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It is worth noting that this term is not analogous with the usual concept of
capillary pressure or suction, which represents the negative pore water pressure
inside the unsaturated material. In this model, the capillary stress depends on the
geometry of the pores and is a tensor rather than a scalar. The capillary stress can
only can be reduced to an isotropic tensor for an isotropic distribution of the branch
lengths l
α
. This can be the case for an initially isotropic structure during isotropic
loading, but during deviatoric loading an induced anisotropy is created and the
capillary tensor is no longer isotropic.
From equations [7.12] and [7.22] we can define a generalized effective stress
tensor σ * by adding the applied and the capillary stresses:
*
cap
σσσ
=+
[7.23]
We can now plot the final states of the unsaturated samples in a generalized
effective stress plane p* , q* . The results are presented in Figure 7.20. We can see
that, in this plane, the critical state is unique for saturated and unsaturated samples.
unsaturated samples
M
500
400
300
200
100
0
0
50
100
150
200
250
300
350
p* (kPa)
Figure 7.20. Maximum strength locus in the generalized effective stress plane
There is no direct relationship between the measured suction and the capillary
stress tensor, but their evolution during the shearing phase is similar and controlled
by the evolution of the degree of saturation due to the volume change. Figures 7.18
and 7.19 show the evolution of the suction and the mean capillary stress,
respectively, with the axial strain for the three unsaturated specimens. We can see a
very similar evolution, even if the absolute values are different.
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