Page 222 - Geotechnical Engineering Soil and Foundation Principles and Practice

Pore Water Pressure, Capillary Water, and Frost Action
Pore Water Pressure, Capillary Water, and Frost Action 217

Figure 11.5
Force balance
inside a soap
bubble.

where r is the radius of the bubble, p is the pressure inside the bubble, and T is
surface tension at a film-air interface. Hence
T
p ¼ ð11:7Þ
r
The internal pressure therefore decreases as the bubble grows larger. Soap lowers
the surface tension and surface energy.

11.4.2 Capillary Rise and Surface Tension
The influence of surface tension on the height of rise in a cylindrical capillary can
be solved by assuming that the half-bubble shown in Fig. 11.5 is rotated 908 to
represent the meniscus in the tube. In this case only one surface is involved and u
can represent negative pressure in water immediately under the capillary surface:
2T
u ¼ ð11:8Þ
r
This may be equated to the weight of the column of suspended water:
2T 2
u ¼ ¼ r h
h
from which
2T
h ¼ ð11:9Þ
2
r
where h is the height of capillary rise, T is surface tension, r is the radius of the
capillary, and is the density of the fluid. The smaller the capillary, the higher the
height of capillary rise.

11.4.3 Negative Pressure in Capillary Water Linking
Two Soil Particles

Capillary water in unsaturated soil can take a doughnut or annular shape around
particle contacts, as illustrated in Fig. 11.6. This problem is somewhat more
complicated because the water-air interface has two radii, r 1 and r 2 , one of which
is convex and the other concave. The concave radius acts to reduce pressure in the

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