Environmental Engineering Reference
In-Depth Information
from the shrinkage of clay soils or from the differential settlement of the embankment or
its foundation. Embankment settlement caused by compression of the foundation materi-
als can result in the breaking of outlet pipes, which permits piping of the embankment
soils into the pipes. Except for overtopping, piping has caused a far greater number of
earth dam failures than any other activity.
Soils susceptible to piping in the natural state, including “dispersive clays,” are
described in
Section 10.5.5.
8.3.3
Flow Systems and Analysis
General
Flow Systems
All flow systems extend physically in three directions. The flow of water through satu-
rated soil is a form of streamlined flow (the tangent of any point on a flow line is in the
direction of the velocity at that point) and can be represented by the Laplace equation for
three-dimensional flow through porous media (DeWeist, 1985). The equation in effect
states that the change in gradient in the
x
direction plus the change in gradient in the
y
direction plus the change in gradient in the
z
direction equals zero.
In practice, seepage problems can be two- or three-dimensional. Fortunately, most engi-
neering problems can be resolved by assuming two-dimensional flow. Most three-dimen-
sional seepage problems are extremely complex in their solutions.
Analytical Methods
A number of analytical methods are available for solving the Laplace equations including:
Electrical analog (Karplus, 1968; Meehan and Morgenstern, 1968)
●
Relaxation method
●
Finite-element method (Zienkiewicz et al., 1966)
●
Conforming mapping configurations
●
Flow nets (this chapter)
●
Well formulas (this chapter)
●
Flow Nets
Description
A flow net is a two-dimensional graphical presentation of flow consisting of a net of flow
lines and equipotential lines, the latter connecting all points of equal piezometric level
along the flow lines.
Applications
Flow nets are used to evaluate:
1.
Seepage quantities exiting through or beneath a dam or other retaining struc-
tures
2.
Flow quantities into wells or other openings in the ground
3.
Seepage pressures that result in uplift below dewatered excavations or at the toe
of dams
4.
Exit gradients and the potential for liquefaction in dams, slopes, or excavations
5.
Pore pressures along potential failure surfaces in slopes
