The document discusses the design of impervious floors for subsurface flow, detailing Bligh's creep theory, Khosla's theory, and Lane's weighted creep theory, along with their limitations and applications in hydraulic engineering. It highlights the importance of understanding creep lengths, uplift pressure, and the exit gradient to ensure safety against structures like weirs and barrages. Khosla's method introduces a more accurate approach to determine pressures and exit gradients via flow nets and critical gradients compared to the earlier theories.

1. Design of Impervious Floor
DIVYA VISHNOI
Assistant Professor

2. DESIGN OF IMPERVIOUS FLOOR FOR
SUBSURFACE FLOW
• Bligh’s creep theory
• Khosla’s theory

3. BLIGH’S CREEP THEORY
• In 1910 W.G. Bligh presented a theory for the subsurface
flow in his book “Practical Design of Irrigation Work. This
theory is known as Bligh’s theory.
• Design of impervious floor or apron
– Directly depend on the possibilities of percolation in
the porous soil on which the apron is built

4. BLIGH’S CREEP THEORY
• Bligh assumed that
– Hydraulic gradient is constant throughout the
impervious length of the apron
– The percolating water creeps along the contact of base
profile of the apron with the sub-soil, losing head
enroute, proportional to the length of its travel
– Stoppage of percolation by cut off (pile) possible only if
it extends up to impermeable soil strata

5. • Bligh designated the length of travel as ‘creep length’
and is equal to the sum of horizontal and vertical
length of creep
BLIGH’S CREEP THEORY

6. • If ‘H’ is the total loss of head, loss of head per unit length of
creep (c),
• c-percolation coefficient
• Reciprocal of ‘c’ is called ‘coefficient of creep’(C)
BLIGH’S CREEP THEORY
321 222 dddb
H
L
H
c



7. • Design criteria
(i) Safety against piping
Length of creep should be sufficient to provide a safe
hydraulic gradient according to the type of soil
Thus, safe creep length,
Where, C= creep coefficient=1/c
BLIGH’S CREEP THEORY

8. • Design criteria
(ii) Safety against uplift pressure
Let ‘h’’ be the uplift pressure head at any point of
the apron
The uplift pressure = wh’
This uplift pressure is balanced by the weight of the
floor at this point
BLIGH’S CREEP THEORY

9. If, t =thickness of floor at this point
G = specific gravity of floor material
Weight of floor per unit area
=
BLIGH’S CREEP THEORY

10. BLIGH’S CREEP THEORY

11. LIMITATIONS OF BLIGH’S THEORY
• Bligh made no distinction between horizontal and vertical
creep
• Did not explain the idea of exit gradient - safety against
undermining cannot simply be obtained by considering a
flat average gradient but by keeping this gradient will be
low critical
• 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

12. • 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
• Bligh did not specify the absolute necessity of
providing a cutoff at the d/s end of the floor,
whereas it is absolutely essential to provide a deep
vertical cutoff at the d/s end of the floor to prevent
undermining.
LIMITATIONS OF BLIGH’S THEORY

13. LANE’S WEIGHTED CREEP THEORY
• An improvement over Bligh’s theory
• Made distinction between horizontal and vertical
creep
• Horizontal creep is less effective in reducing uplift
than vertical creep
• Proposed a weightage factor of 1/3 for horizontal
creep as against the 1 for vertical creep

14. LANE’S WEIGHTED CREEP THEORY
• Lane’s Weighted creep length
Whereas,
N=sum of all the horizontal and sloping contact less
than 45°
V=sum of all the vertical and sloping contact less than
45°
VNLw 
3
1

15. LANE’S WEIGHTED CREEP THEORY
Drawbacks of the Lane’s weighted theory
Most of limitations same as Bligh’s theory.
It is empirical and lacks any rational basis.
Only theoretically important.

16. LANE’S WEIGHTED CREEP THEORY

17. Khosla’s Theory
• Khosla’s Theory and Concept of Flow Nets
• Many of the important hydraulic structures,
such as weirs and barrage, were designed on the
basis of Bligh’s theory between the periods 1910
to 1925. In 1926 – 27, the upper Chenab canal
siphons, designed on Bligh’s theory, started
posing undermining troubles. Investigations
started. During investigations, the actual pressure
measurement were made with the help of pipe
inserted in the floors of these siphons, which
indicated the actual pressures are quite different
from those computed on the basis of Bligh’s
theory.

18. • Khosla’s theory. The main principles of this theory are
summarized below:
• (a) The seepage water does not creep along the
bottom contour of pucca flood as started by Bligh,
but on the other hand, this water moves along a set
of stream-lines. This steady seepage in a vertical
plane for a homogeneous soil can be expressed by
Laplacian equation:
0

19. Khosla’s Theory
• The equation represents two sets of curves
intersecting each other orthogonally. The resultant
flow diagram showing both of the curves is called a
Flow Net.
• Stream Lines: The streamlines represent the paths
along which the water flows through the sub-soil.
• Every particle entering the soil at a given point
upstream of the work, will trace out its own path and
will represent a streamline. The first streamline
follows the bottom contour of the works and is the
same as Bligh’s path of creep. The remaining
streamlines follows smooth curves transiting slowly
from the outline of the foundation to a semi-ellipse, as

20. Khosla’s Theory
• Equipotential Lines: Treating the downstream bed as
datum and assuming no water on the downstream
side, it can be easily started that every streamline
possesses a head equal to h1 while entering the soil;
and when it emerges at the down-stream end into the
atmosphere, its head is zero. Thus, the head h1 is
entirely lost during the passage of water along the
streamlines.

21. Khosla’s Theory
• Further, at every intermediate point in its path,
there is certain residual head (h) still to be dissipated
in the remaining length to be traversed to the
downstream end. This fact is applicable to every
streamline, and hence, there will be points on
different streamlines having the same value of
residual head h. If such points are joined together,
the curve obtained is called an equipotential line.

22. Khosla’s Theory

23. Khosla’s Theory
Every water particle on line AB is having a
residual head h = h1, and on CD is having a
residual head h = 0, and hence, AB and CD
are equipotential lines.
Since an equipotential line represent the
joining of points of equal residual head, hence
if piezometers were installed on an
equipotential line, the water will rise in all of
them up to the same level as shown in figure
below

24. Khosla’s Theory

25. Khosla’s Theory
• The seepage water exerts a force at each point in the
direction of flow and tangential to the streamlines as
shown in figure above. This force (F) has an upward
component from the point where the streamlines turns
upward. For soil grains to remain stable, the upward
component of this force should be counterbalanced by
the submerged weight of the soil grain. This 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.

26. Khosla’s Theory
• For the soil grain to remain stable, the
submerged weight of soil grain should be more
than this upward disturbing force. The
disturbing force at any point is proportional to
the gradient of pressure of water at that point
(i.e. dp/dt). This gradient of pressure of water at
the exit end is called the exit gradient. In order
that the soil particles at exit remain stable, the
upward pressure at exit should be safe. In other
words, the exit gradient should be safe.

27. Critical Exit Gradient
• This 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 to 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
ensured, so as to keep the structure safe
against piping.
• The submerged weight (Ws) of a unit volume
of soil is given as:

28. Critical Exit Gradient

29. KHOSLA’S THEORY
• Dr. A. N. Khosla and his associates done
investigations on structures designed based on
Bligh’s theory and following conclusions were made
– The outer faces of sheet piles are much more
effective than inner ones and the horizontal length
of floor
– The intermediate sheet piles, if smaller in length
than the outer ones were ineffective

30. – Undermining of floors started from the tail end. If
hydraulic gradient at exit is more than the critical
gradient, soil particles will move with water and
leads to failure
– It is absolutely essential to have reasonably deep
vertical cutoff at the d/s end to prevent
undermining
KHOSLA’S THEORY

31. • Khosla and his associates carried out further research
to find out a solution to the problem of subsurface
flow and provided a solution
– Khosla’s theory
– Considered the flow pattern below the impervious
base of hydraulic structures on pervious
foundations to find the distribution of uplift
pressure on the base of the structure and the exit
gradient
KHOSLA’S THEORY

32. KHOSLA’S METHOD OF INDEPENDENT
VARIABLES
• A composite weir section is split up into a number of
simple standard forms
• The standard forms
(a) A straight horizontal floor of negligible thickness with a
sheet pile either at the u/s end or at the d/s end of the
floor

33. (b) A straight horizontal floor of negligible thickness with
a sheet pile at some intermediate point
(c) A straight horizontal floor depressed below the bed
but with no vertical cutoff
KHOSLA’S METHOD OF INDEPENDENT
VARIABLES

34. • These standard cases were analyzed by Khosla and
his associates and expressions were derived for
determining
– The residual seepage head (uplift pressure) at key points
(key points are the junction points of pile and floor, bottom
point of pile and bottom corners of depressed floor)
– Exit gradient
– These results are presented in the form of curves
KHOSLA’S METHOD OF INDEPENDENT
VARIABLES

35. KHOSLA’S METHOD OF INDEPENDENT
VARIABLES
• The curves gives the values of Φ (the ratio of residual
seepage head and total seepage head) at key points
• The directions for reading the curves are given on
the curves itself

36. Khosla’s Method of independent variables for
determination of pressures and exit gradient for
seepage below a weir or a barrage
• In this method, a complex profile like that of a weir is
broken into a number of simple profiles; each of
which can be solved mathematically. profiles which
are most useful are:
• (i) A straight horizontal floor of negligible thickness
with a sheet pile line on the u/s end and d/s end.
• (ii) A straight horizontal floor depressed below the bed
but without any vertical cut-offs.
• (iii) A straight horizontal floor of negligible thickness
with a sheet pile line at some intermediate point.

41. Khosla’s Method of independent variables for
determination of pressures and exit gradient for
seepage below a weir or a barrage
• The key points are the junctions of the floor and the
pole 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 thickness of floor
• (b) Correction for the Mutual interference of Piles
• (c) Correction for the slope of the floor

42. • (i) Straight floor of negligible thickness with pile at u/s end
• (ii) Straight floor of negligible thickness with pile at some
intermediate point
• (iii) Straight floor of negligible thickness with pile at d/s end
• The pressure obtained at the key points from curves are then
corrected for
• (i) Thickness of floor
• (ii) Interference of piles
• (iii) Sloping floor

43. CORRECTION FOR THICKNESS OF FLOOR

44. CORRECTION FOR THICKNESS OF FLOOR
• Pressure at actual points C1 and E1 can be computed by
considering linear variation of pressure between point D
and points E and C
• When pile is at u/s end,
• Correction for
• Pressure at

45. • For the intermediate pile,
• Correction for
• Pressure at
• Correction for
• Pressure at
CORRECTION FOR THICKNESS OF FLOOR

46. • When pile at d/s end,
• Correction for
• Pressure at
CORRECTION FOR THICKNESS OF FLOOR

47. (b) Correction for the Mutual interference of
Piles
The correction C to be applied as percentage of head due to this effect, is given
by
Where,
b′ = The distance between two pile lines.
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
The correction is positive for the points in the rear of back water, and
subtractive for the points forward in the direction of flow. This equation
does not apply to the effect of an outer pile on an intermediate pile, if the
intermediate pile is equal to or smaller than the outer pile and is at a
distance less than twice the length of the outer pile.

48. (b) Correction for the Mutual interference of
Piles

49. (b) Correction for the Mutual interference of Piles

50. (b) Correction for the Mutual interference of
Piles
• Suppose in the above figure, we are considering the influence of
the pile no (2) on pile no (1) for correcting the pressure at C1.
Since the point C1 is in the rear, this correction shall be positive.
While the correction to be applied to E2 due to pile no (1)
shall be negative, since the point E2 is in the forward direction
of flow. Similarly, the correction at C2 due to pile no (3) is
positive and the correction at E2 due to pile no (2) is negative.

51. CORRECTION FOR SLOPE
• The % pressure under a floor sloping down is greater than
that under a horizontal floor
• The % pressure under a floor sloping up is less than that
under a horizontal floor
• Correction is plus for down slopes and minus for up slopes
Slope (vertical/horizontal) Correction (%)
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
1 in 8 2.0

52. • The corrections given table are to be further multiplied by the
proportion of horizontal length of slope to the distance
between the two pile lines in between which the sloping floor
is located
• The slope correction is applicable only to that key points of
pile line which is fixed at the beginning or end of the slope
CORRECTION FOR SLOPE

53. 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 equations. This can be
accomplished either by mathematical solution of the
Laplacian equations, or by Electrical analogy method,
or by graphical sketching by adjusting the streamlines
and equipotential lines with respect to the boundary
conditions. These are complicated methods and are
time consuming. Therefore, for designing hydraulic
structures such as weirs or barrage or pervious
foundations, Khosla has evolved a simple, quick and an
• accurate approach, called Method of Independent
Variables.

54. Exit gradient (GE)
• 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

55. Exit gradient (GE)

56. RTU Questions
• Explain Khosla’s method of independent variables?
• Discuss Bligh’s theory with its limitations?
• Explain Bligh’s Creep Theory in details?
• Compare Khosla and Bligh’s theory?
• Write down the expression for uplift pressure at the
salient point E, D and C of pile at upstream,
downstream and intermediate pile. What is the
effect of mutual interference of piles?
• Describe the exit gradient and critical gradients and
their importance?

57. References
• Irrigation Engineering & Water Power Engineering
– By Prof. P.N.MODI and Dr. S.M. SETH
--- Standard Book House Delhi
• Irrigation Engineering & Hydraulic Structures
– By Prof. Santosh Kumar Garg
– Khanna Publishers
• Irrigation, Water Power Engineering & Hydraulic Structures
– By Prof K.R. Arora
– Standard Publishers Distributions
• Internet Websites
• http://www.aboutcivil.org/
• http://nptel.ac.in/courses/105105110/

58. Thanks
GHT