Page 430 - Civil Engineering Formulas

356 CHAPTER TWELVE

and the effective stress in the soil
s e H

p e p p n D w D w D w (12.207)
1 e L
but 1/L ( i and i N /N , therefore
2
1
p e D w s 1 N 1 H (12.208)
1 e N 2
Were the soil structure of such a nature and the reservoir head H great
enough to create a large amount of percolation or high seepage pressure, the
flow Q would exceed the limits for a safe foundation and the effective pressure
P would be reduced enough to permit soil distortion and sliding of the founda-
e
tion material upon itself.
To reduce under-dam seepage a cutoff wall, Fig. 12.31, can be used. Then,
Darcy’s law, as modified to include the Schliter formula, gives the following
formula for the depth of the cutoff wall:
2
KH b PV
d (12.209)
2PV 2KH
in which d depth of cutoff, ft (m)
K a transmission constant
H head, ft (m)
P porosity of the material expressed as a decimal
V permissible velocity, fpm (m/s)
b effective base width of the dam, ft (m)

Earth Dams

Earth dams, dikes, and levees are the commonest structures used to impound
water, and innumerable instances of their use exist in all parts of the world. The
entire range in soils, from clays to boulders or quarried stone, has been used in
their construction.
Seepage in earth dams through the dam itself and the foundation, should be
kept within the limits prescribed by use of the reservoir, and by economic con-
siderations. The flow of water through all soils except the coarser ones is of the
laminar type and is in accordance with Darcy’s law:
Q kiAt (12.210)
where Q quantity of flow in time, t
k coefficient of permeability
i hydraulic gradient expressed as head lost per unit length of flow path
A superficial area of flow (total cross-sectional area of flow, not
merely cross-sectional area of soil pores)