Page 223 - Geotechnical Engineering Soil and Foundation Principles and Practice

Pore Water Pressure, Capillary Water, and Frost Action
218 Geotechnical Engineering

Figure 11.6
Annular ring of water linking two soil particles. The main attractive force is not from surface tension
but from the negative pore pressure created by the surface tension.

water, whereas the convex radius tends to increase it. As the concave radius is
smaller, the net effect is a decrease in pressure that pulls the grains together.

The equation for negative pressure in this case uses the Laplace function to define
the surface:

1 1
u ¼ T þ ð11:10Þ
r 1 r 2

in which r 1 and r 2 are radii of curvature of a warped surface where it intersects two
orthogonal principal planes. The expression in the parentheses is called the total
curvature of the surface. A negative radius creates a positive pore pressure, so in
Fig.11.5, r 1 , the internal radius of the ring of water, increases pressure in the water
and therefore is negative.

The negative pore pressure in capillary water therefore equals the surface tension
of the water times the total curvature of the meniscus or air-water interface.
This relationship is important because, as the moisture content changes, both
radii of curvature also change.

The influence of total curvature is illustrated in Fig. 11.7, where it will be seen
that, if the moisture content increases such that the outer surface of the annular
ring of connecting water becomes straight-sided (Fig. 11.7(a)), r 1 is infinite so its
reciprocal makes no negative contribution to pore water pressure, which therefore
is positive.
When a soil is dried (Fig. 11.7(b)), the smaller radius is positive so pore pressure
becomes negative. Opposing this tendency is the cross-sectional area of the ring
of water as the soil dries out (Fig. 11.7(c)), which eventually will result in a net
decrease in attraction between the two particles. Finally, r 1 can become so small
that the negative pressure equals the vapor pressure of water, causing the soil to
spontaneously dry out. This does not occur in clay because its adsorptive
properties permit a high negative pressure. When sand dries it crumbles whereas
a clay keeps getting stronger.

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