A Microstructural Model for Soils and Granular Materials - Multiscale Geomechanics: From Soil to Engineering Projects - page 202

identified. The fully saturated regime corresponds to a two-phase material with
water completely filling the voids between grains. The water pressure p w can be
positive or negative (suction) but, in both cases, the effective stress concept
[TER 25] can be applied and the contact forces determined by considering the
effective stresses σ ' as the external stresses [DEB 96, HIC 98]:

σσ I ' =− p [7.18]

w

In the case of partially saturated samples, the liquid phase is distributed in
menisci located between close grains and, as a consequence, capillary forces are
applied on the grains and are added to the contact forces defined above. When the
water content decreases inside a saturated granular sample, the air breaks through at
a given point. The negative water pressure or suction corresponding to that point is
called the air-entry pressure. Its value depends on the pore sizes. Afterwards, the
sample becomes unsaturated, with the water phase being connected inside the pores.

This state is called the funicular regime, in which a constant decrease in the
degree of saturation corresponds to a gentle increase in pore water pressure, which is
homogenized along the continuous water phase. The menisci start to form between
two grains, not necessarily in contact, and are connected to each other. The pendular
regime starts when the water menisci become disconnected. The water is no longer
continuous and equilibrium in the water pressure is obtained by the vapor pressure.
At this stage, the capillary forces start to increase drastically according to the pore
size. If the drying process continues, the water bridges begin to fail, starting with
grains that are not in contact, until a completely dry state is achieved and no
capillary forces are left inside the granular assembly.

Several studies have shown that the attractive capillary forces between two
grains connected by a water bridge are a decreasing function of the distance between
the grains until the bridge fails (see, for example, [BIA 93, CHA 02]). This function
depends on the volume of liquid found between the grains. Different mathematical
expressions have been proposed for these capillary forces, which are the sum of the
pressure forces exerted by the liquid on the wetted area and the surface tension
forces acting along the wetted perimeter. In this study, we retained the following
expression:


−  

d

c

cap R

= f e

[7.19]

n max

where

- f cap is the capillary force between two neighboring grains, not necessarily in
contact;