress areas and its influencing factors. Moreover, the stress distribution characteristics of coal pillars with different coal pillar widths in gob-side entry driving were analyzed by numerical simulation; a reasonable coal pillar width was comprehensively determined, and the yield-anchor mesh-cable support system was proposed. The proposed support system effectively controls the integrity of the roadway surrounding rock and realizes the safety and stability of the roadway support.