Page 224 - Geotechnical Engineering Soil and Foundation Principles and Practice

Pore Water Pressure, Capillary Water, and Frost Action
Pore Water Pressure, Capillary Water, and Frost Action 219

Figure 11.7
Influence of drying
on capillary forces
in soils: more
suction but over
a smaller area.

This relationship was studied in the early 1920s by Haines and Fisher, two soil
scientists at the U.S. Bureau of Soils. A relationship for the negative pressure
inside the water is:
Tð3r 1 2aÞ
u ¼ 2 ð11:11Þ
r
1
where r 1 is as shown in Fig. 11.6 and a is the radius of the spheres. If a is unity,
r 1 ¼ 0.67 for u ¼ 0, which is between (a) and (b) in Fig. 11.7. The compressive force
pulling the particles together is the sum of the surface tension and negative
pressure times the cross-sectional area of the water ring, which can be shown to be
(Kirkham and Powers, 1972):
f ¼ Tð2a r 1 Þ ð11:12Þ
The total force per unit area is the sum of all such forces between particles. If N is
2
the number of particles per unit area, with cubic packing, N ¼ 1/4a . Then
F ¼ N f ¼ f=4a 2

1 r 1
F ¼ T ð11:13Þ
2a 4a 2

This formula indicates that the smaller the particle size, the larger is the cohesive
force per unit area resulting from capillary tension. The maximum force will be
when r 1 is very small, that is, as the soil becomes drier so long as the moisture
films remain intact.

11.5 SOIL MECHANICS OF UNSATURATED SOILS

11.5.1 A Shift in Emphasis
Much of the emphasis in geotechnical engineering has been on saturated soils, as
this normally is the most critical condition when strength is lowest and unit weight
is at a maximum, or is reduced to a minimum by submergence. However, many
soils are not and may never become saturated. An important example is soil that
has been mechanically compacted for support of a road or foundation, because

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