Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 339

q

O

r

lc W

T

f

R

C=cmmc

l

a

R

W

Cm

(a) Resultant cohesive force and other forces (b) Triangle of forces

g

Fig. 9.23 Location of the resultant cohesive force and triangle of forces

The factor of safety with respect to friction, assuming that cohesion is mobilised in full,

is given by:

Fφ =

tan

tan

φ

φ

′

m

...(Eq. 9.39)

where φ′ and φm are the effective friction angle and mobilised friction angle. If the factor of
safety with respect to the total shear strength Fs is required, φm is to be chosen such that Fc
and Fφ are equal. This is common-sense and may also be established mathematically:
Fs = s/τ ...(Eq. 9.40)

where s = c′ + σ tan φ′ (shear strength) ...(Eq. 9.41)

and τ = cm + σ tan φm (shear strength mobilised) ...(Eq. 9.42)

If there were to be neutral pressure due to submergence, it will add to the actuating

force as shown in Fig. 9.24.

B W

U

Fig. 9.24 Effect of neutral pressure on the stability of a slope