floods

Floods

Dr. Mohsin Siddique

Assistant Professor

Dept. of Civil & Env. Engg

1

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.

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.

Flood

4

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.

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.

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

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

� (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 Chezyequation

Estimate, A, P, R, Sn or C for actual site


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

� (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

� (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


� i is equal to the design intensity or critical intensity of rainfall iccorresponding to the time of concentration tc for the catchment for a given recurrence interval T (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


� 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


� Time of concentration: It is defined as the timeneeded for water to flow from the most remotepoint in a watershed to the watershed outlet.

� The time of concentration equals the summationof the travel times for each flow regime along thehydraulic path or hydraulic length.

tc=(L/V)1+(L/V)2+(L/V)3+…..

� The hydraulic length is the distance between themost distant point in the watershed and thewatershed outlet.


16


� 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


� Example: For an area of 20 hectares of 20 minutes concentration time,determine the peak discharge corresponding to a storm of 25-year recurrenceinterval. Assume a runoff coefficient of 0.6.

� From intensity-duration-frequency curves for the area, for T = 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

� 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

� 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

� 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).


21

� Step 3: Determine the time of concentration


22

� Step 4: Find the Rainfall Intensity

i=30mm/h


23

� 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

� 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

� (vi) Unit Hydrograph:

� Peak of unit hydrograph is multiplied by actual precipitation ofdesign 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 hydrograph6-hr Storm Hydrograph


26

� (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-Pearson Type III distribution, and

� 3. Log normal distribution.

27

� Part II

(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 interval T is given as

E.q. 1

E.q. 2

E.q. 3


29


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

� 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.

32

MX**

(cu.m/s) Probability P=m/(N+1)

Return Period T

(years)

1 7826 0.036 28.00

2 6900 0.071 14.00

3 6761 0.107 9.33

4 6599 0.143 7.00

5 5060 0.179 5.60

6 5050 0.214 4.67

7 4903 0.250 4.00

8 4798 0.286 3.50

9 4652 0.321 3.11

10 4593 0.357 2.80

11 4366 0.393 2.55

12 4290 0.429 2.33

13 4175 0.464 2.15

14 4124 0.500 2.00

15 3873 0.536 1.87

16 3757 0.571 1.75

17 3700 0.607 1.65

18 3521 0.643 1.56

19 3496 0.679 1.47

20 3380 0.714 1.40

21 3320 0.750 1.33

22 2988 0.786 1.27

23 2947 0.821 1.22

24 2947 0.857 1.17

25 2709 0.893 1.12

26 2399 0.929 1.08

27 1971 0.964 1.04

N=27Mean of Q,= =4263 cu.m/sStandard deviation of Q= σn-1=1432.6 cu.m/s

x

** X represent Q

33

� From the standard tables of Gumbel’s extreme value distribution, for N = 27, yn =0.5332 and Sn = 1.1004.

34

� Choosing T = 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.

Plot T and XT on semi log scale

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’sextreme value distribution.

0

2000

4000

6000

8000

10000

12000

1 10 100 1000

XT

T

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

37

� Ref: Engineering Hydrology by K subramanaya;Mcgraw hill companies.

Thank you

� Questions….

38

floods

Engineering

flood protection

flood banks

flood4design flood

flood likely

flood risk

spillway design flood

concept of design flood

infrequent flood occurrence