This study focuses on the numerical modelling of concentrated leak erosion of a cohesive soil by a turbulent flow in axisymmetrical geometry, with application to the Hole Erosion Test (HET). The numerical model is based on adaptive remeshing of the water/soil interface to ensure accurate description of the mechanical phenomena occurring near the soil/water interface. The erosion law governing the interface motion is based on two erosion parameters: the critical shear stress and the erosion coefficient. The model is first validated in the case of 2D piping erosion induced by a laminar flow. Then, the numerical results are compared with the interpretation model of the Hole Erosion Test. Three HETs performed on different soils are modelled with a rather good accuracy. Lastly, a parametric analysis of the influence of the erosion parameters on erosion kinetics and evolution of channel diameter is conducted. Finally, after this validation by comparison with both the experimental results and the interpretation of Bonelli et al. [2], our model is now able to reproduce accurately the erosion of a cohesive soil by a concentrated leak. It also gives access to a detailed description of all the averaged hydrodynamic flow quantities. This detailed description is essential in order to achieve a better understanding of the erosion processes.