Page 58 - Water Engineering Hydraulics, Distribution and Treatment

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Water Sources: Surface Water
Chapter 2
favorably to the high-intensity bottom loads. In constant-
angle dams, the upstream face bulges upvalley; the down-
level and elevation of dam crest. Other factors are wave height
stream face curves inward like the small of a man’s back.
(trough to crest), wave runup on sloping upstream faces, wind
setup or tilting of the reservoir surface by the drag exerted in
Dams of this kind fit well into V-shaped valleys, where arch
action becomes their main source of strength at all horizons.
the direction of persistent winds in common with differences
Concrete buttresses are designed to support flat slabs or
in barometric pressure, and (for earth embankments only)
depth of frost.
multiple arches in buttress dams. Here and there, wood and
Overflow sections of masonry and embankment dams
steel structures have taken the place of reinforced concrete.
Their upstream face is normally sloped one on one and may
are designed as masonry structures and separate spillways
terminate in a vertical cutoff wall.
as saddle, side channel, and drop inlet or shaft structures.
Spillways constructed through a saddle normally discharge
All masonry dams must rest on solid rock. Foundation
pressures are high in gravity dams; abutment pressures are namely, the vertical distance between maximum reservoir
into a natural floodway leading back to the stream below the
intense in arched dams. Buttress dams are light on their foun- dam. Usually they take the form of open channels and may
dations. Making foundations tight by sealing contained pock- include a relatively low overflow weir in the approach to the
ets or cavities and seams or faults with cement or cement- floodway proper. Overflow sections and overflow weirs must
and-sand grout under pressure is an important responsibility. be calibrated if weir heads are to record flood discharges
Low-pressure grouting (up to 40 psig or 278 kPa) may be fol- accurately, but their performance can be approximated from
lowed by high-pressure grouting (200 psig or 1390 kPa) from known calculations of similar structures. If their profile con-
permanent galleries in the dam itself, and a curtain of grout forms to the ventilated lower nappe of a sharp-crested weir
may be forced into the foundation at the heel of gravity dams of the same relative height d/h (Fig. 2.12), under the design
to obstruct seepage. Vertical drainage holes just downstream head, h, the rate of discharge, Q, becomes
from the grout curtain help reduce uplift. √ 3/2 3∕2
Q = 2/3c 2gl h = Clh (2.9)
where C = 2/3c is the coefficient of discharge, g the gravity
2.11 SPILLWAYS
constant, and l the unobstructed crest length of the weir. For
Spillways have been built into the immediate structure of both a crest height d above the channel bottom, the magnitude of
embankment and masonry dams, in each instance as masonry C is approximately
sections (see Fig. 2.5). Masonry dams may indeed serve
C = 4.15 + 0.65 h/d for h/d < 4or C = 4.15 − 6.75 (2.10)
as spillways over their entire length. In general, however,
′
spillways are placed at a distance from the dam itself to Under heads h other than the design head h, C approximates
divert flow and direct possible destructive forces—generated, to
for example, by ice and debris, wave action, and the onward ′ 7∕5 ′
C = 4.15(h /h) up to a ratio of h /h = 3.0 (2.11)
rush of waters—away from the structure rather than toward it.
Saddle dams or dikes may be built to a lower elevation than If the entrance to the floodway is streamlined, little if any
2
the main impounding dam in order to serve as emergency energy is lost—certainly no more than 0.05v /2g. As sug-
floodways. gested in Fig. 2.12, substantial quiescence within the reser-
The head on the spillway crest at the time of maxi- voir must be translated into full channel velocity. Discharge
mum discharge is the principal component of the freeboard, is greatest when flow becomes critical. The velocity head h
b
Plan
z
1
2
b b h v = v /2g
h
h v
H d
Figure 2.12 Spillways: (a)
channel spillway and (b) ogee
Longitudinal section spillway (Kindness of Arthur
(a) (b) Casagrande).