Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 63

Equation 2.40 is referred to as Kelvin's capillary model
equation. The radius of curvature of the contractile skin
decreases as the matric suction of a soil increases. The
curved contractile skin is often called a meniscus. When
the difference between the pore-air and pore-water pressure
goes to zero, the radius of curvature R s goes to infinity.
Therefore, a flat air-water interface exists when the matric
suction goes to zero. Interestingly, even under these con-
ditions the surface tension property of water remains at a
constant value.

by considering the surface tension T s acting around the cir-
cumference of the meniscus. The surface tension T s acts
at an angle α 1 from the vertical wall of the capillary tube.
The angle is known as the contact angle, and its magni-
tude depends on the adhesion between the molecules in
the contractile skin and the material comprising the tube
(i.e., glass).
Let us consider the vertical force equilibrium of the cap-
illary water in the tube shown in Fig. 2.40. The vertical
component of surface tension (i.e., 2 πrT s cos α 1 ) is respon-
sible for holding the weight of the water column, which has
a height h c (i.e., πr 2 h c ρ w g ):

2.3.10 Capillary Phenomenon
The capillary phenomenon is associated with the matric suc-
tion component of total suction. The height of water rise in
a capillary tube and the radius of curvature of the air-water
interface have direct implications to the water content-
matric suction relationship in soils (i.e., the soil-water
characteristic curve). The capillary rise is different for the
wetting and drying processes in a soil due to variations in
capillary pore size.

πr 2 h c ρ w g

2 πrT s cos α 1 = (2.41)

where:

r = radius of the capillary tube,

T s = surface tension of water,

α 1 = contact angle,

h c = capillary height, and

g = gravitational acceleration.

2.3.10.1 Capillary Height
Consider a small glass tube inserted into water under atmo-
spheric conditions (Fig. 2.40). Water rises up in the tube as
a result of the surface tension of the contractile skin and the
tendency of water to wet the surface of the glass tube (i.e.,
hygroscopic properties). Capillary behavior can be analyzed

Equation 2.41 can be rearranged to give the maximum
height of water in the capillary tube, h c :

2 T s
ρ w gR s

h c = (2.42)

Figure 2.40 Physical model of capillarity.