Environmental Engineering Reference
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that are smaller than or equal to r . Capillary heights greater
than h c may also develop if the height of the soil column is
extended. The higher capillary rise corresponds to the pore
radii that are smaller than r . However, the water surface
cannot rise within the large openings at the center of the
soil column (Fig. 2.43e).
The above capillary tube analogy also applies to soil con-
ditions in situ. Nonuniform pore size distribution in a soil
can result in hysteresis in the soil-water characteristic curve.
The soil-water contents during the wetting and drying pro-
cesses are different at particular matric suction values, as
illustrated by the examples shown in Figs. 2.43c and 2.43d,
respectively. The contact angle at an advancing interface
during the wetting process is also different from that at a
receding interface during the drying process (Bear, 1979).
The above factors as well as the presence of entrapped air
in the soil are considered to be the main causes for hys-
teresis in the drying and wetting soil-water characteristic
curves.
The capillary model is conceptually simple but has some
limitations when used to explain the mechanical behavior of
unsaturated soils. For example, an apparent anomaly arises
when the capillary model is incorporated into the formula-
tion of pore fluid compressibility, as will be later explained.
The pore radius in the capillary equation (i.e., Eq. 2.46) can-
not be measured and as a result the capillary model is quite
impractical in engineering practice. There are also other fac-
tors, such as the adsorptive forces between clay particles,
that contribute to soils being able to sustain negative pore-
water pressures greater than 1 atm.
Glass tube
Compressive stress
on the wall
T s
T s
Air
Water
Figure 2.42
Forces acting on capillary tube.
The radius or opening of the tube is a significant factor in
the development of capillary rise, as illustrated in Figs. 2.43c
and 2.43d. In both cases, the tube has a bulb with a radius r 1
which is larger than the radius of the tube, r . The presence of
the bulb at the midheight of the capillary height h c prevents
water from rising above the base of the bulb (Fig. 2.43c). In
other words, nonuniform openings along the capillary tube
can prevent the full development of capillary height. On the
other hand, the capillary height h c can be fully developed if
the bulb is filled by submerging it below the water surface
and then raising it above the surface (Fig. 2.43d).
The development of capillary rise in a soil is also
affected by the pore size distribution in the soil, as shown
in Fig. 2.43e. The water surface in the soil can rise to the
capillary height h c through continuous soil pores with radii
2.3.10.4 Capillary Model and Air-Entry Value of a Soil
The air-entry value of a soil consisting of similar-sized spheres
can be estimated using the capillary model (Gvirtzman and
Roberts, 1991). The point of air entry into an arrangement of
spheres occurs when the largest pore allows air to displace the
water within the pore. The air-entry value is a function of the
size of the largest opening between a set of particles.
(a)
(c)
(d)
(e)
Figure 2.43
Height, radius, and shape effects on capillarity (after Taylor, 1948).
 
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