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Hierarchical multiscale numerical modelling of internal erosion with discrete and finite elements

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Abstract

This paper presents a coupled finite and discrete-element model (FEM and DEM) to simulate internal erosion. The model is based on ICY, an interface between COMSOL, an FEM engine, and YADE, a DEM code. With this model, smaller DEM subdomains are generated to simulate particle displacements at the grain scale. Particles in these small subdomains are subjected to buoyancy, gravity, drag and contact forces for short time steps (0.1 s). The DEM subdomains provide the macroscale (continuum) model with a particle flux distribution. Through a mass conservation equation, the flux distribution allows changes in porosity, hydraulic conductivity and hydraulic gradient to be evaluated for the same time steps at a larger, continuum scale. The updated hydraulic gradients from the continuum model provide the DEM subdomains with updated hydrodynamic forces based on a coarse-grid method. The number of particles in the DEM subdomains is also updated based on the new porosity distribution. The hierarchical multiscale model (HMM) was validated with the simulation of suffusion. Results for the proposed HMM algorithm are consistent with results based on a DEM model incorporating the full sample and simulation duration. The proposed HMM algorithm could enable the modelling of internal erosion for soil volumes that are too large to be modelled with a single DEM subdomain.

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Acknowledgements

The authors gratefully acknowledge the support of Hydro-Québec and NSERC for this project and the helpful comments of two reviewers.

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Authors and Affiliations

  1. Laboratory for Geotechnical and Geoenvironmental Engineering (LG2), École de technologie supérieure, 1100 Notre-Dame Ouest, Montreal, QC, H3C 1K3, Canada

    Pouyan Pirnia, François Duhaime, Yannic Ethier & Jean-Sébastien Dubé

Authors
  1. Pouyan Pirnia
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  2. François Duhaime
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  3. Yannic Ethier
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  4. Jean-Sébastien Dubé
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Contributions

Pouyan Pirnia developed the theory and programmed the examples. He wrote the paper. François Duhaime had the original idea of modelling internal erosion with a multiscale model. He supervised the programming of the interface and the examples. He also revised and improved the manuscript. Yannic Ethier supervised the project and edited the manuscript. Jean-Sébastien Dubé supervised the project and edited the manuscript.

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Correspondence to Pouyan Pirnia.

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Pirnia, P., Duhaime, F., Ethier, Y. et al. Hierarchical multiscale numerical modelling of internal erosion with discrete and finite elements. Acta Geotech. 15, 2877–2889 (2020). https://doi.org/10.1007/s11440-020-01009-4

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  • DOI: https://doi.org/10.1007/s11440-020-01009-4

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