The Concept of Effective Stress in Unsaturated Soils - Multiscale Geomechanics: From Soil to Engineering Projects - page 159

Figure 6.5. Relation between capillary pressure and capillary stress

cap σ is given by the following expression, within the limits of
the calculation of the model (Figure 6.5):

The relation

' ( )

c

2

3 − 8 pR + 9

πγ

lg lg lg c lg

σ = 4 R + [6.12]

cap

2

p

2() KeR c

and

2 πγ 4 πγ

lg lg

σ = =

[6.13]

cap max

K eR Ked () ()

with

γ γ

= 7.5 10 -2 N/m at T = 20°) : water-air surface tension ( lg

lg

diameter of the particle

d 2 = R =

K ( e ): parameter depending on the packing type, given by the expression:

K ( e ) = 0.32 e 2 + 4.06 e + 0.11 [6.14]

At large strains, the representation of the critical state of a granular material in
Mohr's plane shows the existence of an apparent cohesion. In general, the solid
skeleton is submitted to an intergranular (or effective) stress, which is the sum of the
total stress and the capillary stress due to capillary pressure: