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

of water.

P+s, = i [gamma]+w,

P+s, = seepage pressure

where

i

= 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,

[gamma]+b,

CRITICAL = ))))))))))))))))))))))) = ))))))))))

;

[gamma]+W,

= [gamma]+W,

i+c,

F+s, = )))) = 2

i

where

i

= actual hydraulic gradient

[gamma]+T, = total unit weight of the soil

[gamma]+W, = unit weight of water

[gamma]b

= 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.

7.1-262

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