Khosla theory

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 P rofessor DEPARTMENT OF CIVIL NAME Aparna Rath Komal Singh Enrollment No. 160860106001 180863106010 Under subject of Irrigation Engineering

2. Topic: khosla theory Made by :- Aparna Rath (160860106001) Komal Singh ( 180863106010)

3. Contents Khosla theory Conclusion over Bligh's theory 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. Khosla’s theory 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. Conclusion over bligh’s theory 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. Modification by Khosla 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. pile at some intermediate point The uplift pressure P E , P d and P c at the three key points E, D and C are given by the following equations . P E = H/ π cos -1 P D = H/ π cos -1 P C = H/ π cos -1 where, 𝛌= 𝛌 1 =

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

11. Pile at the upstream end The pressure at the key points E 1 , D 1 and C 1 are given by the following equations. P E1 = H P D1 = H/ π cos -1 P C1 = H/ π cos -1 where, 𝛌=

12. Exit gradient: 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 (G E ) as follows : G E = 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. Safe Exit gradient 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. Method of independent variable: 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. Correction for the thickness of floor: Pressure were calculated at key points considering floor of negligible thickness i.e. at the top level of the floor, but, points E 1 and C 1 are at the bottom of the floor. Thus, pressures at actual points E 1 and C 1 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 C 1 = Pressure at C 1 = = When pile is at intermediate point Correction for E 1 = Correction for C 1 = Pressure at E 1 = =

20. When pile is at d/s end Correction for C = Pressure at E 1 = =

21. Correction for the mutual interference of piles: 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. Correction for slope: 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 b s /b 1 ’ where, b s = 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

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