Khosla Theory is a topic under the subject Irrigation Engineering of Civil Department.

1. KHOSLA THEORY
LAXMI INSTITUTE OF TECHNOLOGY
SARIGAM – 396155
Presentation by,
Under the Guidance of
RITU SINGH
Assistant Professor
DEPARTMENT OF CIVIL
NAME
Aparna Rath
Komal Singh
Enrollment No.
160860106001
180863106010
Under subject of
Irrigation
Engineering

3. 1. Khosla theory
2. Conclusion over Bligh's theory
3. Modification by Khosla
4. Khosla specific theory
i) Pile at some intermediate point
ii) Pile at downstream point
iii) Pile at the upstream end
5. Exit gradient
6. Safe exit gradient
7. Methods of independent variables
i) Correction for the thickness of floor
ii) Correction for the mutual interference of
piles
iii) Correction for slope

4.  From 1910, Bligh's theory is used for the design of
irrigation structures on permeable foundation.
 Number of structure were design by this Bligh's
theory, some remain stable while others gave
trouble or failed.
 In 1926-1927 , some siphons constructed on the
upper Chenab canal on the basis of bligh’s creep
theory, had piping problems.
 During investigation by Dr. A.N Khosla, Dr. N.K. Bose
and Dr. E.M. Taylor indicated that actual uplift
pressures were quite different from those
computed on the basis of Bligh's theory.

5.  The outer faces of end sheet piles were much
more effective than the inner ones and the
horizontal length of the floor.
 The intermediated piles of smaller length were
ineffective except for local redistribution of
pressure.
 Undermining of the floor started from the tail
end.
 It was absolutely essential to have a reasonably
deep vertical cut off at the downstream end to
prevent undermining.

6. Khosla and his associates carried out further research
work to find the ultimate and complete solution of
the problem. The solution given by them is now
known's as Khosla’s Theory.
They took into account the flow pattern below the
impermeable base of hydraulic structure to calculate
uplift pressure and exit gradient.

7. He thus made it clear that the loss of head does not
take place uniformly in proportion to the length of
creep.
It actually depends in the profile of the base of the
weir.
Secondly, he also established that the safety against
piping is not obtained by flat hydraulic gradient but
the exit gradient should be kept below critical value.

8. Straight horizontal
floor of negligible
thickness with pile
either at u/s end or
at d/s end.
Straight horizontal
floor of negligible
thickness with pile at
intermediate point.
Straight horizontal
floor depressed
below the bed,
but no cut off.
Khosla’s specific theory:

9. The uplift pressure PE, Pd and Pc at the three key points
E, D and C are given by the following equations.
PE = H/π cos-1
PD = H/π cos-1
PC = H/π cos-1
where,
𝛌=
𝛌1=

10. The uplift pressure at the key points E, D and C are
given by the following equations.
PE = H/π cos-1
PD = H/π cos-1
PC = H/π cos-1
where,
𝛌=

11. The pressure at the key points E1 , D1 and C1 are given
by the following equations.
PE1 = H
PD1 = H/π cos-1
PC1 = H/π cos-1
where,
𝛌=

12. The hydraulic gradient or pressure gradient of subsoil
flow at the downstream or the exit end of the floor is
defined as exit gradient.
For a standard form consisting of a floor of length b,
with a vertical cut off of depth d at its downstream
end, khosla derived an expression for the exit
gradient (GE) as follows:
GE = H/d . 1/
where, H = total seepage head
λ =

13. If there is no cut off at the downstream end of the
floor, a higher exit gradient will exist which may lead
to the failure of the floor due to piping.
It is therefore essential that a vertical cutoff should
be provided at the downstream end of the floor to
reduce the exit gradient.

14. The exit gradient should always be less than the
critical hydraulic gradient which is define as the
hydraulic gradient at which the soil particles will be
lifted up and which lead to undermining.
Safe exit gradient = critical hydraulic gradient
factor of safety

15. For alluvial soil, the critical hydraulic gradient is
found to be approximately equal to 1.
Permissible Exit Gradient
Type of soil Exit Gradient
Fine Sand 1/6 to 1/7
Course Sand 1/5 to 1/6
Shingle 1/4 to 1/5

16. 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.
Khosla solved the actual problem by an empirical
method known as method of independent variables.
This method consists of breaking up a complex
profile into a number of simple profiles, each of
which is independently amenable to mathematical
treatment. Then apply corrections due to the mutual
interference of pile and due to thickness and slope
of floor.

17. As an example the complex profile shown in fig is
broken up to the following simple profile and the
pressure at Key Points obtained.
Correction for slope
of the floor
Correction for mutual
interference of piles
Correction for the
thickness of floor

18. Pressure were calculated at key points considering
floor of negligible thickness i.e. at the top level of the
floor, but, points E1 and C1 are at the bottom of the
floor. Thus, pressures at actual points E1 and C1 are
computed by considering linear variation of pressure
between D and hypothetical point E and C.

19. When pile is at u/s end
Correction for C1 =
Pressure at C1 = =
When pile is at intermediate point
Correction for E1 =
Correction for C1 =
Pressure at E1 = =

20. When pile is at d/s end
Correction for C =
Pressure at E1 = =

21. The correction (C) is given by,
C =

22. where,
C = percentage correction to be applied to the
pressure head.
b’ = distance between the piles
b = total length of impervious floor
d = length on pile on which the effect on another pile
of length D is required to determine
D = depth of pile whose effect is required to be
determine on neighboring pile of depth d.
The correction is positive for points in the rear or
back water and subtractive for points in the direction
of flow.

23. The pressures calculated at various key points E, D and
C are considering floor as horizontal. But, the pressure
below sloping floor maybe greater or less than that
under a horizontal floor.
Hence the correction is plus for down slopes and minus
for the up slopes, following the direction of flow.
These corrections are to be multiplied by factor bs/b1’
where, bs = horizontally length of slope
b’ = distance between two piles in between
which the sloping floor is located .

24. The corrections for various slopes are given in
table below:
Slope
(vertical/horizontal)
Correction
(% of pressure)
1 in 1 11.2
1 in 2 6.5
1 in 3 4.5
1 in 4 3.3
1 in 5 2.8
1 in 6 2.5
1 in 7 2.3
1in 8 2.0