Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 64

where: the elevation head at point C . The water pressure at point

C can be calculated as

R s = radius of curvature of the meniscus (i.e., r/ cos α 1 ).

u w =− ρ w gh c (2.44)

The contact angle between the contractile skin for pure
water and clean glass is zero (i.e., α 1 =

where:

0). When the angle
α is zero, the radius of curvature R s is equal to the radius
of the tube, r (Fig. 2.40). Therefore, the capillary height of
pure water in a clean glass tube is

u w = water pressure.

The water pressures above point A in the capillary tube are
negative, as shown in Fig. 2.40. The water in the capillary
tube is said to be under tension. On the other hand, the water
pressures below point A( i.e., water table) are positive due
to hydrostatic pressure conditions. At point C , the air pres-
sure is atmospheric (i.e., u a =

2 T s
ρ w gr

h c = (2.43)

The radius of the tube is analogous to the pore radius in
soils. Equation 2.43 shows that the capillary height increases
as the pore radius gets smaller. The capillary height can be
plotted against the pore radius using Eq. 2.43 where the
contact angle is assumed to be zero (Fig. 2.41).

0) and the water pressure is

ρ w gh c ). The matric suction u a − u w

negative (i.e., u w =−

at point C can then be expressed as follows:

u a − u w = ρ w gh c (2.45)

2.3.10.2 Capillary Pressure
Points A , B , and C in the capillary system shown in Fig. 2.40
are in hydrostatic equilibrium. The water pressures at points
A and B are atmospheric (i.e., the pore-water pressure at
point A is equal to the pore-water pressure at point B , which
is equal to 0.0). The elevation of points A and B on the water
surface is considered as the datum for the system (i.e., zero
elevation). As a result, the hydraulic heads (i.e., elevation
head plus pressure head) at points A and B are equal to zero.
Point C is located at a height h c from the datum (i.e.,
elevation head is equal to h c ). The hydrostatic equilibrium
among points C , B , and A requires that the hydraulic heads
at all three points be equal. In other words, the hydraulic
head at point C is also equal to zero. This means that the
pressure head at point C is equal to the negative value of

Substituting Eq. 2.42 into Eq. 2.45 allows matric suction
to be written in terms of surface tension:

2 T s
R s

u a − u w = (2.46)

Equation 2.46 applies to the pressure difference across a
contractile skin. The radius of curvature R s can be consid-
ered analogous to the pore radius r in a soil by assuming
a zero contact angle (i.e., α 1 = 0). As the pore radius gets

smaller, the matric suction in the soil gets larger, as shown
in Fig. 2.41.
Surface tension has the ability to support a column of
water, h c , in a capillary tube. The surface tension associated
with the contractile skin places a reaction force on the wall
of the capillary tube (Fig. 2.42). The vertical component of
this reaction force produces compressive stresses on the wall
of the tube. In other words, the weight of the water column
is transferred to the tube through the contractile skin. The
contractile skin results in an increased compression on the
soil structure in the capillary zone. As a result, the presence
of matric suction in an unsaturated soil produces a volume
decrease and an increase in the shear strength of the soil.

Surface tension, T s = 72.75 mN/m at t = 20 ° C

1000

100

2.3.10.3 Height of Capillary Rise and Radius Effects
The effect of the height of capillary rise and the radius of
curvature on capillarity is illustrated in Fig. 2.43 (Taylor,
1948). A clean capillary tube of radius r allows pure water
to rise to a maximum capillary height h c (Fig. 2.43a). How-
ever, the water rise in a capillary tube may be restricted by
the limited length of the tube (Fig. 2.43b). A decrease in the
capillary height results in an increase in the radius of curva-
ture R s , as indicated by Eq. 2.42 [i.e., h c =

10

1

Clay

Silt Sand

0.1

0.001 0.01 0.1 1

2 T s / ρ w gR s ].
The increase in R s for a tube with a constant radius causes an
increase in the contact angle since R s is equal to r/ cos α 1 .

Pore radius, r (mm)

Figure 2.41 Relationship of matric suction to pore size for vari-

ous soils.