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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])
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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

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References

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