Analytical solution of coupled soil erosion and consolidation equations by asymptotic expansion approach

In this work, one-dimensional approximation of internal erosion taking place in a soil made from sand and clay mixture was considered. The clay phase that is susceptible to experience erosion under water flow discharge was assumed to be small. A new erosion law fixing the initiation threshold of erosion and integrating the effect of soil consolidation on internal erosion was proposed. Conversely, the effect of erosion on elastic soil deformation was also integrated through damage mechanics concepts. Asymptotic expansion of the coupled equations in terms of a perturbation parameter linked to the total amount of internal erosion that is likely to occur has been performed. This has enabled to view the internal erosion phenomenon occurring inside the soil as a perturbation affecting the classical soil consolidation equation, and further to evaluate the critical discharge gradient for which internal erosion starts. Equations at order zero that are provided by the asymptotic expansion were exactly integrated while an adequate finite difference scheme was introduced to solve the equations at order one. A parametric study was conducted after that in order to assess effects of the main factors on internal erosion and soil deformation.