Water: Surface and Subsurface - Geotechnical Engineering Investigation - page 647

Anisotropic conditions resulting from stratification cause horizontal permeability to be
greater than vertical. This is accounted for in flow net construction by shrinking the
dimensions of the cross section in the direction of the greater permeability. For example, if
k h > k v , the horizontal scale is reduced by multiplying the true distance by

k v / k h , produc-
ing a transformed section, and the flow net is constructed in the ordinary manner.
Anisotropic effects are discussed by Harr (1962) and DeWeist (1965).

√

Analysis
Seepage quantity can be calculated, once the flow net is drawn, from the expression

q ( N f / N e ) k h (8.9)

where N f is the number of flow channels (space between any adjacent pair of flow lines),
N e the number of equipotential drops along each flow channel, k the coefficient of perme-
ability, h the total head loss (sum of h in Figure 8.28) , N f / N e (S) the shape factor, and, q

the discharge or quantity of flow per foot (or meter), commonly given in ft 3 /sec per run-
ning foot in the English system, where k is given in ft/sec or m 3 /sec per meter with k given
in m/sec in the metric or SI system.
Examples of computations of seepage quantities for confined flow conditions are given
in Figure 8.28.
Seepage pressure is equal to the hydraulic gradient times the unit weight of water ( p s

∆

γ w )
and acts in a direction at right angles to the equipotential lines and parallel to the flow lines.
The seepage pressure is resisted by the submerged weight of the overlying soil column.
Therefore, liquefaction or boiling is not imminent where the seepage pressure is greater
than the weight of the overlying soil.
Pore-water pressures may be determined from flow nets as illustrated in Figure 8.28b. The
application to stability analysis of slopes is illustrated in Figure 9.77.

i

Conclusions
Flow nets are useful tools, since even a crude flow net will permit fairly accurate determi-
nations of seepage quantities and pressures in soils. They are somewhat time-consuming
to construct, and each time the dimensions are changed (e.g., when the depth of a cutoff
wall is increased), new flow nets are constructed.
In critical problems where high potential for seepage uplift and pore-water pressures
exist, the values obtained from flow-net analysis should be verified by measurements with
instruments, such as piezometers, to monitor the development of actual pore pressures in
or beneath an embankment, at the toe, or in a slope.

Natural Flow Systems in Slopes
Simplified Regional Flow Systems
Classical descriptions usually consider groundwater flow systems to be hydrostatic,
whereas, in actuality, nonhydrostatic distributions are common in the vicinity of slopes
(Patton and Hendron, 1974). The general flow system in hilly terrain proposed by Hubbert
(1940) is shown in Figure 8.29. In the upland recharge area, the flow tends to be down-
ward, and in the valley lowlands in the discharge area the flow tends to be upward. The
conditions given in the figure are for a relatively uniform material; the nonhydrostatic dis-
tributions along the slope, as illustrated by the equipotential lines, are apparent. If low