Geotechnical Engineering

DHARM

346 GEOTECHNICAL ENGINEERING

\ Safe angle of slope is 8 °.

Example 9.8: A canal is to be excavated through a soil with c = 15 kN/m^2 , φ = 20°, e = 0.9 and
G = 2.67. The side slope is 1 in 1. The depth of the canal is 6 m. Determine the factor of safety
with respect to cohesion when the canal runs full. What will be the factor of safety if the canal
is rapidly emptied?

γsat =

Ge

e w

+

+

F

HG

I

KJ

=

×

+

F

HG

I

KJ

×

1

267 090

1090

. .. 981
.

γ. kN / m^3

=

357

190

. 981
.

×. kN/m^3 = 18.43 kN/m^3

γ ¢ = γsat – γw = 8.62 kN/m^3
β = 45°, φ = 20°.
(a) Submerged condition:
From Taylor’s charts, for these values of β and φ, the stability number N is found to be
0.06.

∴ 0.06 =

c

H

mmc

γ′

=

..862 6×

cm = 8.62 × 6 × 0.06 kN/m^2 = 3.10 kN/m^2.

Factor of safety with respect to cohesion, Fc = c/cm = 15/3.10 = 4.48.

(b) Rapid drawdown condition:

φw = (γ ′/γsat) × φ = (8.62/18.43) × 20° = 9.35°

For β = 45° and φ = 9.35°, Taylor’s stability number from charts is found to be 0.114.

∴ 0.114 =

c

H

mmc

γsat

=

18 43 6 .×

cm = 0.114 × 18.43 × 6 kN/m^2 = 12.60 kN/m^2

Factor of safety with respect to cohesion Fc = c/cm =

15 0

12 6

. 12
.

≈.

(Note: The critical nature of a rapid drawdown should now be apparent).
Example 9.9: The cross-section of an earth dam on an impermeable base is shown in Fig. 9.29.
The stability of the downstream slope is to be investigated using the slip circle shown. Given:

γsat^ = 19.5 kN/m^3
c′ = 9 kN/m^2
φ′ = 27°
r = 9 m.
θ = 88°
For this circle determine the factor of safety by the conventional approach, as well as
the rigorous one.