TECHNIQUES OF IRRIGATION ENGINEERING

1.1 - Surface Drainage

1- DRAIN SECTION DESIGN

Drains are designed by using Chezy, Kutter or Manning’s Formula in addition to Elliott’s open drain formula can be used

V=/ a/P . 3/2 A V = Velocity in feet per second.a = Area of X-Section of drain in Sq. feet.P = Wetted Perimeter.A = Slope in feet per mile.

2- SEEPAGE DISCHARGE OF DRAIN

q = H P . 10-3 q = Discharge in cusecs per thousand feet Length of Drain. = Percolation intensity co-efficient per million Sq. feet at 20o C per unit head in cusecs.H = Percolation headP = Perimeter of drain section.

3- TILE DRAINS “ FLOW”

V = 138 R 2/3 S 1 / 2 V = Mean velocity in feet per secondS = Hydraulic grade or slope = h /lh = Fall of water in feet

Q = a . V l= Length in feet between points.R = a / Pa = Area of tile openingP = Wetted perimeter or circumference of tiles in feet

A = Q / z A = Area in acres drained by the tiles.z = Rate of Run Off.

1.2 - Soil Physics

1 (i ) - Capillary Rise.

h = 2 T g p r h = Height of meniscus above water levelT = Surface tension between water and airg = gravity i.e. 32.2 foot per second per second.p = Density of liquid.r = Radius of tube.

h = 0.15 ŗ г =Equivalent Radius of capillary tube of Elements of pore vacuum

(ii) - Movement of Water V = g h p r t V = Volume of fluid passing in time t. 8 h = Pressure head

= Length of tube = Viscosity of fluid

1.1

(iii) Qx = - x) x = Capillary Potential Qx = Mass of water passing in unit time Through unit cross-section to the

direction of flow x= distance from source.

= Capillary conductivity or transmission constant.

CAPILLARY CONDUCTIVITY OF SOIL

Loosely packed 1.8 x 10 - 3 cm /secWell packed in dry condition 7.4 x 10 - 3

Further packed by moistening and drying 5.4 x 10 - 3

Un- restricted field condition 8.7 x 10 - 3

General mean 5.8 x 10 - 3

2 - Porosity

(i) P = Vv /( Vv + Vs) x 100P = PorosityVv = Total volume of voids in mass of soilVs = Absolute volume of soil particles.

(ii) P = e / (1 + e) x 100e = Voids Ratio

Sand 0.54 Silt 0.71Organic matter 2.00 Clay 2.65Diatom 3.19 Mica 3.44Colloids 8.18

3 - Other soil constants and equilibrium limits

Heat of Wetting

Q = pT2 .( d / dT) . log p/PQ = Heat of dilutionp/P =Ratio of vapour pressure or relative humidity.T = absolute Temperature.P = Gas constant for unit mass of water vapours

4 – Distribution of water in vertical column of soil crust.

i) = 30.5/1033.2 . h – 0.0295 h = Hydrostatic pressure of liquid in atmosphereh = Height in feet above a given datum in feet.

ii) - = A/ - B , A, B = Constants

= Moisture contents.

5 – Soil Analysis

1.2

S2 = 30n / [g(G-G1)V]S = Dia of particles in millimetresn = Co-efficient of viscosity of suspended mediumg = 9.8 meter per second2

G = Specific gravity of particlesG1 = Specific gravity of suspended mediumV = Settlement velocity in centimetre per minute.Assuming n = 0.0102 viscosity at 670 FG = Specific gravity of soil = 2.65G1 = 0.9984 density of water at 670 FS2 = V /5290 or V = 5290 S2 cm / minute. = 173 feet per minute.

6 – Surface evaporation, soil evaporation Effect of Barometric pressure

i) Evaporation = log(P/(P-p)) P = Barometric pressurep = Max. vapour pressure, value

is infinitive at boiling pointII) Meyer’s evaporation formula from small bodies of shallow

water

E =15(V-v)(1+w/10)E = Evaporation in inches in 30 daysV = Max. vapour pressure in inchesv = Actual pressure of vapour in air (Average)w = Average wind velocity.

1.3 – Ground water Reservoir Movement

Sub-soil flow “ Darcy’s & hazen”i) Darcy’s sub-soil flow

Vc = 0.0388P/D Vd = 0.2458P/D Velocity of flow = k . slope of water surface V1 = 52100 f d1

2 (h/l1) feet per secondThis flow is inversely proportion to the viscosity

“Poiseuile’s Ratio”

P = i /(1+0.0337T + 0.000221T2)T = C0

f = i / P = f = 0.337T + 0.000221T2

f = i / P = 0.474 + 0.0147 t +0.0000682 t2

t = F0

V1 = must not exceed 0.039/ f d1 feet per secondf = i / P

Or the flow may cease to be capillary

a) Hazen velocity of percolation

1.3

V = Cd2 . [(t+10)//60] . h / =kh/ and k = Cd

2 . ((t+10)//60)V = Equivalent velocity at which water passesthrough sand.V1 = Velocity of water in pores of sand = Length of path along which percolation occurs in feeth = head producing percolation in feetd = Effective size of sand((t+10)//60 = Approximate factor denoted by f

b) Darcy’s estimation of flow

Q = k . i . A Q = discharge in cusecs = V . Ak = coefficient of permeability of soil cm/secondi = Hydraulic gradientV = k . iA =Area of site for which calculation re needed (Sft)

ii)- Percolation Intensity Coefficient

e . q = (H – h) e = % porosity = e.q /(H-h) = Percolation intensity

e = 40 % = 100/60 . 5/3If h = 0 , = (5/3)3 . q/h cusecs per million sq.feet

iii) Transmission Constant

V = k s = k (H-h)/D k = qD /{603 (H-h)}, q = Rise in feet in 24 hours (if e = 40 %)

iv) Permeability coefficient

“ Theim Method”k = q . log 10 (r1 / r) / (20.4 m (s-s1))

k = Permeability Co-efficient (Cft/minute//Sft on 1:1 gradient at 54o Fq = Rate of pumping in gallon per minuter, r1 = Distance of two observation

points from pumping sitem = Average vertical thickness of saturated portion of water bearing bed.

s & s1 = Draw down of two observation wells in feet.

Seepage Flow from Canals

1) Temperature Effect = 0.00003716 / (1+0.03368T+0.000221 T2)

= ViscosityV = Velocity of flow.T = Temperature oC

1.4

V 1/ (1+0.03368 T+0.000221 T2) A 1/

2) Flux or Loss from Canal “f “ F = Vd1( 1/cos+sin/)

d1 = Horizontal distance of the point of observation on outer most StreamV = Velocity in feet per hour along stream lineF = is flux or rate of loss from cnal.

3) Liquid Limit

= weight of wet soil – weight of dry soil x 100 weight of dry soil

4) Optimum Moisture Contents

W = 24 – 0.14 S W = O.M.C. by weight percentageS = Sand percentageW = Clay (24), Silt Clay (22), Loam (15)

Sand (11)Relation

W ‘ = W / (W + (100/G)) G = Specific Gravity of Soil = 2.65W ‘ = O.M.C by volume percentage

1.4 – Vertical Drainage1) Darcy’s law for determined Ground water

Q = k.i .Ak= Proportionality constant and is

variable with the type of soil and is denoted as Permeability Co-efficient.

i = Hydraulic GradientA = Area

Q/A = k .i = v2) Permeability Co-efficient (k)

S.No Type of Formation App. Av. Value of “k” in cm/Sec

1 Granite, Quartzite 0.6 x 10-5

2 Slate, Shale 4 x 10-5

3 Lime stone 4 x 10-4

4 Sand stone 0.0045 Sand and gravel 0.4006 Gravel 4.0007 Sand 0.0408 Clay and soil 0.04 x 10-5

3) Co-efficient of transmissibility “T”Introduced by Theiss

T = k. dd = depth of water bearing strip

4) Specific YieldSpecific yield = Volume of water obtained by gravity drainage x 100

1.5

Total volume of material drained or dewatered5) Yield of under ground sources

Theoretical MethodQ = A . V

Q = Discharge in cusecs.A = Area of the aquifer and can be found by dia of well and depth of porous strataV = Velocity = k . v v = Actual flow velocity of ground waterk = Constant of permeability.

k = 2.3Qlog10. R/rw

2 .H.(h-hw) = 2.3 Q log10 R/rw

2 H.sQ = 2 k H (d2-hw) 2.3 log 10 (R/rw)

Q = 2 k H (h-hw) 2.3 log 10 (R/rw

H = Total height of confined aquiferhw = Artesian pressure in wellrw = Radius of the wellh = Initial height of piezometric surface from the bottom of the wells = Draw down = h-hw

1.5 – Design of Channels

Hydraulic Formulae1) Chezy

V = C _ R.S V = Mean velocity flowR = Hydraulic mean depthC = Co-efficientS = slope of channel per foot lengthA = Area of Cross SectionPw = Wetted perimeter

i) f ‘ = f w /g w = Weight of one Cft of waterf ‘ = Co-efficient of friction in lbs /Sft at one foot velocity

ii) C = w / f’

2) BazinC = 157.5 / (1 + (k/R0.5 ) k = Co-efficient of roughness

Clean smooth pacca sides and bed = 0.2 Dirty sides of brick or stone etc. = 0.5 Sides of natural earth = 2.35

3) ManningsV = 1.4858/N . R 2/3 . S ½ N = Coefficient of roughness or rugosityQ = k ‘ d 5/3 k = Co-efficient of Area x velocity x

roughnessQ = Discharge in cusecs

4) Kutter

1.6

C = 41.66 + (1.811/N) + (0.0028/S) 1 + (41.66 + 0.0028/S )/ (N/R0.5)

N = Coefficient of roughness or rugosityC = ConstantValues of ‘N’ Well laid brickwork or ashlars =0.013

Rough brick work good stone work =0.015Same in inferior condition =0.017Rubble masonry or coarse brick work =0.020Earthen Canal in good order =0.0225Canals and rivers in bad order =0.030Torrents enumerated with debris =0.050

5) BarnesV0 = 58.4 R0.694 . S 0.496

5) Kennedy’si) V0 = C Dn V0 = Critical velocity in feet per second

D = Depth of water over bedn = Index number

V0 = 0.84 m D0.64 m = Critical velocity ratio. m = V / V0

Values of ‘m’i) Light sandy silt in the river = 1.00 ii) Some what coarse sandy soil = 1.10iii) Sandy loamy silt = 1.20iv) Coarse silt or debris = 1.30v) Silt of river Indus in Sind = 0.70

ii) Silt Transported Qt = a . B . V0

5/2

V0 = Critical velocityQt = Quantity of silt transported by channela = ConstantB = Bed width

iii) Lindley’s Formulae Va = 0.95 D 0.57

Vb = 0.59 B 0.353

B = 3.80 D 1.61

6) acey’s Formulaei) Lacey’s Regime Equation

V0 = k fL R fL = Lacey’s silt factor = 2 /(3)0.5 fL R

= 1.1547 . fL R = (4/3)1/2 . fL R = A . fL

2 = 4.0 V05

ii) Regime Flow Equation V0 = 16 . R 2/3 S ½ S = Slope of water surface per foot run

iii) Perimeter Discharge Relation

1.7

Pw = k Q = 8/3 Q = 2.67 Q k = Co-efficient = 8/3 or 2.67

iv) V, Q , fL Relation Q fL

2 = 4.0 V0

6

V0 = [(Q fL2)/4.0] 1/6

v) Regime slope equation S = fL

5/3 / (1844.3 Q 1/6)

vi) Regime scour depth relationa) R = 0.9(q2/fL) 1/3

R = Scour depthq = Discharge intensity or discharge per foot widthfL = Lacey’s silt factor

b) q = 3/8 . Qc) R = 0.474(Q / fL ) 1/3 Q = Total discharge of channeld) Q = (q/0.375)2

vii) Area of SectionA = 1.26 (Q5/6/ f1/3) = BD + SD2

B = Bed widthD = DepthS = Side Slope Generally ½ :1 or 0.5

P = B + 2.236 D (With ½:1 slope)P = Wetted Perimeter

B = P – 2.236DOrA = D(P-2.236 D) + 0.5 D2

= PD – 2.236D2 + 0.5D2

= 1.736D2 –PD +A = 0

D = P - /P2 – 4x 1.736A2 x 1.736 Evaluating Value of D B can be

calculated Or

D = (A / 2 R K) – (2RK)2 - (A/K)1/2 A = AreaR = Hydraulic mean depth.K = 2x1.736 (for ½:1 side slope)

Lacey’s Flow equation V0 = 1.3458/Na . R 3 / 4 S 1 / 2

viii) N a , fL , CVR Relation (CVR)2 = X2 = (V/V0)2 = fL CVR = Critical velocity ratio

ix) Silt factor grain size ratio FL = 1.76 mr = 8.D1 mr = Silt particle diameter in mm

D1 = Silt particle diameter in inches

Soil/Silt Lacey’s silt factor fL

a) Fine sand = 0.50 – 0.70b) Medium silt = 0.85c) Standard Silt = 1.00

1.8

d) Medium sand = 1.25e) Coarse Sand = 1.50

x) Lacey’s shock formulae a) V0 = 1.3458/Na R3/4 (S – s)1/2

s = Slope required to withstand shock losses

b) =1.3458/0.025 R 3/4 S 1/2

(S-s)1/2 = 0.9 S1/2

s = 0.19 S19% slope for shocks and 21 % for friction

7) Lined Channelsi) V = 1.486 / N . R 2/3 S 1/2

ii) Q = k x 0.8225 C 2/3 D 2/3

Side slope 1:1 Side slope 1.25:1

P = B/D B/DC = R/D R/D

Area = D2(P+1.7854) D2( P+1.9248) Pw = D (P+3.5807) D (P+3.8496)

V0 = 0.826R 2/3 S 1/2 0.826R 2/3 S ½

K = (P+1.7854) (P+1.9248)FL = 0.511C 1/3 D 1/3 0.517C 1/3 D 1/3

9 Super Elevation at curves

i) F = w2 / 2g (B2 + 2 R B) w2 = V2 / R2 Angular velocity in Radians = V2 / 2g [( 2 R B+ B2 ) / R2 ] ii) D1 = q / V1 R = Hydraulic mean depth D2 = q / V2 B = Bed width e = D1 – D2 F = Centrifugal pressure difference in

feetr = Radius of the streamq = Q / B = Discharge / bed widthV = q / D = Discharge per foot/Depth of channelD1= Depth of canal at outside of curveD2=Depth of canal at inside of curve e = Super Elevation

iii) Radius of Canal at bends

Discharge = Q Radius= rLess than 10 cusecs 300 feet10 – 100 cusecs 500 feet100 – 500 cusecs 1000 feet500 – 1000 cusecs 2000 feet1000 - 3000 cusecs 3000 feetAbove 3000 cusecs 5000 feet

iv) Mean velocitiesa) Major Disty . = 0.7. . Central Surface Velocity.

1.9

b) Minor = 0.65. Central Surface Velocity c) Water Course = 0.60. ..Central Surface Velocity v) Bank Widthsa) Discharge of Channel 0 - 49 cusecs = 4.0 feetb) Discharge of Channel 50 - 199 cusecs = 5.0 feetc) Discharge of Channel 200 - 350 cusecs = 6.0 feetd) Main Canals = 20 feetvi) Hydraulic Gradienta) When F.S.D is upto 4.0 feet = 1:4b) When F.S.D is 4.0 to 5.0 feet = 1:5c) When F.S.D is 5.0’ or above = 1:6vii) Berm Widtha) Channel in filling = 3 Db) Channel in cutting = 1.5 Dc) Channel in partially cutting and fiiling = 2 D

10) Absorption Losses

Haigh’s Formulae “

a) “Earthen Channels”

i) k = 5.0 Q0.0625 k =Absorption loss per million Sq.ft of Pw

ii) Qa = 0.0133LQ0.5625 Qa = Absorption losses in cusecQ = Discharge in cusecs.L = Length of reach in 1000 feet

b) “ Lined Channel” iii) k = 1.25Q0.056 k =Absorption loss per million Sq.ft of Pw

1.6 – Hydraulics of Rivers1- Classification of rivers on the Basis of topography

i) River in hillsa) Incised or rocky river stageb) Boulder River stage

ii) Rivers in alluvial plains.a) Aggrading stageb) Dredging stagec) Stabled) Deltaic

iii) Tidal Rivers ( Tail reach adjoining sea or oceans)2. Classification on the basis of Flood

Hydrographsi) Flashy Riversii) Virgin Rivers

3) Behaviour of Riversi) Straight reach, trough shape and high velocity in middle of

section.ii) Bends, silting and scouring continues simultaneously due action

of centrifugal force.iii) Meanders, Deviation from axle, formation of shoals on convex

side and erosion at concave side.Meander Length = ML = Axial length of one meander

1.10

Meander Belt = Mb = Distance between outer edges of clockwise and anti- clockwise loop of meander.Meander Ratio = Mb / ML

ML = 65.8 Qd

Qd = Qdominant = ½ to 2/3 of maximum discharge =Qmax

4) Training of riversi) Marginal Embankments

Runs parallel to river on one or both banks, Main function flood control..

ii) Guide Banksiii) Groynes or spurs.iv) Artificial cut-offs or Leading cutsv) Pitching of banks and provision of launching apronsvi) Pitched islands.vii) Miscellaneous Methods.

5) RunoffQ = K.P

Q = RunoffP = PrecipitationK = Constant depending upon the surface of Drainage AreaValues of “K”

i)ii)iii)iv)

Qv =

6) Flood Dischargesi) Dicken’s Formula.

Qv = High Flood or peak discharge in CumecsC = Constant = 11.5 for Himalyan

RangesA = Catchment area in Sq. kilometres

v) Ryve’s FormulaQv = C1 A 2/3

C1 =Areas within 80 kilometers from the coast = 6.8

S.No. Type of Area Value of “K”

1 Steep bare rock, city pavements of asphalt or concrete commercial and industrial areas 0.90

2 Rock steep but wooded 0.803 Plateaus, lightly covered 0.704 Clayey soils, stiff and bare 0.605 Clayey soils, lightly covered 0.506 Loam lightly cultivated or covered 0.407 Loam largely cultivated , urban residential areas

having single houses0.30

8 Sandy soils of light growth 0.209 Sandy soil covered with heavy brush 0.10

1.11

Areas 80-2400 km from coast = 8.8Limited areas near hills = 10.10Actual observed values upto = 40

vi) Jarvis FormulaQv = C A

C = Varies from 1.77 – 177 . The value of 177 Gives 100 % chance.

vii) Myer’s Modified FormulaQv = 177pA

P = p vary from 0.002 –1.0 usually taken as 1.0

1.7 - Discharge of Notches Orifices and weirs.

1- Notches & weirsa) Discharge through Rectangular Notchesi) Rectangular Notch (Free Fall)

Q =2/3 Cd B 2g . H3/2

Q = Discharge in cusecsB = Width of Notch

= 3.33 B H3/2 Cd= Co-efficient of discharge = 0.60 – 0.62H = G+ha = G + V2 / 2gg = gravity = 32.2 feet per second per second

ii) Rectangular Notch (Submerged)Q = C A V C = Cd (2g)0.5

A = Area of Water over notchV = Velocity

iii_ Rectangular Notch (in thin plate)Q = 2/3 Cd(B-0.2H) (2g)0.5 H3/2

Cd = 0.606 0.2H = End contraction if length of notch is not less than 3H

b) Discharge through triangular notchi) Q = 4/15 Cd B (2g)0.5 H 3/2 Cd = 0.60 – 0.62

ii) Q = 8/15 Cd (2g)0.5 Tan /2 H 3/2 (For any angle)

iii) Q = 8/15 Cd (2g)0.5 H 3/2 ( Right Angle)

c) Discharge through trapezoidal notch Q = Cd -/2g H 3/2 (L+8/15 tan H)

L = Length of cill.

2) Weir Formulae i) Q = 2/3 C B H 3/2 2g H = G + ha = G + V2/2g

Value of “C “ = Cd2gBroad crested or flat top = Cd =0.577 C = 3.09 Narrow crested Cd= 0.623 C= 3.33

1.12

B = Full width of channel= Cd =0.666 C= 3.56Co-efficient “C” includes velocity of approach

i) Francis FormulaQ = 3.58 (B- 0.1n H) H 3/2

n = Nos of end contractionsii) Bazin’s Formula

Q = 2g B H 3/2 No velocity of Approach = 0.405 + 0.00984/H

Q = m 2g B H 3/2

( 1+0.55 H) ( G + H )iii) Partially submerged weir

Discharge through free portion m = Q1 = 2/3 Cd B 2g (H1

3/2 – H3/2)H1 = U/S difference top R.L. of orifice to

Water LevelH = Difference of U/S & D/S Water

Level Cd = 0.62

a) Discharge of submerged portion ( into water)Q2 = Cd1 B 2gH

Description of orifice Value of Cd1

Sluice without side walls 0.66Canal lock and dock gates 0.70Sluice in lock gates 0.83Narrow Bridge opening 0.90Wide bridge opening or very large wellbuilt sluices with side walls 0.94Wide openings the bed of which islevel with bottom of reservoir 0.96 – 0.86

Total Discharge = Q = Q1 +Q2

iv) Discharge over a submerged weir

a) Discharge through free portionQ1 = 2/3 Cd B h 2g .H1

3/2 Cd = 0.577H1 = Difference of u/s & d/s W.L.

b) Discharge through drowned portionQ2 = Cd1 B h 2gH1 Cd1 = 0.80x = 4/3 Cd1Hy h = Drowned height over crest

y = D + 4/g H1

x = Horizontal Distance fro centre of falling water to lip of crest at d/s at any depth D below crest.

y = Depth of falling waterQ = Q1 + Q2

c) Round Crested WeirQ = C1 B H 3/2 C1 = 3 – 4.50

3) Discharge through Syphonsa) Loss of head “ h “

= (1 + f1 + f2.L/R) V2/2g - 2/2gh = Fall of water head through siphon

1.13

L = Length of barrelR = Hydraulic mean depthV = mean velocity through barrel = Mean velocity of approachf1 = 0.08 for bell mouth and 0.505 for cylindrical entry.f2 = ( a + b/R)

Surface Condition “a” “b”Smooth iron pipe 0.00497 0.084Encrusted pipe 0.00996 0.025Smooth cement plaster 0.00316 0.030Ashlars or Brick masonry 0.00401 0.070Rubble masonry or stone work 0.00507 0.250

b) Lacey’s Formulah = (1.08 +0.008 L R-1.05 ) V2/2g - 2/2g

4) NozzlesA/a = 8fL /A’ A/a = Ratio of area of nozzle & supply

pipe8fL/A = Vn

2 / V12Vn = Velocity in nozzle

L = Length of nozzle pipeH = Pressure head at base of nozzle

Projected vertical upward height of water would reach= V2 / 2g = h = H / (1+c .(4L/d1) . (d/d1)4

c = 0.01 For old pipes = 0.005 For New pipes = 0.0026 For varnished surface

d1 = Dia of piped = Dia of nozzleA’ = Area of piece

5) Allowing Air resistantHh = h (1 – 0.003h2) hh = actual height of jet

Qn = k . A 2g (H-h) (H-h) = Jet heightk = Co-efficient 0.95 – 0.99 A = A’

Deduction less due to FrictionHf = (4 f L V2) / (d . 2g)

1.8 - Design of Hydraulic StructuresA – Falls

a. Falls with drop wall or glacisi) Drop fall is recommended when downstream water level is at crest

or below crest.ii) Glacis design is essential when drop is not enough.

b. Requirements of Meter Flume.

i) Length of crest = 2 H to 3 Hii) Minimum modular head

1.14

a) Free over fall = 33 %b) Contracted flume (Crump’s L- Type) = 9 %

4) Contracted meter flume ( 1 in 5 downstream expansion) = 20 %

d) Full channel width with 1 in 5 glacis. = 10 %Safety margin of half a foot is allowed

iii) Fluming Ratio.a) Drop “HL” upto 4.0 feet = 65 %b) Drop “HL” upto 4.0 – 10.0 Feet = 75 %c) Drop “HL” above 10.0 Feet = 85 %

iv) Upstream of Flume.a) Hump

Upstream slope shall be with Radius “R”R =( La

2 +x2) / 2x La = 3 . H1.5

La = Horizontal distance of us bed and crest = 2H

x = Height of crest above u/s bed.R = Radius = 5H – 6 HH = Depth of water over crest.

b) Wing Walls Un-flumed Non Meter Fall may be splayed to an angle of 450 from crest and Junction 3.0

feet in bank of canal. Flumed Meter Fall.

Subtending Angle of 600 and Radius “R” 5H – 6 Hc) Upstream Cut-Off

1/3 of Full Supply Depth of Channel “D”d) Upstream Protection

D.B. Pitching on edge may be laid both in bed and sides for a length = water depth in a slope of 1:10 in bed.

v) Downstream of Flume

a) Glacis Slope 1 in 2 to 1 in 5 is adopted Radius of curves joining glacis with crest and cistern = H

b) Wing Walls Un-flumed Non Meter Fall may be taken as straight upto end of floor and then return wall. Flumed Meter Fall.

Splay of 1 in 3 for small work and for Large works:-Bx = (B1 . B2 . L ) / ( . B2 - (B2 – B1) . x)

B1 = Width of crestB2 = Width of canal at D/SBx = Width at x feet distance from crest. = Length of wing wall.x = Distance from crest

These are kept straight 5-8 times H.HL and then flared out with 1:1 slope at end and end return wall 3.0’ in bank of canal.

HL = Head Loss or difference of U/S & D/S water level

c) Downstream Cut-Off½ of D/S depth “D2”

1.15

d) Inverted FilterF.S.D = D2

e) Downstream ProtectionD.B. or pacca pitching on sides and bed floor = 4-5 times of “D2”

vi) Cistern.a) Etchevery Formula

Length = Lc =3HL . E E = H + V2/2gLc = Length of Cistern

Depth = Dc =1/6 of lengthDc = Depth of cistern.

b) Montague’s Formula Depth = Dc = ½ Ef2

Length= Lc = 4 Ef2

Ef2 can be had from Crump’s Diagram

c) General Equation in use Depth = Dc = ½ D2

Length= Lc = 4 –6 Ef2

d) Lc = 3 (B-Bt)/2B = Designed Bed width D/S sideBt = Width of crest

3) Scours Depthsa) Lacey’s

R = 0.9 (q2/f)1/3

R = Normal scour depth q = Intensity of discharge (Discharge per foot

width)f = Lacey’s silt factor

b) Kennedy’sR = 1.11 q0.61

Max. scour depth to be adopted U/S = 1.5 R, D/S = 2 RMaximum scour Level can be had by deducting Max. Scour Level fromF.S.L. of U/S & D/S side.

4) Hydraulic Jump1)a) 2/g . q2 = 2Dc

3 Dc = Critical depthb) Energy loss in jump

HL = (D2 – D1)3 (4D1-D2)

c) J = (D2 –D1)

d) Position of jump= 3 J on level floor and 3J on Glacis

e) Dr. Rehbock’s FormulaD1

3 –D12 H +( q2/ + g) = V

= Friction co-efficient 0.9 – 0.94f) T – Blench

1.16

D1D2[D2+D1- (2D1D2/(D2-D1))] = 2q2/g

HL = D2 . D1 – D2 +q2/2g(1/D12 – 1/D2

2)

He took trough as fullDL = J = D2 – D1

D1 . D2 (D2 – D1) = 2q2 /g D2 = D1/2 +- D1

2/4 – 2/g . q2/2D1

HL = [(D2+D1)(D2-D1)] / 4D1D2

2) On Glacisa) Crump’s “L” Method

= xy (x+y) = 2q2/g =2C3

x/c . y/c .(x+y/c) = 2L = (y-x)3 / 4xyL/C =(y/c – x/c)3 / (4 . x/c .y/c)

x = Upstream depthy = Downstream depthc = critical depth = (q2/g)1/3

K = Total energy at weir crestF = Vertical distance fro top of crest to point where jump is formed.L = Loss of head in jump.

b) Montague’s method HL = E+F – Ef2 = (D2 – D1)3 / 4D1D2

W (1/2D12+ q2/D1g) = (1/2D2

2+q2/D2g)W

Regulators, Outlets, and Misc. Structures

1) Canal Head Regulators and Cross Regulators.i) Crest Levelsa) Cross Regulator At the U/S Bed Level of channelb) Disty. Head Regulator 1.0 to 3.0 feet higher than crest level of cross Regulator.ii) Waterway

Q = 2/3 . Cd1.2g .B.[(h+ha)3/2 – h03/2] + Cd2.B.h12g(h+ha)

Cd1 = 0.577Cd2 = 0.80B = Clear waterway requiredh = Difference of water level u/s &d/sof crest.ha = Depth of the d/s water above the crest. crest. crest.h0 = Head due to velocity of approach,

which is very small and generally ignored

iii) Downstream Floor or Cistern Levelq and HL is first calculated and then from Crump’s diagram value of Ef2 is foundThe level at which the jump would form i.e. level of d/s floor, is then givenD/S Floor Level = d/s T.E.L - Ef 2

Neglecting velocity head, d/s T.E.L = d/s F.S.L.Level of d/s floor = d/s F.S.L. – Ef 2

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In case d/s floor works out higher than d/s bed of channel then d/s floor level =D/s bed level.

iv) Length of D/S Floor = 5 (y2- y1) or kept inconsideration of Exit gradient = b = a.d.

v) Cut-OffsU/S cut-off = (yd/3 + 2.0) feetD/S cut-off = (yd/2 + 2.0) feet

Yd = Upstream depth of channelvi) Total floor length

‘b’ is worked out from the safe exit gradientvii) Uplift Pressure and floor thickness

The floor thickness are worked out by working out the uplift pressures by Khosla’s Theory.

viii) Protection Works.The protection works are designed for a scour depth ‘D’ equal to (yd/3+2) feetOn the upstream and (yd/2+2) feet on the downstream

ix) Inverted Filter =1.5D

x) Launching Stone apron.= 2.25D cu.ft per foot length

C) Outletsi) Pipe Outlet

Q = C.A.hQ = Discharge in cusecsC = Cd.2g and Cd varies from 0.577 to 0.84 according to Modularty. In general value of C = 5A = Area of pipeh = Working head or difference of W.L. in Distributary and Water courseii) Adjustable Proportionate Module (A.P.M.) or

Orifice Semi Module (O.S.M.)Q = 7.3.B.Yh

Q = Discharge in cusecsB = Width of orifice or throat.Y = Height of orifice or throath = Depth of water over crest – Y

iii) Open Flume (O.F.) and Standing Wave Flume (S.W.F.)Q = C.B.H3/2

Q = Discharge in cusecsC = Coefficient For B = 0.20 to 0.29 = 2.9 For B = 0.30 to 0.39 = 2.95

For B = 0.40 or above = 3.00H = Head or depth of water over crest

iv) ScratchleyQ = 6.4.A.h

Q = Discharge in cusecsA = Area of orifice

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h = Working hed or difference of W.L. in cistern and water course

v) Minimum Modular Head .(M.M.H.)For Open Flume = 0.2 HFor A.P.M. = 0.75 (H – Y)

1.9 - .Affluxx = [( V2 / 58.6 ) + 0.05] . [(A/a)2 – 1]

x = Afflux or rise of waterV = Velocity in normal channelA = Area of Normal channel a = Area of contracted section

L = (d1 – d2) / S + D [1/S – C2/g].[(. d1/D) – ( . d2/D)]d2/D, d1/D are Bresse’s functionT1 = d1/D , T2 = d2/D

1.10 – Bligh’s and Lane’s and Khosla Creep Theories1) Bligh’s Theory

The percolating water follows the outline of the base of the foundation of hydraulic structure. In other words water creep along the bottom contour of the structure. The length of path thus traversed by water is called the Length of Creep. Further it is assumed in this theory that the loss of head is proportional to the length of the creep. If HL is the total head loss between upstream and the downstream, and L is length of creep, then the loss of head per unit of creep length i.e. (HL / L) is called the Hydraulic Gradient. Bligh’s makes no distinction between horizontal and vertical creep.

Head Loss per unit length or Hydraulic Gradient

c [ HL / (b+ 2 (d1+d2+d3)] = HL /L

HL = Head lossb = Total Length of floord1 = Upstream cut-off or sheet piled2 = Intermediate cut-off or sheet pile

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d3 = Downstream cut-off or sheet pile

L = Length or distance for which loss of head is required to be calculated

Losses at Different points are =(HL/L x 2d1) , (HL/L x 2d2) , (HL/L x 2d3)

i) Safety against piping or underminingAs per Bligh, the safety against piping can be ensured by providing sufficient creep length it is given by L = C . HL

C = Bligh’s coefficient for soilS.No Type of soil Value of

“C”Safe Hydraulic Gradient should be less than

1 Fine micaceous sand 15 1/152 Coarse grained sand 12 1/123 Sand mixed with

boulder and gravel, and for loam soil

5 to 9 1/5 to 1/9

4 Light sand and mud 18 1/18ii) Safety against uplift Pressure

The ordinates of the H.G. Line above the bottom of the floor represent the residual water head at each point. For example if at any point the ordinate of H.G. line above the bottom of the floor is one foot then one foot head of water will act as uplift at that point. If h’ feet is this ordinate , then water pressure equal to h’ feet will act at this point, and has to counter balanced the by the weight of floor thickness = t .Uplift Pressure = wh’

W = Ordinary density of water = 62.4 lbs /CftDrowned Pressure = (w.G).t

G = Specific Gravity of floor materialFor equilibrium

wh’ = wGt h’ = Gt

Subtracting t on both sides ( h’-t) = (G.t –t

= t(G-1) t = [(h’ – t )/(G-1)] = [ h / (G-1)]

Where (h’-t) = Ordinate of the H.G. line above the top of floor

(G-1) = Submerged specific gravity of the floor materialFor Concrete G = 2.4After calculating the thickness of floor add 33 % for the factor of safety.

2) Lane’s Weighted Creep Theory

Bligh, in his theory, had calculated the length of the creep, by simply adding the horizontal and vertical creep length, making no

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distinction between two creeps. Lane, on the basis of his analysis carried out on about 200 dams of the world,, stipulated that horizontal creep is less effective in reducing uplift (or in causing loss of head) than the vertical creep. He therefore suggested a weightage factor of 1/3 for the horizontal creep and 1.0 for the vertical creep.

LL = (d1+d1) + 1/3L1 +( d2+d2) + 1/3 L2 +(d3+d3) = 1/3 . (L1+L2) + 2(d1+d2+d3) = 1/3 . b . 2(d1+d2+d3)

LL = Lane’s Creep Length and other features are as per Bligh’s

To ensure safety against piping, the creep length LL must not be less than C1HL

HL = Head causing flow.and C1 is Lane’s Creep Coefficient.C1 = Lane’s coefficient for soil

S.No Type of soil Value of “C1”

Safe Hydraulic Gradient should be less than

1 Very fine sand or silt 8.5 1/8.52 Fine sand 7.0 1/73 Coarse sand 5 1/5 4 Gravel and sand 3.5 to 3.0 1/3.5 to 1/35 Boulders, gravel and

sand2.5 to 3.0 1 / 2.5 to 1/3

6 Clayey soil 3.0 to 1.6 1/3 to 1/1.6

Lane’s theory was an improvement of Bligh’s theory but is still an empirical without any rational basis and hence not adopted in designs. Bligh’s theory is still used even after invention of Khosla’s Modern Theory.

3) Khosla’s Theory and Concept of Flow Nets.Many of the important hydraulic structures , such as weirs and barrages were designed on the -basis of Bligh's theory between the period of 1910 to 1925, In 1926-27, the: Upper Chenab canal syphons were designed on Bligh's theory, started posing undermining troubles. Investigations started. which ultimately , lead to Khosia's theory..-

A detailed description of this theory is available at C.B.1-Publication No. 12. The main principles of this theory are summarised below:-

(i) The seeping water does not creep along the contour of pacca floor as stated by Bligh, but on the other hand this water moves along a set of streamlines. This steady seepage in, a vertical plane for a homogenous soil can be expressed by Laplacian equation.

(d2 /dx2)+(d2 /dz2) = 0

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= Flow potential =kh where k is the coefficient of permeability of soil, as defined by Darcy's law, and h is the residual head at any point within the soil.

The above equation represents two sets of curves intersecting each other orthogonally. One set of lines is called Streammlines and other is called Equipotential Lines. The resultant flow dia gram showing both the sets of curves is called Flow Net.

The streamlines represent, the paths along which the water flows through the sub-soil. Every particle entering the soil at a given point upstream of the work, will trace out its own path and will represent a streamline.The first streamline follows the bottom contour of the works and is same as Bligh's path of creep. The remaining streamlines follow smooth curves transiting slowly, from the outline of the foundation to a "semi-ellipse as shown in above Fig.

Equipotential Limes. Treating the downstream bed as datum and assuming no water on the downstream side, it can be easily stated that every streamline Posses a head equal to h1, while entering the soil, and when it emerges at the down-stream end . into the atmosphere its head is zero. Thus, the head h1 is entirely lost during the passage of water along the streamline. Further at every intermediate in its path there is certain residual head (h) still to be dissipated in the remaining length to be traversed to the downstream end. This fact is applicable to every streamline and hence, there will be points on different streamlines having the same value of residual head h. If such points are joined together, the curve obtained is called Equipotential line.

Every-water Particle on line AB is having a residual head h = hL and on CD is having a residual head h = 0, and hence AB and CD are Equipotential Lines.Since an equipotential line represents the joining of points of equal residual head and hence if piezometers were installed on an Equipotential lines the water will rise in all of them upto the same level as shown in Fig. Above

2) The seepage water exerts a force at each point in the direction of flow and tangential to the streamlines as shown in Fig below

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This force (F) has an upward component from the point where the streamline turns upward. For soil grains to remain stable, the upward component of this force should be counter balanced by the submerged weight of the soil grain. This force has the Maximum disturbing tendency at the exit end, because the direction of this force at the exit point is vertically upward and hence full force acts, as its upward component. For the soil grain to re-main stable, the submerged weight of soil grain should be more than this upward disturbing force. The disturbing force at any point is proportional to the gradient of pressure of water at that Point ( i.e.dp/dl). This gradient of pressure of water at exit is called the Exit Gradient. In order that the soil particles at exit remain stable, the upward pressure at exit should be safe. In other words, the exit gradient should be safeCritical Exit Gradient. This exit gradient is said to be critical when the upward disturbing force on the grain is just equal to the submerged weight of the grain at the exit. When.a factor of safety equal to 4 or 5 is used. the exit gradient can then be taken as safe. In other words, an exit gradient equal to 1/4 to 1/5 of the critical exit gradient is ensured, so as to keep the structure safe against piping.

The submerged weight (ws) of a unit volume of soil is given by w(1 –n)(SS - 1)

where w = unit weight of water.SS = sp. gravity of soil particlesn =. Prosity of soil material

For critical conditions to Occur at the exit point. Table below.

F= WS

Force F= Pressure gradient at that point. = dp/dL = w . dh/-dL

w . dh / dL = w . (1- n) (SS – 1) dh/ dL = (1 – n) (SS – 1)

where dh / dL represents the rate of loss of head or the gradient at the exit end.

=0.6 x 1.65 =0.99 1.0Hence an exit gradient equal to 1/4 to 1/5 g of the critical gradient means that an Exit gradient equal to ¼ to 1/5 has to be provided for keeping the structure safe

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Against piping

Values of safe exit gradient for some of the subsoils are given in below

. Table. Values of Khosla's Safe Exit Gradient.

Type Of Soil Khosla’s SafeExit Gradient Shingle 0.25 to 0.20Coarse sand 0.20 to 0.17Fine sand 0.17 to 0.14

Khosia's theory of flow nets made it very clear that the losshead does not take place uniformly in direct proportion to creep length as statedby Bligh. In fact, it depends upon the geometry of the figure i.e. the shape of foundations boundary and levels of u/s and d/s beds. When the Equipotentiallines are traced to be closer, the rate of loss of head wil ldefinitely be quicker and vice versa.It can, hence, be concluded that the safety against Piping cannot be obtained by providing sufficient floor length, as stated by Bligh, but can be obtained by keeping the exit gradient well below the critical value. The exit gradient may not be safe even if the average hydraulic gradient of Bligh ( i.e. 1 /C) is safe.

(3) Undermining of the floor starts from the downstream end of the d/s pacca floor, and if not checked, it travels upstream towards the weir wall. The undermining starts only when the exit gradient is unsafe for the subsoil on which the weir is founded. It is, therefore, absolutely necessary to have a rreasonably deep vertical cut-oft . at the downstream end of the d/s pacca fi0or to prevent undermining. The depth of this d/s vertical cut-off is governed by two considerations

i) maximum depth of scour; (ii) safe exit gradientWhile designing a weir, downstream cutoff from the maximum scoured depth considerations is, first of all provided, and checked for exit gradient. . If a safe value of exit gradient is not obtained , then the depth of cut-off is increased. The depth of cutoff is also governed and limited by practical considerations, as the execution of very deep cutoffs may be difficult -or un-practicable at site. A weir or a barrage may fait not only due to seepage (i.e. sub-surface flow) as stated by Bligh, but may- also fail due to surface flow. The surface flow (i.e. when flood water flows over the weir crest) may cause scour, dynamic action.; . and in addition, wilt cause uplift Pressures in the jump trough*, (if the hydraulic jump forms on the downstream). These uplift pressures must be investigated for various flow conditions. The maximum uplift due to this dynamic action (i.e. for surface flow) should then be compared with the maximum uplift under steady seepage (ie. for sub-surface flow) ; and the maximum of the two chosen for designing the aprons and the floors of the weirs. -All these modern aspects and other details about designing weirs on permeable foundations, as per the Khosla's theory, have been discussed in article 1 1'6.

Khosla's theory differs from Bligh's theory in all the above respects, but owing to the simplicity, Bligh's theory is still used

1.24

for design of small works. A minimum practical thickness for the floor and a deep vertical cut-off at the downstream end is, however, always provided, in addition to the requirements of Bligh's theory. However, on major works, Blighs theory should never be used, as it would lead to expensive and unsafe erroneous designs.

Khoslas method of independent variables for determination of pressures and exit gradient for seepage below a weir-or a barrage. In order to know as to how the seepage below the foundation of a hydraulic structure is taking place, it is necessary to plot the flownet. In other words, we must solve the Laplacian equations. This can be accomplished either by mathematical solution of the Laplacian equations, or by Electrical analogy method, or by graphical sketching by adjusting the streamlines and equipotential lines w.r .t. the boundary . conditions. These are complicated methods and are time consuming. Therefore for designing hydraulic structures such as weirs or barrages on pervious foundations, Khosla has evolved a simple, quick and an accurate 'approach, called Method of Independent Variables.

In this method, a complex profile like that of a weir is broken into a number of simple profiles, each of which can be solved mathematically.

. Mathematical solutions of. flownets for these standard profiles have been presented in the form of curves (Plate) -which can be used for determining the percentage pressures at the various key points. The simple profiles which are Most useful are :i) A straight horizontal floor of negligible thickness with a sheet pile line on the u/s end or d/s end) and'

ii) A straight horizontal floor depressed below the bed but without any vertical cut-offs (c)iii) A straight horizontal floor of negligible thickness with

are line at some intermediate point (d)

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The key points are the junctions of the floor and the pile lines an either side, and the bottom point of the pile line, and the bottom corners in the case of a depressed floor. The percentage pressures at these key points for the simple forms into which the complex profile has been broken is valid for the complex profile itself, if corrected for

(a) correction for the mutual interference of piles(b) correction for thickness of floor.(c) correction for the slope of the floor.

These corrections are described belowa) Correction for the Mutual Interference of Piles. The Correction C to be applied as percentage of head due to this effect, is given by

C = 19 D/b’[(d+D)/b] b'=The distance between the two pile

lines.D =The depth of the pile line, the influence of which has to be determined on the neighbouring pile of depth d.D is to be measured' below the level at which interference is desiredd=The depth of the pile on which the effect is considered.

b = Total floor lengthThis correction is positive for the points in the rear or back water and subtractive for the points forward in the direction of flow . This equation does not apply to the effect of an outer pile on an intermediate pile , if the intermediate pile is equal to or smaller than the outer pile and is at distance less than twice the length of the outer pile

Suppose in the above Fig. we are considering the influence of pile No. (2) on pile No. (1) for correcting the pressure at Cl, Since the point

C1 is in the rear, and hence, this correction shall be, +ve. While the correction to be applied to. E2 due to pile No. (1) shall be negative since the point E2 is in the forward direction of flow. Similarly, the correction at C2 due to pile No. (3) is positive, and the correction at E2 due to pile No. (2) is negative.

(b). Correction for the thickness of floor.

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In the standard form profiles, the floor is assumed to have negligible thickness.

Hence, the percentage pressures calculated by Khosla's graphs shall pertain to the top levels of the floor. While the actual junction points E & C are at the bottom of the floor. Hence the Pressure at the actual points are calculated assuming a straight line pressure variation. Since the corrected pressure at E’1 should be less then the calculated pressure at E’1, the correction to be applied for the point E1 shall be negative.

Similarly, the pressure calculated at C1 and hence, the correction to be applied at point C1 is positive.

c) Correction for the Slope of the floor.A correction is applied for a sloping floor, and is taken as +ve for

the down and –ve for the up slopes following the direction of flow. Values of correction of standard slopes such as 1:1, 2:1, 3:1 etc. are tabulated below:-

SlopeHorizontal : Vertical

CorrectionFactor

1:111.2

2:16.5

3:14.5

4:13.3

5.:12.8

6:12.5

7:1

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2.3

8:12.0

The correction factor given above is to be multiplied by the horizontal length of the slope and divided by the distance between the two pile lines between which the sloping floor is located. This correction is applicable only to the key points of the pile line fixed at the beginning or the ends of the slope or the ends of the slope.

Thus in Fig. para (a) above correction is applicable only to point E2. Since the slope is down at point E2 in the direction of flow, hence, the correction shall be positive and will be equal to the correction factor for this slope multiplied by b2/b1 where b2 and b1 are shown in above fig. para (a)

Exit Gradient (GE) It has been determined that for a standard form consisting of a floor length b with a vertical cut-off of depth d, the exit gradient aat its downstream end is given by

GE = H/d . 1/()Where =(1+1+2 ) / 2And = b/d

From the Curves of Plate by Khosla for any value of , i.e. b/d the corresponding value of 1 / cn be read off. Knowing H and d the value of GE can easily be calculated. The exit gradient so calculated must lie within the safe limits as given in Table below:

Type of Soil Safe Exit GradientShingle ¼ to 1/5 or 0.25 to 0.20

Coarse Sand 1/5 to 1/6 or 0.20 to 0.17Fine Sand 1/6 to 1/7 or 0.17 to 0.14

The uplift pressure be kept as low as possible consistent with the safety at the exit, so as to keep floor thickness to the minimum.

It is obvious from the above equation of GE that if d=0; GE is infinite. Hence it becomes essential that a vertical cut-off at the downstream end must be provided

1.11 - Examining stability of Hydraulic structures against sub surface flow

The following data required to be collected for checking the stability of the Hydraulic structure.(Falls and Regulators) i) Upstream max. water levelii) Downstream floor leveliii) Length of impervious floor from upstream cut-off to downstream

cut-off.iv) Depth of cut-offsv) The difference of upstream water level and downstream floor

level = Hvi) Length of floor = bvii) Max. depth of any cut-off = d

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viii) Nature or type of foundation soilix) Observation piping, undermining or scour upstream and

downstream which shows sign of any alarming situation for the structure.

x) Now apply Khosla’s Exit Gradient Formula and calculate the GE

xi) GE = H/d . 1/()Where =(1+1+2 ) / 2And = b/dIf the value of GE is less than the specified value for the type of

soil than the structure is safe if not than the remedial measure must be proposed. The remedy may be extending floor length or providing extra deep cut-off on downstream side.For other structures like bridges The upstream and downstream scour pits are thoroughly observed and their stability thus examined againstslipping or overturning in scour pits.For Syphons the observation of piezometric heads are needed to ascertain the safety against uplift pressures caused both by the Channels and drains.

1.12 – Losses of water heads

i. Loss due to friction= {( 4 f L) / d} . (V2 / 2g) f = Co-efficient of friction

ii) Loss due to sudden enlargement= (V1 – V2)2 / 2g V1 = Initial velocity

V2 = Final velocityiii) Loss due to contractionA1/A = 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.9 1.0Cc = 0.624 0.632 0.643 0.659 0.681 0.712 0.755 0.813

0.842 1.0iv) Loss due to obstruction

= A / (0.66(A-a) –1 A = Total areaa = Area of obstruction

v) Loss due to bends and elbows= k . V2 / 2g k = Co-efficient depending radius of

bendsvi) Gradual change

= h = V2(c2R) = (V12

– V22) / 2g

Variable flow in channelsLoss of head right angled bend = 0.84 V2 / 2gLoss in angle subtended by bend = (V2 . Sin2 ) / 1.34Difference in bed slope S’ and water surface slope SS’ – S = (S’ – V2 / (c2 R)) / ( 1 – V2/gd)Strength of pipes and cylinders “Syphon”t = p r / f t = Thickness of pipe in inches

p = Internal pressure in lbs / sq.inchr = Radius of pipe in inchesf = Safe stress per Sq. inch

1.13 – Energy Dissipation Devices1) Friction Blocks

1.29

Rectangular Concrete blocks securely anchored into the floora) For vertical drop fall

Two rows of friction blocks First row ay be started from a distance 1.5 yc from the

downstream toe of crest ( yc = critical depth of water). Spacing in between rows = yc Spacing in between blocks = 2 yc\

Dimension of blocks = 2 yc x yc x yc

In addition, cube blocks of size 1/8th to 1/16th of water depth may be provided at the end of impervious floor.

b) For Glacis Fall. Four rows of staggered blocks in case of flumed falls. The first row may be provided at a distance of 5 x height

of block fro the toe of glacis.. Height of block = 1/8th of water depth. Distance between two rows = h ( h= height of block) Dimension of blocks = 3h x h x h

c) Baffle Fall Two rows of staggered friction blocks when drop is more

than 6 feet. Height = h = 0.26 y2

y2 = Sub critical depth in canal downstream, required for jump formation for parallel downstream sides.

Length = h Top width = 2/3 h Distance between rows = h The first row ay be placed at a distance 2/3rd of the cistern

length fro the upstream end of the cistern.2) Glacis Blocks (Chute Blocks)

Single row of blocks of the sae dimensions as friction blocks may be provided just at the toe of glacis in case of flumed falls drop more than 6 feet

Helps in reducing turbulence and in turn reduces wave

wash, ensures uniform flow.

3) Baffle wall or Deflector wall A baffle or deflector wall is provided at the downstream

end of concrete floor in cast with downstream cut-off. Height above downstream bed level = 1/10th of water depth

1.14 – Retaining wallsRetaining wall is a vertical wall backed with earthy materials is subjected

to a thrust which tends to overturn it as well as cause to slide. In the design of a retaining wall the thrust on the back of the wall due to earth pressure is calculated and the wall made of such a cross section (thickness) the weight of which will resist the movement due to the thrust and the resultant force on the base lies within the middle third to ensure that there is no tension at the base. In cohesive soil the resultant should fall at or near the middle of base because in such soils unequal settlement of the toe may start a vicious circle. It is necessary to check that the stress at the toe does not exceed the allowable bearing

1.30

Section

Glacis

Cistern

capacity of the soil and that the wall does not fail by sliding bodily forward on the base. The pressure at the back of the wall is greater the heavier the material and the less the angle of repose. There are two theories which commonly used for the design of retaining walls:-

i) Rankine’s theoryThis theory assumes the earth a homogeneous incompressible granular mass with no cohesion and is thus appropriate for cohesionless soils e.g., sand, gravel and broken stone. It makes no allowance foe adhesion or for friction between the earth and the backfill of the wall. Although these assumptions are not always correct but give results erring on the side of safety.

ii) Coulomb’s Wedge theory.In this theory it is assumed that there is a wedge having the wall as one side and a plane called the “ plane of rupture” as the other side, and this wedge shaped mass of earth tends breaking away and slide down and forward , thus exerting thrust on the wall, and the wall has to support this wedge. For a vertical without surcharge the plane of rupture bisects the angle between the plane of repose and the back of the wall. This theory, however does not determine the direction of the thrust, and which is taken to act horizontally at 13 the height of the supported backing above the base of the wall, for walls with or without surcharge. For a wall with a vertical back and level backing the overturning moment due to pressure is the same as with Rankine’s formula .Simplified “Wedge theory” Formula:-P = wh2/2 x cos 2 = wh2/2 x K1

sin . sin ( - ) [ 1+ cos ]2

For a wall with vertical back and a levelBacking, = 0

Hence P = wh2/2 x cos 2 = wh2/2 (1-sin / 1+sin) (1+sin)

Rankine’s formula for walls without srcharge:

P = wh2 / 2 x ( 1-sin / 1+sin )Intensity of Pressure at any depth = wh x (1-sin / 1+sin)The earth pressure acts horizontally at 1/3 height of the supported backing above the base of the wall.Overturning moment due to earth pressure = wh2 / 6 x (1-sin / 1+sin )

P = Total lateral earth pressure per foot Length of wall due to the backing.w = Weight of backing per Cft.h = Height of backing. = Angle of repose of backing. = Angle of surcharge

1.31