Finite and discrete element modelling of internal erosion in water retention structures

Internal erosion is a process by which particles from a soil mass are transported due to an internal fluid flow. This phenomenon is considered as a serious threat to earthen structures. Internal erosion is the main cause of damage or failure in the body or foundation of embankment dams. Therefore, it is necessary to have an accurate knowledge of fluid-particle interactions in saturated soils during design and operation. The hydrodynamic behaviour of porous media in geotechnical engineering is typically modelled using continuum methods such as the finite element method (FEM). It has become increasingly common to combine the discrete element method (DEM) with continuum methods such as the FEM to provide microscopic insights into the behaviour of granular materials and fluid–solid interactions. This Ph.D. thesis aims to develop a hierarchical FEM-DEM algorithm to analyze the internal erosion process in large scale earthen structures. To achieve this goal, we (i) programmed a versatile interface between two FEM and DEM codes, (ii) implemented a coarse-grid method (CGM) for the coupled FEM-DEM model to minimize the computations associated with drag force calculation, (iii) developed a multiscale algorithm for the interface to limit the number of discrete particles involved in the simulation, (iv) assessed the accuracy of drag force derived from CGM, and (v) trained an Artificial Neural Network (ANN) to improve the prediction of the drag force on particles. The development of multimethod or hybrid models combining continuum analyses and discrete elements is a promising research avenue to combine the advantages associated with both modelling scales. This thesis first introduces ICY, an interface between COMSOL Multiphysics (commercial finite-element engine) and YADE (open-source discrete-element code). Through a series of JAVA classes, the interface combines DEM modelling at the particle scale with large scale modelling with the finite element method. ICY was verified with a simple example based on Stokes’ law. A comparison of results for the coupled model and the analytical solution shows that the interface and its algorithm work properly. The thesis also presents an application example for the interface. The interface used CGM drag force to model an internal erosion test in a permeameter. The number of particles that can be included in the DEM simulation of ICY is limited, thus restricting the volume of soil that can be modelled. The second part of the thesis proposes a multimethod hierarchical approach based on ICY to model the coupled hydro-mechanical behaviour for saturated granular soils. A hierarchical algorithm was specifically developed to limit the number of particles in the DEM simulations and to eventually allow the modelling of internal erosion for large structures. The number of discrete bodies in the simulations was restricted through employing discontinuous subdomains along the sample. This avoids generating the full sample as a DEM model. Particles in these small subdomains were subjected to buoyancy, gravity, drag force and contact forces for small time steps. The small subdomains provide the continuum model with particle flux. The FEM model solves a particle conservation equation to evaluate porosity changes for longer time steps. The multimethod framework was verified by simulating a numerical internal erosion test. The fluid motion in geotechnical applications is typically solved using CGM. With these methods, an average form of the Navier–Stokes equations is solved. The total drag force derived from CGM can be applied to the particles proportionally to their volume (CGM-V) or surface (CGM-S). However, there is some uncertainty regarding the application of the CGM drag models for polydispersed particle. The accuracy of CGM has not been systematically investigated through comparing CGM results with more precise results obtained from solving the Navier-Stokes equations at the pore scale. The last part of this research investigates the accuracy of CGM-V and CGM-S drag forces in comparison with the pore-scale values obtained by FEM. COMSOL Multiphysics was used to simulate the fluid flow in three unit cells with different porosity values (0.477, 0.319 and 0.259). The unit cell involved a monosize skeleton of large particles with fixed positions and a smaller particle with variable sizes and positions. The results showed that the CGM-V and CGM-S could not predict precisely the drag force on the small particle. An ANN was trained to predict the drag force on the smaller particle. A very good correlation was found between the ANN output and the FEM results. The ANN could thus provide drag force values with accuracy similar to that obtained using flow simulations at the pore scale, but with computational resources that are comparable to CGM. This thesis contributes to the literature by improving our understanding of hybrid DEM-continuum methods and drag force computations in DEM simulations. It provides guidelines to researchers and developers who try to model internal erosion in real scale soil systems