## 1 Introduction  
High-pressure moving water jets are widely used in metal processing [1, 2, 3], coal mining [4, 5], foundation treatment [6], and waterway dredging [7, 8]. In recent years, some scholars [9] have applied high-pressure water jet technology to the liquid collection process in the in situ leaching mining of ionic rare earth ore. In this process, a high-pressure moving water jet breaks soil on both sides of a horizontal diversion hole to form a 'V'-shaped erosion trough. This increases the radiation range of the diversion hole to improve the efficiency of liquid collection. Therefore, it is very necessary to study the soil breaking morphology of high-pressure moving water jets. At present, high-pressure water jet technology is often used to cut hard materials, such as metal, coal rock, and ceramics. Abrasive water jet technology came into being under low working pressure, and a certain amount of abrasive particles are added to a pure water jet to greatly improve the cutting ability of the water jet. The existing literature [1, 2, 3] mainly focuses on factors such as jet pressure, abrasive flow, abrasive particle size, orifice size,and nozzle feed rate in the process of abrasive water jet cutting depth, and it has made a series of research results. However, the floor soil of ionic rare earth mines is cohesive soil, which is obviously different from the physical and mechanical properties of hard materials such as metal and rock. At present, pure water jet technology is often used to cut soil in practical projects such as channel dredging [7; 8]. Therefore, the existing mature abrasive water jet cutting theory cannot provide scientific and effective guidance for pure water jet soil-breaking technology. In view of the above problems, some scholars have carried out targeted research on water jet soil-breaking mechanisms. Of the experimental studies, [PERSON] and [PERSON] [10] analysed the erosion of non-cohesive soil by fluids, proposed erosion parameters, and described the relationship between the parameters and the jet distance with an exponential function. [PERSON] et al. [11] proposed an empirical formula for the erosion pits made by a fixed jet in cohesionless soil. [PERSON] et al. [12] studied the influence of a plane fixed jet on cohesive soil, finding that erosion depth is linearly related to the logarithm of the jet time. [PERSON] et al. [13] carried out submerged water jet soil-breaking tests under different jet angles and distances and analysed the influence of the jet's parameters on the depth of the erosion pit. Of the numerical simulation studies, [PERSON] et al. [14] used the control volume method to calculate the scouring of underwater bedrock and to analyse the degree of bedrock scouring occurring at different jet velocities. [PERSON] et al. [15] carried out a numerical study on the problem of the two-dimensional-plane fixed-jet scouring of sediment. An F-equation was constructed to describe the shear stress conversion between the flow phase and sediment phase, and a general governing equation for calculating the two phases at the same time was obtained. [PERSON] et al. [16] used Flow-3D software to simulate the three-dimensional fixed jet erosion process and found that the jet erosion angle has an important influence on the shape of the erosion pit. [PERSON] et al. [17] used computational fluid dynamics and discrete element methods to quantitatively analyse the influence of jet velocity and sediment characteristics on erosion pit morphology. These studies have greatly promoted the development of fixed jet soil breaking. However, in the application of water jet technology in ionic rare earth mines, most of the encountered problems are soil breaking by moving water jets, and more concern is given to the geometric shape of the erosion surface formed after soil breaking. In-depth research on this issue has not yet been conducted. In recent years, some scholars have used erosion theory to analyse the process of water jets breaking clay [18; 19; 20].