EMBANKMENT LECTURE 12

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Infinite and finite length of blanket:

Infinite and finite length of blanket 1/27/2014 1 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

(a) Infinite length of blanket ::

(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 1/27/2014 2 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET. v

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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 3 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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1/27/2014 4 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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In this case for the convenience, the point x = 0 is taken at the downstream end of the blanket and hence h 0 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 5 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

equivalent resistance Xr of the foundation ::

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 equ ivalent to the flow which passes the blanket system under the same loss of head. Thus vi 1/27/2014 6 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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Also from equation (v), we have Equating the values of vii 1/27/2014 7 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

(2) Solution for finite length of blanket ::

(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. * viii 1/27/2014 8 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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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 9 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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Again if Xr is the equivalent resistance of the foundation, we have from equation 1/27/2014 10 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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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 11 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

Loss of head through the blanket ::

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 12 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

reduction in quantity of seepage due to provision of blanket ::

reduction in quantity of seepage due to provision of blanket : When no blanket With blanket 1/27/2014 13 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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1/27/2014 18 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

The value of constant 'a' is given by:

The value of constant 'a' is given by 1/27/2014 19 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

The optimum length of blanket,:

The optimum length of blanket, 1/27/2014 20 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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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 21 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

Sample calculations for blanket length x =50 m, are given below:

Sample calculations for blanket length x =50 m, are given below 1/27/2014 22 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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1/27/2014 23 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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The results for other values of x are tabulated below. 1/27/2014 24 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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1/27/2014 27 PREPARED BY V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.

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