Modelling of internal erosion based on mixture theory: General framework and a case study of soil suffusion

Abstract

Summary A general thermo‐hydro‐mechanical framework for the modelling of internal erosion is proposed based on the theory of mixtures applied to two‐phase porous media. The erodible soil is partitioned in two phases: one solid phase and one fluid phase. The solid phase is composed of nonerodible grains and erodible particles. The fluid phase is composed of water and fluidized particles. Within the fluid phase, species diffuse. Across phases, species transfer. The modelling of internal erosion is contributed directly by mass transfer from the solid phase towards the fluid phase. The constitutive relations governing the thermomechanical behaviour, generalised diffusion, and transfer are structured by the dissipation inequality. The particular case of soil suffusion is investigated with a focus on constitutive laws. A new constitutive law for suffusion is constructed based on thermodynamic conditions and experimental investigations. This erosion law is linearly related to the power of seepage flow and to the erosion resistance index. Owing to its simplicity, this law tackles the overall trend of the suffusion process and permits the formulation of an analytical solution. This new model is then applied to simulate laboratory experiments, by both analytical and numerical methods. The comparison shows that the newly developed model, which is theoretically consistent, can reproduce correctly the overall trend of the cumulated eroded mass when the permeability evolution is small. In addition, the results are provided for four different materials, two different specimen sizes, and various hydraulic loading paths to demonstrate the applicability of the new proposed law.

Analysis of volumetric internal erosion in cohesionless soils: Model, experiments and simulations

“…To describe the suffusive behaviour of a porous medium, the mass exchange term needs to be formulated. Considerations based on the thermodynamics of irreversible processes can be found in several references 5,18,33,47 . The committed position of this work is to favour relationships that use measurable material parameters and that take into account experimentally‐based observations.…”

“…Throughout, the overhead bar will refer to a volumetric quantity with respect to the initial volume V 0 . The volumetric flow power is computed from the fluid flow and the flow head gradient, 5 …”

“…Discrete approaches are key methods to understand better the physics of this complex coupled process 15,34,39,43 ; yet they are still restricted by a relatively low number of particles with respect to that of laboratory specimens or geotechnical structures. On the other hand, continuous models use relationships and averaged variables dedicated to the scale of a representative elementary volume 3,5,8,27,28,38,41,44,47 . Most of these studies describe internal erosion by a mass transfer law.…”

“…Some of these laws describe the detachment and transport of finer soil particles from a porous medium towards an open exit such as a borehole or a cavity, that is, the detached particles are not concerned by a possible self‐filtration. In fact, few models or relationships are dedicated to the simultaneous detachment, transport and self‐filtration that cannot be experimentally distinguished, 5,19,35,45,47 and fewer are concerned by the experimental measurement of the averaged parameters 5,19,35 . In contrast to other works which lack a clear chain of validation from laboratory specimens, physical models and full‐sale structures, 45,47 the present work is based on experimental observations and data to fill the gap between laboratory testing and field applications.…”