###### Abstract  
In underground coal mines, high-pressure water jet slotting is effective at improving coal seams' permeability. The slotting depth determines the effect of pressure relief and permeability enhancement in coal seams. However, there is no effective and feasible way of determining the slotting depth; thus, the operational parameters and borehole layout are unknown. This study determined the effects of key parameters, including the nozzle diameter, jet pressure, rotation speed, and slotting time, on the slotting depth. A water jet slotting depth calculation model was established and verified according to the slotting experiments under different operational conditions. The slotting depths were investigated based on the results of field slotting experiments. The results revealed that there exists an optimal nozzle diameter for a higher jet impact velocity. The slotting depth linearly increased with the jet pressure and decreased as a power function with the increase of the jet translation speed. The slotting depth increased with the slotting time, but the growth rate gradually decreased and tended to be stable. As the rotation speed increased, the slotting depth became greater at the initial period and the limit depth was reached faster. Laboratory and field slotting experiments were conducted to verify the model, and the experimental results are approximately in agreement with the theoretical predictions. The results of this study can be useful as guidelines for the hydraulic parameter selection of water jet slotting and for optimizing the layout of coal gas drainage boreholes.  
Keywords:gas drainage; water jet slotting; slotting depth; coal and gas outburst +
Footnote †: journal: Applied Soft  
to effectively extract coalbed methane and ensure mining safety, effective measures must be taken to improve the coal seam permeability and control the risk of gas disasters.  
In coal seams, high-pressure water jet slotting is an effective method of improving the coal seam permeability [6; 7; 8; 9]. As shown in Figure 1, this technology can form a disc slot in the coal seam by using a high-pressure water jet, which effectively increases the area of exposed coal. Additionally, the pressure in the coal seam surrounding the slot is fully relieved, which results in the deformation of coal and the formation of cracks. This increases the gas flow channels and improves the flow conditions, which in turn accelerate the gas desorption and discharge, to result in permeability improvement [10; 11]. Therefore, it can be seen that the slotting depth directly affects the pressure relief range and determines the gas drainage effect. Many studies have investigated water jet slotting. However, most existing studies have focused on improving the permeability mechanism [12; 13; 14] and rock-breaking capability of the water jet [15], optimizing and improving the slotting system [16; 17], and so on. A few studies have investigated the effects of hydraulic parameters and operational parameters on the slotting depth, but there is no applicable theoretical model for determining the slotting depth in water jet slotting applications. This leads to the operational parameters and borehole layout being unknown when applying high-pressure water jet slotting technology.  
This study investigated the effects of hydraulic parameters (nozzle diameter and jet pressure) and operational parameters (rotation speed and slotting time) on the slotting depth. Based on the rock-cutting model of a water jet, a model for calculating the water jet slotting depth was established. Water jet slotting experiments were conducted under different operational conditions to verify the calculation model. Additionally, water jet slotting field tests were conducted, and the slotting depths were investigated. The results of this study can be useful as guidelines for selecting the hydraulic parameters of water jet slotting and optimizing the layout of coal gas drainage boreholes in coal seams.