# Internal erosion in embankment dams fluid flow through and deformation of porous media

Sammanfattning: A basic understanding of fluid flow through a porous media facilitates a comprehensive understanding of internal erosion in embankment dams. Hence, it is necessary to reveal the detailed seepage flow, the flow-induced forces acting within the porous media and the fluid flow deformation of the porous media. In order to increase the knowledge of the fluid flow a Computational Fluid Dynamics approach is applied to investigate different flow regimes. The regimes ranges from creeping flow, where a Darcy law formulation is sufficient, via an inertia dominated region, where a non-linear term must be added to the Darcy's law such as the Ergun equation, to the turbulent region, where the full Navier- Stokes equations must be solved including a Reynolds decomposition. Since it is not obvious when these transitions takes place the CFD-simulations are used to calculate the apparent permeability, the Blake-type friction factor and the normal and shear forces for a variety of model geometries. This includes quadratic and hexagonal packing of cylinders as well as spheres. One result is that the Reynolds number, where inertia-effects become significant, varies with the packing and the porosity. For a quadratic arrangement of cylinders this occurs around a Reynolds number about 10 while for a hexagonal arrangement it takes place between 30 and 50 depending on the porosity. Another result is that for quadratic arrangement the turbulent set-up at high Reynolds number gives higher forces than a corresponding laminar set-up regardless of the porosity. For hexagonal packing a turbulent set-up can, however, give lower forces. These ranges, regarding the Reynolds number, have been utilized in order to develop an expression for theoretical limits of the effective diameter and the applied pressure gradient to be applied when designing down-scaled geotechnical experimental setups. Regarding the deformation of the porous media there are several methods that has the potential to model the internal erosion process. One way is a mesh deformation approach where the normal and shear forces acting on the particles generate the motion. This methodology requires that the computational mesh is upgraded in every time-step resulting in rather computational heavy simulations. Another way is to combine CFDsimulations of flow in the vicinity of single particles with Monte-Carlo simulations of a system of a large number of particles by using the fact that the distribution of the stream function follows the known principle of minimal dissipation rate of energy. Main result is that the more compact the system is the larger is the possible relative change of permeability by applying a high flow rate. When applying this technique on a classical geotechnical experimental setup, the No Erosion Filter test, results indicate that the developed model captures the main characteristics of the sought particle transportation, both for a sealing as well as a non-sealing design of the filter and fine combination.

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