Technical Paper
Dec 30, 2015

Pore-Scale Modeling of Fine-Particle Migration in Granular Filters

Publication: International Journal of Geomechanics
Volume 16, Issue 3

Abstract

Fine-particle migration and associated internal erosion are major concerns for dam safety. Granular filters are used to prevent fine-particle migration, and several empirical models have been introduced for the design of these filters. Few computational techniques have tracked particle transport through the filters. This paper presents a three-dimensional transient fully coupled pore-scale model used to study the mechanism of fine-particle migration in granular filters. A pore-scale idealization of the fluid was achieved by using the lattice Boltzmann method, and the solid phase was modeled at a microscale using a discrete element method. The fluid forces applied on the particles were calculated on the basis of the momentum exchange between the fluid and particles. The proposed numerical technique was used to model the migration of base-soil particles through granular filters of different particle sizes. Results of conducted simulations provided the erosion percentages and flow rates during the simulations. The general behavior of the filters agreed with observations in laboratory experiments and with filter-design criteria reported in the literature. The proposed computational framework can be used effectively to model fine-particle migration at a pore scale with minimal assumptions, which would add a new dimension to filter-design problems.

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Acknowledgments

This research was partially supported by the U.S. National Science Foundation, Grant Number CMMI-1000908, and the U.S. Army Corps of Engineers Engineer Research and Development Center, Grant No. W9132V-13-C-0004. This support is gratefully acknowledged.

References

Abdelhamid, Y. (2015). “A universal coupled computational framework for saturated granular materials.” Ph.D. thesis, Southern Methodist Univ., Dallas, TX.
Abdelhamid, Y., and El Shamy, U. (2014). “Pore-scale modeling of surface erosion in a particle bed.” Int. J. Numer. Anal. Methods Geomech., 38(2), 142–166.
Aidun, C. K., Lu, Y., and Ding, E.-J. (1998). “Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation.” J. Fluid Mech., 373, 287–311.
Allen, H. (1900). “XXXI. The motion of a sphere in a viscous fluid.” Philos. Mag., 50(304), 323–338.
Arnold, H. (1911). “LXXIV. Limitations imposed by slip and inertia terms upon Stoke’s law for the motion of spheres through liquids.” Philos. Mag., 22(131), 755–775.
Bhatnagar, P. L., Gross, E. P., and Krook, M. (1954). “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems.” Phys. Rev., 94(3), 511–525.
Bouillard, J. X., Lyczkowski, R. W., and Gidaspow, D. (1989). “Porosity distributions in a fluidized bed with an immersed obstacle.” AlChE J., 35(6), 908–922.
Brauer, H. (1973). “Impuls-, stoff- und wärmetransport durch die grenzfläche kugelförmiger partikeIn.” Chem. Ing. Tech., 45(18), 1099–1103 (in German).
Carman, P. (1937). “Fluid flow through granular beds.” Trans. Inst. Chem. Eng., 15, 150–166.
Cividini, A., Bonomi, S., Vignati, G., and Gioda, G. (2009). “Seepage-induced erosion in granular soil and consequent settlements.” Int. J. Geomech., 187–194.
Cividini, A., and Gioda, G. (2004). “Finite-element approach to the erosion and transport of fine particles in granular soils.” Int. J. Geomech., 191–198.
Cleary, P. W., Sinnott, M., and Morrison, R. (2006). “Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media.” Miner. Eng., 19(15), 1517–1527.
Cook, B. (2001). “A numerical framework for the direct simulation of solid fluid systems.” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Cundall, P., and Strack, O. (1979). “A discrete numerical model for granular assemblies.” Géotechnique, 29(1), 47–65.
Dennis, S. C. R., and Walker, J. D. A. (1971). “Calculation of the steady flow past a sphere at low and moderate Reynolds numbers.” J. Fluid Mech., 48(4), 771–789.
Derksen, J. (2011). “Simulations of granular bed erosion due to laminar shear flow near the critical Shields number.” Phys. Fluids, 113303(23), 1–12.
Edwards, S. (1998). “The equations of stress in a granular material.” Physica A, 249(1), 226–231.
El Shamy, U. (2004). “A coupled continuum-discrete fluid-particle hydromechanical model for granular soil liquefaction.” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY.
El Shamy, U., and Abdelhamid, Y. (2014). “Modeling granular soils liquefaction using coupled lattice Boltzmann method and discrete element method.” Soil Dyn. Earthquake Eng., 67, 119–132.
El Shamy, U., and Aydin, F. (2008). “Multi-scale modeling of flood-induced piping in river levees.” J. Geotech. Geoenviron. Eng., 1385–1398.
Fell, R., Wan, C., Cyganiewicz, J., and Foster, M. (2003). “Time for development of internal erosion and piping in embankment dams.” J. Geotech. Geoenviron. Eng., 307–314.
Feng, Y., Han, K., and Owen, D. (2010). “Combined three-dimensional lattice Boltzmann method and discrete element method for modeling fluid-particle interactions with experimental assessment.” Int. J. Numer. Methods Eng., 81(2), 229–245.
Filippova, O., and Hänel, D. (1997). “Lattice-Boltzmann simulation of gas-particle flow in filters.” Comput. Fluids, 26(7), 697–712.
Ginzburg, I., and D’Humières, D. (2003). “Multireflection boundary conditions for lattice Boltzmann models.” Phys. Rev. E, 68(6), 1–30.
Hadj-Hamou, T., Tavassoli, M., and Sherman, W. (1990). “Laboratory testing of filters and slot sizes for relief wells.” J. Geotech. Eng., 1325–1346.
Han, Y. and Cundall, P. (2013). “LBM-DEM modeling of fluid–solid interaction in porous media.” Int. J. Numer. Anal. Methods Geomech., 37(10), 1391–1407.
Honjo, Y., and Veneziano, D. (1989). “Improved filter criterion for cohesionless soils.” J. Geotech. Eng., 75–94.
Ihme, F., Schmidt-Traub, H., and Brauer, H. (1972). “Theoretische untersuchung über die umströmung und den stoffübergang an kugeIn.” Chem. Ing. Tech., 44(5), 303–313.
Indraratna, B., Dilema, E., and Vafai, F. (1996). “An experimental study of the filtration of a lateritic clay slurry by sand filters.” Proc. ICE-Geotech. Eng., 119(2), 75–83.
Indraratna, B., and Vafai, F. (1997). “Analytical model for particle migration within base soil-filter system.” J. Geotech. Geoenviron. Eng., 100–109.
ITASCA. (2008). PFC3D: Particle flow code in 3 dimensions, version 4.0. Itasca Consulting Group, Minneapolis, MN.
Jenson, V. (1959). “Viscous flow round a sphere at low Reynolds numbers (<40).” Proc. R. Soc. A, 249(1258), 346–366.
Kovács, G. (1981). Seepage hydraulics. Elsevier, Amsterdam, Netherlands.
Ladd, A. (1994a). “Numerical simulations of particulate suspensions via a discretized Boltzmann equation: Part 1. Theoretical foundation.” J. Fluid Mech., 271, 285–309.
Ladd, A. (1994b). “Numerical simulations of particulate suspensions via a discretized Boltzmann equation: Part 2. Numerical results.” J. Fluid Mech., 271, 311–339.
Lafleur, J., Mlynarek, J., and Rollin, A. (1989). “Filtration of broadly graded cohesionless soils.” J. Geotech. Eng., 1747–1768.
Lafleur, J., Montes, P., Alicescu, V., and Phoung, N. (2000). “Laboratory simulations of filtration through dam cores made of broadly graded moraines.” Proc., 3rd Int. Conf.: Geofilters 2000, A. A. Balkema, The Netherlands, 135–144.
Liebster, H. (1927). “Über den widerstand von kugeln.” Ann. Phys., 387(4), 541–562 (in German).
Locke, M., Indraratna, B., and Adikari, G. (2001). “Time-dependent particle transport through granular filters.” J. Geotech. Geoenviron. Eng., 521–529.
Lominé, F., Scholts, L., Sibillè, L., and Poullain, P. (2011). “Modeling of fluid-solid interaction in granular media with coupled lattice Boltzmann/discrete element methods: Application to piping erosion.” Int. J. Numer. Methods Eng., 37(6), 577–596.
Mei, R., Yu, D., Shyy, W., and Luo, L.-S. (2002). “Force evaluation in the lattice Boltzmann method involving curved geometry.” Phys. Rev. E, 65(4), 1–14.
Mohamad, A. (2011). Lattice Boltzmann method: Fundamentals and engineering applications with computer codes. Springer, London.
Nguyen, V., Rujikiatkamjorn, C., and Indraratna, B. (2013). “Analytical solutions for filtration process based on constriction size concept.” J. Geotech. Geoenviron. Eng., 1049–1061.
Patankar, N., Huang, P., Ko, T., and Joseph, D. (2001a). “Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation.” J. Fluid Mech., 438, 67–100.
Patankar, N., Ko, T., Choi, H., and Joseph, D. (2001b). “A correlation for the lift-off of many particles in plane Poiseuille flows of Newtonian fluids.” J. Fluid Mech., 445, 55–76.
Peck, R. (1990). “Interface between core and downstream filter.” Proc., H. Bolton Seed Memorial Symposium, San Francisco, CA, 237–251.
Potapov, A., Hunt, M., and Campbell, C. (2001). “Liquid-solid flows using smoothed particle hydrodynamics and the discrete element method.” Powder Technol., 116, 204–213.
Reboul, N., Vincens, E., and Cambou, B. (2010). “A computational procedure to assess the distribution of constriction sizes for an assembly of spheres.” Comput. Geotech., 37, 195–206.
Reddi, L. N., Lee, I. M., and Bonala, M. V. S. (2000). “Comparison of internal and surface erosion using flow pump tests on a sand-kaolinite mixture.” ASTM Geotech. Test. J., 23(1), 116–122.
Schuler, U. (1996). “Scattering of the composition of soils an aspect for the stability of granular filters.” Proc., Geofilters ’96, J. Lafleur and A. Rollin, eds., Bitech Publications, Montreal, QB, Canada, 21–34.
Sherard, J., and Dunnigan, L. (1989). “Critical filters for impervious soils.” J. Geotech. Eng., 927–947.
Sherard, J., Dunnigan, L., and Talbot, J. (1984a). “Basic properties of sand and gravel filters.” J. Geotech. Eng., 684–700.
Sherard, J., Dunnigan, L., and Talbot, J. (1984b). “Filters for silts and clays.” J. Geotech. Eng., 701–718.
Silveira, A., de Lorena Peixoto, T., and Nogueira, J. (1975). “On void size distribution of granular materials.” Proc., V Pan-American Conf. on Soil Mechanics and Foundation Engineering, 161–176.
Sterpi, D. (2003). “Effects of the erosion and transport of fine particles due to seepage flow.” Int. J. Geomech., 111–122.
Terzaghi, K. (1922). “Der grundbruch an stauwerken und seine verhutung.” Die Wasserkraft, 17, 445–449 (in German).
Tomlinson, S., and Vaid, Y. (2000). “Seepage forces and confining pressure effects on piping erosion.” Can. Geotech. J., 37(1), 1–13.
USACE (United States Army Corps of Engineers). (1953). “Filter experiments and design criteria.” No. 3-360, Waterway Experiment Station, Vicksburg, MS.
Vafai, F. (1996). “Analytical modelling and laboratory studies of particle transport in filter media.” Ph.D. thesis, Univ. of Wollongong, NSW, Australia.
Vaughan, P., and Soares, H. (1982). “Design of filters for clay cores of dams.” J. Geotech. Geoenviron. Eng., 108(1), 17–31.
Wan, C., and Fell, R. (2004). “Investigation of rate of erosion of soils in embankment dams.” J. Geotech. Geoenviron. Eng., 373–380.
White, F. (1974). Viscous fluid flow. McGraw-Hill, New York.
Witt, K. (1993). “Reliability study of granular filters.” Filters in geotechnical and hydraulic engineering, M. H. J. Brauns and U. Schuler, eds., A. A. Balkema, Rotterdam, The Netherlands.
Yu, D., Mei, R., Luo, L., and Shyy, W. (2003). “Viscous flow computations with the method of lattice Boltzmann equation.” Prog. Aerosp. Sci., 39(5), 329–367.
Zak, D. (2010). An introduction to programming with C++, 6th Ed., Cengage Learning, Boston.
Zhu, Y., Fox, P., and Morris, J. (1999). “A pore-scale numerical model for flow through porous media.” Int. J. Numer. Anal. Methods Geomech., 23(9), 881–904.
Zou, Q., and He, X. (1997). “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model.” Phys. Fluids, 9(6), 1591–1598.
Zou, Y., Chen, Q., Chen, X., and Cui, P. (2013). “Discrete numerical modeling of particle transport in granular filters.” Comput. Geotech., 47, 48–56.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 16Issue 3June 2016

History

Received: Jul 24, 2014
Accepted: Jul 23, 2015
Published online: Dec 30, 2015
Discussion open until: May 30, 2016
Published in print: Jun 1, 2016

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Yasser Abdelhamid
Graduate Student, Civil and Environmental Engineering Dept., Southern Methodist Univ., P.O. Box 750340, Dallas, TX 75275.
Usama El Shamy, M.ASCE [email protected]
P.E.
Associate Professor, Civil and Environmental Engineering Dept., Southern Methodist Univ., P.O. Box 750340, Dallas, TX 75275 (corresponding author). E-mail: [email protected]

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