A process called piping, which often occurs in the soil at dams, levees, and dykes, involves the formation and development of a continuous tunnel between upstream and downstream ends. The hole erosion test is commonly used to quantify the critical stress and the rate of piping erosion progression. The aim of this study is to draw up a model for interpreting the results of this test. A characteristic internal erosion time is defined and expressed as a function of the initial hydraulic gradient and the coefficient of surface erosion. It is established here that the product of the coefficient of erosion and the flow velocity is a significant dimensionless number: when this number is small, the kinetics of erosion are low, and the particle concentration does not have any effect on the flow. This finding applies to most of the available test results. Theoretical and experimental evidence is presented showing that the evolution of the pipe radius during erosion with a constant pressure drop obeys a scaling exponential law.