Environmental Engineering Reference
In-Depth Information
8.3.10 Example of Water Flow through Earth Dam
The example problem involving water flow through an earth-
fill dam is first discussed. The soil is assumed to be isotropic
with respect to its coefficient of permeability and the perme-
ability function along with the SWCC and the water storage
modulus function are shown in Fig. 8.51. The saturated coef-
ficient of permeability
k
s
is 1
.
0
10
−
6
coefficients of permeability are equal
to 5
.
0
×
and
10
−
5
m/s for the liner and the surrounding soil,
respectively. A water storage modulus
m
2
1
.
0
×
of for both soils
is shown in Fig. 8.56c.
The discretized cross section of the soil liner and its sur-
rounding soil are depicted in Fig. 8.57. Initially the ground-
water table was located 5 m below the ground surface.
The lagoon was assumed to be instantaneously filled with
water to a depth of 1 m. No-flow boundary conditions were
assumed along the ground surface outside the lagoon, the
bottom boundary, and the vertical axis of symmetry. On the
right-hand boundary, a hydrostatic condition was assumed
to exist below the groundwater table. A no-flow condition
was assumed to exist above the groundwater table to the
ground surface. The exit point of the groundwater table was
assumed to be fixed with elapsed time.
The transient modeling process commenced as the lagoon
was filled with water to the 1-m height which gave rise
to a 1-m pore-water pressure head. The water commenced
seeping from the lagoon, causing the groundwater to grad-
ually mound to its final steady-state condition. Figure 8.57
illustrates the transient positions of the water table at an
elapsed time of 24 h. Figure 8.57a shows the pressure head
contours, including the phreatic line, along with the automat-
ically generated finite element mesh required for solving the
problem at 24 h of elapsed time. It can be seen that there is
a slight rise in the groundwater table 5 m below the ground
surface. At the same time there is a phreatic line that has
developed at the 0.5-m depth below ground surface as water
moves downward from the lagoon. Figure 8.57b shows the
equipotential heads along with the flow vectors correspond-
ing to an elapsed time of 24 h. The water level in the lagoon
remains constant at a 1-m height throughout the transient
process.
The seepage flow pattern and the development of pore-
water pressures in the soil below the lagoon after an elapsed
time of 40 h are shown in Figs. 8.58a and 8.58b. At the
beginning of the transient process, water moved downward
from the lagoon, while the position of the groundwater table
showed little effect. With time, the wetting front moves
deeper into the soil mass while the groundwater begins to
mound upward. After 52 h, the downward wetting front from
the lagoon joins the rising groundwater table, as shown in
Fig. 8.59. Steady-state conditions are approached after an
elapsed time of about 200 h, as shown in Fig. 8.60. The
length of time required to approach steady-state seepage
conditions is largely controlled by the saturated coefficients
of permeability for the soils.
10
−
7
m/s. The pore-air
pressure is assumed to remain at atmospheric pressure. The
base of the dam is selected as the datum for elevation head.
The reservoir is initially assumed to be empty so the water
level is at 0 m (i.e., the datum). The water level in the
reservoir is then instantaneously raised to a level of 10 m
above datum. The water level remains constant at 10 m as
transient or unsteady-state seepage takes place in the dam.
The rise of the phreatic line from the initial steady-state
condition to an elapsed time of 1500 days is computed.
The development of equipotential lines, the phreatic sur-
face, and water flow vectors through the dam are illus-
trated for four elapsed times during the transient process.
Figure 8.52 shows the development of the phreatic lines,
the flow vectors, and the equipotential lines after an elapsed
time of 25 days. The dynamically generated finite element
mesh corresponding to the converged solution is also shown.
Similar plots of the phreatic lines, the flow vectors, and
the equipotential lines after an elapsed time of 60 days are
shown in Fig. 8.53. Likewise, the development of seepage
toward steady-state conditions is shown for elapsed times of
120 and 1500 days in Figs. 8.54 and 8.55, respectively.
The increase in the reservoir level results in an increase in
pore-water pressures with time. This is demonstrated by the
advancement of equipotential lines from upstream to down-
stream of the dam with elapsed time. It should also be noted
that the equipotential lines extend from the saturated through
the unsaturated zones. In other words, water flows in both
the saturated and the unsaturated zones as a result of the
hydraulic head differences between the equipotential lines.
The flow of water in both zones can be observed directly
from the flow rate vectors that exist in both the saturated and
unsaturated zones. The amount of water flowing in the unsat-
urated zone depends on the rate of change in the coefficient
of permeability with respect to matric suction changes.
×
8.3.11 Example of Groundwater Seepage below
Lagoon
The second example problem illustrates unsteady-state
groundwater seepage below a lagoon. The lagoon is placed
on top of a 1-m-thick soil liner. The geometry of the
problem is symmetrical, and the liner and the surrounding
soil are assumed to be isotropic with respect to coefficient
of permeability. The problem is analyzed by considering
half of the geometry. The SWCC is assumed to be the same
for the soil liner and the underlying soil and is shown in
Fig. 8.56a. The permeability functions for the soil liner and
the surrounding soil are shown in Fig. 8.56b. The saturated
8.3.12 Example of Seepage within Layered Hill Slope
The third example problem illustrates unsteady-state seepage
within a layered hill slope under constant-infiltration condi-
tions. Rulon and Freeze (1985) studied this problem using a
sandbox model of the layered hill slope. Details of the geom-
etry of the slope and the applied surface moisture flux are
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