Contents preface (VII) introduction 1—37

(vi) Horizontal Upstream Impervious Blanket
When the foundation soil is homogeneous and extends to large depths, a horizontal upstream impervious blanket (Fig. 15.17) offers an effective method of reducing the underseepage by increasing the length of the seepage path. Such blankets must be constructed using impervious soil in the same manner as the impervious core of the dam. At sites where a natural surface blanket of impervious soil already exists, it may be necessary only to scarify the upper surface and recompact it with proper water content and also fill the gaps to make a continuous impervious seal. The thickness and length of such blankets depend on the permeability of the blanketing material, the stratification and thickness of the pervious foundation, and the reservoir depth. Thickness ranging from 0.6 to 3 m is generally used. If the blanket material is very impervious compared to the natural foundation soil so that the seepage through the blanket is negligible, the length of the blanket can be related to the reduction in underseepage. Considering Fig. 15.17, the underseepage Q in the absence of the blanket is given as

H	Zf
^Q = Kf xd		(15.17)

in which K_f is the coefficient of permeability of the foundation soil, and Z_f is the thickness of the foundation. If the provision of the blanket of length x reduces the underseepage to pQ, then

	pQ =	K f		H	Zf	(15.18)
	x d + x
Combining Eqs. (15.17) and (15.18)
		p =			^xd					(15.19)
	x d + x
or	x = x			(1 − p)			(15.20)
d			p

H Core
Z_b

Blanket

x			xd		z	f

Fig. 15.17 Horizontal upstream impervious blanket

EMBANKMENT DAMS

509

It may, however, not always be possible to have an impervious blanket through which the seepage can be considered negligible. In such cases, there is an optimum length of the blanket and there is no significant reduction in the underseepage with further increase in the length of the blanket. The effectiveness of such blankets (Fig. 15.18) is analysed by using the following Bennett’s fundamental differential equation (10):

d ^2 h	= a^2h	(15.21)
dx^2

where, h is the head loss through the blanket which equals the difference of the head on the two sides of the blanket under which percolation takes place and a is given as:

a^2	=	Kb		(15.22)
K f Z f
			Zb

Here, K_f and K _b are coefficients of permeability of the foundation, and the blanket material, respectively. For a blanket of constant thickness Z_b and infinite horizontal extent, Bennett (10) obtained

xr =	1	(15.23)
a

where, x_r is termed the effective length of the blanket and is defined as the length of the prism of foundation which will be able to carry the actual foundation seepage under the same head loss h₀ (up to the end of the blanket) with a linear hydraulic gradient, i.e.,

q = K		h0	Z		(15.24)
f	^f xr	f

For the case of blanket of constant thickness and finite length (i.e., the part of the foundation seepage enters from the reservoir bed upstream of the blanket), Bennett (10) obtained

x		=	e^2^ax − 1	=	1	tan h (ax)	(15.25)
r	a (e^2^ax + 1)	a

Here, x_r represents the effective length of the blanket up to a distance x downstream from its upstream end (x = 0). If L is the total length of the blanket, then its effective length is given as

x

=

1

tan h

(aL) =

e2aL − 1

(15.26)

r

a

a (e^2^aL + 1)

F.R.L.

h

Foundation HGL

^ho

dx

Zb

H

qf

qf

x

r

x

d

o

z

L

f