Encyclopedia of Environmental Science and Engineering, Volume I and II

HYDROLOGY 487

Experience of similar structures is very useful at this stage,

especially in evaluating such added constraints as possible

log jams or the infl uence of siltation or erosion (Bureau of

Reclamation^54 ).

Major Spillway Design Floods

Large dams are a particularly challenging design problem

from many viewpoints. In particular, the consequences of

failure due to inadequate spillway design have given rise to

numerous extensive hydrological studies and the develop-

ment of suitable techniques. For such a major structure it is

usual to calculate design fl oods by several methods, as dis-

cussed in such references as Kuiper and Linsley. 52,53

The fi rst method is based on extreme probability theory

as previously discussed in the statistics section. The analy-

sis of extreme independent time series is based on the work

of Fisher and Tipper^11 and is well illustrated by Gumbel.^12

The big question is what level of risk to assume, and prob-

abilities of 1:1000 to 1:10,000 are not uncommon for such

projects. The economic arguments reveal that the spillway

cost is often small compared with the havoc that could

occur if the dam failed. Hence it is quite usual for spillways

to be designed for much more rare events than the design

fl ood used for the rest of the system. Clearly the determina-

tion of the spillway design fl ood involves the incorporation

of a large safety factor, but it is still necessary to make as

good an estimate as possible of the true probability of such

an event.

The second method for estimation of design fl oods is the

maximum probable fl ood^1 approach. The physical processes

involved in producing a fl ood are studied. In some areas,

such as the North-Western part of North America, snowmelt

is the principal factor for large rivers. Elsewhere rain fl oods

may be limiting. Probable maximum precipitation can be

estimated by storm maximization,^55 or by statistical methods.

A simple approach was developed by Hershfi eld^56 and has

been called the poor man’s probable maximum precipita-

tion, the PMPMP. It is necessary to study the weather pat-

terns which produce either high snowmelt or high rainfall

Step Approximation

of unit Hydrograph

Sum of two

unit Hydrograph

Ins. of Rain

C.F.S

500

1000

1500

C.F.S

500

1000

1500

C.F.S

500

1000

1500

(^21)
1
2
2
2
3
3
(^4456)
4
6
6
8
(^24688)
10
(^1010)
Hours
Hours
1Hr.U.H.
2Hr.U.H.
Hours
Hours
1 HOUR UNIT HYDROGRAPH
RAIN-DURATION CURVE
CONSTRUCTION OF 2 HOUR
UNIT HYDROGRAPH 2 HOUR UNIT HYDROGRAPH
PEAK RUN-OFF RAIN
Critical Duration is 4 Hour Storm of 2.5 ins. of Rain,
which produces maximum Run – off of 2810 C.F.S.
U.H.PEAK RUN-OFF-RAIN x U.H.PEAK
1
2
3
4
5
Hour Storm 1.0 inch
1.7
2.0
2.5
2.75
(^1540) 1540 C.F.S
1290
1290
1125
990
2190
2580
2810
2720
Max.
FIGURE 14 Determination of critical storm duration for a given catchment.
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