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Numerical estimation of the permeability of granular soils using the DEM and LBM or FFT-based fluid computation method

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Abstract

Numerical packings of spheres with uniform grain size distribution and maximum to minimum diameter ratio up to 15 are generated using the Discrete Element Method (DEM). Two numerical methods are used to compute their permeability by homogenization: the Lattice Boltzmann Method (LBM) and a Fast Fourier Transform (FFT) based method. The results given by both methods are shown to be consistent with semi-analytical and experimental results. For an identical discretization grid, the FFT method has the lowest memory and computational time requirements. The LBM is more accurate for coarse to moderately fine discretizations, while the FFT method converges linearly with the voxel size h with a relative discretization error below 1.5 times \(h/D_{25}\), where \(D_{25}\) is the 25% passing by mass grain diameter. The issue of the variability of the permeability computed on finite sized samples is determined either directly by many realizations of similar random samples or indirectly by a faster filtering method on a single sample. Both methods yield similar results and indicate that a Representative Volume Element (RVE) size greater than 7\(D_{40}\) guarantees a variability of permeability below 5%.

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Notes

  1. \(\mu = \rho \nu\) where \(\rho\) is the fluid density and \(\nu\) its kinematic viscosity.

  2. In this section, as opposed to Sect. 2, the microscale denotes the molecular scale, the macroscale denotes the scale at which the fluid is homogeneous (which is the microscale of Sect. 2) and the mesoscale denotes the scale of a collection of molecules.

  3. The bold letter \({\varvec{f}}\) denotes a body force in this section, and must not be confused with the letter f which denotes the distribution function in the LBM method.

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Acknowledgements

This work was partly funded by the French National Research Agency under grant ANR-21-CE22-0005-01.

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  1. Nantes Université, École Centrale Nantes, CNRS, GeM, UMR 6183, 44600, Saint-Nazaire, France

    Ngoc Son Nguyen & François Bignonnet

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  1. Ngoc Son Nguyen
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Nguyen, N.S., Bignonnet, F. Numerical estimation of the permeability of granular soils using the DEM and LBM or FFT-based fluid computation method. Granular Matter 25, 53 (2023). https://doi.org/10.1007/s10035-023-01330-1

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