design of weirs

PREPARED
BY
ER. SANJEEV SINGH
SNJV432GMAIL.COM

TYPES OF WEIRS
1. Types of Weirs based on Shape of the Opening
• Rectangular weir
• Triangular weir
• Trapezoidal weir
2. Types of Weirs based on Shape of the Crest
• Sharp-crested weir
• Broad- crested weir
• Narrow-crested weir
• Ogee-shaped weir
3. Types of weirs based on Effect of the sides on the emerging
nappe
• Weir with end contraction (contracted weir)
• Weir without end contraction (suppressed weir)

CLASSIFICATION BASED ON
SHAPE OF OPENING
Rectangular weir:
• It is a standard shape of weir. The top edge of weir may be sharp crested or
narrow crested.
• It is generally suitable for larger flowing channels.

FLOW OVER RECTANGULAR
WEIR
• To find the discharge over rectangular weir, consider an elementary
horizontal strip of water thickness dh and length L at a depth h from the
water surface.
Area of strip = L x dh
Theoretical velocity of water
Theoretical velocity of water formula
Therefore, discharge through strip
• Where Cd = coefficient of discharge
• By integrating above equation with limits 0 to H we can get the total discharge Q.

Finally discharge over the weir

TRIANGULAR WEIR
• The shape of the weir is actually reverse triangle like V. so, it is also
called V-notch weir.
• This type of weirs are well suitable for measuring discharge over small
flows with greater accuracy.

FLOW OVER TRIANGULAR WEIR
• Here also consider an elementary horizontal strip of water of thickness dh
at a depth h from the water surface.
Therefore, area of strip

• Theoretical velocity of water
• Therefore, discharge through strip dQ = Cd x area of strip x velocity of
water
• By integrating the above equation with limits 0 to H we can get the total
discharge Q
Therefore,
Finally, we get

TRAPEZOIDAL WEIR
• Trapezoidal weir is also called as Cippoletti weir. This is trapezoidal in
shape and is the modification of rectangular weir with slightly higher
capacity for same crest strength.
• The sides are inclined outwards with a slope 1:4 (horizontal : vertical)

FLOW OVER CIPPOLETTI WEIR
OR TRAPEZOIDAL WEIR
• In cippoletti weir both sides are having equal slope. So, we can divide the
trapezoid into rectangle and triangle portions.
• So, Total discharge over trapezoidal weir Q = discharge over rectangular
weir + discharge over triangular weir.

CLASSIFICATION ACCORDING TO
SHAPE OF THE CREST
Sharp-crested weir
• The crest of the weir is very sharp such that the water will springs clear of
the crest.
• The weir plate is bevelled at the crest edges to obtain necessary thickness.
And weir plate should be made of smooth metal which is free from rust and
nicks.
• Flow over sharp-crested weir is similar as rectangular weir.

BROAD-CRESTED WEIR
• These are constructed only in rectangular shape and are suitable for the
larger flows.
• Head loss will be small in case of broad crested weir.

NARROW-CRESTED WEIR
• It is similar to rectangular weir with narrow shaped crest at the top.
• The discharge over narrow crested weir is similar to discharge over
rectangular weir.

OGEE-SHAPED WEIR
• Generally ogee shaped weirs are provided for the spillway of a storage dam.
• The crest of the ogee weir is slightly rises and falls into parabolic form.
• Flow over ogee weir is also similar to flow over rectangular weir

CLASSIFICATION BASED ON END
CONTRACTIONS
Contracted weir
• The crest is cut in the form of notch and then it is similar to rectangular
weir. Head loss will occur in this type.
Suppressed weir
• The crest is running all the way across the channel so head loss will be
negligible.

COMPONENT PARTS OF A WEIR
Body wall of weir:-
• It is a wall which is constructed to raise the water level on u/s
• To raise water level on u/s
• Strong enough to resist water pressure
• Strong enough to resist uplift pressure

UPSTREAM APRON
• Protect weir from erosive forces during floods.
• Length of apron depends upon discharge in river and length of weir.
• Strong enough to withstand downward water pressure.
• Strong enough to prevent any leakage in the sub soil.

DOWNSTREAM APRON
• To reduce the kinetic energy of water.
• Length depends upon height of fall of water nature of soil discharge in
river.
• Apron is extended up to the point where there is no scope for erosion.
• Should have sufficient thickness to resist uplift pressure.

UPSTREAM CURTAIN WALL
• To reduce uplift pressure.
• Length depends on nature of sub soil.
• To increase length of the creep.
• To reduce exit gradient.

DOWNSTREAM CURTAIN WALL
• Protect downstream flow from uplift pressure.
• Strong enough to resist kinetic energy of water increase length of creep
CREEP:-
• Top of weir is called crest
• Strong enough to resist excessive pressure during floods
• Shutter will laid flat during floods over the crest

SHUTTERS:-
• Provide on the crest
• Can be raised during flood
• Strong enough to resist water pressure

CAUSES OF FAILURE OF WEIRS &
THEIR REMEDIES
Common causes of failure of weirs include:
• Excessive and progressive downstream erosion, both from within the
stream and through lateral erosion of the banks
• Erosion of inadequately protected abutments
• Hydraulic removal of fines and other support material from
downstream protection (gabions and aprons) resulting in erosion of
the apron protection
• Deterioration of the cutoff and subsequent loss of containment
• Additional aspects specific to concrete, rockfill or steel structures

PIPING
• Piping is caused by groundwater seeping out of the bank face. Grains are
detached and entrained by the seepage flow and may be transported away
from the bank face by surface runoff generated by the seepage, if there is
sufficient volume of flow. The exit gradient of water seeping under the base
of the weir at the downstream end may exceed a certain critical value of
soil. As a result the surface soil starts boiling and is washed away by
percolating water. The progressive erosion backwash at the upstream
results in the formation of channel (pipe) underneath the floor of weir.
Since there is always a differential head between upstream & downstream,
water is constantly moving form upstream to downstream from under the
base of weir. However, if the hydraulic gradient becomes big, greater than
the critical value, then at the point of existence of water at the downstream
end, it begins to dislodge the soil particles and carry them away. In due
course, when this erosion continues, a sort of pipe or channel is formed
within the floor through which more particles are transported downstream
which can bring about failure of weir.

• Piping is especially likely in high banks backed by the valley side, a terrace,
or some other high ground. In these locations the high head of water can
cause large seepage pressures to occur. Evidence includes: Pronounced
seep lines, especially along sand layers or lenses in the bank; pipe shaped
cavities in the bank; notches in the bank associated with seepage zones and
layers; run-out deposits of eroded material on the lower bank.

REMEDIES
• Decrease Hydraulic gradient i.e. increase path of percolation by providing
sufficient length of impervious floor
• Providing curtains or piles at both upstream and downstream

RUPTURE OF FLOOR DUE TO
UPLIFT
• If the weight of the floor is insufficient to resist the uplift pressure, the
floor may burst. This bursting of the floor reduces the effective length of
the impervious floor, which will resulting increasing exit gradient, and can
cause failure of the weir.
REMEDIES:
• Providing impervious floor of sufficient length of appropriate thickness.
• Pile at upstream to reduce uplift pressure downstream

• Rupture of floor due to suction caused by standing waves
• Hydraulic jump formed at the downstream of water
REMEDIES:
• Additional thickness
• Floor thickness in one concrete mass
• Scour on the upstream and downstream of the weir
• Occurs du to contraction of natural water way.
REMEDIES:
• Piles at greater depth than scour level
• Launching aprons:

DESIGN CONSIDERATIONS
• The problems involved in the hydraulic design of weirs on permeable
foundations may be treated under the following classification :
SURFACE FLOW
1. Depth of sheet piles with respect to scour considerations,
2. Level and length of the horizontal part of the downstream floor,
3. The thickness of the floor on the sloping glacis considering the hydraulic
jump formation,
4. Length and thickness of upstream and downstream loose aprons, and
Length, shape, &d free board of the guide banks

DESIGN FOR SURFACE FLOW
• Two considerations are to be fulfilled in determining the depth of the
downstream pile line L .
a) That with a suitable length of thc floor, it gives a safe exit gradient under
the maximum head. This is dealt with in the treatment of subsurface flow.
b) That its bottom is nearly at or below the level of the flood scour for that
• section of the work for which the depth is being determined.
• The depth of upstream pile line is determined only by the second of the
above considerations. The normal depth of scour, R, in metres, below the
high flood level, for a discharge intensity, q, in cumec/m, is given by
Lacey's equation as
R=1.34 𝑞2/𝑓 1/2

• The value of q would he different for the weir and the undersluices section and
should be taken separately for each. Here f is the silt factor which can be
determined by observing the water surface slope of the river during high flood and
substituting in Lacey's slope equation
S =0.00030
𝑓5
/
3
𝑄1
/
6
• Lacey's depth of scour, R, applies to regime flow only. Due to curved flow or
otherwise, where there is a likelihood of disturbance to flow, the depth of scour
would be more. Lacey has suggested the following classes of scour:
CLASS REACH DEPTH OF SCOUR
A STRAIGHT 1.25R
B MODERATE BEND 1.50R
C SEVERE BEND 1.75R
D RIGHT ANDLED BEND 2.00R

• Class A is likely to occur anywhere below the loose aprons, Class B is likely to occur
anywhere along the aprons of guide banks in a straight reach and Classes C and D at
and below the noses of guide banks or at the loose weir aprons in case heavy swirls
develop for some reason For the design of the sheet piles, it will be generally
sufficient to take them down to the level obtained by measuring the normal depth of
scour, R, below the high flood level (HFL), though sometimes upto 1.5 R on the
upstream side and 2.0 R on the downstream side is taken in conservative designs,
• For the design of the launching aprons, the maximum depth of scour below HFL
may be taken as:
• Upstream of the concrete floor 1.5 R
• Downstream of the concrete floor 2.0 R
• At noses of guide banks 2.25 R
• In transition from nose to straight portion of guide banks 1.5 R
• Straight portions 1.25R

LOOSE PROTECTION DOWNSTREAM
OF THE CONCRETE FLOOR
• Just below the end of the concrete floor an inverted filter 1.5D to 2 D long
should be provided, where D is the depth of scour below the bed (Figure
5.5). In the figure, xR is the depth of scow below HFL where x is the
coefficient of R for different situations as mentioned in the previous
paragraph. The depth of the inverted filter is kept equal to the depth of
dawnstream launching apron. It may comprise of concrete blocks 1.0 to 1.2
m deep placed over a 0.6 m thick layer filled with graded filter material.
The space between the blocks are filled with clean fine gravel. The inverted
filter is required from considerations of subsurface flow. The design
criterion for inverted filter is given by Terzaghi as
𝐷15 𝑂𝐹 𝐹𝐼𝑇𝐸𝑅
𝐷15 𝑂𝐹 𝐹𝑂𝑈𝑁𝐷𝐴𝑇𝐼𝑂𝑁
≥ 5 ≥
𝐷15 𝑂𝐹 𝐹𝐼𝑇𝐸𝑅
𝐷85 𝑂𝐹 𝐹𝑂𝑈𝑁𝐷𝐴𝑇𝐼𝑂𝑁

• Here, D15 and D85 represent the particle sizes which are, respectively, coarser than the finest
15 and 85 per cent of the soil, by weight.
The loose apron is provided after the inverted filter. The quantity of stone included in the
apron should be enough to provide a cover of approximately 1 m thickness over a slope of 2:1
(H:V) below the level at which. originally laid down to the bottom of the deepest scour that is
likely to take place at a given location. The length of the apron after having been launched will
be 5 D and its thickness being 1 m, the sectional area of the launching apron will be 1.0 x √5
D = 2.24 D . The apron as initially laid must have the same quantity of stone hence the same
sectional area. It may be laid in a length equal to 1.5 D and thickness will correspondingly be
almost 1.5 m. as scour takes place the apron launches the itself and provides a stone pitching
on the side of the soil. For this reason, such aprons are also called launching aprons.

LOOSE PROTECTION UPSTREAM
OF THE CONCRETE FLOOR
• Just upstream of the concrete floor of the weir, a block protection of 0.6 m
thick concrete blocks over 0.85 m packed stone should be provided for a
length equal to D. Upstream of the block protection, loose apron should be
provided in the same manner as for the downstream apron. D in this case
will refer to depth of scour hole below upstream bed, the bottom of scour
hole being determined after applying the appropriate coefficient to R.
• The launching aporns for protection of guide bunds or‘ flux bunds are also
designed in the same manner.

DESING OF BARRAGE OR WEIR
There are two aspects of the design of a barrage i.e:
• Surface flow / Overflow consideration
• Safety against subsoil flow i.e. (by Bligh’s creep theory, Lane’s weighted
creep theory and Khosla’s theory)

SURFACE FLOW / OVERFLOW
CONSIDERATION
Following items have to be estimated / designed in case
of overflow considerations:
• Estimation of design flood.
• Length of barrage i.e. (Width between abutments)
• Retrogression
• Barrage profile i.e. upstream floor level, D/S floor level, crest level

1. Estimation of design flood:
• The design flood (maximum flood) is estimated for which the barrage
is to be designed depending upon the life of structure. The design
flood estimation may be for 50 years, 100 years etc.
2. Length of Barrage (Width b/w Abutments):
• Lacey’s formula can be used for fixing the length of barrage i.e. Pw =
4.75 Q
Where, Pw = Wetted perimeter Q = Maximum flood discharge
• From t the length of barrage can be evaluated as, Length of barrage =
L.L.C x Pw
• Where, L.L.C = Lacey’s looseness coefficient Take L.L.C = 1.8, if not
mentioned

3. Retrogression:
• It is a temporary phenomenon which occurs after the construction of
barrage in the river flowing through alluvial soil. As a result of back water
effect and increase in the depth, the velocity of water decreases resulting in
deposition of sedimentation load. The water flowing through the barrage
have less silt, so water picks up silt from downstream bed. This results in
lowering d/s river bed to a few miles. This is known as retrogression.
• It may occur for the first few years and bed levels often recover their
previous level. Within a few years, water flowing over the weir has a
normal silt load and this cycle reverses. Then due to greater depth, silt is
deposited and d/s bed recovers to equilibrium. Retrogression value is
minimum for flood discharge and maximum for low discharge. The values
vary (2 - 8.5) ft.

4. Accretion:
• It is the reverse of retrogression and normally occurs upstream, although it may
occur d/s after the retrogression cycle is complete. There is no accurate method for
calculating the values of retrogression and accretion but the values which have been
calculated from different barrages can be used as a guideline.
5. Barrage profile:
• • crest level: The crest level is fixed by the total head required to pass the design
flood over the crest. The pond level is taken as the H.F.L. Maximum scour depth can
be calculated from Lacey’s scour formula,
R = 1.35 (q2f)1/3 (M.K.S) R = 0.9 (q2f) 1/3 (F.P.S)
Discharge per unit width, q = QL Velocity of Approach, V = qR Velocity head = v22g
And discharge can be found using discharge formula, Q = CLH 3/2
Where C = Coefficient of discharge Taken as 2.03 (M.K.S), Q = Flood Discharge, L = Length of
barrage crest , H=Total Energy Head = v22g + h •

ESTIMATION OF DESIGN FLOOD
Basis of Estimation
• The design flood for any given return period is usually estimated by the
frequency analysis method. Appropriate type of frequency distribution will
be selected from among the following:
• Pearson & Log Pearson Type III distributions
• Gumbel's Extreme Value distributions
• Normal & Log Normal distributions
• It is pertinent to point out that Log Pearson Type III distribution has been
adopted by United States Federal Agencies whereas Gumbel distribution
has generally been found to be suitable for most of the streams in Pakistan
including river Indus and its tributaries.

Hydraulic Units
• The dimensions and units of properties used in solving hydraulic problems
are expressed in three fundamental quantities of Mass (M), Length (L),
and time (T). All analyses and designs will be carried out in the Foot-
Pound-Second system of units and conversion to S.I Units will be made
only of important results as necessary.
Width of Barrage
• Three considerations govern the width of a barrage. They are the design
flood, the Lacey design width and the looseness factor. It is generally
thought that by limiting the waterway, the shoal formation upstream can
be eliminated. However, it increases the intensity of discharge and
consequently the section of the structure becomes heavier with excessive
gate heights and cost increases, though the length of the structure is
reduced.

Lacey's Design Width
• The Lacey's Design or Stable width for single channel is expressed as:
W = 2.67 v Q
Where Q is the Design Discharge in cusecs (ft3/sec).
• The Barrage is designed for a width exceeding W, partly to accommodate
the floodplain discharge and partly to take advantage of the dispersion of
the channel flow induced by the obstruction caused by the barrage itself.
The Looseness Factor
• The ratio of actual width to the regime width is the "looseness factor", the
third parameter affecting the barrage width. The values used have varied
from 1.9 to 0.9, the larger factor being applied in the earlier design.
Generally it varies from 1.1 to 1.5. From the performance of these
structures, a feeling arises in certain quarters that with high Looseness
Factor, there is a tendency for shoal formation upstream of the structures,
which causes damages and maintenance problems. The Consultants will
use the most appropriate looseness factor to provide reasonable flexibility
keeping the ill effects to the minimum.

Afflux
• The rise in maximum flood level of the river upstream of the barrage as a
result of its construction is defined as Afflux. Afflux, though confined in the
beginning to a short length of the river above the barrage, extends
gradually very far up till the final slope of the river upstream of the barrage
is established.
• In the design of barrages/weirs founded on alluvial sands, the afflux is
limited to between 3 and 4 feet - more commonly 3 feet. The amount of
afflux will determine the top levels of guide banks and their lengths, and
the top levels and sections of flood protection bunds. It will govern the
dynamic action, as greater the afflux or fall of levels from upstream to
downstream the greater will be the action. It will also control the depth and
location of the standing wave. By providing a high afflux the width of the
barrage can be narrowed but the cost of training works will go up and the
risk of failure by out flanking will increase. Selection and adoption of a
realistic medium value is imperative.

Tail Water Rating Curve
• Tail water rating curve for the barrages will be established through analysis
of gauge discharge data. The proposed tail water levels for new designs will
be established by subtracting the designed retrogression values from the
existing average tail water levels.
Crest Levels
• Fixation of crest level is clearly related with the permissible looseness
factor and the discharge intensity in terms of discharge per foot of the
overflow section of the barrage. After considering all the relevant factors
and the experience on similar structures the crest levels will be fixed in
order to pass the design flood at the normal pond level with all the gates
fully open.

• Discharges through a Barrage (Free Flow Conditions)
• The discharge through a Barrage under free flow conditions shall be
obtained from the following formula:
Q = C. L . H3/2 .......(1)
• Where,Q = discharge in cusecs
C = Coefficient of Discharge
L = Clear waterway of the Barrage (ft)
H = Total Head causing the flow in ft
• The value of C is generally taken as 3.09, but may approach a maximum
value of 3.8 for modular weir operation (Gibson). However to design a new
barrage it will be determined by physical model studies.

Discharge through a Barrage (Submerged Flow Conditions)
• The flow over the weir is modular when it is independent of variations in
downstream water level. For this to occur, the downstream energy head
over crest (E2) must not rise beyond eighty (80) percent of the upstream
energy head over crest (E1). The ratio (E2/E1) is the "modular ratio" and
the "modular limit" is the value (E2/E1= 0.80) of the modular ratio at
which flow ceases to be free.
Fane's Curve
• For submerged (non - modular) flow the discharge coefficient in equation
(1) above should be multiplied by a reduction factor. The reduction factor
depends on the modular ratio (E2/E1) and the values of reduction factor
(Cr) given in the table below are from Fane's curve (Ref: 2.3) which is
applicable to weirs having upstream ramp and sloping downstream with
slope 2H:1V or flatter:

E2/E1 Value of "Cr"
0.80 0.99
0.85 0.99
0.90 0.98
0.92 0.96
0.94 0.90
0.95 0.84
0.96 0.77
0.97 0.71
0.98 0.61
The submerged discharge is given by the equation:
Q = 3.09. Cr.b .E1
1.5

Gibson Curve
• Q = C'bE
1.5
• Where:Q = submerged discharge over crest (cusecs)
C' = submerged discharge coefficient
B = width of weir (ft)
E1 = upstream energy head above crest = h1+ v12/2g (ft)
• For submerged discharges the free flow discharge coefficient (C=3.80) is
multiplied by a reduction factor (C'/C). The coefficient factor depends on
the modular ratio (h/E), where his downstream depth of flow above crest.
The values of reduction factor "C'/C" given in the table below are from
Gibson curve applicable to the broad crested weirs:

h/E C'/C C'
0.70 0.86 3..27
0.80 0.78 2.96
0.90 0.62 2.36
0.95 0.44 1.67

design of weirs

More Related Content

What's hot (20)

Similar to design of weirs (20)

More from SANJEEV Wazir (20)

Recently uploaded (20)

design of weirs