The Concept of Effective Stress in Unsaturated Soils - Multiscale Geomechanics: From Soil to Engineering Projects - page 155

with

S : Saturation in gas (air + water vapor) at pressure p g

S : Saturation in liquid water at pressure p l

S =− 1 S

g l

p = p − p

= capillary pressure

g

U is a function derived from the wetting curve and by taking into account the
strain of the skeleton. Following an energy approach, Coussy and Dangla [COU 02]
showed that the effective properties derived from the analysis at the microscopic
scale could be combined to the relations deduced from thermodynamics to interpret
the effects of the pore pressure and the scale effects. This approach leads to the same
expression of π:

π = Sp + Sp − UST

[6.8]

gg ll l

where

SU l , is the free energy stored in the interfaces (solid-liquid; solid-gas and
liquid-gas) reported to the unit volume of porous space n 0 d Ω in which these
interfaces are physically located ( n 0 : initial porosity; d Ω: infinitesimal volume
element).

T

Dangla [DAN 02] extended this energy approach to the study of elastoplasticity
in unsaturated soils. By idealizing the capillary pressure - degree of saturation
relation and decomposing the degree of saturation into a reversible part and a
non-reversible part, he obtained a definition of capillary cohesion as

() () C = p − π t g φ = p S S U + S t g φ

[6.9]

cap g c l l l

with

p : gas pressure

π : equivalent pore pressure
φ : internal friction angle, assumed independent from capillary pressure