Stability of Slopes - Elements of Soil Mechanics - page 420

Fig. 13.30 Example 13.13: Rigorous method.

Example 13.14: Geo limit state (planar failure)

Consider an infinite slope, constructed at an angle of β = 20° to the horizontal using the
granular soil described in Example 13.1. Check the GEO limit state against failure along
a plane parallel and 2 m beneath the surface of the slope, using Design Approach 1.

Solution:

(ii) Combination 1 (partial factor sets A1 + M1 + R1)
From Table 5.1, the relevant partial factors are: γ G;unfav = 1.35; γ φ ′ = 1.0.
From Section 13.1 it was seen that the sliding force, per unit area = W sin β

Design sliding force per unit area G , = × × γ z sin β γ × d G unfav ;

= 18 × × 2 sin 20 °× 1 35 .

= 16 6 . kPa

No other actions contribute to the sliding force so E d = G d = 16.6 kPa.

′

tan φ tan

.

30
1 0

°

= °

=

′ =

− 1 − 1

φ tan tan 30 d

γ φ ′

′

Design resisting force per unit area R , = × × γ z cos β × tan φ

d d

= 18 × × 2 cos 20 °× tan 30 °

= 19 5 . kPa

Therefore the limit state requirement is satisfied since E d ≤ R d .
(ii) Combination 2 (partial factor sets A2 + M2 + R1)
From Table 5.1: γ G;unfav = 1.0; γ φ ′ = 1.25.
Design sliding force per unit area G , = × × γ z sin β γ ×

d G unfav ;

= 18 × × 2 sin 20 °× 1 0 .

= 12 3 . kPa