Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T05:55:18.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Homogenization Theory Applied to Unsaturated Solid-Liquid Mixture

Published online by Cambridge University Press:  08 May 2012

K.-F. Liu ,
Y.-H. Wu  and
Y.-C. Hsu
K.-F. Liu*
Affiliation:
Department of Civil engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Y.-H. Wu
Affiliation:
Department of Civil engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Y.-C. Hsu
Affiliation:
Department of Civil engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Corresponding author ([email protected])
Get access

Abstract

In this study, we present theoretical derivation of seepage flow in unsaturated and static soil using Homogenization theory. The derivation started in the microscopic scale in the soil. The representative elementary volume (REV) in the soil is set to be one order larger than the scale of characteristic length of pore. Solids in the REV are assumed to be rigid and cohesionless. The liquid velocity in the pore is slow. By no-slip boundary condition on the solid boundary in REV, we could obtain the microscopic flow conditions. Using spatial ensemble average under the microscopic scale, we obtain the relation between water content, pressure head and velocities in macroscopic scale. This macroscopic averaged equation is validated to be equal to Richards' equation.

Keywords

Homogenization theoryUnsaturatedSolid-liquid mixtureRichards' equation
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 2 , June 2012 , pp. 329 - 335
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Ancey, C., “Plasticity and Geophysical Flows: A Review,” Journal of Non-Newtonian Fluid Mechanics, 142, pp. 4–35 (2007).CrossRefGoogle Scholar
2. Iverson, R. M., Reid, M. E. and LaHusen, R. G., “Debris-Flow Mobilization from Landslide,” Annual Review of Earth and Planetary Sciences, 25, pp. 85–138 (1997).Google Scholar
3. Iverson, R. M., “Landslide Triggering by Rain Infiltration,” Water Resources Research, 36, pp. 1897–1910 (2000).Google Scholar
4. Auriault, J.-L., “Heterogenous Medium. is an Equivalent Macroscopic Description Possible?,” International Journal of Engineering Science, 29, pp. 785–795 (1991).CrossRefGoogle Scholar
5. Richards, L. A., “Capillary Conduction of Liquids Through Porous Mediums,” Physics, 1, pp. 318–333 (1931)Google Scholar
6. White, F. M., Viscous Fluid Flow, 3rd Ed., McGraw Hill (2006).Google Scholar
7. Chow, V. T., Maidment, D. R. and Mays, L. W., Applied Hydrology, McGraw-Hill (1998).Google Scholar
8. Mei, C. C. and Auriault, J.-L., “The Effect of Weak Inertia on Flow Through a Porous Medium,” Journal of Fluid Mechanics, 222, pp. 647–663 (1991).Google Scholar
9. Mei, C. C. and Vernescu, B., Homogenization Methods for Multiscale Mechanics, World Scientific (2010).CrossRefGoogle Scholar