Solving Saturated/Unsaturated Water Flow Problems - Unsaturated Soil Mechanics in Engineering Practice - page 409

The phreatic line resulting from the saturated-unsaturated
seepage analysis is in close agreement with the empiri-
cal free surface from the conventional flownet construction
(Casagrande, 1937). This observation supports the assump-
tion that the empirical free surface is approximately equal to
a phreatic line. However, water can flow across the phreatic
line, as indicated by the nodal flow rate vectors. Water flow
across the phreatic line into the unsaturated zone indicates
that the phreatic line is not the uppermost flow line as
assumed in the flownet solution technique.
The difference between the phreatic line (from the finite
element analysis) and the free surface (from the flownet
technique) decreases as the permeability function for the
unsaturated zone becomes steeper. A steep permeability
function indicates a rapid reduction in the water coefficient
of permeability for a small increase in matric suction. In
this case, the quantity of water flow into the unsaturated
zone is considerably reduced. This condition approaches
the assumption associated with the conventional flownet
technique.
Equipotential lines extend from the saturated zone through
the unsaturated zone, as shown in Fig. 8.43. Changes in
hydraulic head between equipotential lines demonstrate
that water flows in both the saturated and unsaturated
zones. The amount of water flowing in the unsaturated
zone depends upon the rate at which the coefficient of
permeability changes with respect to matric suction.
The pore-water pressure heads are computed at all nodes
throughout the dam. Pore-water pressure heads are com-
puted by subtracting the elevation head from the hydraulic
head. Contour lines of equal-pressure heads or isobars are of
little value for the interpretation of the computer results for
this problem (apart from the phreatic line or zero-pressure
line).
The flow of water in the saturated and unsaturated zones is
approximately parallel to the phreatic line as observed from
the flow rate vectors in the central section of the dam. This
is not the situation for sections close to the upstream face
and the toe of the dam. Near the upstream face of the dam,
water flows across the phreatic line from the saturated to the
unsaturated zone and continues to flow in the unsaturated
zone. The water in the saturated and unsaturated zones then
flows essentially parallel to the phreatic line in the central
section of the dam. The water in the saturated zone then
flows across the phreatic line into the unsaturated zone at
the toe of the dam.
Figure 8.44 shows steady-state seepage through the
above dam cross section when the soil is assumed to be
anisotropic. The water coefficient of permeability in the
horizontal direction is assumed to be six times larger than
in the vertical direction (i.e., k wx =

for the anisotropic case (Fig. 8.44). The saturated zone
could exit on the downstream face of the dam for higher
anisotropy ratios for the horizontal-to-vertical coefficients of
permeability.
The third example shows an isotropic earth dam having
a core with a lower coefficient of permeability and a hor-
izontal drain, as illustrated in Fig. 8.45. The soil forming
the shell of the dam has a saturated coefficient of perme-
ability k s of 1 . 0

10 − 7 m/s, and the permeability function
is in accordance with function A in Fig. 8.42. The core has
a saturated coefficient of permeability k s of 1 . 0

×

10 − 9 m/s
and a permeability function in accordance with function B
in Fig. 8.42. The boundary conditions used in the analysis
are the same as those applied to the previous problems.
The results show that most of the hydraulic head change
occurs in the region around the core as depicted by the
concentrated distribution of equipotential lines in the core
zone. As the difference in the coefficients of permeability
between the soil and the core increases, greater hydraulic
head changes take place in the core. The nodal flow rate
vectors also indicate that a significant amount of water flows
upward into the unsaturated zone and over the top of the rel-
atively impermeable core (i.e., the siphon effect), as shown
in Fig. 8.45b.
The fourth example demonstrates the effect of a mois-
ture flux boundary condition (i.e., infiltration) placed on
the isotropic earth dam (Fig. 8.43). The seepage analysis
results are presented in Fig. 8.46. Steady-state infiltration is
simulated by applying a positive nodal flow Q w of 1 . 0

×

×
10 − 8 m 2 /s to each of the nodes along the upper boundary
of the dam. The results can be compared to the case of zero
flux across the upper boundary by comparing Figs. 8.43
and 8.46. Infiltration results in a rise in the phreatic line.
Consequently, the pore-water pressures in the unsaturated
zone increase relative to the case where there is zero infil-
tration at the ground surface.
The fifth example demonstrates the development of a
seepage face on the downstream of the dam. In this case,
there is no horizontal drain and zero nodal flows are
specified along the entire lower boundary. There is close
agreement between the phreatic line obtained from the finite
element analysis and the free surface obtained using the
flownet technique (Fig. 8.47). The phreatic line extends to
the downstream face of the dam. The phreatic line exits on
the downstream face and the portion below the exit point
is called the seepage face. The seepage face has a zero
pore-water pressure (i.e., atmospheric pressure), boundary
condition. In other words, the hydraulic head is equal to
the gravitational or elevation head along the seepage face.
The location of the exit point is not known prior to per-
forming the analysis. Therefore, the location of the exit
point must be assumed in order to commence the analy-
sis. The exit point is revised following each solution of the
finite element solver. The seepage face boundary condition
is reevaluated and the solution is repeated.

6 k wy ). The anisotropy
ratio is assumed to be constant throughout the dam. One
permeability function (i.e., function A in Fig. 8.42) is used
for the x - and y -directions. The phreatic line is elongated
in the direction of the major coefficient of permeability