4.

RIVER DIVERSION HEAD WORKS

 River diversion headwork is constructed at the head of the canal to divert the
regulated continuous
river water towards the canal, so as to ensure a
supply of silt-free water with a certain minimum head into the
canal.
 It usually provides a small storage capacity.
 Purposes of diversion headwork
 It raises the water level in the river so that the commanded area is increased 
 It regulates the supply of water into the canal
 It provides storage of water for a short period
 It controls the entry of silt into the canal
 It reduces the fluctuations in the level of supply in the river.
Selection of site for canal head works

1. A narrow, straight, well defined channel confined b/n banks not submerged by
the highest flood;

2. It should be possible to align the offtaking canal in such a way that the
command of its area is obtained without excessive digging.

3. The material of construction such as stone, sand, etc. should be available in

the vicinity of the site.

4. The site should be accessible by road. And there should be (enough) workers
available in the vicinity of project site.
Components of Diversion Head Works
 Weir or barrage

 Divide wall

 Fish ladder

 Pocket or approach channel

 Undersluices or

scouring sluices
 Silt excluder

 Canal head regulator

 River training works, such as marginal bunds, guide banks

 Weirs and Barrages
o are permanent river diversion works and are relatively low dams constructed across

a river to raise the river level sufficiently to divert the flow in full, or in part, into a
supply canal or conduit for the purpose of irrigation, power generation, domestic and
industrial uses, etc.
o Weirs are with or without gates, whereas barrages are always gate controlled

o Weirs may be classified according to the material of construction and certain design

features as
1) Masonry weirs with vertical drop or vertical drop weirs

2) Rockfill weirs with sloping aprons

3) Concrete weirs with a downstream glacis
 Masonry Weir (Vertical Drop Weir): Consists of:
 An impervious horizontal floor or apron
 A masonry weir wall (with both upstream and downstream faces vertical; or both
faces inclined; or upstream face vertical and downstream face inclined)
 Block protection at upstream end of floor, and a graded inverted filter at the
downstream end of floor
 Launching aprons or pervious aprons (or floors) after block protection and inverted
filters.

 This type of weir is suitable for any type of foundation

 Rockfill Weir With Sloping Aprons: is the simplest type of construction
and Consists of:
 Masonry weir wall

 Dry packed boulders

laid in the form of glacis or

sloping aprons in the
upstream and downstream
sides of the weir wall
 The downstream slope is generally made very flat.

 It requires a very large quantity of stone. It also has few intervening core walls.
 Concrete weir with downstream glacis

 It is of recent origin
 Its design is based on sub-surface flow concept.
 Hydraulic jump is developed on the glacis due to which considerable energy is
dissipated.
 Protection works such as inverted filter; block protection and launching apron
are provided.
 Sheet piles of sufficient depths are provided both at upstream and
downstream ends of the floor.
 Divide wall
 masonry or concrete wall with top width of 1.5 to 3m constructed at right angles to
the axis of the weir and separates the ‘weir proper’ from under sluices.
 extends on the upstream side beyond the beginning of the canal head regulator and
on the downstream side, up to the end of downstream protection of the under
sluices.
 The main functions :
o To separate the floor of the under sluices which is at lower level from the weir
proper;
o To help in providing a comparatively less turbulent pocket near the canal head
regulator resulting in deposition of silt in this pocket and, thus, to help entry of
silt-free water into the canal;
o To isolate the pocket upstream of the canal head regulator and facilitate
scouring operation;
o To prevent formations of cross-currents to avoid their damaging effects on the
weir.
 Fish Ladder
 enables the fish to pass upstream.
 the device dissipates energy thereby providing smooth flow at sufficiently low
velocity, ≤ 3 to 3.5m/s.
 This object is accomplished by providing a narrow opening adjacent to the
divide wall and provide suitable baffles or staggering devices in it, so as to
control the flow velocity.
Types
(i) pool type,
(ii) steep channel type,
(iii) fish lock type and
(iv) fish lift or elevator type.
 Types (iii) and (iv) are suitable
for high dams only.
 Types (i) and (ii) are generally
provided for barrages.
FISH LADDER
FISH LADDER
FISH LADDER
 Undersluices or Scouring Sluices
 They are openings provided in the weir wall with their crest at low level.
 The openings are fully controlled by gates.
 They are located on the same side of the off-taking canal.

 Functions :
i. They preserve a clear and well defined river channel towards the canal
head regulator;
ii. They scour the silt deposited on the river bed in the pocket upstream of
the canal head regulator;
iii. They pass low floods without the necessity of dropping the weir crest
shutters;
iv. They help to lower the high flood level by supplementing the discharge
over the weir during high floods.
 Capacity :

i. To ensure proper scouring, its capacity should be at least two times the
maximum discharge of the off-taking canal;

ii. It should have sufficient capacity to discharge maximum winter flood – without the
necessity of dropping the weir shutter;

iii. 10 to 20% of the maximum flood discharge – to supplement the discharge over
the weir during high floods.

 Canal head regulator

 provided at the head of the offtaking canal and serves the following functions:

 It regulates the supply of water entering in the canal;

 It controls the entry of silt in the canal;

 It prevents the river floods from entering the canal

 The head regulator is generally aligned at right angle
to the weir, but slightly larger angles
(between 900 and 1100) are now considered
preferable for providing smooth entry of water into the regulator.
 The regulation is done by means of gates.

 An important consideration in designing the regulator is silt exclusion from canals.

 Silt-excluder tunnels are provided in the barrage bays adjacent to the regulator
 The entry of silt into the canal is controlled by keeping the crest of the head
regulator by about 1 to 1.5m higher than the crest of the under sluices.

 Guide banks (river training works)

 Guide banks direct the main river flow as centrally as possible to the diversion
structure.
 They also safeguard the barrage/weir from erosion and may be designed so that a
desirable curvature is induced to the flow for silt exclusion from the canals.
 The side slopes of the guide banks must be protected by stone pitching, with a
sufficient 'self-launching' stone apron at the lowest feasible level.
 Protection Works
 The concrete floor of a weir or barrage is protected on the upstream as well as
downstream by loose apron.
 In the immediate vicinity of the floor, a certain portion of the loose apron is made
non-launching.
 The non-launching apron prevents the scour hole travel close to the floor or sheet
pile line;
 Launching apron is designed to launch along the slope of the scour hole to prevent
further scooping out of the underlying river bed material.
 Designs of Weirs and Barrages
 Causes of Failures of Weirs on Permeable Foundation
1. Due to seepage or subsurface flow
2. Due to surface flow
 Failures due to seepage or subsurface flow
 The seepage may cause the failure of a weir in two ways
 By piping or undermining
o Prevention measures:
i. Provide sufficient length of the impervious floor (so that the path of
percolation is increased) and reduce exit gradient.
ii. Provide piles at upstream and downstream ends of the impervious floor
 By uplift pressure: If the uplift pressure is not counterbalanced by the weight
of the floor, it may fail by rupture.
 o To prevent failure by uplift:
i. Provide sufficient thickness of the impervious floor

ii. Provide pile at the upstream end of the impervious floor so that uplift pressure is
reduced on the downstream side.

 Failures due to surface flow

 The surface flow may cause the failure of a weir in the following two ways:
 By suction due to standing wave or hydraulic jump:
o The following measures may be taken to prevent such kind of failure:
i. Providing additional thickness of the impervious floor to counterbalance the suction
pressure due to standing wave.

ii. Constructing floor as monolithic concrete mass instead of in different layers of

masonry.
 By scour on the upstream and downstream of the weir:
o Preventive measures which should be taken against failure due to scour
are:
i. Providing deep piles both at upstream and downstream ends of the
impervious floor. The piles should be driven much below the calculated scour
depth.
ii. Providing launching aprons of suitable length and thickness at upstream and
downstream ends of the impervious floor.
 Criteria for the Design of Weirs and Barrages
 Design of weirs and barrages consists of;
1. Hydraulic design
2. Structural design
 The hydraulic design deals with the evaluation of the hydraulic forces acting on the
structure and the determination of the configurations of the structure which will be most
economical and will have the best functional efficiency.
 The structural design consists of dimensioning the various parts of the structure to enable
it to resist safely all the forces acting on it.
 The hydraulic design is treated in respect of both subsurface and surface flows.
 Design w.r.t. subsurface flow involves determination of;
 Uplift pressure,
 Exit gradient,
 Length of impervious floor,
 Depth of sheet piles or cutoffs at upstream and downstream ends of the
impervious floor;
 Protection works
 The design in respect of surface flow involves determination of;
Pond level;
 Afflux;
 Levels of upstream floor and crest of weir or barrage;
 Shape of weir crest;
 Waterway;
 Effect of retrogression.
 Pond level:
 Pond level, in the undersluice pocket, u/s of the canal head regulator may be
obtained by adding the working head to the designed full supply level in the canal.
 The working head should include the head required for passing the design discharge
into the canal and the head loss in the regulator.
 Afflux
 Is the rise in water level on the u/s of a weir or barrage as a result of its construction.
 Afflux corresponding to the design flood is important for the design of the length of
the weir, crest levels, river training works, etc.
  Levels of u/s floor and crest of weir or barrage

 The u/s floor level of a weir or a barrage bays (other than undersluice bays) is fixed at the
general river bed level, at or below the level of the crest of the weir or barrage.
 The floor level is kept at 0.5 to 1.0 m higher than the u/s floor level of the undersluice bays.
o The crest levels of weirs or barrages are fixed as follows:

i. For weirs without shutters, the crest level should be at the required pond level;
ii. For weirs with shutters, the crest level should not be lower than 2 m below the pond level
as the maximum height of the falling shutters is limited to 2 m.
iii. For barrages, the crest level is determined by the depth required to pass the design flood
at the desired afflux. The level of crest in this case should be fixed by adjustment of the
waterway. It should in any case be kept higher than the undersluice crest level.
 Shape of the weir crest

A vertical drop weir is usually trapezoidal in cross section and its dimensions may be
obtained on the basis of stability considerations;
A glacis type weir is provided with a top width of about 2.0 m, and u/s slope of 2:1 to 3:1
depending on site conditions and d/s slope as required for the glacis of stilling basin.
 Waterway:

 The length of waterway which is equal to the length of the weir or barrage is fixed to pass
safely the maximum flood discharge.
 The length of the waterway should be equal to the stable river width for the maximum flood

discharge so that shoaling upstream is mostly eliminated and a nearly straight and stable
approach to the weir or barrage is obtained.
 The clear waterway to be provided between guide banks or abutments, excluding thickness of piers, is usually
taken equal to the Lacey’s regime perimeter given by
P  4.75 Q

P = Lacey’s regime perimeter in m,

Q = design flood discharge (m3/s)
 To account for the silt load carried by the alluvial rivers, the clear waterway of 1.1 to 1.25 times Lacey’s regime
perimeter is provided.
 Effect of Retrogression:

 Construction of a weir or barrage results in progressive retrogression or degradation of the downstream river bed

 This results in lowering of the downstream river stages and the same has to be suitably provided for in the design
of downstream cisterns.
 Design of Impervious Floor for Subsurface Flow
 Bligh’s Creep Theory
 Bligh assumed that the percolating water creeps along the base profile of the
structure, which is in contact with the subsoil.
 The length of the path thus traversed by the percolating water is called the creep
length.
 Bligh also assumed that the head loss per unit length of creep (called hydraulic
gradient) is proportional to the distance of the point from the upstream of the
foundation.
 The total creep length, L, is given by

L = (L1 + L2) + 2d1 + 2d2 + 2d3

L= b + 2(d1 + d2 + d3)
 The hydraulic gradient or the loss of head per unit length of creep is,

H H H
 
L b  2 d1  2 d 2  2 d 3  b  2 d1  d 2  d 3  

 Therefore, for any point the head loss is proportional to the creep length.

 As the hydraulic gradient is constant, if L1 is the creep length up to any point, then head loss up to
this point will be (H/L) L1, and
 the residual head at this point will be (H - (H/L) L1).
 The head losses at the three vertical cutoffs will be:
[(H/L) 2d1], [(H/L) 2d2] and [(H/L) 2d3]
  The reciprocal of the hydraulic gradient, i.e., L/H is known as Bligh’s coefficient of
creep, C.
 Safety against piping and undermining
 safety against piping can be ensured by providing sufficient creep length, given by
L = C.H, where C is the Bligh’s Coefficient for the soil
 According to Bligh if the hydraulic gradient H/L  C1 (for the soil) there is no danger
of piping
Safe
Type of soil Value of Hydraulic Gradient
C
Fine micaceous sand 15 1/15
Coarse grained sand 12 1/12
Sand mixed with boulder and gravel; and 5 to 9 1/9 to1/5
for loam soil
Light sand & mud 8 1/8
 Safety against uplift pressure
 The ordinate of the subsoil hydraulic gradient line above the bottoms of the floor at
any point represents the residual seepage head or the uplift pressure at that point.
 If h´ is the uplift pressure head at a point under the floor, the pressure intensity is,

P  gh 

 This is to be resisted by the weight of the floor, the thickness of which is t and

density ρm (for concrete, m = 2400 kg/m3).

 Downward force per unit area due to the weight of the floor is

W  mg t
 Therefore, equating
 m g t  gh'

 which gives

h   m t  Sm t

 where Sm is the relative density
of the floor material.
 Thus, we can write, h   t  S m t  t
which gives the thickness of the floor,
h  t h
t 
Sm  1 Sm  1
 where h is the pressure head (ordinate of hydraulic gradient) measured above the
top of floor, and (Sm-1) is submerged specific gravity of the floor material.
 4 h 3 h
 Considering a safety factor of 4/3 to 3/2 t to
3 Sm  1 2 Sm  1

with Sm= 2.24, t ≈ 1.08 h to 1.2 h

 The design will be economical if the greater part of the creep length (i.e. of the impervious floor) is provided
upstream of the weir where nominal floor thickness would be sufficient.
 The downstream floor has to be thicker to resist the uplift pressure.
 However, a minimum floor length is always required to be provided on the downstream side from the consideration
of surface flow to resist the action of fast flowing water whenever it is passed to the downstream side of the weir
 Moreover, the provision of maximum creep length on the upstream side of the weir (barrier) also reduces uplift
pressures on the portion of the floor provided on the downstream side of the barrier
 This is because a large portion of the total creep having taken place up to the barrier; the residual heads on the
downstream floor are reduced (Fig a).
 Further, (Fig b) a vertical cutoff at the upstream end of the floor reduces uplift all over the floor.
 Thus, according to Bligh’s theory a vertical cutoff at the upstream end of the floor is more useful than the one at the
downstream end of the floor.
Lane’s Weighted Creep Theory
Lane made distinction between vertical and horizontal creep.
He indicated that the horizontal creep is less effective in reducing uplift (or in
causing head loss) than the vertical creep.
 He, therefore, used a weightage factor of (1/3) for the horizontal creep.
Thus, the weighted creep length, Lw, is given by
N = sum of all the horizontal contacts and all the sloping
1 contacts less than 450 to the horizontal.
Lw  N V V = sum of all the vertical contacts and all sloping contacts
3
greater than 450 to the horizontal.
 To ensure safety against piping Lw > C1H
H = Total seepage head (difference in water head between u/s and
downstream)
C1 = Lane’s coefficient (empirical) of creep
 H   1 
    
 Further if the hydraulic gradient  Lw   C1 
safety against piping can be ensured.

Recommended values of Lane’s coefficient of creep C1 and safe hydraulic Gradient

 1 
Type of Soil (Material) Value of C1 Safe Hydraulic Gradient  
 C1 

Very fine sand or silt 8.5 1/8.5

Fine sand 7.0 1/7
Coarse sand 5.0 1/5
Gravel & Sand 3.5 to 3.0 1/3.5 to 1/3
Boulders, with some cobble & 2.5 1/2.5
gravel
Boulders, gravel and sand 2.5 to 3.0 1/2.5 to 1/3
Clayey Soils 3.0 to 1.6 1/3 to 1/1.6
 Khosla’s Theory and Concept of Flow Nets
The main principles of this theory are summarized below:
a) The seepage water does not creep along the bottom contour of impervious floor as
stated by Bligh, but moves along a set of streamlines .
 This steady seepage in a vertical plane for a homogeneous soil can be expressed by
Laplacian equation:

Where, φ = Flow potential = Kh; K = 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.
 The resultant flow diagram showing both of the curves is called a 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 the same as Bligh’s
path of creep.
 Flownet for seepage flow through soil
below a hydraulic structure

b) The seepage water exerts a force at each point in the direction of flow and tangential to the
streamlines.
This force (F) has an upward component from the point where the streamlines turns upward.
For soil grains to remain stable, the upward component of this force should be counterbalanced by
the submerged weight of the soil grain.
This gradient of pressure of water at the exit end 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 safe.
 Khosla’s Theory of Independent Variables
 In order to know how the seepage below the foundation of a hydraulic structure is taking
place, it is necessary to plot the flow net, i.e., we must solve the Laplacian equations.
 This can be accomplished either
 by mathematical solution of the Laplacian equations, or

 by graphically sketching and by adjusting the streamlines and equipotential lines with

respect to the boundary conditions.

 These are complicated methods and are time consuming.

 Therefore, for designing hydraulic structures such as weirs or barrage 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 flow nets for these simple standard profiles have been
presented in the form of equations and curves which can be used for determining the
percentage pressures at the various key points.
 The simple standard profiles used are:
a) A straight horizontal floor of negligible thickness with a sheet pile at either end,
i.e. at upstream or downstream end

b) A straight horizontal floor depressed below the bed but with no vertical cut-offs.
c) A straight horizontal floor of negligible thickness with a sheet pile line at some

intermediate position.
 The usual weir section consists of a combination of all or some of the three forms
mentioned above.
 Each elementary form is treated as independent of the others.
 The pressures as a percentage of the water head are read from Khosla’s curves at
the key points.
 The key points are the junction of the floor and the pile or cut-off walls, the bottom
points of the pile or walls, and the bottom corners in the case of depressed floor.
 The percentage pressure observed from the curves for the simple form into which the profile has been
broken up, is valid for the profile as a whole if corrected for:
1) Mutual interference of piles;
2) The floor thickness; and
3) The slope of the floor
i) Correction for Mutual Interference of Piles
The correction C to be applied as a percentage of head is given by;
D d  D
C  19  
b  b 

Where b’= the distance between two pile lines

D= the depth of pile line, the influence of

which has to be determined on

the neighboring pile of depth d. D is to be measured below the level at which interference is desired.
d= the depth of pile on which the effect is to be determined.
b= total floor length.
 The correction is positive for points in the rear or backwater and subtractive
for 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
a distance less than twice the length of the outer pile .
ii) Correction for Floor Thickness
 In the standard forms with cutoffs, the thickness of the floor is assumed to be negligible.

 Thus, as observed from Khosla’s curves, the percentage pressures at the junction
points E and C pertain to the level at the top of the floor whereas the actual junction is
with the bottom of the floor.
 The percentage pressures at the actual points E and C are interpolated by assuming a
straight line pressure variation from the hypothetical point E to D and also from D to C
 For pile no. 1, since the corrected pressure at E1

should be less than the calculated pressure at E,

the correction to be applied for the joint E1

shall be negative.
 Similarly, the pressure calculated at C

is less than the corrected pressure at C1, and hence, the correction to be applied at point C1
is positive. Slope
(V: H)
Correction
(% of pressure)
iii) Correction for Slope of the Floor 1:1 11.2
1:2 6.5
1:3 4.5
1:4 3.3
1:5 2.8
1:6 2.5
1:7 2.3
1:8 2.0

 A correction is applied for a sloping floor, and is taken as positive for the down and
negative for the up slopes following the direction of flow.
 The correction 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
iv) Exit Gradient (GE)
 For standard form consisting of a floor length b with a vertical cutoff of depth d, the exit
gradient at its end is given by:
H 1 Type of soil Safe exit gradient
GE  .
d  
Shingle ¼ to 1/5
Coarse sand 1/5 to 1/6
1 12
 , and Fine sand 1/6 to 1/7
2

b H = maximum seepage head

 The exit gradient so calculated must lie within safe limits as given in the table
d
Depth of sheet piles on upstream and downstream of impervious floor
 The sheet pile must be taken up to the level of possible deepest scour below the bed
of the river. 1
q2  3
 According to Lacey the depth of scour in alluvial soils is given by R  1 . 35  
 f 
R = scour depth measured below the highest flood level (HFL),
q = discharge per unit length,
f = Lacey’s silt factor.
√ In order to ensure further safety, for the design of sheet piles the scour depth is
considered as 1.25 to 2 times R given by the above equation.
Design of protection works at the u/s and d/s ends of the impervious floor
 In order to further safeguard the impervious floor against failure due to piping certain
protection works are provided at both the u/s and d/s ends of the impervious floor.
 These protection works consist of

Inverted filter,
Block protection, and
Launching apron or pervious apron
 Inverted Filter: consists of layers of materials of
increasing permeability from bottom to top.
Provided immediately at the d/s end of the
impervious floor to relieve the uplift pressure
Thickness: varies from 0.5 to 1.25 m.
The length depends on the scour depth D below
the river bed and it usually varies from 1.5 D to 2 D
D = XR – Y
XR = depth of deepest scour level below high flood
level
X = a multiplying factor (varies from 1.25 to 2)
Y = depth of the river bed or impervious floor below
high flood level
Y = High flood level – River bed level (or floor
level)
To prevent the filter material from dislocation by surface flow they are loaded with large size
stones or concrete blocks.
Thickness of blocks: 0.9 to 1.2 m and are placed with open joints filled with river sand or filter
material.
Block Protection: provided immediately at the u/s end of the impervious floor.
 Consists of 0.6 to 1.0 m thick stone or concrete blocks laid on 0.4 to 0.6 m thick loosely
packed stone.
 The length equals to the depth of scour, D, below the river bed at the u/s end of the
impervious floor.
Launching apron or pervious apron: is an apron of loosely packed stones.
 Its function is to protect the impervious floor and the pile from the scour holes
progressing towards the floor and the pile.

 The protection is provided by

a launching apron by forming a
protective covering of stones
over a certain slope below the
bed of the river at which the
apron is originally laid to the
bottom of the deepest scour likely to occur.
 The size of the stones (that shall not be washed away during maximum flood) is given
by USBR as  V 
2

d A 
 4.915 

Where VA = average velocity of flow in m/s and d = mean diameter of stones in m.

 The stones are assumed to launch at a slope of 2:1.

 The quantity of stone in a launching apron should be sufficient to provide about 1.0 m
thick cover over a slope of 2:1 in the launched position.
 Thus if D is the depth of scour, the length of the launched apron would be about

5D  2.236D.

 Since the thickness of the launched apron is 1 m, the quantity of stone required is
2.236D m3 per m length of the apron
 Design of vertical drop weir
The design of a vertical drop weir consists of: The following data must be known
i. Hydraulic calculations to fix various elevations, for the design of the vertical drop
ii. Design of weir wall, weir:
iii. Design of impervious floor (apron),
iv. Design of protection works on u/s & a) Maximum flood discharge,
d/s sides. b) High flood level (H.F.L.) before
construction of weir,
c) Downstream bed level,
d) Full supply level (F.S.L.) of
canal taking off from the river,
e) Allowable afflux,
f) Lacey’s silt factor.
Hydraulic Calculations
I. The length of the waterway, L is calculated from Lacey’s regime formula. P  4.75 Q
II. The discharge per unit length of the waterway, q is calculated as q = Q/L.
III. The regime scour depth is calculated using Lacey’s formula 1
q2  3
R  1 . 35  
 f 
IV. The regime velocity and velocity head are calculated from
V = q/R, and velocity head = v2/(2g)
V. Water levels and total energy line (T.E.L.) on the d/s & u/s side are calculated as
Level of d/s T.E.L. = (H.F.L. before construction) + v2/(2g)
Level of u/s T.E.L. = Level of d/s T.E.L. + Afflux
Level of u/s H.F.L. = Level of u/s T.E.L. – v2/(2g)
VI. Discharge over the crest of the weir is determined from,
2 3
and  q 
K
q  1.70 K 3 2 
 1.70 

Therefore, crest level = u/s T.E.L. - K

VII. Pond level = Level of top of gates

= F.S.L. of canal + Head loss through regulator

Head loss through regulator may be taken as 0.5 to 1.0 m.
Height of shutters = S = Level of top of gates – Crest level
VIII. Protection against scour

Level of bottom of u/s pile = u/s H.F.L. – 1.5 R

Level of bottom of d/s pile = H.F.L. after retrogression – 2 R
Design of Weir Wall
 A weir wall is usually trapezoidal in cross-section with either both u/s and d/s faces
inclined; or u/s face vertical and d/s face inclined.
 The design of the weir wall involves the determination of its top and bottom widths
such that the section will be stable under the condition of maximum stress.
 In general the condition of maximum pressure is that in which the head water is at the level
of the crest of the weir or at the top of the crest of the shutters (if any) and no water is
flowing over the weir so that there is no water on the d/s side.
 However, the condition of maximum stress on the weir may be different in certain
cases. Hence, it is necessary to check the stability of the weir under the following three
states:
State 1. When the u/s water or head
water is at crest level or at the top of
the crest shutter (if any)
and there is no flow .
State 2. When water is flowing over the
weir crest and the weir is submerged

State 3. When water is flowing

over the weir crest and weir is
discharging with a clear overfall.
Top width of weir wall
 Top width of the weir wall is obtained using three methods:
1) No tension criterion (for elementary profile) d
B1 
Sm
Where B1 = top width of the weir
d = maximum depth of water above the weir crest, which is equal to u/s
H.F.L. – crest level,
d
2) No sliding criterion (for elementary profile) B1 
 Sm

Where µ = coefficient of friction. Assuming µ = 2/3 as a safe value, we get

3d
B1 
2 Sm
3) Considering the height of the crest shutter
The top width of the weir is affected by height of crest shutter and it is given by,
B1 = S + 1 (meters)
Then, the largest of the three values is taken as the top width of the weir wall.
Bottom width of weir wall, B
 Determined by equating the overturning moments to the resisting moments taken at
the outer middle third of the bottom width of the weir wall.
 In determining the bottom width all the three states discussed above are considered.
State 1. Head water is at crest level or at the top of the crest shutter (if any)
 Considering the pressure diagram in Fig. (a) above, the overturning moment is given
  H  S
3
by M0 
6

 The resisting moment about the outer middle third point of the bottom is given by,
  1 
M r    S m  1.5 H  2.5S B 2  B1  Sm H  H  S B  B12  H  3S 
12  2 
 The above expression is valid when u/s and d/s faces have the same slope.
 If the u/s faceisHSkept vertical, the resisting moment is given by
Mr 
6
m
 B 2  BB1  B12 

 By equating the overturning moment to the resisting moment, the bottom width B is
determined.
State 2. Water is flowing over the weir crest and the weir is submerged (Fig. b).
 The overturning moment is given by,
hH 2
M0 
2
 For maximum value of M0, h is taken corresponding to the case when the weir is just
submerged.
 The resisting moment about the outer middle third of the bottom, with tail water at weir
crest level, is given by,
H  S m  1 2
 if both u/s and d/s faces have the same slope Mr 
12
 B  B1 B 
H  S m  1 2
 If the u/s face is vertical, Mr 
6
 B  B1 B  B12 

 Equating M0 and Mr, B can be determined.

State 3. Water is flowing over the weir crest and weir is discharging with a clear over-fall

(Fig. c). M 0   H 3  3dH 2  D 3 
6
 In the above equation there are two unknowns, viz. d and D and the relation between
the two must be known to find the maximum overturning moment.
 When the weir extends over the entire width of the river and the width of the river is of
considerable width in comparison to its depth, d is roughly proportional to D, i.e. d =
kD; where k is a constant and can be known if the river discharge for any one depth is
known (i.e. gauged).
 3
 Introducing this relation, M0 will be, M0 
6

H  3kDH 2  D 3 

 The maximum value of M0 is obtained from

dM 0 
dD

 3kH 2  3D 2  0
6

Or
 Hence, the maximum value of M0 is given by
DH k

M0 
H 3
6

1  2k 3 2

 The resisting moment may be considered to be approximately the same as that given for state 2.
 Like the previous cases, by equating M0 and Mr, B is determined.
 The greatest of the three values of B obtained above is adopted.
Design of impervious floor (or apron)
 For underseepage the worst condition occurs when the water on the u/s side is at the
level of the weir crest or at the top of the crest shutters and there is no tailwater.
 If the floor is designed on the basis of Bligh’s theory, the total creep length is given by

L = CHs

 If the floor is to be designed on the basis of Khosla’s theory, the horizontal length b of the
impervious floor is foundHby the consideration of the permissible exit gradient, GE, given by
1
GE  S

d  
1
 
 Knowing the permissible value of GE for the soil 1and values of Hs and d, may be
calculated.  
 From the exit gradient curve, for this value of , the corresponding value of α may be
found.
 Then from α = b/d, knowing α and d, the value of b can be determined
 Out of the total impervious floor length b (or creep length L), the lengths L 1 and L2 on the
d/s and u/s of the weir wall, respectively are fixed on the basis of Bligh’s recommendation
as
 Downstream impervious floor length, L1
 for weirs without crest shutters Hs
L1  2.21C
10

 for weirs with crest shutters L1  2.21C

Hs
13

 Upstream impervious floor length, L 2

L2 = L – L1 – (B + 2d1 + 2d2) (according to Bligh’s theory)
L2 = b – L 2 – B (according to Khosla’s theory)
Design of protection works on upstream and downstream sides
 Upstream side
 Immediately at u/s end of the impervious floor, a block protection of length d 1 is provided, where d1 is the depth of
pile below the river bed or the impervious floor at the u/s end.
 U/s of the block protection a launching apron of length equal to 1.5d 1 is provided.
ii) Downstream side
 The total length of the impervious floor, inverted filter, and launching apron on the d/s side of the
weir wall is also fixed on the basis of Bligh’s recommendations as
 for weirs without crest shutters L 3  18C
Hs q
x
10 75
Hs q
L 3  18C x
 for weirs with crest shutters 13 75

 The minimum length of the inverted and the launching apron is then equal to L3
– L1.

 However, an inverted filter of minimum length equal to 1.5d 2 is to be provided immediately at the d/s

end of the impervious floor, where d2 is depth of d/s sheet pile.

 After the inverted filter, a launching apron of length equal to 1.5 d 2 and thickness of 1.5 m is provided.

 If the required length (L3 – L1) is more than 3d2 the lengths of the inverted filter and launching apron

may be suitably increased.