Embankment lecture 12
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. Infinite and finite length of blanket 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 1
- 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. 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
- 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. 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. Also from equation (v), we have vii Equating the values of 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 7
- 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. 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. 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. 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. 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. 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
- 19. The value of constant 'a' is given by 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 19
- 20. The optimum length of blanket, 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 20
- 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. Sample calculations for blanket length x =50 m, are given below 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 22
- 24. The results for other values of x are tabulated below. 1/27/2014 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. 24