Solution of internal erosion equations by asymptotic expansion
1 Laboratory MAS, Faculty of Sciences, Tetouan, Morocco
2 High Polytechnic School of Algeciras, University of Cadiz, Spain
3 Laboratory LTDS, University of Lyon, Saint-Etienne, France
One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.
Key words: Porous media / internal erosion / Darcy law / consolidation / asymptotic expansion
© Owned by the authors, published by EDP Sciences, 2012