Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 30

cause an unsaturated soil to change water content, change
volume, and change shear strength. It is the contractile skin
that forms a barrier between air and water, determining the
ratio of the volume of air to the volume of water in the
voids (i.e., degree of saturation). It is particularly important
to view an unsaturated soil as a four-phase mixture when
considering the stress state of an unsaturated soil. Equilib-
rium stress equations can be written for each phase within
the context of multiphase continuum mechanics. The equi-
librium analysis reveals the stress state variables associated
with maintaining equilibrium conditions in the unsaturated
soil (see Chapter 3).
An unsaturated soil should be viewed as having two phases
that flow under the influence of a stress gradient (i.e., air
and water) and two phases that come to equilibrium under
the influence of a stress gradient (i.e., structural arrangement
of soil particles and the contractile skin forming a partition
between the fluid phases) (Fredlund and Rahardjo, 1993a).
The contractile skin has physical properties differing from
the contiguous air and water phases and interacts with the
soil structure to influence soil behavior. The contractile skin
can be considered as part of the water phase when consid-
ering changes in the volume-mass soil properties; however,
the contractile skin must be considered as an independent
phase when describing the stress state and phenomenological
behavior of an unsaturated soil.
Terzaghi (1943) emphasized the important role played by
surface tension property associated with the air-water inter-
face (i.e., contractile skin). The important role played by the
contractile skin can be demonstrated by simply observing the
shrinkage of an initially saturated ball of clay from which
water is allowed to evaporate. There may be essentially no
changes in the total stress state as water evaporates; how-
ever, the contractile skin can result in a significant overall
volume change of the soil mass. In other words, the con-
tractile skin acts like an elastic membrane pulling the soil
particles closer together as water is removed.

Thickness of the
contractile skin

Liquid water density

Hyperbolic tangent function
thickness:
1.5 - 2 water molecules
or about 5 Å

Water vapor density

0

Figure 2.1 Density distribution across air-water interface (con-
tractile skin) (after Kyklema, 2000).

of ordinary water and have a molecular structure similar to
that of ice (Derjaguin and Churaev, 1981; Mitsuhiro and
Kataoka, 1988).
The Young-Laplace and Kelvin equations describe funda-
mental behavioral aspects of the contractile skin, but both
equations have limitations. The Young-Laplace equation is
not able to explain why an air bubble can gradually dissolve
in water without any apparent difference between the air
pressure and the water pressure. The validity of the Kelvin
equation becomes suspect as the radius of curvature reduces
to the molecular scale (Adamson and Gast, 1997; Christen-
son, 1988).
Terzaghi (1943) recognized the limitations of the Kelvin
equation and stated that if the radius of a gas bubble
“approaches zero, the gas pressure—approaches infinity”.
However, within the range of molecular dimensions, “the
equation loses its validity.” Terzaghi (1943) recognized
the limitations associated with the Kelvin equation but
later researchers have attempted to incorporate the Kelvin
equation into formulations for the compressibility of
air-water mixtures to no avail (Schuurman, 1966). Details
pertaining to the behavior of the contractile skin are still not
fully understood, but the contractile skin is known to play an
important role in unsaturated soil behavior. Terzaghi (1943)
stated that surface tension “ is valid regardless of the physical
causes. ” He went on to say, “The views concerning the
molecular mechanism which produces the surface tension
are still controversial. Yet the existence of the surface film
was established during the last century beyond any doubt.”
The statements of Terzaghi in 1943 are still relevant today.

2.1.3 Distinctive Features of Contractile Skin
Numerous research studies on the nature of the contrac-
tile skin point toward its significant and independent role
in unsaturated soil mechanics (Wang and Fredlund, 2003).
Terzaghi (1943) suggested that the contractile skin might be
on the order of 10 − 6 mm in thickness. More recent studies
suggest that the thickness of the contractile skin is in the
order of 1.5 to 2 water molecules in diameter (i.e., 5

A)

2.1.4 Terminology for Continuum Mechanics
Variables of State
The authors are reticent to introduce many new variables
and terms for the synthesis of a science for unsaturated
soil mechanics; however, the terminology associated with
saturated soil behavior has some limitations when consider-
ing unsaturated soil behavior. As a result, some universally
acceptable terms from continuum mechanics and thermody-
namics are introduced. Definitions for the following terms

(Israelachvili, 1991; Townsend and Rice, 1991).
If the contractile skin is about 5 A thick, then a lineal
surface tension value of 75 mN/m translates into a unit
stress in the order of 140,000 kPa (i.e., stress per unit area
or surface tension divided by the thickness of the contrac-
tile skin). Kyklema (2000) showed that the distribution of
water molecules across the contractile skin takes the form of
a hyperbolic tangent function as shown in Fig. 2.1. Proper-
ties of the contractile skin are different from the properties