Measurement and Estimation of State Variables - Unsaturated Soil Mechanics in Engineering Practice - page 111

with the soil-water relative to the partial pressure of
water vapor in equilibrium with free pure water.
Total suction or free energy of soil-water: Total suction is
the equivalent suction derived from the measurement of
the partial pressure of the water vapor in equilibrium
with the soil-water relative to the partial pressure of
water vapor in equilibrium with free pure water.

The above definitions state that total suction corresponds
to the free energy of the soil-water, while the matric and
osmotic suctions are the components of the free energy. The
mathematical relationship between the components of soil
suction can be written as follows:
ψ = u a − u w + π

(4.3)

where:

u a − u w = matric suction, kPa,

u a = pore-air pressure, kPa,

u w = pore-water pressure, kPa, and

π = osmotic suction, kPa.

Figure 4.2 illustrates the concept of total suction and its
components relative to the free energy of the soil-water.
Matric suction is commonly associated with the capillary
phenomenon arising from the surface tension of water. The
capillary phenomenon can be illustrated by the rise of water
in a capillary tube (Figure 4.2).

Figure 4.3 Capillary tubes showing air-water interfaces at vary-
ing heights for different radii of curvature (after Janssen and
Dempsey, 1980).

The pores in a soil are analogous to capillary tubes with
small radii. Soil-water rises above the water table because
of the capillaries created by the soil (Fig. 4.3). The capillary
water has a negative pressure with respect to the air pressure.
The air pressure in the field is generally atmospheric (i.e.,
u a = 0). The pore-water pressures can be highly negative

at low degrees of saturation (Olson and Langfelder, 1965).
The adsorptive forces between soil particles and water are
believed to play an important role in sustaining highly neg-
ative pore-water pressures.
Let us consider a capillary tube filled with water squeezed
from a soil. The surface of the water in the capillary tube
is curved and is called a meniscus. The same soil water will
have a flat surface when placed in a large container. The partial
pressure of the water vapor above the curved surface of soil
water, u v , is less than the partial pressure of water vapor above

a flat surface of the same soil water,

u v < u v 1 ). In
other words, the relative humidity in a soil will decrease due
to the presence of the curved water surface produced by the
capillary phenomenon. The water vapor pressure or the rela-
tive humidity decreases as the radius of curvature of the water
surface decreases. The radius of curvature is inversely propor-
tional to the difference between the air and water pressures
across the surface (i.e., u a − u w ) and is called matric suction.
Therefore, one component of total suction is matric suction,
and it contributes to a reduction in the relative humidity.

u v 1 (i.e.,

Figure 4.2 Total suction and components of matric suction and
osmotic suction.