Mathematical modelling of cumulative erosion ratio for suffusion in soils

Internal erosion induced by suffusion is a progressive process that can have negative consequences for dams, foundations and tunnel projects. The erosion ratio (denoting the ratio of the weight of cumulative eroded soils to the total weight of soils) is an important parameter in characterising this process, reflecting variations in porosity and hydraulic conductivity during suffusion. In this study, an erosion equation expressing the variation in the erosion ratio with respect to the hydraulic gradient and time is derived under arbitrary hydraulic loading conditions. This equation is based on investigations into the influence of both the hydraulic gradient and of time on the process of soil erosion. The derived erosion equation is applied in a case study and the results are compared with existing test data. It is shown that the expression proposed in this paper is in good agreement with observations. Finally, the influences of the hydraulic loading history and an erosion rate coefficient on the soil erosion process are discussed.