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Mechanical Equilibrium in Externally Loaded Unsaturated Granular Similar Media¹

ABSTRACT

The physics of soil deformation under applied external loads is still very poorly understood. This is especially true in the case of unsaturated soils, where very complex internal force systems arise as a result of applied loads, stresses in the pore fluid phases, and surface tension forces in the air-water interface. The present paper attempts a theoretical description of these forces, for the relatively simple case of nonswelling cohesionless granular soils in static equilibrium. The analysis concentrates on systems which are similar according to the rules defined by Miller and Miller (1956) in their theory of capillary flow phenomena in granular media. Applied loads, gravity, and stresses in the pore fluid phases are analyzed in terms of their effects on the interparticle contact forces which determine soil behavior. For isotropic similar media under similar applied loads, interparticle contact forces can be approximated as linear combinations of the scalar groups (-µ_a) ²₁, g³₁ and ₁, where is the mean applied stress, µ_a is the pore-air pressure, is particle density, g is the gravitational constant, is the surface tension of the air-water interface, and ₁ is the microscopic characteristic length. The coefficients of these groups are dimensionless vector arrays (each vector corresponding to a particular interparticle contact point) which depend on the geometry of the soil-air-water system, but are independent of its characteristic length when gravitational effects on pore-water pressure can be neglected relative to surface tension effects. The relationship of the theory to continuum mechanics and probabilistic approaches to force transmission in soils is briefly discussed.

¹ Contribution from the Dep. of Agronomy, Cornell Univ., Ithaca, NY 14853. Supported in part by Hatch Project no. 405.

² Formerly Assistant Professor, Dep. of Agronomy, Cornell Univ., Ithaca NY. Currently Associate Professor, Dep. of Agronomy and Soils, Univ. of Puerto Rico, Mayaguez, Puerto Rico.

Received for publication December 20, 1985.