Research Spotlight: Hydro-mechanical coupling in Yade-DEM

Hydro-mechanical coupling in Yade-DEM

by Thomas Sweijen¹ and Bruno Chareyre²

1 Utrecht University, Environmental Hydrogeology group, the Netherlands t.sweijen @uu.nl
2 Université Grenoble Alpes, CNRS, Grenoble INP, 3SR lab., France bruno.chareyre@grenoble-inp.fr

Yade is an extensible open-source framework for discrete numerical models, focused on the Discrete Element Method (DEM) – a Lagrangian method for simulating granular media at the particle scale. It enables mechanical simulations of porous materials at the particle scale, possibly coupled with multi-phase processes occurring inside the pore-space, such as poromechanical coupling, fracturing, saturated flow, capillarity phenomena, unsaturated flow. The environment of Yade allows for lower-level (C++) and higher-level (python) tailoring of the code to specific problems, making it a versatile code for many academic and industrial interests. Most parts of the code are parallelized in the shared memory paradigm, some modules also support execution in distributed memory environments (MPI) or on GPU.

The code is accompanied by extensive documentation and a forum, which aims to assist users and developers. Recently, Yade has been extended to include various options for hydromechanical coupling. In what follows, we would like to introduce various highlights of available hydromechanical couplings and examples. For more detailed information and to download Yade, please visit https://yade-dem.org.

Fig. 1. Regular triangulation is used to subdivide the pore space into tetrahedra which are referred to as a pore unit. Based on these pore units, flow computations and capillarity phenomena can be computed. A) a pore unit that is enclosed by four particles. B) a pore unit C) An inscribed sphere in a pore unit. (figure from Sweijen et al., 2016)

One-phase flow

Pore-Finite Volume Method: In order to simulate micro-hydromechanical effects in granular materials, the DEM is combined with a pore-scale finite volume (PFV) discretization of the pore fluid flow (Chareyre et al. 2012). Dedicated solvers have been developed for compressible and strictly incompressible viscous flow, respectively. In this approach the pore space is discretized into tetrahedra (Fig. 1) using the regular triangulation algorithms of the CGAL library (Clément et al. 2018). The governing equations at this scale bare similarities with the classical equations of poromechanics. This coupling allows for efficient computations of hydromechanical processes such as consolidation in soils, liquefaction/fluidization (Movie 1), hydrofracturing (Figs. 2 and 3).

Movie 1: fluidization of a granular layer by localized injection (3D coupled DEM-PFV). Video available at: https://www.youtube.com/watch?v=gH585XaQEcY

Fig. 2. Simulated sequences of crack propagation by fluid injection, for different orientations of the initial cracks relative to in situ principal stresses (Papachristos et al. 2017)

Fig. 3. Analysis of micromechanical crack events and pore pressure (Caulk 2017).

Averaged Euler-Lagrange Coupling: An alternative of the above for turbulent flow is based on a mesoscale averaging of the fluid problem (Maurin et al. 2015). It is particularly adapted to bedload and possibly other kinds of flow on inclines. Lubrication and Grain/Fiber Suspensions: The properties of flowing suspensions of particles can be approached by adding relevant lubrication terms on the top of the PFV coupling (Marzougui et al. 2015). Yet another coupling was achieved by Kunhappan et al. (2017) for turbulent fiber suspensions based on the immersed boundary method (Movie 2).

Movie 2: A fiber suspension flowing in a pipe (see Kunhappan et al. 2017). Video available at: https://youtu.be/JqQ0RnLHmhE

Capillarity and two-phase flow

Pendular Regime: In partial saturation the capillary effects can greatly contribute to the mechanical properties of porous materials. When the wetting phase is present in a small amount, dominant effects can be captured by considering pendular bridges between the solid grains. A dedicated module of Yade makes the introduction of pendular bridges in DEM easy. It has been used in a number of previous researches on partially saturated soils.

Across Regimes: To tackle more general situations – e.g. to construct water retention curves (SWRC) beyond the pendular regime – a more advanced capillarity module inspired by pore-network approaches (but not exactly equivalent) can be used. The effect of porosity, particle size distribution and loading history on the SWRC can be investigated (Yuan et al., 2016; Sweijen et al., 2016) with ab-initio simulations, as well as the coupling with deformation of the solid phase (Yuan et al., 2017).

Fig. 4. Distribution of fluid phases during a simulated drainage (dark blue is the wetting phase), after Yuan et al. (2016).

Dynamic flow: Recently, a module for dynamic unsaturated flow has been included based on various pore-network concepts. This module is based on the pore-unit assembly method (Sweijen et al. 2017) and is capable to simulate flow during deformation of a particle packing. Toward multiscale models:Some of the current developments aim at embedding a lattice-boltzman solver (Palabos) in the network construction to determine, from simulated subdomains, local parameters such as entry capillary pressure of pore throats and hydraulic conductivity (Chareyre et al. 2017).

Movie 3: A pore throat formed by three spherical particles invaded by a non-wetting (yellow) phase – simulation by E.P. Montella (unpublished) using a 2-component Shan-Chen method implemented in Palabos. Video available at: https://www.youtube.com/watch?v=BoB0w_pVghg

Example studies

Application to Super Absorbent Polymer (SAP) particles: To study grain-scale phenomena inside a bed of swelling particles, Yade is employed to simulate a bed of swelling particles. For each particle, a swelling rate is assigned and the particles can soften during swelling. Using this setup, swelling under saturated conditions (Sweijen et al., 2017), swelling under unsaturated conditions, and various capillarity effect are investigated (Sweijen et al., 2016). New insights are achieved that could not be found using continuum-scale simulations or experiments (see Fig. 5).

Fig 5. Illustration of using DEM for upscaling of swelling particles; 1) properties of individual SAP particles are measured in experiments; 2) using the properties of individual particles, a bed of particles can be simulated using DEM; 3) macro-scale quantities can be extracted from DEM, in this case, the height of a particle bed (solid line) vs. experiments (black dots).

Open source softwares and libraries

https://yade-dem.org
http://www.palabos.org/
https://www.cgal.org/

References

References can be viewed here (download 477 KB).