Multi Scale Modelling of Particle Transport in Soils – TRANSOL

Particle transport in a granular medium presents specific characteristics due to the possible evolution of this medium by addition or pulling out of particles. Phenomena linked to the transport of solid particles can be found in many engineering fields. Such examples include civil and environmental engineering.This project will involve two research teams: a team from the GeM UMR 6183 reinforced by a member of the laboratory of Mathematics Jean Leray UMR 6629, a team from the LTDS UMR 5513 and a team from CEMAGREF. The main objective is to develop a numerical modelling of transport phenomena taking into account the mechanisms of filtration and erosion in granular media. The two teams are already working on this subject by means of discrete numerical analysis for LTDS (one PhD is currently in process) and CEMAGREF and continuous numerical analysis for GeM (one PhD finished, one PhD in process). These two approaches are complementary and, if combined, can provide pertinent solutions to the complex scientific problems linked to these particular fluid flows. In particular, the discrete element method can provide a more precise evaluation of several parameters which appear in the continuous formulation and determined up to now in a phenomenological way.The continuous approach, based on a macroscopic description of the granular medium, presents us with the difficult task of having to establish evolution laws of the granular structure which account for the adding or the elimination of solid particles. The main originality of this project is to propose a multi-scale analysis which should permit a better understanding of the local mechanisms in the fluid-solid interactions, depending on the medium topology. We propose an analysis which takes into account three different scales: a micro scale corresponding to the particles and pores size; a meso scale corresponding to the scale of the Representative Volume Element in which variables characterising the continuum are defined; a macro scale which represents a large domain for which conditions must be specified at the limits of the continuum medium.The project is comprised of three parts.The part concerning the discrete modelling will account for the phenomena at the particle scale. It will allow an accurate description of the internal void distribution and particularly of its topology and the use of this local information to propose a better and more precise modelling of the fluid-particles interaction. The numerical approach is based on Discrete Element Codes (such as PFC3D) for the solid particles and a finite volume method to account for the fluid flow.The continuous modelling will account for the phenomena at the meso and macro scales. In practice, the models of transfer in porous media rarely take into account the phenomenon of mass exchange. Furthermore, if this exchange were considered, the problem of transport would often be simplified. Therefore, the originality of the continuous modelling part of this project is to propose a model which considers transport as a whole, by means of non linear coupled equations, and in addition takes into account filtration or erosion which can occur in the granular medium. The objectives are to integrate in the modelling the results obtained from the experimental part as well as the results from the discrete modelling for defining and identifying the evolution laws of the solid part.The experimental part will be conducted so that we can obtain valuable information at the three scales. The results will allow the modelling approaches (discrete and continuous) to be validated and will also provide the values of the physical parameters used in the proposed models. The product of this research will be the construction of a finite element code allowing us to treat various problems linked to fluid flows in granular media. One of these problems concerns the phenomenon of internal erosion, due to the dragging of the smallest particles of a soil subjected to a water flow. This phenomenon can occur particularly in dykes, earth dams or embankments. A better knowledge achieved through modelling would allow us to improve the design of such earth structures. Another application deals with the reinforcement of soils by injection of fine cement grout in order to improve its mechanical and hydraulic characteristics. The main purpose of modelling is to be able to predict accurately the soil volume affected by the treatment and the parameters which condition grout injection, in order to optimize the process. Analysing and subsequently controlling soil and groundwater pollution that is caused by pollutants in the form of divided solids is a third potential application in the domain of geo-environmental engineering.