Stability of Slopes - Elements of Soil Mechanics - page 417

Example 13.12: Taylor's charts to Eurocode 7

Using Taylor's charts, determine the margin of safety of a proposed motorway cutting
slope, as detailed below, using the procedures of Eurocode 7 GEO limit state Design
Approaches 1 and 2 for both the short- and the long-term conditions.
The slope will be constructed from a regular, homogeneous clay deposit and will have
the following properties:

Height of slope, H = 15 m
Angle of slope, β = 21°
Weight density, γ k = 20 kN/m 3
Undrained shear strength, c u; k = 90 kPa
Effective cohesion,

′ =

k 5
Effective angle of shearing resistance

c kPa

′ = °

φ k 25

Solution:

As seen in Section 13.3.1 , when using Taylor's chart, the factor of safety applied to each
component of the shear strength (c ′ and tan φ ′ ) is the same. However, when applying
partial factors of safety in a Eurocode 7 design, different factors are applied to these
two components and thus the use of Taylor's charts in a Eurocode 7 design is slightly
more complex. The stability number is calculated using the design values of shear
strength, together with the design weight of the slope (i.e. the permanent, unfavourable
design action acting).

(a) Design Approach 1
1. Combination 1 (partial factor sets A1 + M1 + R1)
From Table 5.1: γ G; unfav = 1.35; γ cu = 1.0; γ c ′ = 1.0; γ φ ′ = 1.0;

c 90

1

u

Design material properties c :

; =

= = 90 kPa

u d

γ

cu

′ = =
′

c 5

1

′ =

c 5 kPa d

γ

c

′

tan φ

= °

′ =

− 1

φ tan 25 d

γ φ ′

c 90

15 20 1 35

u d ;

Short-term: N = = = 0 222 .

d

H × × γ γ × × .

G

From Fig. 13.24: For N = 0.222, φ u;d = 0°:
maximum achievable slope angle, β = 77°
i.e. the GEO limit state requirement is satisfied since 77° > 21°

′
× ×

c 5

15 20 1 35

d

Long-term: N = = = 0 012 . d

H γ γ × × . G

′ = °

From Fig. 13.24: For N = 0.012, φ d 25 :

maximum achievable slope angle, β = 32°
i.e. the GEO limit state requirement is satisfied since 32° > 21°