## 1 Introduction  
Borehole extraction is the main technical means of gas control at present. Effective extraction radius is an important basis for borehole design, which directly affects the extraction effect. If the hole spacing is too large, it is easy to form a blind area of extraction. If the hole spacing is too small, the effective extraction radius overlaps with each other, which is easy to cause unnecessary waste of manpower and material resources [1, 2]. For this reason, researchers have carried out shock waves [3], loose blasting [4, 5], hydraulic fracturing [6, 7], CO\({}_{2}\) fracturing [8, 9] and large borehole [10, 11] in improving the permeability-increasing of coal seam and increasing the effective extraction radius. It achieved a certain effect of increasing permeability and increasing flow. In addition, many researchers have carried out a lot of fruitful research work on the theoretical solution of gas flow channels and effective radius of extraction, field test technology and other key issues, and achieved a series of results [12]. [PERSON] et al. [13] studied the evolution law of mining gas channels and its influence on the law of gas-guided flow. They established the judgment method of the gas channel flow state. [PERSON] et al. [14] divided the gas flow channel into mesoscopic channels and macroscopic channels according to the fracture degree of the coal body. They analyzed their formation mechanism and evolution law of them. [PERSON] et al. [15] studied the unloading damage range of gas channels under different mining heights. [PERSON] et al. [16, 17] established the model of the plastic zone of a borehole surrounding a rock and gas permeability-increasing circle. He put forward the concept of a high-quality gas channel. [PERSON] et al. [18] used a similar simulation method to study the formation and evolution mechanism of gas channels in close-distance coal seams.  
In summary, the formation of the plastic zone of the surrounding rock of the borehole provides a high-quality channel for gas flow. The distribution pattern of the plastic zone and the characteristics of the connection network are very important for the optimal layout of the gas extraction borehole. However, the current research mainly focuses on the formation and evolution of the plastic zone of the single-hole surrounding rock and the expansion of the plastic zone between the surrounding rock of each borehole. The research on the scientific rationality of the hole spacing is relatively lagging behind, and it also ignores the influence of gas pressure on the plastic zone of the surrounding rock of the borehole. Resulting in a certain blindness and randomness in the actual engineering application, which seriously affects the efficient extraction of gas. Therefore, considering the gas pressure parameter, the implicit equation of the plastic zone boundary of the borehole surrounding rock is derived based on the modified Terzaghi effective stress principle and Mohr-Coulomb strength criterion. The distribution pattern of the plastic zone of the borehole surrounding rock and the variation law of the permeability-increasing circle with the confining pressure ratio, the mechanical parameters of the coal body, the gas pressure and the aperture are analyzed. The distribution pattern of the plastic zone of the borehole surrounding rock is used to establish the honeycomb gas flow network channel structure, which is beneficial to gas extraction. Based on this, the main criterion of the borehole spacing is proposed, and the engineering test is carried out.