_hydronic structure _II_Diversion Structures_Unity_University.pdf
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Aug 08, 2024
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About This Presentation
Its a module for engineers
Slide Content
4.0 Diversion Head Works
•The works which are constructed at the head of the canal,
in order to divert the river water towards the canal, so as
to ensure a regulated continuous supply of silt-free water
with a certain minimum head into the canal, are known as
diversion head works.
•The diversion of flow can be accomplished by constructing
a barrier across the river, so as to raise the water level on
the upstream side of the obstruction, and thus, to feed the
main canals taking off from its upstream side at one or
both of its flanks
4/16/2021 1 Daniel A. Unity University-HS-II-2013A.Y
•The works which are constructed at the head of the canal,
in order to divert the river water towards the canal, so as
to ensure a regulated continuous supply of silt-free water
with a certain minimum head into the canal, are known as
diversion head works.
•The diversion of flow can be accomplished by constructing
a barrier across the river, so as to raise the water level on
the upstream side of the obstruction, and thus, to feed the
main canals taking off from its upstream side at one or
both of its flanks
4/16/2021 1 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The ponding of water can be achieved either only by a
permanent pucca raised crest across the river or by a raised
crest supplemented by failing counter-balanced gates or
shutters, working over the crest.
•If the major part or the entire ponding of water is achieved
by a raised crest and a smaller part or nil part of it is
achieved by the shutters then the barrier is known as WEIR
•If most of the ponding is done by gates and a smaller or nil
part of it is done by the raised crest then the barrier is known
as a BARRAGE
4/16/2021 2 Daniel A. Unity University-HS-II-2013A.Y
•The ponding of water can be achieved either only by a
permanent pucca raised crest across the river or by a raised
crest supplemented by failing counter-balanced gates or
shutters, working over the crest.
•If the major part or the entire ponding of water is achieved
by a raised crest and a smaller part or nil part of it is
achieved by the shutters then the barrier is known as WEIR
•If most of the ponding is done by gates and a smaller or nil
part of it is done by the raised crest then the barrier is known
as a BARRAGE
4/16/2021 2 Daniel A. Unity University-HS-II-2013A.Y
Contd
4/16/2021 3 Daniel A. Unity University-HS-II-2013A.Y
4/16/2021 3 Daniel A. Unity University-HS-II-2013A.Y
Difference between Barrage and Weir --Contd
S.No
Barrage Weir
1 Low set crest High set crest
2 Ponding is done by means of gates Ponding is done against the raised crest or
partly against crest and partly by shutters
3 Gated over entire length Shutters in part length
4 Gates are of greater height Shutters are of smaller height, 2m
5 Gates are raised clear off the high floods
to pass floods
Shutters are dropped to pass floods
6 Perfect control on river flow No control of river in low floods
7 Gates convenient to operate Operation of shutters is slow, involve labor and
time
8 High floods can be passed with minimum
afflux
Excessive afflux in high floods
9 Less silting upstream due to low set crest Raised crest causes silting upstream
10 Longer construction period Shorter construction period
11 Silt removal is done through under sluices No means for silt disposal
12 Road and/or rail bridge can be
constructed at low cost
Not possible to provide road-rail bridge
13 Costly Structure Relatively cheaper structure
4/16/2021 4 Daniel A. Unity University-HS-II-2013A.Y
S.No
Barrage Weir
1 Low set crest High set crest
2 Ponding is done by means of gates Ponding is done against the raised crest or
partly against crest and partly by shutters
3 Gated over entire length Shutters in part length
4 Gates are of greater height Shutters are of smaller height, 2m
5 Gates are raised clear off the high floods
to pass floods
Shutters are dropped to pass floods
6 Perfect control on river flow No control of river in low floods
7 Gates convenient to operate Operation of shutters is slow, involve labor and
time
8 High floods can be passed with minimum
afflux
Excessive afflux in high floods
9 Less silting upstream due to low set crest Raised crest causes silting upstream
10 Longer construction period Shorter construction period
11 Silt removal is done through under sluices No means for silt disposal
12 Road and/or rail bridge can be
constructed at low cost
Not possible to provide road-rail bridge
13 Costly Structure Relatively cheaper structure
4/16/2021 4 Daniel A. Unity University-HS-II-2013A.Y
Objective of Diversion Head Works ---Contd
It raises the water level on its upstream side.
It regulates the supply of water into canals.
It controls the entry of silt into canals
It creates a small pond (not reservoir) on its upstream
and provides some pondage.
It helps in controlling the vagaries(change) of the river.
4/16/2021 5 Daniel A. Unity University-HS-II-2013A.Y
It raises the water level on its upstream side.
It regulates the supply of water into canals.
It controls the entry of silt into canals
It creates a small pond (not reservoir) on its upstream
and provides some pondage.
It helps in controlling the vagaries(change) of the river.
4/16/2021 5 Daniel A. Unity University-HS-II-2013A.Y
Location of Diversion Headwork ---Contd
•If there are a number of sites which are suitable, the final
selection is done on the basis of cost
•The site which gives the most economical arrangement for the
diversion head works and the distribution works (canals) is
usually selected.
•The factors/conditions to be considered in site selection for
diversion head work are:
The river section at the site should be narrow and well-
defined.
The river should have high, well-defined, inerodible and
non-submersible banks so that the cost of river training works
is minimum.
4/16/2021 6 Daniel A. Unity University-HS-II-2013A.Y
•If there are a number of sites which are suitable, the final
selection is done on the basis of cost
•The site which gives the most economical arrangement for the
diversion head works and the distribution works (canals) is
usually selected.
•The factors/conditions to be considered in site selection for
diversion head work are:
The river section at the site should be narrow and well-
defined.
The river should have high, well-defined, inerodible and
non-submersible banks so that the cost of river training works
is minimum.
4/16/2021 6 Daniel A. Unity University-HS-II-2013A.Y
Contd
The canals taking off from the diversion head works
should be quite economical and should have a large
commanded area.
There should be suitable arrangement for the diversion
of river during construction.
The site should be such that the weir (or barrage) can be
aligned at right angles to the direction of flow in the river.
The site should be easily accessible by road or rail.
The overall cost of the project should be a minimum.
4/16/2021 7 Daniel A. Unity University-HS-II-2013A.Y
The canals taking off from the diversion head works
should be quite economical and should have a large
commanded area.
There should be suitable arrangement for the diversion
of river during construction.
The site should be such that the weir (or barrage) can be
aligned at right angles to the direction of flow in the river.
The site should be easily accessible by road or rail.
The overall cost of the project should be a minimum.
4/16/2021 7 Daniel A. Unity University-HS-II-2013A.Y
Layout of Diversion Head Works and its
Components
•Typical layout of a canal head-works is shown in figure
below. Such a head-works consists of:
Weir proper
Under-sluices
Divide wall
River Training works
Fish Ladder
Canal Head Regulator
River Training Works e.g. Guide bank, Marginal bunds,
spur and groyne etc.
Shutters and Gates
Silt Regulation Works
4/16/2021 8 Daniel A. Unity University-HS-II-2013A.Y
Components
•Typical layout of a canal head-works is shown in figure
below. Such a head-works consists of:
Weir proper
Under-sluices
Divide wall
River Training works
Fish Ladder
Canal Head Regulator
River Training Works e.g. Guide bank, Marginal bunds,
spur and groyne etc.
Shutters and Gates
Silt Regulation Works
4/16/2021 8 Daniel A. Unity University-HS-II-2013A.Y
Contd
Typical layout of diversion head-works
4/16/2021 9 Daniel A. Unity University-HS-II-2013A.Y
Typical layout of diversion head-works
4/16/2021 9 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Weir Proper: It is a barrier constructed across the river. It aims
to raise the water level in order to feed the canal.
•Under-sluices/Scouring Sluices: The under sluices are the
openings provided at the base of the weir or barrage. These
openings are provided with adjustable gates.
The crest of the under-sluice portion of the weir is
kept at a lower level (1 to 1.5 m) than the crest of the
normal portion of the weir
When the suspended silt goes on depositing in front
of the canal head regulator and silt deposition becomes
appreciable the gates are opened and the deposited
silt is loosened with an agitator mounting on a boat. 4/16/2021 10 Daniel A. Unity University-HS-II-2013A.Y
•Weir Proper: It is a barrier constructed across the river. It aims
to raise the water level in order to feed the canal.
•Under-sluices/Scouring Sluices: The under sluices are the
openings provided at the base of the weir or barrage. These
openings are provided with adjustable gates.
The crest of the under-sluice portion of the weir is
kept at a lower level (1 to 1.5 m) than the crest of the
normal portion of the weir
When the suspended silt goes on depositing in front
of the canal head regulator and silt deposition becomes
appreciable the gates are opened and the deposited
silt is loosened with an agitator mounting on a boat. 4/16/2021 10 Daniel A. Unity University-HS-II-2013A.Y
Contd
4/16/2021 11 Daniel A. Unity University-HS-II-2013A.Y
4/16/2021 11 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The main functions of under-sluices are:
To maintain a well defined deep channel approaching
the canal head regulator.
To ensure easy diversion of water into the canal
through the canal head regulator even during low flow.
To control the entry of silt into the canal
To help passing the low floods without dropping the
shutters of the weir.
4/16/2021 12 Daniel A. Unity University-HS-II-2013A.Y
•The main functions of under-sluices are:
To maintain a well defined deep channel approaching
the canal head regulator.
To ensure easy diversion of water into the canal
through the canal head regulator even during low flow.
To control the entry of silt into the canal
To help passing the low floods without dropping the
shutters of the weir.
4/16/2021 12 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The divide wall: The divide wall is a long wall constructed at
right angles in the weir or barrage, it may be constructed with
stone masonry or cement concrete.
On the upstream side, the wall is extended just to
cover the canal head regulator and on the downstream
side, it is extended up to the launching apron.
•The main functions of the divide walls:
It separates the ‘under-sluices’ with lower crest level from
the ‘weir proper’ with higher crest level.
It helps to keep cross-current, if any, away from the weir.
It helps in providing a comparatively less turbulent
flow
4/16/2021 13 Daniel A. Unity University-HS-II-2013A.Y
•The divide wall: The divide wall is a long wall constructed at
right angles in the weir or barrage, it may be constructed with
stone masonry or cement concrete.
On the upstream side, the wall is extended just to
cover the canal head regulator and on the downstream
side, it is extended up to the launching apron.
•The main functions of the divide walls:
It separates the ‘under-sluices’ with lower crest level from
the ‘weir proper’ with higher crest level.
It helps to keep cross-current, if any, away from the weir.
It helps in providing a comparatively less turbulent
flow
4/16/2021 13 Daniel A. Unity University-HS-II-2013A.Y
Contd
Cross section of divide wall on Pucca floor
4/16/2021 14 Daniel A. Unity University-HS-II-2013A.Y
Cross section of divide wall on Pucca floor
4/16/2021 14 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Fish Ladder: the fish ladder is provided just by the side of
the divide wall for the free movement of fishes
In the fish ladder, the walls are constructed in a
zigzag manner so that the velocity of flow within the
ladder does not exceed 3 m/sec
Section and plan of
a typical fish
ladder
4/16/2021 15 Daniel A. Unity University-HS-II-2013A.Y
•Fish Ladder: the fish ladder is provided just by the side of
the divide wall for the free movement of fishes
In the fish ladder, the walls are constructed in a
zigzag manner so that the velocity of flow within the
ladder does not exceed 3 m/sec
Section and plan of
a typical fish
ladder
4/16/2021 15 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Canal Head Regulator or Head sluices: A structure which is
constructed at the head of the canal to regulate flow of water
is known as Canal Head Regulator(C.H.R)
It consists of a number of piers which divide the total
width of the canal into a number of spans which are known
as bays
The piers consist of number tiers on which the adjustable
gates are placed. The gates are operated form the top by
suitable mechanical device.
Alignment of a canal head regulator
4/16/2021 16 Daniel A. Unity University-HS-II-2013A.Y
•Canal Head Regulator or Head sluices: A structure which is
constructed at the head of the canal to regulate flow of water
is known as Canal Head Regulator(C.H.R)
It consists of a number of piers which divide the total
width of the canal into a number of spans which are known
as bays
The piers consist of number tiers on which the adjustable
gates are placed. The gates are operated form the top by
suitable mechanical device.
Alignment of a canal head regulator
4/16/2021 16 Daniel A. Unity University-HS-II-2013A.Y
Contd
Alignment of a
canal head regulator
A typical section through a Canal Head Regulator 4/16/2021 17 Daniel A. Unity University-HS-II-2013A.Y
Alignment of a
canal head regulator
A typical section through a Canal Head Regulator 4/16/2021 17 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Functions of Canal Head Regulator:
It regulates the supply of water entering the canal
It controls the entry of silt in the canal
It prevents the river-floods from entering the canal
•The water from the under-sluice pocket is made to enter the
regulator bays, so as to pass the full supply discharge into
the canal.
•The maximum height of gated openings, called head sluices
will be equal to the difference of Pond Level and Crest Level
of the regulator.
4/16/2021 18 Daniel A. Unity University-HS-II-2013A.Y
•Functions of Canal Head Regulator:
It regulates the supply of water entering the canal
It controls the entry of silt in the canal
It prevents the river-floods from entering the canal
•The water from the under-sluice pocket is made to enter the
regulator bays, so as to pass the full supply discharge into
the canal.
•The maximum height of gated openings, called head sluices
will be equal to the difference of Pond Level and Crest Level
of the regulator.
4/16/2021 18 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The entry of silt into the canal is controlled by keeping the crest
of the head regulator by about 1.2 to 1.5 meters higher than
the crest of the under-sluices.
4/16/2021 19 Daniel A. Unity University-HS-II-2013A.Y
•The entry of silt into the canal is controlled by keeping the crest
of the head regulator by about 1.2 to 1.5 meters higher than
the crest of the under-sluices.
4/16/2021 19 Daniel A. Unity University-HS-II-2013A.Y
Silt Control Devices ---Contd
•Silt Control Devices: The entry of silt into a canal, which
takes off from a head-works can be reduced by constructing
certain special works called silt control works. The works may
be classified into the following two types:
a)Silt Excluders: Silt excluders are those works which
are constructed on the bed of the river, upstream of the
head regulator.
The clearer water enters the head regulator
and the silted water enters the silt excluder. In this
type of works, the silt is, therefore removed from
the water before it enters the canal 4/16/2021 20 Daniel A. Unity University-HS-II-2013A.Y
•Silt Control Devices: The entry of silt into a canal, which
takes off from a head-works can be reduced by constructing
certain special works called silt control works. The works may
be classified into the following two types:
a)Silt Excluders: Silt excluders are those works which
are constructed on the bed of the river, upstream of the
head regulator.
The clearer water enters the head regulator
and the silted water enters the silt excluder. In this
type of works, the silt is, therefore removed from
the water before it enters the canal 4/16/2021 20 Daniel A. Unity University-HS-II-2013A.Y
Contd
Silt Excluder 4/16/2021 21 Daniel A. Unity University-HS-II-2013A.Y
Silt Excluder 4/16/2021 21 Daniel A. Unity University-HS-II-2013A.Y
Contd
b) Silt Ejectors: Silt ejectors also called silt extractors
are those devices which extract the silt from the
canal-water after the silted water has travelled a
certain distance in the off-taking canal. These works
are therefore constructed on the bed of the canal and a
little distance downstream from the head regulator
Plan of Silt Ejector
4/16/2021 22 Daniel A. Unity University-HS-II-2013A.Y
b) Silt Ejectors: Silt ejectors also called silt extractors
are those devices which extract the silt from the
canal-water after the silted water has travelled a
certain distance in the off-taking canal. These works
are therefore constructed on the bed of the canal and a
little distance downstream from the head regulator
Plan of Silt Ejector
4/16/2021 22 Daniel A. Unity University-HS-II-2013A.Y
Principles of Silt Control ----Contd
The fundamental principle behind silt control is that most of
the silt tries to settle down in water thus confining itself mostly
in the bottom layers of water.
The silt is kept in suspension by the force of the vertical
eddies generated by the friction of the flowing water against
the bed.
If bed friction is more the upward force of eddies shall be
more and hence lesser chance of silt settlement will exist.
The friction between flowing water and bed can be reduced
by constructing a smooth approach channel, hence more
settlement of silt and its consequent removal is possible.
4/16/2021 23 Daniel A. Unity University-HS-II-2013A.Y
The fundamental principle behind silt control is that most of
the silt tries to settle down in water thus confining itself mostly
in the bottom layers of water.
The silt is kept in suspension by the force of the vertical
eddies generated by the friction of the flowing water against
the bed.
If bed friction is more the upward force of eddies shall be
more and hence lesser chance of silt settlement will exist.
The friction between flowing water and bed can be reduced
by constructing a smooth approach channel, hence more
settlement of silt and its consequent removal is possible.
4/16/2021 23 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The chances of less disturbance and that of providing a
smooth approach channel can be better attained in a canal
rather than in the river bed.
The works which are constructed in the canal (i.e. silt
extractors or silt ejectors) will definitely be superior and
more effective than the works which are constructed in the
river bed(i.e. silt excluders)
Silt extractor is therefore better than a silt excluder,
however the silt extractor shall be costlier because surplus
water has to be taken into the canal from the head, and an
escape channel which will feed the highly silted water back
into the river shall be constructed
4/16/2021 24 Daniel A. Unity University-HS-II-2013A.Y
•The chances of less disturbance and that of providing a
smooth approach channel can be better attained in a canal
rather than in the river bed.
The works which are constructed in the canal (i.e. silt
extractors or silt ejectors) will definitely be superior and
more effective than the works which are constructed in the
river bed(i.e. silt excluders)
Silt extractor is therefore better than a silt excluder,
however the silt extractor shall be costlier because surplus
water has to be taken into the canal from the head, and an
escape channel which will feed the highly silted water back
into the river shall be constructed
4/16/2021 24 Daniel A. Unity University-HS-II-2013A.Y
The Diversion Weir and it Types
•The weirs may be divided into the following three classes
1.Masonry weir with vertical drop
2.Rock fill weirs with sloping aprons
3.Concrete weirs with sloping glacis
1.Masonry weirs with vertical drop: This type of a weir consists
of a horizontal floor and a masonry crest with vertical or
nearly vertical downstream face.
The raised masonry crest does the maximum
ponding of water, but a part of it is usually done by
shutters at the top of the crest.
4/16/2021 25 Daniel A. Unity University-HS-II-2013A.Y
•The weirs may be divided into the following three classes
1.Masonry weir with vertical drop
2.Rock fill weirs with sloping aprons
3.Concrete weirs with sloping glacis
1.Masonry weirs with vertical drop: This type of a weir consists
of a horizontal floor and a masonry crest with vertical or
nearly vertical downstream face.
The raised masonry crest does the maximum
ponding of water, but a part of it is usually done by
shutters at the top of the crest.
4/16/2021 25 Daniel A. Unity University-HS-II-2013A.Y
Contd
The shutters can be dropped down during floods, so
as to reduce the afflux by increasing the waterway
opening
Suitable for hard clay and consolidated gravel
foundation. However, this type of weir is becoming
obsolete
Masonry Weir
4/16/2021 26 Daniel A. Unity University-HS-II-2013A.Y
The shutters can be dropped down during floods, so
as to reduce the afflux by increasing the waterway
opening
Suitable for hard clay and consolidated gravel
foundation. However, this type of weir is becoming
obsolete
Masonry Weir
4/16/2021 26 Daniel A. Unity University-HS-II-2013A.Y
Contd
2) Rock-fill weirs with sloping aprons: Such a weir is also
called-Dry stone slope weir.
It is the simplest type of construction, and is suitable
for fine sandy foundations like those in alluvial areas
Such a weir requires huge quantities of stone and is
economical only when stone is easily available.
Rock fill weirs
4/16/2021 27 Daniel A. Unity University-HS-II-2013A.Y
2) Rock-fill weirs with sloping aprons: Such a weir is also
called-Dry stone slope weir.
It is the simplest type of construction, and is suitable
for fine sandy foundations like those in alluvial areas
Such a weir requires huge quantities of stone and is
economical only when stone is easily available.
Rock fill weirs
4/16/2021 27 Daniel A. Unity University-HS-II-2013A.Y
Contd
3. Modern Concrete Weirs with sloping downstream glacis:
Weir of this type are of recent origin and their design is
based on modern concepts of sub surface flow (i.e. Khosla`s
Theory)
Sheet piles of sufficient depths are driven at the ends of
upstream and downstream floor. Sometimes, an intermediate
pile is also provided.
The hydraulic jump is formed on the downstream sloping
glacis, so as to dissipate the energy of the flowing water
This type of weirs are now exclusively used especially on
permeable foundations, and are generally provided with
low crest with counter balanced gates
4/16/2021 28 Daniel A. Unity University-HS-II-2013A.Y
3. Modern Concrete Weirs with sloping downstream glacis:
Weir of this type are of recent origin and their design is
based on modern concepts of sub surface flow (i.e. Khosla`s
Theory)
Sheet piles of sufficient depths are driven at the ends of
upstream and downstream floor. Sometimes, an intermediate
pile is also provided.
The hydraulic jump is formed on the downstream sloping
glacis, so as to dissipate the energy of the flowing water
This type of weirs are now exclusively used especially on
permeable foundations, and are generally provided with
low crest with counter balanced gates
4/16/2021 28 Daniel A. Unity University-HS-II-2013A.Y
Contd
Fig. A typical cross-section of a Barrage founded on pervious foundations
Fig. A typical cross-section of a modern concrete weir founded on permeable foundations
4/16/2021 29 Daniel A. Unity University-HS-II-2013A.Y
Fig. A typical cross-section of a Barrage founded on pervious foundations
Fig. A typical cross-section of a modern concrete weir founded on permeable foundations
4/16/2021 29 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Afflux: The rise in the maximum flood level(HFL) upstream of
the weir caused due to the construction of the weir across the
river is called-Afflux
•Pond level: The water level required in the under sluice
pocket upstream of the canal head regulator, so as to feed
the canal with its full supply is known as pond level
The Full Supply Level(FSL) of the canal at the head,
depends up on the level of the irrigated areas and the
slope of the canal. The pond level is generally
obtained by adding 1.0 to 1.2 m to canal full supply
level
4/16/2021 30 Daniel A. Unity University-HS-II-2013A.Y
•Afflux: The rise in the maximum flood level(HFL) upstream of
the weir caused due to the construction of the weir across the
river is called-Afflux
•Pond level: The water level required in the under sluice
pocket upstream of the canal head regulator, so as to feed
the canal with its full supply is known as pond level
The Full Supply Level(FSL) of the canal at the head,
depends up on the level of the irrigated areas and the
slope of the canal. The pond level is generally
obtained by adding 1.0 to 1.2 m to canal full supply
level
4/16/2021 30 Daniel A. Unity University-HS-II-2013A.Y
Theories of Seepage and Design of Weirs and
Barrages
•Hydraulic structures such as dams, weirs, barrages, head
regulators, cross drainage structures etc may either be founded
on an imperious solid rock foundation or on a pervious
foundation
•When ever, any hydraulic structure is founded on a pervious
foundation, it is subjected to seepage of water beneath the
structure, in addition to all other forces to which it will be
subjected when founded on an impervious rock foundation.
4/16/2021 31 Daniel A. Unity University-HS-II-2013A.Y
Barrages
•Hydraulic structures such as dams, weirs, barrages, head
regulators, cross drainage structures etc may either be founded
on an imperious solid rock foundation or on a pervious
foundation
•When ever, any hydraulic structure is founded on a pervious
foundation, it is subjected to seepage of water beneath the
structure, in addition to all other forces to which it will be
subjected when founded on an impervious rock foundation.
4/16/2021 31 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The water seeping below the body of the hydraulic structure
endangers the stability of the structure and may cause its
failure either by:
Piping
Direct Uplift
•Failure by piping or undermining: When the seepage water
retains sufficient residual force at the emerging downstream
end of the work, it may lift up the soil particles.
This leads to increased porosity of the soil by progressive
removal of the soil from beneath the foundation. The
structure may ultimately subside into the hollow so formed
resulting in the failure of the structure
4/16/2021 32 Daniel A. Unity University-HS-II-2013A.Y
•The water seeping below the body of the hydraulic structure
endangers the stability of the structure and may cause its
failure either by:
Piping
Direct Uplift
•Failure by piping or undermining: When the seepage water
retains sufficient residual force at the emerging downstream
end of the work, it may lift up the soil particles.
This leads to increased porosity of the soil by progressive
removal of the soil from beneath the foundation. The
structure may ultimately subside into the hollow so formed
resulting in the failure of the structure
4/16/2021 32 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Failure by Direct Uplift :
•The water seeping below the structure, exerts an uplift
pressure on the floor of the structure.
•If this pressure is not counter balanced by the weight of the
concrete or masonry floor, the structure will fail by a rupture
of a part of the floor.
The above concepts of the failure of hydraulic structures
due to sub-surface flow were introduced by Bligh
4/16/2021 33 Daniel A. Unity University-HS-II-2013A.Y
•Failure by Direct Uplift :
•The water seeping below the structure, exerts an uplift
pressure on the floor of the structure.
•If this pressure is not counter balanced by the weight of the
concrete or masonry floor, the structure will fail by a rupture
of a part of the floor.
The above concepts of the failure of hydraulic structures
due to sub-surface flow were introduced by Bligh
4/16/2021 33 Daniel A. Unity University-HS-II-2013A.Y
Bligh`s Creep Theory for Seepage Flow
•According to Bligh`s Theory, the percolating water follows the
outline of the base of the foundation of the hydraulic structure.
•Water Creeps along the bottom contour of the structure, the
length of the path thus traversed by water is called the length
of the creep
•It is assumed in this theory that the loss of head is proportional
to the length of the creep
4/16/2021 34 Daniel A. Unity University-HS-II-2013A.Y
•According to Bligh`s Theory, the percolating water follows the
outline of the base of the foundation of the hydraulic structure.
•Water Creeps along the bottom contour of the structure, the
length of the path thus traversed by water is called the length
of the creep
•It is assumed in this theory that the loss of head is proportional
to the length of the creep
4/16/2021 34 Daniel A. Unity University-HS-II-2013A.Y
Contd
•If H
L is the total head loss between the upstream and the
downstream, and L is the length of the creep then the loss of
head per unit of creep Length (i.e. H
L/L) is called the hydraulic
gradient.
•Bligh makes no distinction between horizontal and vertical
creep
Fig. Bligh`s creep
4/16/2021 35 Daniel A. Unity University-HS-II-2013A.Y
•If H
L is the total head loss between the upstream and the
downstream, and L is the length of the creep then the loss of
head per unit of creep Length (i.e. H
L/L) is called the hydraulic
gradient.
•Bligh makes no distinction between horizontal and vertical
creep
Fig. Bligh`s creep
4/16/2021 35 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Consider a section as shown in the figure (Bligh`s creep). Let
H
L be the difference of water levels between upstream and
downstream ends (no water is shown on downstream side).
•Water will seep along the bottom contour as shown by
arrows. It starts percolating at A and emerges at B. The total
length of creep is given by
)(2
2)(
22)(2
321
32121
32211
33222111
dddbL
dddLLL
ddLLdL
ddLddLddL
Fig. Vertical and Horizontal seepage
A B
4/16/2021 36 Daniel A. Unity University-HS-II-2013A.Y
•Consider a section as shown in the figure (Bligh`s creep). Let
H
L be the difference of water levels between upstream and
downstream ends (no water is shown on downstream side).
•Water will seep along the bottom contour as shown by
arrows. It starts percolating at A and emerges at B. The total
length of creep is given by
)(2
2)(
22)(2
321
32121
32211
33222111
dddbL
dddLLL
ddLLdL
ddLddLddL
Fig. Vertical and Horizontal seepage
A B
4/16/2021 36 Daniel A. Unity University-HS-II-2013A.Y
Contd
•Head loss per unit length or hydraulic gradient L
H
dddb
H
LL
3212
12d
L
H
L
2
2d
L
H
L
32d
L
H
L
•Head loss equal to
,
,
will occur respectively in the planes of three vertical cut offs.
The hydraulic gradient line (H.G. Line) can then be drawn as
shown in the figure.
Fig. HGL and head loss at
vertical cutoffs
4/16/2021 37 Daniel A. Unity University-HS-II-2013A.Y
•Head loss per unit length or hydraulic gradient L
H
dddb
H
LL
3212
12d
L
H
L
2
2d
L
H
L
32d
L
H
L
•Head loss equal to
,
,
will occur respectively in the planes of three vertical cut offs.
The hydraulic gradient line (H.G. Line) can then be drawn as
shown in the figure.
Fig. HGL and head loss at
vertical cutoffs
4/16/2021 37 Daniel A. Unity University-HS-II-2013A.Y
Safety against Piping or Undermining --Contd
,
, •According to Bligh, the safety against piping can be ensured
by providing sufficient creep length, given by L = CH
L where
C is Bligh`s coefficient for the soil.
•Different values of C for different types of soils are given in
the table below
S.
No
Types of Soil Value
of C
Safe Hydraulic Gradient
should be less than
1 Fine sand 15 1/15
2 Coarse grained sand 12 1/12
3 Sand mixed with boulder and
gravel and for loam soil
5 to 9 1/5 to 1/9
4 Light sand and mud 8 1/8
Table: Values of Bligh`s Safe Hydraulic Gradient for different types of Soils
4/16/2021 38 Daniel A. Unity University-HS-II-2013A.Y
,
, •According to Bligh, the safety against piping can be ensured
by providing sufficient creep length, given by L = CH
L where
C is Bligh`s coefficient for the soil.
•Different values of C for different types of soils are given in
the table below
S.
No
Types of Soil Value
of C
Safe Hydraulic Gradient
should be less than
1 Fine sand 15 1/15
2 Coarse grained sand 12 1/12
3 Sand mixed with boulder and
gravel and for loam soil
5 to 9 1/5 to 1/9
4 Light sand and mud 8 1/8
Table: Values of Bligh`s Safe Hydraulic Gradient for different types of Soils
4/16/2021 38 Daniel A. Unity University-HS-II-2013A.Y
Safety against Piping or Undermining --Contd
,
,
Note: The hydraulic gradient, i.e. H
L/L is then equal to 1/C.
Hence, it may be stated that the
hydraulic gradient must be kept
under a safe limit in order to
ensure safety against piping
4/16/2021 39 Daniel A. Unity University-HS-II-2013A.Y
,
,
Note: The hydraulic gradient, i.e. H
L/L is then equal to 1/C.
Hence, it may be stated that the
hydraulic gradient must be kept
under a safe limit in order to
ensure safety against piping
4/16/2021 39 Daniel A. Unity University-HS-II-2013A.Y
Safety against uplift pressure --Contd
,
,
•The ordinates of the H.G. line above the bottom of the floor
represent the residual uplift water head at each point
•For example if at any point, the ordinates of H.G. line above
the bottom of the floor is 1m, then 1m head of water will act
as uplift at that point.
•If h
`
meters is this ordinate, then water pressure equal to h
`
meters will act at this point, and has to be counter balanced
by the weight of the floor of thickness say, t
4/16/2021 40 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The ordinates of the H.G. line above the bottom of the floor
represent the residual uplift water head at each point
•For example if at any point, the ordinates of H.G. line above
the bottom of the floor is 1m, then 1m head of water will act
as uplift at that point.
•If h
`
meters is this ordinate, then water pressure equal to h
`
meters will act at this point, and has to be counter balanced
by the weight of the floor of thickness say, t
4/16/2021 40 Daniel A. Unity University-HS-II-2013A.Y
Safety against uplift pressure --Contd
,
,
•Uplift Pressure h
w
tG
w
)(
•Downward Pressure where G is the specific
gravity of the floor
material
•For equilibrium Gth
tGh
ww
11
1
G
h
G
th
t
GtttGth
Subtracting t on both sides, we get
4/16/2021 41 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Uplift Pressure h
w
tG
w
)(
•Downward Pressure where G is the specific
gravity of the floor
material
•For equilibrium Gth
tGh
ww
11
1
G
h
G
th
t
GtttGth
Subtracting t on both sides, we get
4/16/2021 41 Daniel A. Unity University-HS-II-2013A.Y
Safety against uplift pressure --Contd
,
,
Where
(G-1) is the submerged specific gravity of the floor material.
For concrete, G may be taken equal to 2.4. 11
G
h
G
th
t
is the ordinate of the H.G.line above the top of the
floor.
Hence, the thickness of the floor can be easily
determined by using the above equation and
this is generally increased by 33%, so as to
allow a suitable factor of safety hth
4/16/2021 42 Daniel A. Unity University-HS-II-2013A.Y
,
,
Where
(G-1) is the submerged specific gravity of the floor material.
For concrete, G may be taken equal to 2.4. 11
G
h
G
th
t
is the ordinate of the H.G.line above the top of the
floor.
Hence, the thickness of the floor can be easily
determined by using the above equation and
this is generally increased by 33%, so as to
allow a suitable factor of safety hth
4/16/2021 42 Daniel A. Unity University-HS-II-2013A.Y
Safety against uplift pressure --Contd
,
,
•The floor thickness has to be designed according to the
above equation only for the downstream floor and for the
worst condition i.e. when maximum ordinates of H.G. line occur.
•The water standing on the upstream floor, more than counter
balances the uplift caused by the same water, hence, only a
nominal floor thickness is required on the upstream side, so
as to resist wear, impact of flowing water
•While designing aprons of hydraulic structures on Bligh`s
theory for sub surface flow, the floor thickness is designed in
accordance with the above rules and sufficient length of pucca
floor given by L = CH
L is provided so as to ensure a safe
value of hydraulic gradient
4/16/2021 43 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The floor thickness has to be designed according to the
above equation only for the downstream floor and for the
worst condition i.e. when maximum ordinates of H.G. line occur.
•The water standing on the upstream floor, more than counter
balances the uplift caused by the same water, hence, only a
nominal floor thickness is required on the upstream side, so
as to resist wear, impact of flowing water
•While designing aprons of hydraulic structures on Bligh`s
theory for sub surface flow, the floor thickness is designed in
accordance with the above rules and sufficient length of pucca
floor given by L = CH
L is provided so as to ensure a safe
value of hydraulic gradient
4/16/2021 43 Daniel A. Unity University-HS-II-2013A.Y
Lane`s Weighted Creep Theory
,
,
•Bligh, in his theory, had calculated the length of the creep,
by simply adding the horizontal creep length and the vertical
creep length, thereby making no distinction between the two
creeps
•Lane, on the basis of his analysis carried out on about 200
dams all over the World, stipulated that the horizontal creep is
less effective in reducing uplift(or in causing loss of head) than
the vertical creep
•Lane, therefore, suggested a weighted factor of 1/3 for the
horizontal creep as against 1 for the vertical creep
4/16/2021 44 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Bligh, in his theory, had calculated the length of the creep,
by simply adding the horizontal creep length and the vertical
creep length, thereby making no distinction between the two
creeps
•Lane, on the basis of his analysis carried out on about 200
dams all over the World, stipulated that the horizontal creep is
less effective in reducing uplift(or in causing loss of head) than
the vertical creep
•Lane, therefore, suggested a weighted factor of 1/3 for the
horizontal creep as against 1 for the vertical creep
4/16/2021 44 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
Thus, the total Lane`s creep length (L
l) is given by:
33222111
3
1
)(
3
1
ddLddLddL
l
322
32121
2
3
1
2)(
3
1
dddbL
dddLLL
l
l
4/16/2021 45 Daniel A. Unity University-HS-II-2013A.Y
,
,
Thus, the total Lane`s creep length (L
l) is given by:
33222111
3
1
)(
3
1
ddLddLddL
l
322
32121
2
3
1
2)(
3
1
dddbL
dddLLL
l
l
4/16/2021 45 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
•To ensure safety against piping according to Lane theory, the
creep length L
l must not be less than C
1H
L where H
L is the head
causing flow and C
1 is Lane`s creep coefficient
S.N
o
Types of Soil Value of Lane`s
Coefficient , C
1
Safe Lane`s
Hydraulic gradient
should be less than
1 Very fine sand or silt 8.5 1/8.5
2 Fine Sand 7.0 1/7
3 Coarse Sand 5.0 1/5
4 Gravel and Sand 3.5 to 3.0 1/3.5 to 1/3
5 Boulders, gravels and
Sand
2.5 to 3.0 1/2.5 to 1/3
6 Clayey Soils 3.0 to 1.6 1/3 to 1/1.6
Values of Lane`s Safe Hydraulic Gradient for different types of soils
4/16/2021 46 Daniel A. Unity University-HS-II-2013A.Y
,
,
•To ensure safety against piping according to Lane theory, the
creep length L
l must not be less than C
1H
L where H
L is the head
causing flow and C
1 is Lane`s creep coefficient
S.N
o
Types of Soil Value of Lane`s
Coefficient , C
1
Safe Lane`s
Hydraulic gradient
should be less than
1 Very fine sand or silt 8.5 1/8.5
2 Fine Sand 7.0 1/7
3 Coarse Sand 5.0 1/5
4 Gravel and Sand 3.5 to 3.0 1/3.5 to 1/3
5 Boulders, gravels and
Sand
2.5 to 3.0 1/2.5 to 1/3
6 Clayey Soils 3.0 to 1.6 1/3 to 1/1.6
Values of Lane`s Safe Hydraulic Gradient for different types of soils
4/16/2021 46 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
•Lane`s theory was an improvement over Bligh`s theory, but
however, was purely empirical without any rational basis and
hence is generally not adopted in any designs.
•Bligh`s theory is still used(even after the invention of modern
Khosla`s theory), but Lane`s theory is practically no where
used and is having only a theoretical importance.
4/16/2021 47 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Lane`s theory was an improvement over Bligh`s theory, but
however, was purely empirical without any rational basis and
hence is generally not adopted in any designs.
•Bligh`s theory is still used(even after the invention of modern
Khosla`s theory), but Lane`s theory is practically no where
used and is having only a theoretical importance.
4/16/2021 47 Daniel A. Unity University-HS-II-2013A.Y
Khosla`s Theory and Concept of Flow Nets
,
,
•The seeping water does not creep along the bottom contour
of pucca floor as stated by Bligh, but on the other hand, this
water moves along a set of stream-lines as shown in the figure.
•The steady seepage in a vertical plane for a homogeneous
soil can be expressed by Laplacian equation. 0
2
2
2
2
dz
d
dx
d
= 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.
4/16/2021 48 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The seeping water does not creep along the bottom contour
of pucca floor as stated by Bligh, but on the other hand, this
water moves along a set of stream-lines as shown in the figure.
•The steady seepage in a vertical plane for a homogeneous
soil can be expressed by Laplacian equation. 0
2
2
2
2
dz
d
dx
d
= 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.
4/16/2021 48 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
•The above equation represents two sets of curves intersecting
each other orthogonally (Figure above). One set of lines is
called streamlines and the other set is called equipotential
lines. The resultant flow diagram showing both the sets of
curves is called a Flow Net
Khosla`s Flow Net 0
2
2
2
2
dz
d
dx
d
4/16/2021 49 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The above equation represents two sets of curves intersecting
each other orthogonally (Figure above). One set of lines is
called streamlines and the other set is called equipotential
lines. The resultant flow diagram showing both the sets of
curves is called a Flow Net
Khosla`s Flow Net 0
2
2
2
2
dz
d
dx
d
4/16/2021 49 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
•The seepage water exerts a force at each point in the
direction of flow and tangential to the streamlines as shown in
the figure below. This force (F) has an upward component from
the point where streamline 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.
4/16/2021 50 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The seepage water exerts a force at each point in the
direction of flow and tangential to the streamlines as shown in
the figure below. This force (F) has an upward component from
the point where streamline 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.
4/16/2021 50 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
•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.
•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 the exit end is called the exit
gradient.
•In order that the soil particles at exit remain stable, the
upward pressure at the exit should be safe. In other words,
the exit gradient should be safe.
4/16/2021 51 Daniel A. Unity University-HS-II-2013A.Y
,
,
•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.
•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 the exit end is called the exit
gradient.
•In order that the soil particles at exit remain stable, the
upward pressure at the exit should be safe. In other words,
the exit gradient should be safe.
4/16/2021 51 Daniel A. Unity University-HS-II-2013A.Y
Critical Exit Gradient: ---Contd
,
,
•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 ¼ to 1/5 of
the critical exit gradient is ensured so as to keep the
structure safe against piping
4/16/2021 52 Daniel A. Unity University-HS-II-2013A.Y
,
,
•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 ¼ to 1/5 of
the critical exit gradient is ensured so as to keep the
structure safe against piping
4/16/2021 52 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•The submerged weight (W
s) of a unit volume of soil is given
as: )1)(1(
swS
SnW
Unit weight of Water
Ss = Specific gravity of soil particles
n = Porosity of the soil material
w
Where
•For critical conditions to occur at the exit point:
F = W
S
Where F- is the upward disturbing force on the grain
Force F = Pressure gradient at that point = dl
dh
dl
dp
w
4/16/2021 53 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The submerged weight (W
s) of a unit volume of soil is given
as: )1)(1(
swS
SnW
Unit weight of Water
Ss = Specific gravity of soil particles
n = Porosity of the soil material
w
Where
•For critical conditions to occur at the exit point:
F = W
S
Where F- is the upward disturbing force on the grain
Force F = Pressure gradient at that point = dl
dh
dl
dp
w
4/16/2021 53 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
, )1)(1(
)1)(1(
s
sww
Sn
dl
dh
Sn
dl
dh
Where
represents the rate of loss of head or the
gradient at the exit end dl
dh
4/16/2021 54 Daniel A. Unity University-HS-II-2013A.Y
,
, )1)(1(
)1)(1(
s
sww
Sn
dl
dh
Sn
dl
dh
Where
represents the rate of loss of head or the
gradient at the exit end dl
dh
4/16/2021 54 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•Under critical conditions, the critical exit gradient is equal
to (1-n)(S
s-1). For, most of the rivers , S
s = 2.65 and n = 0.4,
then the value of critical exit gradient 0.199.0)65.16.0()165.2)(4.01(
Hence, an exit gradient equal to ¼ to 1/5 of the critical
gradient means that an exit gradient equal to ¼ to 1/5 has
to be provided for keeping the structure safe against piping
4/16/2021 55 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Under critical conditions, the critical exit gradient is equal
to (1-n)(S
s-1). For, most of the rivers , S
s = 2.65 and n = 0.4,
then the value of critical exit gradient 0.199.0)65.16.0()165.2)(4.01(
Hence, an exit gradient equal to ¼ to 1/5 of the critical
gradient means that an exit gradient equal to ¼ to 1/5 has
to be provided for keeping the structure safe against piping
4/16/2021 55 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
Type of Soil Khosla`s Safe Exit Gradient
Shingle 0.25 to 0.20
Course Sand 0.20 to 0.17
Fine Sand 0.17 to 0.14
Values of Khosla`s Safe Exit Gradient different types e soils
4/16/2021 56 Daniel A. Unity University-HS-II-2013A.Y
,
,
Type of Soil Khosla`s Safe Exit Gradient
Shingle 0.25 to 0.20
Course Sand 0.20 to 0.17
Fine Sand 0.17 to 0.14
Values of Khosla`s Safe Exit Gradient different types e soils
4/16/2021 56 Daniel A. Unity University-HS-II-2013A.Y
Khosla Vs Bligh ---Contd
,
, •Khosla`s theory of flow nets made it very clear that the loss
of head does not take place uniformly, in direct proportion to
the creep length, as stated by Bligh
Loss of head depends up on the whole geometry
of the figure, i.e. the shape of foundation, depth of
impervious boundary and levels of U/S and D/S beds.
•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
gradient of Bligh(i.e.1/C) is safe
4/16/2021 57 Daniel A. Unity University-HS-II-2013A.Y
,
, •Khosla`s theory of flow nets made it very clear that the loss
of head does not take place uniformly, in direct proportion to
the creep length, as stated by Bligh
Loss of head depends up on the whole geometry
of the figure, i.e. the shape of foundation, depth of
impervious boundary and levels of U/S and D/S beds.
•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
gradient of Bligh(i.e.1/C) is safe
4/16/2021 57 Daniel A. Unity University-HS-II-2013A.Y
Khosla Vs Bligh ---Contd
,
, •A weir or a barrage may fail not only due to seepage (i.e.
Sub-surface flow) as stated by Bligh, but may also fail due to
the surface flow.
•The surface flow (i.e. when flood water flows over the weir
crest) may cause scour, dynamic action; and in addition, will
cause uplift pressures in the jump trough (if the hydraulic jump
forms on the downstream)
•The 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 (i.e. for
sub-surface flow) and the maximum of the two chosen for designing the
aprons and the floors of the weirs
4/16/2021 58 Daniel A. Unity University-HS-II-2013A.Y
,
, •A weir or a barrage may fail not only due to seepage (i.e.
Sub-surface flow) as stated by Bligh, but may also fail due to
the surface flow.
•The surface flow (i.e. when flood water flows over the weir
crest) may cause scour, dynamic action; and in addition, will
cause uplift pressures in the jump trough (if the hydraulic jump
forms on the downstream)
•The 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 (i.e. for
sub-surface flow) and the maximum of the two chosen for designing the
aprons and the floors of the weirs
4/16/2021 58 Daniel A. Unity University-HS-II-2013A.Y
Khosla Vs Bligh ---Contd
,
,
•Khosla`s theory differs from Bligh`s theory in all the above
respects, but owing to the simplicity, Bligh`s theory is still used
for design of small works.
A minimum practical thickness for the floor and a
deep vertical cutoff at the downstream end is however
always provided in addition to the requirements of
Bligh`s theory.
However , on major works, Bligh`s theory should never
be used as it would lead to expensive and unsafe
erroneous designs.
4/16/2021 59 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Khosla`s theory differs from Bligh`s theory in all the above
respects, but owing to the simplicity, Bligh`s theory is still used
for design of small works.
A minimum practical thickness for the floor and a
deep vertical cutoff at the downstream end is however
always provided in addition to the requirements of
Bligh`s theory.
However , on major works, Bligh`s theory should never
be used as it would lead to expensive and unsafe
erroneous designs.
4/16/2021 59 Daniel A. Unity University-HS-II-2013A.Y
Khosla`s 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 flow net. In other words, we must solve the Laplacian
equation
•Solution of laplace equation can be either by
•Mathematical solution of the laplacian equation or
•By Electrical analogy method or graphical sketching by
adjusting the streamlines and equipiotential lines with
respect to the boundary conditions. These are complicated
methods
4/16/2021 60 Daniel A. Unity University-HS-II-2013A.Y
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 flow net. In other words, we must solve the Laplacian
equation
•Solution of laplace equation can be either by
•Mathematical solution of the laplacian equation or
•By Electrical analogy method or graphical sketching by
adjusting the streamlines and equipiotential lines with
respect to the boundary conditions. These are complicated
methods
4/16/2021 60 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•For designing hydraulic structures such as weirs or barrages on
pervious foundation, Khosla has evolved a simple, quick and an
accurate approach called Method of Independent Variables
•In Khosla 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 given
in the figure and curves shown which can be used for
determining the percentage pressures at the various key
points
4/16/2021 61 Daniel A. Unity University-HS-II-2013A.Y
,
,
•For designing hydraulic structures such as weirs or barrages on
pervious foundation, Khosla has evolved a simple, quick and an
accurate approach called Method of Independent Variables
•In Khosla 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 given
in the figure and curves shown which can be used for
determining the percentage pressures at the various key
points
4/16/2021 61 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•The simple profiles which are most useful are:
1.A straight horizontal floor of negligible thickness with a
sheet pile line on the U/S end and D/S end
Fig. Khosla`s Simple Profiles for
a weir of complex profile
4/16/2021 62 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The simple profiles which are most useful are:
1.A straight horizontal floor of negligible thickness with a
sheet pile line on the U/S end and D/S end
Fig. Khosla`s Simple Profiles for
a weir of complex profile
4/16/2021 62 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
2.A straight horizontal floor depressed below the bed but
without any vertical cut-offs
Fig. Khosla`s Simple Profiles
for a weir of complex profile
4/16/2021 63 Daniel A. Unity University-HS-II-2013A.Y
,
,
2.A straight horizontal floor depressed below the bed but
without any vertical cut-offs
Fig. Khosla`s Simple Profiles
for a weir of complex profile
4/16/2021 63 Daniel A. Unity University-HS-II-2013A.Y
Khosla`s Pressure Curves
4/16/2021 64 Daniel A. Unity University-HS-II-2013A.Y
4/16/2021 64 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
3.A straight horizontal floor of negligible thickness with a
sheet pile line at some intermediate point
Fig. Khosla`s Simple Profiles for a
weir of complex profile
4/16/2021 65 Daniel A. Unity University-HS-II-2013A.Y
,
,
3.A straight horizontal floor of negligible thickness with a
sheet pile line at some intermediate point
Fig. Khosla`s Simple Profiles for a
weir of complex profile
4/16/2021 65 Daniel A. Unity University-HS-II-2013A.Y
Khosla`s Pressure Curves
4/16/2021 66 Daniel A. Unity University-HS-II-2013A.Y
4/16/2021 66 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
Khosla`s Pressure Curves
4/16/2021 67 Daniel A. Unity University-HS-II-2013A.Y
,
,
Khosla`s Pressure Curves
4/16/2021 67 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•The key points are:
The junctions of the floor and the pile lines on 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 the floor
c)Correction for the slope of the floor
4/16/2021 68 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The key points are:
The junctions of the floor and the pile lines on 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 the floor
c)Correction for the slope of the floor
4/16/2021 68 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
a)Correction for the mutual interference of piles
•The correction C to be applied as percentage of head due to
this effect is given by:
b
Dd
b
D
C19 b
The distance between two pile line
D = The depth of the 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 the pile on which the effect is considered
b = Total floor length
Where
4/16/2021 69 Daniel A. Unity University-HS-II-2013A.Y
,
,
a)Correction for the mutual interference of piles
•The correction C to be applied as percentage of head due to
this effect is given by:
b
Dd
b
D
C19 b
The distance between two pile line
D = The depth of the 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 the pile on which the effect is considered
b = Total floor length
Where
4/16/2021 69 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•The correction(mutual interference) is positive for the points in
the rear or back water and subtractive for the points forward
in the direction of flow.
•The equation(mutual interference) doesn’t 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.
4/16/2021 70 Daniel A. Unity University-HS-II-2013A.Y
,
,
•The correction(mutual interference) is positive for the points in
the rear or back water and subtractive for the points forward
in the direction of flow.
•The equation(mutual interference) doesn’t 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.
4/16/2021 70 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•Suppose in the above figure, we are considering the influence
of the pile No. (2) on pile No.(1) for correcting the pressures at
C
1. Since the point C
1 is in the rear, this correction shall be +ve,
•The correction to be applied to E
2 due to pile No. (1) shall be
negative since the point E
2 is in the forward direction of flow.
a) Influence of Pile No(2) on Pile No.(1)-Point C
1
b) Influence of Pile No(1) on Pile No.(2)-Point E
2
c) Influence of Pile No(3) on Pile No.(2) Point E
2 & C
2
•The correction at C
2 due to pile No.(3) is positive and the
correction at E
2 due to pile No(3) is negative
4/16/2021 71 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Suppose in the above figure, we are considering the influence
of the pile No. (2) on pile No.(1) for correcting the pressures at
C
1. Since the point C
1 is in the rear, this correction shall be +ve,
•The correction to be applied to E
2 due to pile No. (1) shall be
negative since the point E
2 is in the forward direction of flow.
a) Influence of Pile No(2) on Pile No.(1)-Point C
1
b) Influence of Pile No(1) on Pile No.(2)-Point E
2
c) Influence of Pile No(3) on Pile No.(2) Point E
2 & C
2
•The correction at C
2 due to pile No.(3) is positive and the
correction at E
2 due to pile No(3) is negative
4/16/2021 71 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
b) Correction for the Thickness of Floor
•In the standard form profiles, the floor is assumed to have
negligible thickness.
•The percentage pressures calculated by Khosla`s equations or
graphs shall pertain to the top levels of the floor. While the
actual junction points E and C are at the bottom of the floor.
•The pressures at the actual points
are calculated by assuming a
straight line pressure variation.
4/16/2021 72 Daniel A. Unity University-HS-II-2013A.Y
,
,
b) Correction for the Thickness of Floor
•In the standard form profiles, the floor is assumed to have
negligible thickness.
•The percentage pressures calculated by Khosla`s equations or
graphs shall pertain to the top levels of the floor. While the
actual junction points E and C are at the bottom of the floor.
•The pressures at the actual points
are calculated by assuming a
straight line pressure variation.
4/16/2021 72 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
•Since the corrected pressures at E
1 should be less than the
calculated pressures at the correction to be applied for
the point E
1 shall be –Ve. 1E 1C
•The pressure calculated at is less than the corrected
pressure at C
1, and hence the correction to be applied at point
C
1 is +Ve
4/16/2021 73 Daniel A. Unity University-HS-II-2013A.Y
,
,
•Since the corrected pressures at E
1 should be less than the
calculated pressures at the correction to be applied for
the point E
1 shall be –Ve. 1E 1C
•The pressure calculated at is less than the corrected
pressure at C
1, and hence the correction to be applied at point
C
1 is +Ve
4/16/2021 73 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
, t
td
DE
EE
11
11
Sketch for correction for floor thickness t
td
Correction
DE
11
Correction for floor thickness t
td
Correction
CD
11
t
td
CD
CC
11
11
4/16/2021 74 Daniel A. Unity University-HS-II-2013A.Y
,
, t
td
DE
EE
11
11
Sketch for correction for floor thickness t
td
Correction
DE
11
Correction for floor thickness t
td
Correction
CD
11
t
td
CD
CC
11
11
4/16/2021 74 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
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 shown
in the table
Slope(H:V) Correction Factor
1:1 11.2
2:1 6.5
3:1 4.5
4:1 3.3
5:1 2.8
6:1 2.5
7:1 2.3
8:1 2.0
4/16/2021 75 Daniel A. Unity University-HS-II-2013A.Y
,
,
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 shown
in the table
Slope(H:V) Correction Factor
1:1 11.2
2:1 6.5
3:1 4.5
4:1 3.3
5:1 2.8
6:1 2.5
7:1 2.3
8:1 2.0
4/16/2021 75 Daniel A. Unity University-HS-II-2013A.Y
---Contd
,
,
This correction is applicable only to the key points of the pile
line fixed at the start or the end of the slope.
•The correction factor given above(table) 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.
Correction Factor 1b
b
s
4/16/2021 76 Daniel A. Unity University-HS-II-2013A.Y
,
,
This correction is applicable only to the key points of the pile
line fixed at the start or the end of the slope.
•The correction factor given above(table) 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.
Correction Factor 1b
b
s
4/16/2021 76 Daniel A. Unity University-HS-II-2013A.Y
Exit Gradient (G
E)
,
, •It has been determined that for a standard form consisting of
a floor length b with a vertical cutoff of depth d, the exit
gradient at its downstream end is given by
1
d
H
G
E 2
11
2
d
b
Where
•From the curve of plate , for any value of i.e. b/d the
corresponding value of can be read. Knowing H and d,
the value of G
E can be easily calculated. The exit gradient so
calculated must lie within safe limit as given in table
1
4/16/2021 77 Daniel A. Unity University-HS-II-2013A.Y
E)
,
, •It has been determined that for a standard form consisting of
a floor length b with a vertical cutoff of depth d, the exit
gradient at its downstream end is given by
1
d
H
G
E 2
11
2
d
b
Where
•From the curve of plate , for any value of i.e. b/d the
corresponding value of can be read. Knowing H and d,
the value of G
E can be easily calculated. The exit gradient so
calculated must lie within safe limit as given in table
1
4/16/2021 77 Daniel A. Unity University-HS-II-2013A.Y
Contd
,
,
Type of Soil Safe Exit Gradient
Shingle ¼ to 1/5(0.25 to 0.20)
Coarse Sand 1/5 to 1/6(0.20 to 0.17)
Fine Sand 1/6 to 1/7(0.17 to 0.14)
Plate Curves
4/16/2021 78 Daniel A. Unity University-HS-II-2013A.Y
,
,
Type of Soil Safe Exit Gradient
Shingle ¼ to 1/5(0.25 to 0.20)
Coarse Sand 1/5 to 1/6(0.20 to 0.17)
Fine Sand 1/6 to 1/7(0.17 to 0.14)
Plate Curves
4/16/2021 78 Daniel A. Unity University-HS-II-2013A.Y
Contd
•The uplift pressures must be kept as low as possible consistent
with the safety at the exit, so as to keep the floor thickness to
the minimum
•It is obvious from equation that if d = 0 ; G
E
is infinite. Hence,
it becomes essential that a vertical cutoff at the downstream
end must be provided
4/16/2021 79 Daniel A. Unity University-HS-II-2013A.Y
•The uplift pressures must be kept as low as possible consistent
with the safety at the exit, so as to keep the floor thickness to
the minimum
•It is obvious from equation that if d = 0 ; G
E
is infinite. Hence,
it becomes essential that a vertical cutoff at the downstream
end must be provided
4/16/2021 79 Daniel A. Unity University-HS-II-2013A.Y
Example
#Determine the percentage pressures at various key points in
the figure. Also determine the exit gradient and plot the
hydraulic gradient line for pond level on U/S and no flow on
D/S, find also the required floor thickness.
Figure: Weir Structure
4/16/2021 80 Daniel A. Unity University-HS-II-2013A.Y
#Determine the percentage pressures at various key points in
the figure. Also determine the exit gradient and plot the
hydraulic gradient line for pond level on U/S and no flow on
D/S, find also the required floor thickness.
Figure: Weir Structure
4/16/2021 80 Daniel A. Unity University-HS-II-2013A.Y
Contd
Solution:
A. For upstream pile line No.(1)
Total length of the floor = b = 57m
Depth of U/S pile line = d = 154.00-148.00 = 6.0m 5.9
6
57
d
b
Formula for determining key points pressure at Pile 1: DD
EC
E
100
100
0
1
1
1
4/16/2021 81 Daniel A. Unity University-HS-II-2013A.Y
Solution:
A. For upstream pile line No.(1)
Total length of the floor = b = 57m
Depth of U/S pile line = d = 154.00-148.00 = 6.0m 5.9
6
57
d
b
Formula for determining key points pressure at Pile 1: DD
EC
E
100
100
0
1
1
1
4/16/2021 81 Daniel A. Unity University-HS-II-2013A.Y
Contd
Using the Khosla pressure curve 105.0
5.9
11
%8020100
%7129100
1
1
D
C
4/16/2021 82 Daniel A. Unity University-HS-II-2013A.Y
Using the Khosla pressure curve 105.0
5.9
11
%8020100
%7129100
1
1
D
C
4/16/2021 82 Daniel A. Unity University-HS-II-2013A.Y
Contd
2
cos
1
1
E 28.5
2
5.911
2
11
22
OR using the formula %3.717.28100100
%7.28..,287.0%100
180
65.51
1
28.5
228.5
cos
1
1
1
EC
o
o
E
ei
(as against 71% read out earlier)
Where
Similarly %9.19199.0
28.5
128.5
cos
11
cos
1
11
say
D
%1.809.19100
1
D
(as against 80% read out earlier) DD 100
1
4/16/2021 83 Daniel A. Unity University-HS-II-2013A.Y
2
cos
1
1
E 28.5
2
5.911
2
11
22
OR using the formula %3.717.28100100
%7.28..,287.0%100
180
65.51
1
28.5
228.5
cos
1
1
1
EC
o
o
E
ei
(as against 71% read out earlier)
Where
Similarly %9.19199.0
28.5
128.5
cos
11
cos
1
11
say
D
%1.809.19100
1
D
(as against 80% read out earlier) DD 100
1
4/16/2021 83 Daniel A. Unity University-HS-II-2013A.Y
Contd
Correction for key Point C
1
1.Correction for Mutual Interference of piles( the point C
1
is
affected by intermediate pile No.2)
b
Dd
b
D
Correction 19
Where:
D = Depth of pile No.2
D = 153.00-148.00 = 5.0m
d = Depth of pile No.1 = 153.0-148.0 = 5.0m
b
`
= Distance between two piles = 15.8m
b = Total floor length = 57.0m
4/16/2021 84 Daniel A. Unity University-HS-II-2013A.Y
Correction for key Point C
1
1.Correction for Mutual Interference of piles( the point C
1
is
affected by intermediate pile No.2)
b
Dd
b
D
Correction 19
Where:
D = Depth of pile No.2
D = 153.00-148.00 = 5.0m
d = Depth of pile No.1 = 153.0-148.0 = 5.0m
b
`
= Distance between two piles = 15.8m
b = Total floor length = 57.0m
4/16/2021 84 Daniel A. Unity University-HS-II-2013A.Y
Contd %88.1
57
55
7.15
5
19
Correction
Since the point C
1 is in the rear in the direction of flow, the
correction is +ve. Therefore, correction due to pile
interference on C
1 is 1.88%(+ve)
2.Correction at C
1 due to thickness of floor:
•Pressure calculated from curve/equation is at but we want
the pressure at C
1. Pressure at C
1 shall be more than at as
the direction of flow is from C
1 to as shown; and hence the
correction will be +ve 1C 1C 1C t
td
Correction
CD
11
4/16/2021 85 Daniel A. Unity University-HS-II-2013A.Y
57
55
7.15
5
19
Correction
Since the point C
1 is in the rear in the direction of flow, the
correction is +ve. Therefore, correction due to pile
interference on C
1 is 1.88%(+ve)
2.Correction at C
1 due to thickness of floor:
•Pressure calculated from curve/equation is at but we want
the pressure at C
1. Pressure at C
1 shall be more than at as
the direction of flow is from C
1 to as shown; and hence the
correction will be +ve 1C 1C 1C t
td
Correction
CD
11
4/16/2021 85 Daniel A. Unity University-HS-II-2013A.Y
Contd )%(5.11
6
9
153154
148154
%71%80
11
vet
td
Correction
CD
3.Correction due to slope at C
1
•Correction due to slope at C
1 is nil, as this point is neither
situated at the start nor at the end of a slope %38.74%5.1%88.1%71
1
CCorrected
Hence corrected %38.74
1
C %80
1
D 125.2
4.1
9752.2
14.2
%38.744
1
G
h
t
Required thickness will be %100
1
E 4/16/2021 86 Daniel A. Unity University-HS-II-2013A.Y
6
9
153154
148154
%71%80
11
vet
td
Correction
CD
3.Correction due to slope at C
1
•Correction due to slope at C
1 is nil, as this point is neither
situated at the start nor at the end of a slope %38.74%5.1%88.1%71
1
CCorrected
Hence corrected %38.74
1
C %80
1
D 125.2
4.1
9752.2
14.2
%38.744
1
G
h
t
Required thickness will be %100
1
E 4/16/2021 86 Daniel A. Unity University-HS-II-2013A.Y
Contd
B. For Intermediate pile line No.(2)
d = 154-148 = 6m
b = 57m 5.9
6
57
d
b
Using the Khosla curve
Formula for determining key points pressure at Pile 2: CE 100
2 )1(
1
and
b
b
for
C )(
1
2
andvalue
b
b
chartfromDirect
C DD 100
2 )1(
1
and
b
b
for
D 702.0298.011
298.0
57
4.16
1
1
b
b
b
b
4/16/2021 87 Daniel A. Unity University-HS-II-2013A.Y
B. For Intermediate pile line No.(2)
d = 154-148 = 6m
b = 57m 5.9
6
57
d
b
Using the Khosla curve
Formula for determining key points pressure at Pile 2: CE 100
2 )1(
1
and
b
b
for
C )(
1
2
andvalue
b
b
chartfromDirect
C DD 100
2 )1(
1
and
b
b
for
D 702.0298.011
298.0
57
4.16
1
1
b
b
b
b
4/16/2021 87 Daniel A. Unity University-HS-II-2013A.Y
Contd %70%30100
2
E %56
2
C %63%37100
2
D
(Where ɸ
C = 30% is for a base ratio of 0.702 and α = 9.5)
(For a base ratio 0.298 and α = 9.5)
Where 37% is ɸ
D for a base ratio of 0.702 and α =
9.5)
4/16/2021 88 Daniel A. Unity University-HS-II-2013A.Y
2
E %56
2
C %63%37100
2
D
(Where ɸ
C = 30% is for a base ratio of 0.702 and α = 9.5)
(For a base ratio 0.298 and α = 9.5)
Where 37% is ɸ
D for a base ratio of 0.702 and α =
9.5)
4/16/2021 88 Daniel A. Unity University-HS-II-2013A.Y
Contd
OR Using the Formula
11
11
11
1
1
cos
1
1
cos
1
2
2
2
Cos
DD
CC
EE d
b
d
b
2
2
1
1
2
2
2
1
1
2
2
2
1
;
2
11
2
11
d = Depth of intermediate pile = 154-148 = 6m
b
1 = Floor length U/S of intermediate pile = 16.4m
b
2 = Floor length D/S of intermediate pile = 40.6m 77.6
6
6.40
73.2
6
4.16
2
1
968.1
2
843.6907.2
875.4
2
843.6907.2
2
77.6173.21
1
22
4/16/2021 89 Daniel A. Unity University-HS-II-2013A.Y
OR Using the Formula
11
11
11
1
1
cos
1
1
cos
1
2
2
2
Cos
DD
CC
EE d
b
d
b
2
2
1
1
2
2
2
1
1
2
2
2
1
;
2
11
2
11
d = Depth of intermediate pile = 154-148 = 6m
b
1 = Floor length U/S of intermediate pile = 16.4m
b
2 = Floor length D/S of intermediate pile = 40.6m 77.6
6
6.40
73.2
6
4.16
2
1
968.1
2
843.6907.2
875.4
2
843.6907.2
2
77.6173.21
1
22
4/16/2021 89 Daniel A. Unity University-HS-II-2013A.Y
Contd
(as against 70% read out earlier) %2.63632.0
875.4
968.1
cos
1
%100
180
cos
1
1
11
2
2
DD
DD %8.70;708.0
875.4
1968.1
cos
1
%100
180
1
cos
1
1
11
2
2
E
E
(as against 63% read out earlier) %4.56564.0
875.4
1968.1
cos
1
100
180
1
cos
1
1
11
2
2
CC
CC
(as against 56% read out earlier)
4/16/2021 90 Daniel A. Unity University-HS-II-2013A.Y
(as against 70% read out earlier) %2.63632.0
875.4
968.1
cos
1
%100
180
cos
1
1
11
2
2
DD
DD %8.70;708.0
875.4
1968.1
cos
1
%100
180
1
cos
1
1
11
2
2
E
E
(as against 63% read out earlier) %4.56564.0
875.4
1968.1
cos
1
100
180
1
cos
1
1
11
2
2
CC
CC
(as against 56% read out earlier)
4/16/2021 90 Daniel A. Unity University-HS-II-2013A.Y
Contd
Correction for key Point E
2
•Pile No.(1) will affect the pressure at E
2 and since E
2 is in the
forward direction of flow, this correction shall be –ve. The
amount of this correction is given as:
b
Dd
b
D
19
Where
D = Depth of pile No.1, the effect of which is considered
=153-148=5m
d = depth of pile No.2, the effect on which is considered =
153-148 = 5m
b
`
= distance between the two piles = 15.8m
b = Total floor length =57m
1.Correction for Mutual Interference of piles( the point E
2 is
affected by pile No.1)
4/16/2021 91 Daniel A. Unity University-HS-II-2013A.Y
Correction for key Point E
2
•Pile No.(1) will affect the pressure at E
2 and since E
2 is in the
forward direction of flow, this correction shall be –ve. The
amount of this correction is given as:
b
Dd
b
D
19
Where
D = Depth of pile No.1, the effect of which is considered
=153-148=5m
d = depth of pile No.2, the effect on which is considered =
153-148 = 5m
b
`
= distance between the two piles = 15.8m
b = Total floor length =57m
1.Correction for Mutual Interference of piles( the point E
2 is
affected by pile No.1)
4/16/2021 91 Daniel A. Unity University-HS-II-2013A.Y
Contd )%(88.1
57
55
7.15
5
19 veCorrection
2. Correction at E
2 due to floor thickness %17.11
6
7
1
148154
%63%70
22
t
td
Correction
DE
Since the pressure
observed/calculated is at
and not at E
2 (as shown in the
figure) and by looking at the
direction of flow, it can be stated
easily that the pressure at E
2
shall be less than that at ,
hence this correction is negative
2E 2E 2E
Correction at E
2 due to
floor thickness =
1.17%(-Ve)
4/16/2021 92 Daniel A. Unity University-HS-II-2013A.Y
57
55
7.15
5
19 veCorrection
2. Correction at E
2 due to floor thickness %17.11
6
7
1
148154
%63%70
22
t
td
Correction
DE
Since the pressure
observed/calculated is at
and not at E
2 (as shown in the
figure) and by looking at the
direction of flow, it can be stated
easily that the pressure at E
2
shall be less than that at ,
hence this correction is negative
2E 2E 2E
Correction at E
2 due to
floor thickness =
1.17%(-Ve)
4/16/2021 92 Daniel A. Unity University-HS-II-2013A.Y
Contd
3) Correction at E
2 due to slope : Correction at E
2 due to slope
is nil as the point E
2 is neither situated at the start of a slope
nor at the end of a slope AnsCorrected
E %95.66%17.1%88.1%70
2
Correction for key Point C
2
1.Correction for Mutual Interference of piles( the point C
2 is
affected by pile No.3)
•Pressure at C
2 is affected by pile No.(3) and since the point
C
2 is in the back water in the direction of flow, this correction
is +Ve. The amount of this correction is given as
b
dD
b
D
Correction19 913.1
4.1
678.2
14.2
%95.664
1
G
h
t
Required thickness will be
4/16/2021 93 Daniel A. Unity University-HS-II-2013A.Y
3) Correction at E
2 due to slope : Correction at E
2 due to slope
is nil as the point E
2 is neither situated at the start of a slope
nor at the end of a slope AnsCorrected
E %95.66%17.1%88.1%70
2
Correction for key Point C
2
1.Correction for Mutual Interference of piles( the point C
2 is
affected by pile No.3)
•Pressure at C
2 is affected by pile No.(3) and since the point
C
2 is in the back water in the direction of flow, this correction
is +Ve. The amount of this correction is given as
b
dD
b
D
Correction19 913.1
4.1
678.2
14.2
%95.664
1
G
h
t
Required thickness will be
4/16/2021 93 Daniel A. Unity University-HS-II-2013A.Y
Contd
D= Depth of pile No.3, the effect of which is considered below the level
at which interference is desired =153-141.7 = 11.3m
d = Depth of pile No.2, the effect on which is considered= 153-148 =
5m )%(89.2
57
53.11
40
11
19 VeCorrection
2. Correction at C
2 due to floor thickness –It can be easily
stated that the pressure at C
2 shall be more than that at
and since the observed pressure is at
2C 2C %13.11
6
8.6
1
148154
%4.56%2.63
2
t
td
Correction
CD
Hence the correction at C
2 due to floor thickness =1.13%(+Ve) b
= Distance between pile 2 and pile 3 =40m
b = Total floor length = 57m
4/16/2021 94 Daniel A. Unity University-HS-II-2013A.Y
D= Depth of pile No.3, the effect of which is considered below the level
at which interference is desired =153-141.7 = 11.3m
d = Depth of pile No.2, the effect on which is considered= 153-148 =
5m )%(89.2
57
53.11
40
11
19 VeCorrection
2. Correction at C
2 due to floor thickness –It can be easily
stated that the pressure at C
2 shall be more than that at
and since the observed pressure is at
2C 2C %13.11
6
8.6
1
148154
%4.56%2.63
2
t
td
Correction
CD
Hence the correction at C
2 due to floor thickness =1.13%(+Ve) b
= Distance between pile 2 and pile 3 =40m
b = Total floor length = 57m
4/16/2021 94 Daniel A. Unity University-HS-II-2013A.Y
Contd
3. Correction at C
2 due to slope: Since the point C
2 is situated
at the start of a slope of 3:1. I.e. An up slope in the direction
of flow, the correction is negative
Correction factor for 3:1 slope from table is 4.5
Horizontal Length of the slope =3m
Distance between two pile lines between which the
sloping floor is located = 40.0m )%(34.0
40
3
5.4 VeCorrectionActual
%68.59%34.0%13.1%89.2%56
2
CCorrected 705.1
4.1
387.2
14.2
%68.594
1
G
h
t
4/16/2021 95 Daniel A. Unity University-HS-II-2013A.Y
3. Correction at C
2 due to slope: Since the point C
2 is situated
at the start of a slope of 3:1. I.e. An up slope in the direction
of flow, the correction is negative
Correction factor for 3:1 slope from table is 4.5
Horizontal Length of the slope =3m
Distance between two pile lines between which the
sloping floor is located = 40.0m )%(34.0
40
3
5.4 VeCorrectionActual
%68.59%34.0%13.1%89.2%56
2
CCorrected 705.1
4.1
387.2
14.2
%68.594
1
G
h
t
4/16/2021 95 Daniel A. Unity University-HS-II-2013A.Y
Contd
C. Downstream pile line
Downstream pile line
d = 152-141.7 = 9.3m
b = 57m 181.0
57
3.101
b
d
1
0
1
3
3
3
chartfromDirect
chartfromValueDirect
D
C
E
Formula for determining key points pressure at pile -3 %26
%38
3
3
D
E
From Khosla Curve
4/16/2021 96 Daniel A. Unity University-HS-II-2013A.Y
C. Downstream pile line
Downstream pile line
d = 152-141.7 = 9.3m
b = 57m 181.0
57
3.101
b
d
1
0
1
3
3
3
chartfromDirect
chartfromValueDirect
D
C
E
Formula for determining key points pressure at pile -3 %26
%38
3
3
D
E
From Khosla Curve
4/16/2021 96 Daniel A. Unity University-HS-II-2013A.Y
Contd 31.3
2
53.511
2
11
22
53.5
3.10
57
d
b
OR Using the Formula %37..37.0
180
65.66
1
31.3
231.3
cos
1
2
cos
1
01
1
2
2
ei
oEE
EE
%4.25.254.0
31.3
131.3
cos
1
1
cos
1
1
1
2
2
ei
DD
DD
(as against 38% read out earlier)
(as against 26% read out earlier)
4/16/2021 97 Daniel A. Unity University-HS-II-2013A.Y
2
53.511
2
11
22
53.5
3.10
57
d
b
OR Using the Formula %37..37.0
180
65.66
1
31.3
231.3
cos
1
2
cos
1
01
1
2
2
ei
oEE
EE
%4.25.254.0
31.3
131.3
cos
1
1
cos
1
1
1
2
2
ei
DD
DD
(as against 38% read out earlier)
(as against 26% read out earlier)
4/16/2021 97 Daniel A. Unity University-HS-II-2013A.Y
Contd
1.Correction for Mutual Interference of piles( the point E
3 is
affected by pile No.2)
Correction for key Point E
3
•The point E
3 is affected by pile No.2 and since E
3 is in the
forward direction of flow from pile No.3, this correction is
negative and its amount is given by
b
Dd
b
D
Correction19
D = Depth of pile No.2, the effect of which is considered = 150.7-148= 2.7m
d = Depth of pile No.3, the effect on which is considered = 150.7-141.7=9m b
= Distance between piles =40m
b = Total floor length = 57m )%(02.1
57
7.29
40
7.2
19 VeCorrection
4/16/2021 98 Daniel A. Unity University-HS-II-2013A.Y
1.Correction for Mutual Interference of piles( the point E
3 is
affected by pile No.2)
Correction for key Point E
3
•The point E
3 is affected by pile No.2 and since E
3 is in the
forward direction of flow from pile No.3, this correction is
negative and its amount is given by
b
Dd
b
D
Correction19
D = Depth of pile No.2, the effect of which is considered = 150.7-148= 2.7m
d = Depth of pile No.3, the effect on which is considered = 150.7-141.7=9m b
= Distance between piles =40m
b = Total floor length = 57m )%(02.1
57
7.29
40
7.2
19 VeCorrection
4/16/2021 98 Daniel A. Unity University-HS-II-2013A.Y
Contd
2. Correction due to floor thickness
•It can be stated easily that the pressure at E
3 shall be less
than and since the pressure observed from curves/equation
is at this correction shall be –Ve and its amount
3
E 3
E )%(76.03.1
7.141152
%32%38
33
Vet
td
Correction
DE
4/16/2021 99 Daniel A. Unity University-HS-II-2013A.Y
2. Correction due to floor thickness
•It can be stated easily that the pressure at E
3 shall be less
than and since the pressure observed from curves/equation
is at this correction shall be –Ve and its amount
3
E 3
E )%(76.03.1
7.141152
%32%38
33
Vet
td
Correction
DE
4/16/2021 99 Daniel A. Unity University-HS-II-2013A.Y
Contd
3) Correction due to slope at E
3: As the point E
3 is neither
situated at the start nor the end of any slope correction due to
slope at E
3 is nil %22.36%76.0%02.1%38
3
ECorrected 035.1
4.1
45.1
14.2
%22.364
1
G
h
t
4/16/2021 100 Daniel A. Unity University-HS-II-2013A.Y
3) Correction due to slope at E
3: As the point E
3 is neither
situated at the start nor the end of any slope correction due to
slope at E
3 is nil %22.36%76.0%02.1%38
3
ECorrected 035.1
4.1
45.1
14.2
%22.364
1
G
h
t
4/16/2021 100 Daniel A. Unity University-HS-II-2013A.Y
Contd
The corrected pressures at various key points are shown
in the table below
Upstream Pile
No.1
Downstream
stream Pile No.2
Downstream Pile
No.3
%100
1
E %80
1
D %38.74
1
C %95.66
2
E %63
2
D %72.59
2
C %22.36
3
E %32
3
D %0
3
C
4/16/2021 101 Daniel A. Unity University-HS-II-2013A.Y
The corrected pressures at various key points are shown
in the table below
Upstream Pile
No.1
Downstream
stream Pile No.2
Downstream Pile
No.3
%100
1
E %80
1
D %38.74
1
C %95.66
2
E %63
2
D %72.59
2
C %22.36
3
E %32
3
D %0
3
C
4/16/2021 101 Daniel A. Unity University-HS-II-2013A.Y
Exit Gradient
•Let the water be headed up to pond level, i.e. on level 158m
on the upstream side with no flow downstream
The maximum seepage head = H =158-152 = 6m
The depth of D/S cut-off = d =152-141.7 = 10.3m
Total floor length = b = 57m 53.5
3.10
57
d
b
For a value of α = 5.53, 31.3
2
53.511
2
11
22
4/16/2021 102 Daniel A. Unity University-HS-II-2013A.Y
•Let the water be headed up to pond level, i.e. on level 158m
on the upstream side with no flow downstream
The maximum seepage head = H =158-152 = 6m
The depth of D/S cut-off = d =152-141.7 = 10.3m
Total floor length = b = 57m 53.5
3.10
57
d
b
For a value of α = 5.53, 31.3
2
53.511
2
11
22
4/16/2021 102 Daniel A. Unity University-HS-II-2013A.Y
Contd
Hence 102.0
82.9
1
92.58
6
72.5
1
3.10
6
31.3
1
3.10
61
d
H
G
E
Hence, the exit gradient shall be equal to 0.102, i.e. 1 in
9.82 which is very much safe
OR
For a value of α = 5.53, 18.0
1
The value of
from the curve
4/16/2021 103 Daniel A. Unity University-HS-II-2013A.Y
Hence 102.0
82.9
1
92.58
6
72.5
1
3.10
6
31.3
1
3.10
61
d
H
G
E
Hence, the exit gradient shall be equal to 0.102, i.e. 1 in
9.82 which is very much safe
OR
For a value of α = 5.53, 18.0
1
The value of
from the curve
4/16/2021 103 Daniel A. Unity University-HS-II-2013A.Y
Plotting the Hydraulic Gradient Line
•The percentage pressures, computed and tabulated can be
used to work out the elevation of H.G. line above the datum
is given by:
Flow
Condition
U/S
Water
level
in m
D/S
Water
level in
m
Head
in m
Elevation of subsoil H.G. Line above Datum
Upstream pile Line Intermediate Pile Line Downstream pile Line
Pond
level U/S
with no
flow D/S
158 152 6 6 4.8 4.46 4.02 3.78 3.58 2.68 1.92 0
158 156.8 156.
46
156.02 155.7
8
155.5
8
154.1
7
153.9
2
152 %100
1E
%80
1D
%38.74
1C
%95.66
2E
%63
2D
%72.59
2
C %22.36
3E %32
3
D %0
3
C
4/16/2021 104 Daniel A. Unity University-HS-II-2013A.Y
•The percentage pressures, computed and tabulated can be
used to work out the elevation of H.G. line above the datum
is given by:
Flow
Condition
U/S
Water
level
in m
D/S
Water
level in
m
Head
in m
Elevation of subsoil H.G. Line above Datum
Upstream pile Line Intermediate Pile Line Downstream pile Line
Pond
level U/S
with no
flow D/S
158 152 6 6 4.8 4.46 4.02 3.78 3.58 2.68 1.92 0
158 156.8 156.
46
156.02 155.7
8
155.5
8
154.1
7
153.9
2
152 %100
1E
%80
1D
%38.74
1C
%95.66
2E
%63
2D
%72.59
2
C %22.36
3E %32
3
D %0
3
C
4/16/2021 104 Daniel A. Unity University-HS-II-2013A.Y
Contd
The subsoil H.G. Line is then plotted in figure
4/16/2021 105 Daniel A. Unity University-HS-II-2013A.Y
The subsoil H.G. Line is then plotted in figure
4/16/2021 105 Daniel A. Unity University-HS-II-2013A.Y
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