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# Embankment lecture 12

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Infinite and finite length of blanket
A natural impervious blanket of large areal extent if available may be considered as a balnket of infinite length
For a blanket of infinite length, the solution of equation (iv) is
In this case for the convenience, the point x = 0 is taken at the downstream end of the blanket and hence h0 is the total loss of head through the blanket upto the end of the blanket.
As a measure of the efficiency of a blanket of any length x (where x may be infinite or a finite length) a length Xr is considered which is known as equivalent resistance of the foundation and is defined below.
It may be defined as the length of a prism of the foundation soil of thickness Zf and coefficient of permeability kf which under the loss of head h would carry flow equivalent to the flow which passes the blanket system under the same loss of head. Thus
(2) Solution for finite length of blanket :
For a blanket of uniform thickness and finite length of blanket ihe solution equation (iv) is

which h is the loss of head through the blanket upto any point at a distance and hn is a constant for computing h. hn depends on the total head loss of the system of which the blanket is a part and on the ratio of the blanket to the remainder of system. *
From equation (viii) at x - 0, h = 0, and hence in this case the point x = 0 is taken at the upstream end of the blanket.
Differentiating both sides of equation (viii) with respect to x, we get

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### Embankment lecture 12

1. 1. Infinite and finite length of blanket 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 1
2. 2. (a) Infinite length of blanket : A natural impervious blanket of large areal extent if available may be considered as a balnket of infinite length For a blanket of infinite length, the solution of equation (iv) is v 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 2
3. 3. where, h = loss of -head through the blanket up to any point at a distance x. h0 = loss of head through the blanket up to a point x = 0. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 3
4. 4. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 4
5. 5. In this case for the convenience, the point x = 0 is taken at the downstream end of the blanket and hence h0 is the total loss of head through the blanket upto the end of the blanket. As a measure of the efficiency of a blanket of any length x (where x may be infinite or a finite length) a length Xr is considered which is known as equivalent resistance of the foundation and is defined below. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 5
6. 6. equivalent resistance Xr of the foundation : It may be defined as the length of a prism of the foundation soil of thickness Zf and coefficient of permeability kf which under the loss of head h would carry flow vi equivalent to the flow which passes the blanket system under the same loss of head. Thus 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 6
7. 7. Also from equation (v), we have vii Equating the values of 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 7
8. 8. (2) Solution for finite length of blanket : For a blanket of uniform thickness and finite length of blanket ihe solution equation (iv) is viii which h is the loss of head through the blanket upto any point at a distance and hn is a constant for computing h. hn depends on the total head loss of the system of which the blanket is a part and on the ratio of the blanket to the remainder of system. * 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 8
9. 9. From equation (viii) at x - 0, h = 0, and hence in this case the point x = 0 is taken at the upstream end of the blanket. Differentiating both sides of equation (viii) with respect to x, we get 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 9
10. 10. Again if Xr is the equivalent resistance of the foundation, we have from equation 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 10
11. 11. If the length of the blanket is L then by substituting x = L in equation (ix) the value of Xr for the entire blanket is obtained. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 11
12. 12. Loss of head through the blanket : h0 is the loss of head upto the end of the blanket; H is the total reservoir head Xd is the base width of the impervious core 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 12
13. 13. reduction in quantity of seepage due to provision of blanket : When no blanket With blanket 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 13
14. 14. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 14
15. 15. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 15
16. 16. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 16
17. 17. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 17
18. 18. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 18
19. 19. The value of constant 'a' is given by 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 19
20. 20. The optimum length of blanket, 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 20
21. 21. Let us vary the length of blanket as 25 m, 75 m, 100 m, 125 m, 151.78 AND infinite, and calculate the values of Xr , h0 and % reduction in the discharge. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 21
22. 22. Sample calculations for blanket length x =50 m, are given below 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 22
23. 23. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 23
24. 24. The results for other values of x are tabulated below. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 24
25. 25. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 25
26. 26. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 26
27. 27. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 27