2. Outcome of Lecture
2
After completing this lecture…
The students should be able to:
Understand Floods, Concept of design flood and Calculation of
peak flood discharge.
3. Flood
3
A flood is an unusual high stage of a river due to runoff from rainfall
and/or melting of snow in quantities too great to be confined in the
normal water surface elevations of the river or stream, as the result
of unusual meteorological combination.
5. Design Flood
5
The maximum flood that any structure can safely pass is called the ‘design
flood’ and is selected after consideration of economic and hydrologic
factors.
The design flood is related to the project feature; for example, the spillway
design flood may be much higher than the flood control reservoir design
flood or the design flood adopted for the temporary coffer dams.
6. Design Flood
6
A design flood is selected by considering the cost of structure to provide
flood control and the flood control benefits
Benefit can be categorized into direct and indirect.
Direct(tangible) prevention of damage to structures downstream, disruption
communication, loss of life and property, damage to crops and under utilization
of land
Indirect: (Intangible) the money saved under insurance and workmen’s
compensation laws, higher yields from intensive cultivation of protected lands
and elimination of losses arising from interruption of business, reduction in
diseases resulting from inundation of flood waters.
When the structure is designed for a flood less than the maximum
probable, there exists a certain amount of flood risk to the structure,
nor is it economical to design for 100% flood protection. Protection
against the highest rare floods is uneconomical because of the large
investment and infrequent flood occurrence.
7. Design Flood
7
Standard Project Flood (SPF).This is the estimate of the flood likely to occur from
the most severe combination of the meteorological and hydrological
conditions, which are reasonably characteristic of the drainage basin being
considered, but excluding extremely rare combination.
Maximum Probable Flood (MPF).This differs from the SPF in that it includes the
extremely rare and catastrophic floods and is usually confined to spillway
design of very high dams.The SPF is usually around 80% of the MPF for the
basin.
Design Flood. It is the flood adopted for the design of hydraulic structures like
spillways, bridge openings, flood banks, etc
8. ESTIMATION OF PEAK FLOOD
8
The maximum flood discharge (peak flood) in a river may be determined by
the following methods:
(i) Physical indications of past floods—flood marks and local enquiry
(ii) Empirical formulae and curves
(iii) Concentration time method
(iv) Overland flow hydrograph
(v) Rational method
(vi) Unit hydrograph
(vii) Flood frequency studies
9. ESTIMATION OF PEAK FLOOD
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(i) Physical indications of past floods—flood marks and local enquiry
By noting the flood marks (and by local enquiry), depths, affluxes (heading
up of water near bridge openings, or similar obstructions to flow) and
other items actually at an existing bridge, on weir in the vicinity, the
maximum flood discharge may be estimated by use of Manning’s or Chezy
equation
Estimate,A, P, R, S
n or C for actual site
10. ESTIMATION OF PEAK FLOOD
10
(ii) Empirical formulae and curves
There are plenty of empirical formulae relating Q with drainage area,A, of basin.
For example:
Burkli Ziegler formula for USA: Q = 412 A3/4
DICKENS Formula (1865): Q=CDA3/4
RYVES Formula (1884): Q=CRA2/3
INGLIS Formula (1930): Q=124A/(A+10.4)0.5
Where, Q is the peak flood in m3/s and A is the area of the drainage basin in
km2. CD and CR dickens constant and Ryves coefficient respectively.
11. ESTIMATION OF PEAK FLOOD
11
(iii) Envelope Curves.
Areas having similar topographical features and climatic conditions are
grouped together. All available data regarding discharges and flood
formulae are compiled along with their respective catchment areas.
12. ESTIMATION OF PEAK FLOOD
12
(v) Rational Method:
The Rational Method is most effective in urban areas with drainage areas of
less than 200 acres. The method is typically used to determine the size of
storm sewers, channels, and other drainage structures.
The rational method is based on the application of the formula
Q=kCiA
where C is a coefficient depending on the runoff qualities of the catchment
called the runoff coefficient (0.2 to 0.8), A is the area of catchment, i is
rainfall intensity and k is conversion factor.
For English units of acres and in/hr, k = 1.008 to give flow in cfs
For SI units of hectares and mm/hr, k = 0.00278 to give flow in m3/sec.
13. ESTIMATION OF PEAK FLOOD
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(v) Rational Method:
i is equal to the design intensity or critical intensity of rainfall ic
corresponding to the time of concentration tc for the catchment for a given
recurrence intervalT (also called return period);
ic can be found from the intensity-duration-frequency (IDF) curves, for the
catchment corresponding to tc and T.
Typical IDF Curve
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Duration, hr
Intesity,cm/hr
T = 25 years
T = 50 years
T = 100 years
tc
i
14. ESTIMATION OF PEAK FLOOD
14
(v) Rational Method:
If the intensity-duration-frequency curves, are not available for the
catchment and a maximum precipitation of P cm occurs during a storm
period of tR hours, then the design intensity i (= ic) can be obtained from the
empirical formulae as given below
when the time of concentration, tc is not known, ic ≈ P/tR.
15. ESTIMATION OF PEAK FLOOD
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(v) Rational Method:
Time of concentration: It is defined as the time
needed for water to flow from the most remote
point in a watershed to the watershed outlet.
The time of concentration equals the summation
of the travel times for each flow regime along the
hydraulic path or hydraulic length.
tc=(L/V)1+(L/V)2+(L/V)3+…..
The hydraulic length is the distance between the
most distant point in the watershed and the
watershed outlet.
16. ESTIMATION OF PEAK FLOOD
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(v) Rational Method:
Kirpich Formula
tc = 0.0078 L0.77S-0.385
where
tc = time of concentration in minutes.
L = maximum length of flow (ft)
S = the watershed gradient (ft/ft )or the difference in elevation between
the outlet and the most remote point divided by the length L.
17. ESTIMATION OF PEAK FLOOD
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(v) Rational Method:
Example: For an area of 20 hectares of 20 minutes concentration time,
determine the peak discharge corresponding to a storm of 25-year recurrence
interval. Assume a runoff coefficient of 0.6.
From intensity-duration-frequency curves for the area, forT = 25-yr, t = 20 min, i
= 12cm/hr.
Solution
For t = tc = 20 min,T = 25-yr, i = ic = 12 cm/hr= 120 mm/hr
Q = kCiA = (0.00278) 0.6 × 120 × 20 = 0.00278 (1440)
Q = 4 cumec
18. ESTIMATION OF PEAK FLOOD
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Example
For a culvert project, in the foothills of Alberta, Canada, determine the peak
flow using rational formula
Return Period for design: 50 years
http://culvertdesign.com/rational-method-example/
19. ESTIMATION OF PEAK FLOOD
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Step 1: Calculate the Drainage Area
Mark the drainage area and use planimeter or count squares to determine
net area.
The calculated drainage area was 8.0 km2, or 800 hectares
20. ESTIMATION OF PEAK FLOOD
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Step 2: Determine the Runoff Coefficient
Area may be composed of different surface characteristics, so we have to
determine average value of Coefficient C.
The drainage basin is 90% treed and 10% exposed rock (mountainous).
22. ESTIMATION OF PEAK FLOOD
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Step 4: Find the Rainfall Intensity
i=30mm/h
23. ESTIMATION OF PEAK FLOOD
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Step 5: Calculate Flood Peak Discharge
Q = 0.00278 C i A (metric)
= 0.00278 x 0.44 x 30 mm/hr x 800 ha
= 29.5 m3/s
24. ESTIMATION OF PEAK FLOOD
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Example:A 500 ha watershed has the land use/cover and corresponding
coefficients as given below
The maximum length of travel of water in the water shed is about 300m and the
elevation difference between the highest and outlet points of the watershed is 25m.
The maximum intensity duration frequency relationship of the watershed is given
by
i=6.311T0.1523/(D+0.5)0.945
Where I is the intensity in cm/h,T=return period in years and D=duration of the
rainfall in hours.
Estimate the 25 year peak runoff from the watershed using rational formula.
Land use Area (ha) Runoff Coefficient
Forest 250 0.1
Pasture 50 0.11
Cultivated land 200 0.3
25. ESTIMATION OF PEAK FLOOD
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(vi) Unit Hydrograph:
Peak of unit hydrograph is multiplied by actual precipitation of
design event to get expected peak of flood.
-10
10
30
50
70
90
110
130
-12 -6 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120
Discharge(cumecs)
Time, hours
6-hr Unit hydrograph
6-hr Storm Hydrograph
26. ESTIMATION OF PEAK FLOOD
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(vi) Flood Frequency studies:
Return period
Probablity of occurrence.
(similar like discussed in rainfall)
Some of the commonly used frequency distribution function for the
prediction of extreme flood values are:
1. Gumbel’s extreme-value distribution,
2. Log-PearsonType III distribution, and
3. Log normal distribution.
28. (vi) Flood Frequency studies:
Gumbel’s extreme-value distribution
28
This extreme value distribution was introduced by Gumbel (1941) and is
commonly known as Gumbel’s distribution. It is one of the most widely
used probability-distribution functions of extreme values in hydrological
and meteorologic studies for prediction of flood peaks, maximum rainfalls,
maximum wind speed, etc.
Gumbel’s Equation for Practical Use
The value of variate X with intervalT is given as
E.q. 1
E.q. 2
E.q. 3
30. Gumbel’s extreme-value distribution
30
Procedure
1.Assemble the discharge data and note the sample size N. Here the
annual flood value is the variate X. Find and σn-1 for the given
data.
2. Using standard tables determine and Sn appropriate to given
N.
3. Find yT for a given T by Eq. (3).
4. Find K by Eq. (2).
5. Determine the required xT by Eq. (1).
x
ny
31. Gumbel’s extreme-value distribution
31
Example: Annual maximum recorded floods in the river Bhima at Deorgaon, a
tributary of the river Krishna, for the period 1951 to 1977 is given below.Verify
whether the Gumbel extreme-value distribution fit the recorded values.
Estimate the flood discharge with recurrence interval of (i) 100 years and (ii) 150
years by graphical extrapolation.
33. 33
From the standard tables of Gumbel’s extreme value distribution,
for N = 27, yn =0.5332 and Sn = 1.1004.
34. 34
ChoosingT = 10 years, determine yT, K and xT by Eq. 3, Eq. 2 and Eq. 1
Similarly, values of xT are calculated for 5 and 20 and are shown below.
PlotT and XT on semi log scale
35. 35
It is seen that due to the property of Gumbel’s extreme probability these
points lie on a straight line.A straight line is drawn through these points. It
is seen that the observed data fit well with the theoretical Gumbel’s
extreme value distribution.
0
2000
4000
6000
8000
10000
12000
1 10 100 1000
XT
T
36. 36
By extrapolation of the theoretical xT vs T relationship, from Fig.,
At T = 100 years, xT = 9600 m3/s
At T = 150 years, xT = 10700 m3/s
By using Eq. (1 ) to (3),
x100 = Q100 = 9558 m3/s and
x150 = Q150 = 10088 m3/s
