Multiphase LBM-DEM Coupling for Unsaturated Granular Media

  • Younes, Nabil (University of Calgary, Calgary)
  • Wan, Richard (University of Calgary, Calgary)
  • Millet, Olivier (LaSIE, University of La Rochelle, La Rochelle)
  • Wautier, Antoine (INRAE, Aix-en-Provence)
  • Nicot, François (University of Savoie Mont Blanc, Chambéry)

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The hydraulic and mechanical properties of unsaturated granular media as to how they relate to complex air, liquid, and solid grain interactions in a three-phase system is an important question in geomechanics. The difficulty lies in the crossing of the various unsaturated regimes in a seamless manner, whereas several studies have focussed exclusively on the pendular regime [1 – 4]. In such a particular case, isolated capillary bridges found between pairs of grains can be considered as point-wise capillary forces at grain contacts with the air phase being continuous. Extending into the two other regimes, namely the funicular and capillary regimes where capillary bridges merge, this approach is unfortunately no longer valid. To simulate partially saturated media over a large range of degrees of saturation, we thus propose to couple a phase-field-based Lattice Boltzmann Method (LBM) model with another one based on the Discrete Element Method (DEM). The LBM model lends itself well to handling the complex formation and coalescence of capillary bridges within the system [5], whereas DEM [6] readily computes grain kinematics following Newton’s Second Law of motion. Combining these two methods eventually gives rise to a numerical tool that accounts for the coupled grain-fluid dynamics as the topology of capillary bridges and air clusters continually evolve. Using this coupling, we capture the so-called Soil Water Characteristic Curve (SWCC) which describes the fundamental relationship between matric suction and water saturation. This curve has important practical applications such as the determination of shear strength and permeability of unsaturated soils. Capillarity, as an apparent cohesion conferred to the unsaturated medium, is further investigated by evaluating the capillary stress tensor σ^cap for different degrees of water saturation. The proposed LBM-DEM coupled model provides a viable numerical framework within which one can explore pore-scale phenomena governed by grain connectivity, liquid distribution, surface tension, contact angle, and pore size distribution in unsaturated granular media.