Jet erosion is a frequent occurrence in maritime engineering and in river erosion. This study was based on a self-developed water jet experimental platform, and conducted experimental and simulation studies on the vertical jet erosion of cohesive soil under different velocities ( \(U_{0}\) ) and target distances (h). To describe in detail the three-dimensional dynamic changes in the soil jet scouring hole. Build a custom function (UDF) model for soil erosion, embed the experimentally measured Bingham rheological model parameters into the solver, and combine them with the Krieger–Dougherty model to determine the threshold of \(\phi_{c} = 0.35\) for the soil initiation volume on the iso-surface during the simulation process. According to the dynamic size changes of the simulated jet scouring holes, jet scouring is divided into four stages: initial stage, expansion stage, unstable expansion stage, and stable development stage. The experimental data for jet erosion holes is fitted, and dimensionless equations \(\varepsilon_{m\infty }\) , \(\sqrt[3]{\xi }\) , and \({\text{r}}_{0\infty }\) for viscous soil erosion holes under equilibrium erosion conditions are proposed, with a correlation coefficient of 0.94, 0.90 and 0.91. By comparing the simulation and experimental data, it was found that the scour hole depth developed logarithmically with dimensionless time, further verifying the effectiveness of the simulation model.
