Stability of Slopes - Elements of Soil Mechanics - page 418

2. Combination 2 (partial factor sets A2 + M2 + R1)
From Table 5.1: γ G; unfav = 1.0; γ cu = 1.4; γ c ′ = 1.25; γ φ ′ = 1.25.
Design material properties:

′ = ′

c 90

1 4

c 5

1 25

t an φ

=

u

c = = = 64 3 . kPa c ; ′ = = 4 kPa ; φ ′ = tan

− 1

20 5 . °

u d ; d d

γ . γ . γ φ

cu c ′ ′

c 64 3

15 20 1 0

.

u d ;

Short-term: N = = = 0 214 .

d

H × × γ γ × × .

G

From Fig. 13.24: For N = 0.214, φ u;d = 0°:
maximum achievable slope angle, β = 72°
i.e. the GEO limit state requirement is satisfied since 72° > 21°

′
× ×

c 4

15 20 1 0

d

Long-term: N = = = 0 013 .

d

H γ γ × × .

G

′ =

From Fig. 13.24: For N = 0.013, φ d 20 . :

maximum achievable slope angle, β = 25°
i.e. the GEO limit state requirement is satisfied since 25° > 21°

°

(b) Design Approach 2
(Partial factor sets A1 + M1 + R2)
From Table 5.1: γ G; unfav = 1.35; γ cu = 1.0; γ c ′ = 1.0; γ φ ′ = 1.0; γ Rh = 1.1.
Design material properties:

′ = = ′

c 90

1

c 5

1

tan φ

= °

u

c = = = 90 kPa c ; ′ = 5 kPa ; φ ′ = tan

− 1

25

u d ; d d

γ γ γ φ

cu c ′ ′

In Design Approach 2, the design resistance is obtained by reducing the character-
istic resistance by the relevant partial factor on resistance (see Section 5.4.7 and
EN1977-1:2004, Annex B). In this case, it is clear that the partial factor on sliding
resistance is to be used.

c 90 0

15 20 1 35 1 1

.

u d ;

Short-term : N = = = 0 0 . 2 2

d

H × × × γ γ γ × × . × .

G Rh

From Fig. 13.24: For N = 0.202, φ u;d = 0°:
maximum achievable slope angle, β = 65°
i.e. the GEO limit state requirement is satisfied since 65° > 21°

′
× × ×

c 5

15 20 1 35 1 1

d

Long-term: N = = = 0 011 .

d

H γ γ γ × × . × .

G Rh

′ = °

From Fig. 13.24: For N = 0.011, φ d 25 :

maximum achievable slope angle, β = 32°
i.e. the GEO limit state requirement is satisfied since 32° > 21°
It is seen that the proposed design satisfies the requirements of both Design
Approach 1 and Design Approach 2.