Geotechnical Engineering

DHARM

186 GEOTECHNICAL ENGINEERING

1

ht

E

a

a

F

2 4

3

d

0

Fig. 6.20 Graphical solution based on L. Casagrande’s method

z 1

z 2

M

Ds=z 22

L

Ds=z 11

C

a sin^2 a

a sina

Daz = a sin 1 2

Daz = a sin 2 2

Fig. 6.21 Graphical method for sketching the top flow line, based on

L. Casagrande’s method (After Taylor, 1948)

Let us assume that the top flow line is divided into sections of constant head drop, say,

∆z (a convenient choice is a given fraction of a sin^2 α).

From Eq. 6.22,

if ∆z = C 1 a sin^2 α, where C 1 is a constant,

s = C 1. Z ...(Eq. 6.23)

C 1 has been conveniently chosen as unity, for the illustration given in Fig. 6.21.

The head drop ∆z 1 is laid-off equal to a sin^2 α, z 1 being the average ordinate

ejaasin^2 αα+^12 sin^2. By setting ∆s 1 equal to z 1 , point L on the top flow line is obtained. By

repeating this process, we plot a number of points on the top flow line. A smaller value of C 1

would yield more points and a better determination of the top flow line.

Schaffernak and Iterson’s Solution for ααααα < 30°

Shcaffernak and Iterson (1917) assumed the energy gradient as tan α or dz/dx. This is approxi-

mately true as long as the slope is gentle–say α < 30°.

Referring to Fig. 6.22, flow through the vertical section EJ is given by

q = k. dz

dx

. z