b. Seepage Quantity. Total seepage computed from flow net depends
primarily on differential head and mean permeability of the most pervious
layer. The ratio of permeabilities of separate strata or their anisotropy
has less influence. The ratio n+f,/n+d, in Figure 1 usually ranges from 1/2
to 2/3 and thus for estimating seepage quantity a roughly drawn flow net
provides a reasonably accurate estimate of total flow. Uncertainties in the
permeability values are much greater limitations on accuracy.
For special cases, the flow regime can be analyzed by the finite
element method. Mathematical expressions for the flow are written for each
of the elements, considering boundary conditions. The resulting system of
equations is solved by computer to obtain the flow pattern (see Appendix A).
2. SEEPAGE FORCES. The flow of water through soil exerts a force on the
soil called a seepage force. The seepage pressure is this force per unit
volume of soil and is equal to the hydraulic gradient times the unit weight
P+s, = i [gamma]+w,
P+s, = seepage pressure
= hydraulic gradient
[gamma]+w, = unit weight of water
The seepage pressure acts in a direction at right angles to the
equipotential lines (see Figure 1).
The seepage pressure is of great importance in analysis of the stability
of excavations and slopes (see Chapter 7 and DM-7.2, Chapter 1) because it
is responsible for the phenomenon known as boiling or piping.
a. Boiling. Boiling occurs when seepage pressures in an upward
direction exceed the downward force of the soil. The condition can be
expressed in terms of critical hydraulic gradient. A minimum factor of
safety of 2 is usually required, i.e.,
i+c, = i
[gamma]+T, - [gamma]+W,
CRITICAL = ))))))))))))))))))))))) = ))))))))))
F+s, = )))) = 2
= actual hydraulic gradient
[gamma]+T, = total unit weight of the soil
[gamma]+W, = unit weight of water
= buoyant unit weight of soil
b. Piping and Subsurface Erosion. Most piping failures are caused by
subsurface erosion in or beneath dams. These failures can occur several
months or even years after a dam is placed into operation.