Development of a saturation-based Mu(I)-rheology for wet granular materials using discrete element method

Document Type : Article

Authors

School of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155/9567, Iran

Abstract

The discrete element method (DEM) is used to establish a rheological model that relates the apparent viscosity of a granular material to shear rate, normal stress, and water saturation. A theoretical model is developed to determine water distribution and water-induced forces between particles for different saturations. The resulting forces are embedded in a 3D shear cell as a numerical rheometer and a wet specimen is sheared between two walls. A power law rheological model is obtained as a function of inertia number and saturation. It was found that up to a critical saturation, the apparent viscosity increases with saturation and is higher than that of the dry specimen. However, when the saturation exceeds a critical value, the viscosity suddenly drops below that of dry condition. To evaluate the model, the collapse of two-dimensional granular material on a horizontal rigid bed is studied using continuum-based numerical simulation which utilizes the proposed rheological model.

Keywords


References
1. Iverson, R. “Landslide triggering by rain infiltration”. Water Resources Research. 36, pp. 1897-1910 (2000).
2. Iverson, R., George, D. “Modelling landslide liquefaction, mobility bifurcation and the dynamics of the 2014 Oso disaster”. Géotechnique. 66, pp. 175-187 (2016).
3. Coussot, P. Rheometry of pastes, suspensions, and granular materials. Wiley, Hoboken, N.J (2010).
4. Saramito, P., Wachs, A. “Progress in numerical simulation of yield stress fluid flows”. Rheologica Acta. 56, pp. 211-230 (2017).
5. De Blasio, F. Introduction to the physics of landslides. Springer (2011).
6. Midi GDR. “On dense granular flows”. The European Physical Journal E, 14, pp. 341-365 (2004).
7. Fall, A., Ovarlez, G., Hautemayou, et al. “Dry granular flows: Rheological measurements of the μ(I)-rheology”. Journal of Rheology. 59, pp. 1065-1080 (2015).
8. Jop, P., Forterre, Y., Pouliquen, O. “A constitutive law for dense granular flows”. Nature. 441, pp. 727-730 (2006).
9. Gesenhues, L., Camata, J., Coutinho, A. “Simulation of a column collapse for dense granular flows”. American Congress on Computational Methods in Engineering (2017).
10. Valette, R., Riber, S., Sardo, L., et al. “Sensitivity to the rheology and geometry of granular collapses by using the μ(I) rheology”. Computers & Fluids. 191, pp. 104260 (2019).
11. Gesenhues, L., Camata, J., Côrtes, A., et al. “Finite element simulation of complex dense granular flows using a well-posed regularization of the μ(I)-rheology”. Computers & Fluids. 188, pp. 102-113 (2019).
12. Cundall, P., Strack, O. “Discussion: A discrete numerical model for granular assemblies”. Géotechnique. 30, pp. 331-336 (1980).
13. Bhateja, A., Khakhar, D. “Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow,” Physical Review Fluids. 3, pp. 062301 (2018).
14. Mandal, S., Khakhar, D. “A study of the rheology and micro-structure of dumbbells in shear geometries,” Physics of Fluids. 30, pp. 013303 (2018).
15. Shi, H., Roy, S., Weinhart, T., et al. “Steady state rheology of homogeneous and inhomogeneous cohesive granular materials”. Granular Matter. 22, pp. 14 (2020).
16. Binaree, TH., Azéma, E., Estrada, N., et al. “Combined effects of contact friction and particle shape on strength properties and microstructure of sheared granular media”. Physical Review E. 102, pp. 022901 (2020).
17. Vo, TT., Nguyen-Thoi, T. “The role of inter-particle friction on rheology and texture of wet granular flows”. The European Physical Journal E. 43, pp. 65 (2020).
18. Scheel, M., Seemann, R., Brinkmann, M., et al. “Morphological clues to wet granular pile stability”. Nature Materials. 7, pp. 189-193 (2008).
19. Willett, C., Adams, M., Johnson, S., et al. “Capillary Bridges between Two Spherical Bodies”. Langmuir. 16, pp. 9396-9405 (2000).
20. Zhao, C., Kruyt, N., Millet, O. “Capillary bridge force between non-perfectly wettable spherical particles: an analytical theory for the pendular regime”. Powder Technology. 339, 827–837 (2018).
21. Kruyt, N., Millet, O. “An analytical theory for the capillary bridge force between spheres”. Journal of Fluid Mechanics. 812, pp. 129–151 (2017).
22. Nguyen, H., Millet, O., Gagneux, G. “On the capillary bridge between spherical particles of unequal size: analytical and experimental approaches”. Continuum Mechanics and Thermodynamics. 31, pp. 225–237 (2019).
23. Zhao, C., Kruyt, N., Millet, O. “Capillary bridges between unequal-sized spherical particles: Rupture distances and capillary forces”. Powder Technology. 346, pp. 462-476 (2019).
24. Schwarze, R., Gladkyy, A., Uhlig, F., et al. “Rheology of weakly wetted granular materials: a comparison of experimental and numerical data”. Granular Matter. 15, pp. 455-465 (2013).
25. Obermayr, M., Vrettos, C., Eberhard, P., et al. “A discrete element model and its experimental validation for the prediction of draft forces in cohesive soil”. Journal of Terramechanics. 53, pp. 93-104 (2014).
26. Dullien, F., El-Sayed, M., Batra, V. “Rate of capillary rise in porous media with nonuniform pores”. Journal of Colloid and Interface Science. 60, pp. 497-506 (1977).
27. Urso, M., Lawrence, C., Adams, M. “Pendular, Funicular, and Capillary Bridges: Results for Two Dimensions”. Journal of Colloid and Interface Science. 220, pp. 42-56 (1999).
28. Seville, J., Wu, C. Particle technology and engineering. Elsevier (2016).
29. Kloss, C., Goniva, C., Hager, A., et al. “Models, algorithms and validation for opensource DEM and CFD-DEM”. Progress in Computational Fluid Dynamics, An International Journal. 12, pp. 140 (2012).
30. Shojaaee, Z., Roux, J., Chevoir, F., et al. “Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region”. Physical Review E. 86, pp. 011301 (2012).
31. da Cruz, F., Emam, S., Prochnow, M., et al. “Rheophysics of dense granular materials: Discrete simulation of plane shear flows”. Physical Review E. 72, pp. 021309 (2005).
32. Iverson, R., Reid, M., Logan, M., et al. “Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment”. Nature Geoscience. 4, pp. 116-121 (2010).
33. Nikooei, M., Manzari, M. “Studying effect of entrainment on dynamics of debris flows using numerical simulation”. Computers & Geosciences. 134, pp. 104337 (2020).
34. Hashemi, M., Fatehi, R., Manzari, M. “A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows”. International Journal of Non-Linear Mechanics. 47, pp. 626-638 (2012).
35. Nguyen, C., Bui, H., Fukagawa, R. “Failure Mechanism of True 2D Granular Flows”. Journal of Chemical Engineering of Japan. 48, pp. 395-402 (2015).