Technical Papers
Feb 28, 2024

Applying Network Modeling to Determine Seepage-Induced Forces on Soil Particles

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 150, Issue 5

Abstract

A pore network model (PNM) idealizes the pore space in a soil as voids (network nodes) connected by pore throats (network edges). Along each edge the fluid flow rate is linearly related to the pressure drop by a hydraulic conductance. This study demonstrates the benefit of using a pore network model (PNM) with an appropriate conductance model in coupled particle–fluid simulations that use the discrete-element method (DEM) to simulate the particle phase. PNM simulations and fully resolved finite-volume method computational fluid dynamics (CFD) simulations are used to obtain the fluid–particle interaction force vectors on particles in virtual samples of sand created using DEM simulations. Linearly graded and bidisperse samples are considered. The study assesses the predictive capabilities of existing conductance models considering local flow rates, global permeability, and particle–fluid interaction force magnitude for the packings. A new refined conductance model that is developed upon models available in the literature is also proposed. Taking the fully resolved CFD data as a benchmark, the PNM approach is shown to better capture the heterogeneity in the magnitude of the particle–fluid interaction force acting on particles with a similar size than the coarse-grid CFD-DEM approach for all the samples considered. The orientation of particle–fluid interaction force vectors obtained from the fully resolved CFD is compared with the direction of the force vector predicted by a coarse-grid CFD-DEM and a PNM with the novel conductance model, where the PNM demonstrates a better accuracy. This work enables more realistic and more accurate coupled simulations of phenomena including liquefaction and internal erosion than has hitherto been possible.

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Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

Dr. Tokio Morimoto was funded by the European Union’s Horizon 2020 research and innovation program Marie Skłodowska-Curie grant agreement MATHEGRAM No. 813202. OpenFOAM simulations were conducted on the Research Computing Service facilities at Imperial College London (DOI: 10.14469/hpc/2232).

References

Ahrens, J., B. Geveci, and C. Law. 2005. “Paraview: An end-user tool for large data visualization.” In The visualization handbook, 717. Argonne, IL: Argonne National Laboratory.
Balay, S., et al. 2021. PETSc users manual. Lemont, IL: Argonne National Laboratory.
Balay, S., W. D. Gropp, L. C. McInnes, and B. F. Smith. 1997. “Efficient management of parallelism in object-oriented numerical software libraries.” In Modern software tools for scientific computing, 163–202. Boston: Birkhäuser.
Beetstra, R., M. A. van der Hoef, and J. A. M. Kuipers. 2007. “Drag force of intermediate Reynolds number flow past mono-and bidisperse arrays of spheres.” AIChE J. 53 (2): 489–501. https://doi.org/10.1002/aic.11065.
Bryant, S., and M. Blunt. 1992. “Prediction of relative permeability in simple porous media.” Phys. Rev. A 46 (4): 2004. https://doi.org/10.1103/PhysRevA.46.2004.
Catalano, E., B. Chareyre, and E. Barthélemy. 2014. “Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects.” Int. J. Numer. Anal. Methods Geomech. 38 (1): 51–71. https://doi.org/10.1002/nag.2198.
Chareyre, B., A. Cortis, E. Catalano, and E. Barthélemy. 2012. “Pore-scale modeling of viscous flow and induced forces in dense sphere packings.” Transp. Porous Media 94 (2): 595–615. https://doi.org/10.1007/s11242-012-0057-2.
Che, H., C. O’Sullivan, A. Sufian, and E. R. Smith. 2021. “A novel CFD-DEM coarse-graining method based on the Voronoi tessellation.” Powder Technol. 384 (Apr): 479–493. https://doi.org/10.1016/j.powtec.2021.02.025.
Cundall, P. A., and O. D. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Di Felice, R. 1994. “The voidage function for fluid-particle interaction systems.” Int. J. Multiphase Flow 20 (1): 153–159. https://doi.org/10.1016/0301-9322(94)90011-6.
Edelsbrunner, H., and N. R. Shah. 1996. “Incremental topological flipping works for regular triangulations.” Algorithmica 15 (3): 223–241. https://doi.org/10.1007/BF01975867.
El Shamy, U., and F. Aydin. 2008. “Multiscale modeling of flood-induced piping in river levees.” J. Geotech. Geoenviron. Eng. 134 (9): 1385–1398. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:9(1385).
Ergun, S. 1952. “Fluid flow through packed columns.” Chem. Eng. Prog. 48 (Sep): 89–94.
Hutabarat, D., and J. D. Bray. 2021. “Effective stress analysis of liquefiable sites to estimate the severity of sediment ejecta.” J. Geotech. Geoenviron. Eng. 147 (5): 04021024. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002503.
Kawano, K., T. Shire, and C. O’Sullivan. 2018. “Coupled fluid-particle simulations of the initiation of suffusion.” Soils Found. 58 (4): 972–985. https://doi.org/10.1016/j.sandf.2018.05.008.
Knight, C. 2019. “Fluid flow and drag in polydisperse granular materials subject to laminar seepage flow.” Ph.D. thesis, Dept. of Physics, Imperial College London.
Knight, C. 2021. “Mesh-sphere-packing.” Accessed May 14, 2021. https://github.com/chrisk314/mesh-sphere-packing.
Knight, C., C. O’Sullivan, B. van Wachem, and D. Dini. 2020. “Computing drag and interactions between fluid and polydisperse particles in saturated granular materials.” Comput. Geotech. 117 (Aug): 103210. https://doi.org/10.1016/j.compgeo.2019.103210.
Kress, J., T. S. Yun, G. A. Narsilio, T. M. Evans, and D. S. Lee. 2012. “Evaluation of hydraulic conductivity in 3D random and heterogeneous particulate materials using network model.” Comput. Geotech. 40 (May): 45–52. https://doi.org/10.1016/j.compgeo.2011.09.007.
Ladd, A. J. 1994a. “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation.” J. Fluid Mech. 271 (Apr): 285–309. https://doi.org/10.1017/S0022112082000627.
Ladd, A. J. 1994b. “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results.” J. Fluid Mech. 271 (Jul): 311–339. https://doi.org/10.1017/S0022112094001783.
Lam, C., and S. A. Jefferis. 2018. Polymer support fluids in civil engineering. London: ICE Publishing.
Mason, G., and N. R. Morrow. 1991. “Capillary behavior of a perfectly wetting liquid in irregular triangular tubes.” J. Colloid Interface Sci. 141 (1): 262–274. https://doi.org/10.1016/0021-9797(91)90321-X.
Morimoto, T. 2023. “LAMMPS with heat pipe network model and pore network model.” Zenodo. https://doi.org/10.5281/zenodo.7817369.
Morimoto, T., B. Zhao, D. M. Taborda, and C. O’Sullivan. 2022. “Critical appraisal of pore network models to simulate fluid flow through assemblies of spherical particles.” Comput. Geotech. 150 (Aug): 104900. https://doi.org/10.1016/j.compgeo.2022.104900.
Mostaghimi, P., M. J. Blunt, and B. Bijeljic. 2013. “Computations of absolute permeability on micro-CT images.” Math. Geosci. 45 (1): 103–125. https://doi.org/10.1007/s11004-012-9431-4.
Rong, L. W., K. J. Dong, and A. B. Yu. 2013. “Lattice-Boltzmann simulation of fluid flow through packed beds of uniform spheres: Effect of porosity.” Chem. Eng. Sci. 99 (Aug): 44–58. https://doi.org/10.1016/j.ces.2013.05.036.
Rong, L. W., K. J. Dong, and A. B. Yu. 2020. “Lattice-Boltzmann computation of hydraulic pore-to-pore conductance in packed beds of uniform spheres.” Chem. Eng. Sci. 224 (Feb): 115798. https://doi.org/10.1016/j.ces.2020.115798.
Sanvitale, N., B. D. Zhao, E. T. Bowman, and C. O’Sullivan. 2023. “Particle-scale observation of seepage flow in granular soils using PIV and CFD.” Géotechnique 73 (1): 71–88. https://doi.org/10.1680/jgeot.20.P.432.
Sari, H., B. Chareyre, E. Catalano, P. Philippe, and E. Vincens. 2011. “Investigation of internal erosion processes using a coupled dem-fluid method.” In Proc., 2nd Int. Conf. on Particle-Based Methods: Fundamentals and Applications, 820–830. Barcelona, Spain: Springer.
Sarkar, S., M. A. van der Hoef, and J. A. M. Kuipers. 2009. “Fluid–particle interaction from lattice Boltzmann simulations for flow through polydisperse random arrays of spheres.” Chem. Eng. Sci. 64 (11): 2683–2691. https://doi.org/10.1016/j.ces.2009.02.045.
Si, H. 2015. “TetGen, a Delaunay-based quality tetrahedral mesh generator.” ACM Trans. Math. Software 41 (2): 1–36. https://doi.org/10.1145/2629697.
Skempton, A. W., and J. M. Brogan. 1994. “Experiments on piping in sandy gravels.” Géotechnique 44 (3): 449–460. https://doi.org/10.1680/geot.1994.44.3.449.
Šmilauer, V., et al. 2015. “Yade documentation.” Preprint, submitted January 2, 2023. http://arxiv.org/abs/2301.00611.
Sufian, A., C. Knight, C. O’Sullivan, B. van Wachem, and D. Dini. 2019. “Ability of a pore network model to predict fluid flow and drag in saturated granular materials.” Comput. Geotech. 110 (Aug): 344–366. https://doi.org/10.1016/j.compgeo.2019.02.007.
Tang, Y., E. A. J. F. Peters, J. A. M. Kuipers, S. H. L. Kriebitzsch, and M. A. van der Hoef. 2015. “A new drag correlation from fully resolved simulations of flow past monodisperse static arrays of spheres.” AIChE J. 61 (2): 688–698. https://doi.org/10.1002/aic.14645.
Tenneti, S., R. Garg, and S. Subramaniam. 2011. “Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres.” Int. J. Multiphase Flow 37 (9): 1072–1092. https://doi.org/10.1016/j.ijmultiphaseflow.2011.05.010.
Tong, A. T., E. Catalano, and B. Chareyre. 2012. “Pore-scale flow simulations: Model predictions compared with experiments on bi-dispersed granular assemblies.” Oil Gas Sci. Technol.–Revue d’IFP Energies Ouvelles 67 (5): 743–752. https://doi.org/10.2516/ogst/2012032.
Tsuji, Y., T. Kawaguchi, and T. Tanaka. 1993. “Discrete particle simulation of two-dimensional fluidized bed.” Powder Technol. 77 (1): 79–87. https://doi.org/10.1016/0032-5910(93)85010-7.
Uhlmann, M. 2005. “An immersed boundary method with direct forcing for the simulation of particulate flows.” J. Comput. Phys. 209 (2): 448–476. https://doi.org/10.1016/j.jcp.2005.03.017.
van der Hoef, M. A., R. Beetstra, and J. A. M. Kuipers. 2005. “Lattice-Boltzmann simulations of low-Reynolds-number flow past mono-and bidisperse arrays of spheres: Results for the permeability and drag force.” J. Fluid Mech. 528 (Sep): 233–254. https://doi.org/10.1017/S0022112004003295.
Van Oosterom, A., and J. Strackee. 1983. “The solid angle of a plane triangle.” IEEE Trans. Biomed. Eng. BME-30 (2): 125–126. https://doi.org/10.1109/TBME.1983.325207.
Wautier, A., S. Bonelli, and F. Nicot. 2017. “Scale separation between grain detachment and grain transport in granular media subjected to an internal flow.” Granular Matter 19 (2): 1–15. https://doi.org/10.1007/s10035-017-0706-9.
Weller, H. G., G. Tabor, H. Jasak, and C. Fureby. 1998. “A tensorial approach to computational continuum mechanics using object-oriented techniques.” Comput. Phys. 12 (6): 620–631. https://doi.org/10.1063/1.168744.
Wu, Y., Q. Hou, Z. Qi, and A. Yu. 2021. “Particle–pore scale modeling of particle–fluid flows.” Chem. Eng. Sci. 235 (Mar): 116500. https://doi.org/10.1016/j.ces.2021.116500.
Wu, Y., Q. Hou, and A. Yu. 2019. “Pore-scale study of fluid flow and drag force in randomly packed beds of different porosities.” Ind. Eng. Chem. Res. 58 (12): 5041–5053. https://doi.org/10.1021/acs.iecr.8b06418.
Xu, B. H., and A. B. Yu. 1997. “Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics.” Chem. Eng. Sci. 52 (16): 2785–2809. https://doi.org/10.1016/S0009-2509(97)00081-X.
Yang, Z., and R. Juanes. 2018. “Two sides of a fault: Grain-scale analysis of pore pressure control on fault slip.” Phys. Rev. E 97 (2): 022906. https://doi.org/10.1103/PhysRevE.97.022906.
Zeghal, M., and U. El Shamy. 2004. “A continuum-discrete hydromechanical analysis of granular deposit liquefaction.” Int. J. Numer. Anal. Methods Geomech. 28 (14): 1361–1383. https://doi.org/10.1002/nag.390.
Zhao, B., and C. O’Sullivan. 2022. “Stokes flow through periodic arrays of spheres.” Powder Technol. 395 (4): 133–148. https://doi.org/10.1016/j.powtec.2021.09.022.
Zick, A. A., and G. M. Homsy. 1982. “Stokes flow through periodic arrays of spheres.” J. Fluid Mech. 115 (1): 13–26. https://doi.org/10.1017/S0022112082000627.

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Go to Journal of Geotechnical and Geoenvironmental Engineering
Journal of Geotechnical and Geoenvironmental Engineering
Volume 150Issue 5May 2024

History

Received: Apr 12, 2023
Accepted: Dec 12, 2023
Published online: Feb 28, 2024
Published in print: May 1, 2024
Discussion open until: Jul 28, 2024

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Assistant Professor, Dept. of Civil Engineering, Univ. of Tokyo, Tokyo 113-8656, Japan; formerly, Ph.D. Student, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK (corresponding author). ORCID: https://orcid.org/0000-0002-8524-9766. Email: [email protected]
Catherine O’Sullivan, M.ASCE https://orcid.org/0000-0002-0935-1910
Professor, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK. ORCID: https://orcid.org/0000-0002-0935-1910
Reader, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK. ORCID: https://orcid.org/0000-0001-5391-2087

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