Micro-mechanical modelling of unsaturated particle packings

Unsaturated soils consist of three phases: the solid phase (soil grains), the water phase (pore water) and the air phase (pore air). The content of pore water in the soil structure is defined by the degree of saturation. Depending on the degree of saturation different gas-solid-liquid interfaces are formed such as bubbles, liquid bridges or capillary interfaces. That in mind, it becomes obvious that stability, transport phenomena and forces within unsaturated soils highly depend on the degree of saturation. Further, the degree of saturation is a local property at soil grain scale rather than a global property. Within a soil, regions of high saturation can be spatially close to regions of low saturation. In order to describe, model and understand the behaviour of unsaturated soils, it is therefore necessary to understand the physical phenomena at soil grain scale. The proposed research project is concerned with the investigation of micro-hydraulic and micro- mechanical processes in partially saturated granular porous media by means of new modelling approaches and imaging experiments. In these experiments the imaging technique of computed tomography (CT) is used. These experimental techniques deliver detailed information of the behaviour of gas-liquid-solid granular systems. Based on that information numerical models based on Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) will be developed and further refined. The goal is to develop numerical models that are able to predict the behaviour of saturated soils and produce even deeper understanding of the underlying phenomena. In contrast to the visual experimental techniques, the numerical models can provide lots of additional information that is not easily accessible by experiments. For instance forces acting on the gas, liquid and solid phase are calculated at a scale smaller than the granular particles. This is of fundamental importance for understanding and modelling effects such as stability of such soils or other geotechnical questions. Given the wide field of expertise needed for the planned tasks, researchers at DCS Computing GmbH, who will focus on the development of numerical models, have teamed up with the Institute of Geotechnical Engineering and Construction Management at the Hamburg University of Technology.

Goal of the DACH Cooperation project (FWF project number I 5374) between Prof. Grabe (Institute of Geotechnical Engineering and Construction Management at Hamburg University of Technology (TUHH)) and Dr. Christoph Kloss (DCS Computing GmbH) was the investigation of two phase-fluid flow in the pore space of sand packings. Water retention within the pores between sand grains creates capillary forces and substantially alters the overall mechanical properties of the soil. The goal was to develop high-fidelity computational methods to simulate these processes. Experimental investigations were performed as part of the project and generated high-resolution volumetric CT data. These will be used, on the one hand, to validate the developed computational methods and, on the other hand, to create simulation setups that are digital twins of the experiment, for instance by using the same initial particle positions and shapes as observed in the experiments. The first case investigated is the imbibition of a sand column, i.e. water entering an initially dry sand packing from the bottom. This case can be simulated with standard CFD methods for liquid-gas two-phase flows by a body-fitted mesh directly meshing the pore space between the grains. This approach, however, does not easily permit the motion of individual grains. Doing so requires deforming the mesh to the particle motion, an operation which quickly becomes very costly and often generates low-quality meshes giving rise to numerical instabilities. Instead, the Immersed Boundary Method (IBM) was chosen which operates on a static mesh and models the impact of particles on the fluid by a volumetric force term. This method is substantially more stable than the body-fitted mesh approach and permits arbitrary particle motions. For combining the IBM and the Volume-of-Fluid approach chosen to model the liquid-gas interface, it is crucial to correctly handle the propagation of the latter at the surface of immersed objects. A coupled CFD-DEM solver doing so has been implemented and successfully validated. Imbibition cases of decreased domain size compared to the experiments were run with particles directly extracted from the experimental data. The second setup of interest is the triaxial test where an upright cylindrical packing of sand grains is supported by an outside confining pressure and compressed between two plates in axial direction. Depending on the confining pressure, the sample will fail to support the vertical load beyond a certain threshold that depends on the grain sizes, packing density and various other parameters. As for the previous case, volumetric measurement data from experiments is available and simulations are set up using the particle packing as extracted from the measurements. Simulations in dry conditions were performed by coupling the particle motion with a dedicated solver for the membrane deformation. Their results agree very well with experiments.