Mathematical descriptions of grading linked with prediction of mechanical consequences of suffusion

Internal erosion is a leading cause of disfunctions and failures of earth embankments when used as water retaining structures. Internal erosion results from water flowing through the embankments, removing particles from the soils forming the embankments. It may even occur in the embankment foundations if they are made of soils. It changes a soil’s particle size distribution, increases its void ratio, shifts its critical state line upwards in the compression plane and alters its stress–strain behavior. This paper presents new mathematical links and constitutive model ingredients to capture these effects. They apply to a gap-graded soil and a particular type of erosion known as suffusion. The evolution of the particle size distribution is characterised through a grading state index, defined in terms of geometrical properties which are fractal. These new ingredients are incorporated into the Severn-Trent model to simulate stress–strain responses of the soil, subjected to drained triaxial compression, having experienced different amounts of suffusion. The simulations match the experimental data well. The model and its ingredients are also used to simulate other property changes to the gap-graded soil which follow different amounts of suffusion, especially the soil’s reduced strength and increased tendency for compression.