Slope Stability Model and Landslide Susceptibility Using Geo-technical Properties of Soil - Semi-quantitative Approaches for Landslide Assessment and Prediction - page 168

depth based on equal factor of safety. However, it is not simple to analyze 2D
rotational slide due to variation in depth of sliding surface. Hence, 2D depth of
rotational slide (Eq. 6.2 ) was then converted to equivalent translational depth
without the impact of ground water (Eq. 6.3 ) keeping the same factor of safety.

þ c tan [ P i 1 z i cos 2 b
c P i 1 z i

c

FS Rotational ð Þ ¼

sin b cos b ð 6 : 2 Þ

þ c cos 2 b tan u

c z

FS Translational ð Þ ¼ ð 6 : 3 Þ

c z sin b cos b

where, ʳ = unit weight of the soil; z = depth of the failure surface below the terrain

surface; ʲ = the terrain surface inclination; φ = angle of internal friction;

c = cohesion.
The safety factor (FS) under the influence of ground water (semi-saturated and
saturated condition) of cohesive soil could also be calculated by applying the
revised 1D slope stability model with the help Eq. 6.4 .

c þ c ð m c w Þ cos 2 b tan u

FS ¼ ð 6 : 4 Þ

c z sin b cos b

where, = unit weight of soil; m = soil saturation index; Z w = height of water table

above failure surface; Z = depth of failure surface below the terrain surface;
ʳ w = unit weight of water;

γ

ʲ = the terrain surface inclination; φ = angle of internal

friction and c = cohesion.
In completely dry condition, cohesion (c) and wetness index value (m) become
zero (0) and in case of cohesion less soil, safety factor could be determined with the
help of following equation.

2

¼ c

D cos h tan u

Fs ð 6 : 5 Þ

c D sin h cos h

¼ tan u
tan €

Or ; FS ð 6 : 6 Þ

The safety factor for cohesion less soil with the influence of ground water can be
estimated by:

2

¼ c

ð m

€ tan u
c D sin € cos €

c w Þ D cos

ð 6 : 7 Þ

FS