Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 58

Recognizing the uniqueness of the fourth phase (i.e., con-
tractile skin) assists in understanding the stress state vari-
ables for an unsaturated soil (Fredlund and Morgenstern,
1977). From a physical behavioral standpoint, an unsatu-
rated soil can be visualized as a mixture with two phases
that come to equilibrium under applied stress gradients (i.e.,
soil particles and contractile skin) and two phases that flow
under applied stress gradients (i.e., air and water). From the
standpoint of the volume-mass relations for an unsaturated
soil, it is possible to consider the soil as a three-phase sys-
tem since the volume of the contractile skin is small and its
mass can be considered as part of the mass of the water.
Geotechnical engineers are familiar with a shrinkage type
of experiment where a small soil specimen (i.e., initially
saturated) is allowed to dry by exposure to the atmosphere.
The total stresses on the specimen remain unchanged near
zero while the specimen undergoes a decrease in volume.
The pore-water pressure goes increasingly negative during
the experiment. It is the contractile skin (or air-water inter-
face) that acts like a thin rubber membrane that pulls the
particles together, causing volume change.

B

C

22,090

Fusion
curve

Vaporization
curve

Solid

Liquid

101.3

A

0.61

Vapor

D

Sublimation
curve

0 100 374

Temperature, ° C

Figure 2.35 State diagram for water (not to scale; from van Hav-
eren and Brown, 1972).

2.3.6 Water Vapor
The vaporization curve AB in Fig. 2.35 represents an equi-
librium condition between the liquid and vapor states of
water. In this equilibrium state, evaporation and condensa-
tion processes occur simultaneously at the same rate. The
rate of condensation depends on the pressure in the water
vapor which reaches its saturation value on the vaporization
line. On the other hand, the evaporation rate depends only on
temperature. Therefore, a unique relationship exists between
the saturation water vapor pressure and temperature, which
is referred to as the vaporization curve. Saturation water
vapor pressures u v 0 are presented in Table 2.11.
Water vapor is mixed with air in the atmosphere. The
presence of the air has no effect on the behavior of the
water vapor. This phenomenon is expressed by Dalton's law
of partial pressures. Dalton's law states that the pressure of a
mixture of gases is equal to the sum of the partial pressures
at which each individual component of the gas would exert if
it alone filled the entire volume. In other words, the behavior

2.3.5 Interaction of Air and Water
Air and water behave as both an immiscible mixture and
as a miscible mixture. The immiscible mixture is a combi-
nation of free air and pure water without any interaction.
The immiscible mixture is characterized by a separation of
liquid and gas produced by the contractile skin. A miscible
air-water mixture can have two forms. First, air dissolves
in water and can occupy approximately 2% of the water by
volume (Dorsey, 1940). Second, water vapor can be present
in the air. Various types of air-water mixtures are discussed
in the following sections. Consideration is also given to the
possible “states” for water.

2.3.5.1 Solid, Liquid, and Vapor States of Water
Water can be found in one of three “states”: the solid state
as ice, the liquid state as water, or the gaseous state as water
vapor (Fig. 2.35). The state of water depends on the pressure
and temperature environment. Three lines are drawn on the
water state diagram (Fig. 2.35): the vaporization curve AB ,the
fusion curve AC , and the sublimation curve AD. The vaporiza-
tion curve AB is also called the vapor pressure curve of water.
It gives combination values of temperature and pressure for
which the liquid and vapor states of water can coexist in equi-
librium. The fusion curve AC separates the solid and liquid
states of water, and the sublimation curve AD separates the
solid and the vapor states of water. The solid state can coexist
in equilibrium with the liquid state along the fusion curve and
with the vapor state along the sublimation curve.
The vaporization, fusion, and sublimation curves meet at
point A . This point is called the triple point of water where
the solid, liquid, and vapor states of water can coexist in
equilibrium. The triple point of water is achieved at a tem-
perature of 0 ◦ C and a (gauge) pressure of 0.61 kPa.

Table 2.11 Saturation Pressures of Water Vapor
at Various Temperatures

Temperature ( ◦ C) Saturation Vapor Pressure (kPa)

0 0.6107

10 1.2276

20 2.3384

30 4.2451

40 7.3812

60 19.933

80 47.375

100 101.325

120 198.49

Source: From Kaye and Laby, 1973.