Download - Embankment lecture 12
![Page 1: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/1.jpg)
Infinite and finite length of blanket
1/27/2014 1 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 2: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/2.jpg)
(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
![Page 3: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/3.jpg)
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.
![Page 4: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/4.jpg)
1/27/2014 4 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 5: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/5.jpg)
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 5 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 6: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/6.jpg)
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 equivalent 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.
![Page 7: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/7.jpg)
Also from equation (v), we have
Equating the values of
vii
1/27/2014 7 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 8: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/8.jpg)
(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.
![Page 9: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/9.jpg)
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.
![Page 10: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/10.jpg)
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.
![Page 11: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/11.jpg)
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.
![Page 12: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/12.jpg)
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.
![Page 13: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/13.jpg)
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.
![Page 14: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/14.jpg)
1/27/2014 14 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 15: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/15.jpg)
1/27/2014 15 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 16: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/16.jpg)
1/27/2014 16 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 17: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/17.jpg)
1/27/2014 17 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 18: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/18.jpg)
1/27/2014 18 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 19: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/19.jpg)
The value of constant 'a' is given by
1/27/2014 19 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 20: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/20.jpg)
The optimum length of blanket,
1/27/2014 20 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 21: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/21.jpg)
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.
![Page 22: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/22.jpg)
Sample calculations for blanket length x =50 m, are
given below
1/27/2014 22 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 23: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/23.jpg)
1/27/2014 23 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 24: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/24.jpg)
The results for other values of x are tabulated below.
1/27/2014 24 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 25: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/25.jpg)
1/27/2014 25 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 26: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/26.jpg)
1/27/2014 26 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.
![Page 27: Embankment lecture 12](https://reader034.vdocuments.us/reader034/viewer/2022042513/54c219cd4a7959c5778b466e/html5/thumbnails/27.jpg)
1/27/2014 27 PREPARED BY
V.H.KHOKHANI,ASSISTANT PROFESSOR, DIET.