Theory for impervious floor

This presentation covers topic theory for impervious floor. It includes bligh thoery and khsola theory.

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

7. Design criteria 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°

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 Result: - Bligh’s theory is still using but Lane’s theory is not being.

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:

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 shown below.

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.

37. 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

38. ( 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

39. CORRECTION FOR THICKNESS OF FLOOR

40. 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

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

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

43. (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.

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

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

46. (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.

47. 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

48. 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

49. 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.

50. 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

51. Exit gradient (GE)

52. 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?

53. 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/

54. Thanks GHT