Solving Saturated/Unsaturated Water Flow Problems - Unsaturated Soil Mechanics in Engineering Practice - page 415

problems as long as the soil is isotropic. Heterogeneity with
respect to the coefficient of permeability results in varying
distances between either flow lines or equipotential lines;
however, the respective lines must cross at 90 ◦ .
The pore-water pressure distribution in the unsaturated
zone can be analyzed by considering a horizontal datum
through an arbitrary point (e.g., point A in Fig. 8.49) on
the phreatic line. The pore-water pressure distribution in a
direction perpendicular to the phreatic line (i.e., in the a -
direction) is first examined. The results are then used to ana-
lyze the pore-water pressure distribution in the y -direction
(i.e., vertically). The gravitational head distribution in the
a -direction is zero at point A( i.e., datum) and increases lin-
early to a gravitational head of H cos 2 α at ground surface.
The pore-water pressure head at a point in the a -direction
must be negative and equal in magnitude to its gravitational
head because the hydraulic heads are zero in the a -direction.
Therefore, the pore-water pressure head distribution in the
a -direction must start at zero at the datum (i.e., point A ) and
decrease linearly to

negative pore-water pressure head at a point on a vertical
plane can therefore be expressed as follows:

y cos 2 α h pi =− (8.49)

where:

h pi = negative pore-water pressure head on a vertical

plane (i.e., the y -direction) for an infinite slope,

y = vertical distance from the point under consideration

to the datum (i.e., point A ), and

α = inclination angle of the slope and the phreatic line.

When the ground surface and the phreatic line are hori-
zontal (i.e., α

=

0 or cos α

=

1), the negative pore-water
pressure head at a point along a vertical plane, h ps , is equal
to

y . This is the condition of static equilibrium above
and below a horizontal water table. The ratio between the
pore-water pressure heads on a vertical plane through an
infinite slope (i.e., h pi =−

−

y cos 2 α ) and the pore-water pres-
sure heads associated with a horizontal ground surface (i.e.,
h ps =−

H cos 2 α at ground surface. A pore-

−

H cos 2 α applies to any point along
the ground surface since every line parallel to the phreatic
line is also an isobar.
The pore-water pressure head distribution in a vertical
direction also commences with a zero value at point A and
decreases linearly to a head of

water pressure head of − y ) is plotted in Fig. 8.50. The ratio of pressure heads

indicates the reduction in the pore-water pressures on a ver-
tical plane as the slope α becomes steeper.
The gravitational head at a point along a vertical plane
is equal to its elevation from the datum, y( Fig. 8.49). The
hydraulic head is computed as the sum of the gravitational
and pore-water pressure heads:
h wi = 1

H cos 2 α at ground sur-
face. However, the pore-water pressure head is distributed
along a length H cos α in the a -direction, while the head is
distributed along a length H in the vertical direction. The

−

cos 2 α y

− (8.50)

y

- H cos 2

α a

Hydraulic head is equal to
zero along the a-direction

Pressure
head

H

Pressure
head

H cos 2

α

y

α

α

Gravitational
head

Datum

A

Saturated zone

α

α

Figure 8.49 Pore-water pressure distribution above phreatic line in unsaturated zone during
steady-state seepage through infinite slope.