This document discusses theories for designing weirs on permeable foundations to prevent failures from seepage. It describes Bligh's creep theory, Lane's weighted creep theory, and Khosla's theory. Bligh's theory calculates creep length and floor thickness but does not distinguish horizontal from vertical creep. Lane's theory assigns higher weight to vertical creep. Khosla's theory accounts for pressure distributions and recommends cut-offs and aprons. It is commonly used but requires corrections for floor thickness, pile interference, and slope. Inverted filters and launching aprons are also discussed.

1. WEIRS ON PERMEABLE
FOUNDATIONS
(WATER RESOURCES ENGINEERING – II)
UNIT – VI
Rambabu Palaka, Assistant ProfessorBVRIT

2. Diversion Headworks

4. Learning Objectives
1. Causes of Failures of Weirs on Permeable
Foundations
2. Find Uplift Pressure and Thickness of Floor using
 Bligh’s Creep Theory
 Lane’s Weighted Creep Theory
 Khosla’s Theory
 Application of Correction Factors
3. Launching Apron

5. Causes of Failures of Weirs on Permeable Foundations
Causes of Failure:
1. Due to Seepage or Sub-surface Flow
a) Piping or Undermining
b) Rupture of Floor by Uplift Pressure
2. Due to Surface Flow
a) By Suction due to Hydraulic Jump
b) By Scour on the u/s and d/s of the weir

7. Design of Impervious Floor
 Directly depended on the possibilities of percolation in porous subsoil
 Water from upstream percolates and creeps (or travel) slowly through weir base
and the subsoil below it.
 The head lost by the creeping water is proportional to the distance it travels (creep
length) along the base of the weir profile.
 The creep length must be made as big as possible so as to prevent the piping
action. This can be achieved by providing deep vertical cut-offs or sheet piles
1. Bligh’s Creep Theory (1912)
2. Lane’s Weighted Creep Theory (1932)
3. Khosla’s Theory (1936)

8. Bligh’s Creep Theory (1912)
Assumptions:
1. Hydraulic Gradient is constant throughout the impervious length of the apron.
2. Creep Length is the sum of horizontal and vertical creep.
3. Stoppage of percolation by cut off or sheet pile possible only if it extends up to
impermeable soil strata.

9. Creep Length:
Coefficient of Percolation:
(Loss of head per unit length of creep)
Coefficient of Creep:

11. Bligh’s Creep Theory (1912)
Design Criteria:
a) Safety against Piping
Safe Creep Length, L = C.H
where C = Coefficient of Creep = 1/c
b) Safety against Uplift Pressure
Floor Thickness,
where
h = Ordinate of Hydraulic Gradient Line measures above the top of floor
ρ = Specific Gravity of Floor Material

14. Nominal Thickness of 1 m
Nominal Thickness of 1.5 m
L2 = L – l1 – (b + 2d1 + 2d2)
b
Safe Creep Length, L = C.H
d1 = HFL – Max. Scour Depth d2 = HFL after Retrogation – Max. Scour Depth
DESIGN

15. Bligh’s Creep Theory (1912)
Limitations:
1. No distinction between horizontal and vertical creep.
2. Holds good so long as horizontal distance between the pile lines is greater than
the twice their depth
3. Did not explain about Exit Gradient
4. No distinction between outer and inner faces of sheet piles or the intermediate
sheet piles, whereas from investigation it is clear that the outer faces of the end
sheet piles are much more effective than inner ones.
5. Losses of head does not take place in the same proportions as the creep length.
Also the uplift pressure distribution is not linear but follow a sine curve
6. Bligh does not specify the absolute necessity of providing a sheet pile at
downstream which is essential to prevent undermining or piping.

16. Lane’s Weighted Creep Theory (1932)
From the analysis of 200 dams all over the world, Lane’s concluded that horizontal
creep is less effective in reducing uplift than vertical creep. Therefore, he suggested
a factor of 1/3 for horizontal creep against 1 for the vertical creep
Assumptions:
1. Slopes steeper than 450 are taken as Verticals (d)
2. Slopes less than 450 are taken as Horizontals (l)
Creep Length:
Safe Creep Length, L = C.H

18. Khosla’s Theory (1936)
After studying a dam failures constructed based on Bligh’s theory, Khosla came out
with the following;
1. Outer faces of end sheet piles were much more effective than the inner ones
and the horizontal length of the floor.
2. Intermediated piles of smaller length were ineffective except for local
redistribution of pressure.
3. Undermining of floor started from tail end.
4. It was absolutely essential to have a reasonably deep vertical cut off at the
downstream end to prevent undermining.

19. Khosla’s Theory (1936)
Horizontal Floor with negligible small thickness:

21. Khosla’s Theory (1936)
Special Cases:
Straight horizontal floor of negligible thickness with
1. Pile at upstream ends.
2. Pile at downstream end.
3. Pile at intermediate points.
4. Depressed below the bed
(with no cutoff)

23. Where
b = Length of weir foundation
d = depth of pile
Φ = Percentage of Pressure at a
given point
H = Height of Water
Example:
PD = (ΦD /H) 100

24. Khosla’s Curve for Exit Gradient

26. Khosla’s Theory (1936)
Most designs do not confirm to elementary profiles (specific cases). In actual cases,
we may have a number of piles at upstream level, downstream level and
intermediate points and the floor also has some thickness.
Method of independent variable:
This method consists of breaking up a complex profile into a number of simple
profiles. The pressures obtained at the key points by considering simple profile are
then corrected for the following:
1. correction for the thickness of floor
2. correction for mutual interference of piles
3. correction for slope of the floor.

27. U/S Pile
Intermediate Pile:
D/S Pile:

28. Where
C = Percentage of Correction to
be applied the pressure head

31. Inverted Filter and Launching Apron
Inverted Filter:
An inverted filter is provided immediately at the end of d/s impervious apron to
relieve the pressure.
Approximate length is 1.5 d2
Launching Apron:
After the inverted filter, a launching apron is provided to protect the d/s pile from
scour holes progressing in the u/s direction.
Approximate length is 2.5 d2
A similar launching apron is provided to the u/s side with a length equal to 2d1

33. Previous Questions
1. Describe with the help of suitable sketches Bligh's creep theory for the safe
design of apron in an irrigation work
2. How does Lane’s theory differ from Bligh’s Creep Theory
3. Discuss Khosla's theory for design of weirs on permeable foundations,
Enumerate the various corrections that are needed in its application
4. Discuss utility and limitations of Khosla`s theory
5. Explain salient features of Khosla’s theory and how it is used in the design of
permeable foundations
6. Compare the Bligh’s and Khosla’s theories for the design of impervious floor

34. Reference
Chapter 12
Irrigation and Water Power Engineering
By Dr. B. C. Punmia,
Dr. Pande Brij Basi Lal,
Ashok Kr. Jain,
Arun Kr. Jain