Stability of Slopes - Elements of Soil Mechanics - page 416

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2

W = × 152 18 × = 39 672 kN ; φ = ° 23 2 m

As the directions of P and T 2 are known, the value obtained for N 2 will be correct. The
error of closure, E, can therefore be assessed by comparing the value of T 2 determined
from the force diagram with the value calculated from N 2 tan φ m .
The force diagrams for the four chosen values for F are shown superimposed on each
other in Fig. 13.28d . The corresponding values of N 2 and T 2 are set out below.

F N 2 (kN) T 2 (kN) N 2 tan φ m (kN) E (kN)

1.0 42 750 15 080 35 871 20 791

1.2 42 500 16 700 29 759 13 059

1.5 42 250 18 800 23 420 4 620

2.0 41 500 21 000 17 616 − 3 384

By plotting F against E we see that the value of E = 0 when F = 1.8. Hence, for the
wedge failure surfaces chosen, F = 1.8 (Fig. 13.28e ).

13.5 Slope stability analysis to Eurocode 7

The principles of Eurocode 7, described in Chapter 5 , apply to the assessment of slope stability and the
reader is advised to refer back to that chapter whilst studying the following few pages.
The overall stability of slopes is covered in Section 11 of Eurocode 7, and the GEO limit state is the
principal state that is considered. The procedure to check overall stability uses the methods described
earlier in this chapter and applies to both the undrained and drained states. Partial factors are applied to
the characteristic values of the soils shear strength parameters, and to the representative values of the
actions (e.g. weights of slices) to obtain the design values.
For circular failure surfaces, during a method of slices analysis, the weight of a single slice can contribute
to the disturbing moment or it may contribute to the restoring moment, as illustrated by Example 13.4
(Fig. 13.19) . In that example, slices 2-5 contribute to the disturbing moment and slice 1 contributes to
the restoring moment. This follows from the particular choice of position of the centre of the slip circle:
had the centre of the slip circle been in a different location the directions of the moment of each slice
might have been different.
As explained in Chapter 5, an action is considered as either favourable or unfavourable. However, as
we have just seen, the choice of the position of the centre of the circle influences whether the weight of
a slice would be favourable or unfavourable and because of this it is impossible to know from the outset
whether an action will be favourable or unfavourable. When using Design Approach 1 Combination 1, the
partial factors (see Table 5.1) are different for favourable and unfavourable actions, whereas for Combina-
tion 2 the partial factors are the same ( = 1.0). To this end, when using Design Approach 1 for circular
failure surfaces, Combination 2 will almost always be used to check the overall stability.
The GEO limit state requirement is satisfied if the design effect of the actions (E d ) is less than or equal
to the design resistance (R d ), i.e. E d ≤ R d . Here E d is the design value of the disturbing moment (or force,
for planar failure surfaces) and R d is the design value of the restoring moment (or force). By representing
the ratio of the restoring moment (or force) to the disturbing moment (or force) as the over-design factor,
Γ , it is seen that the limit state requirement is satisfied if Γ ≥ 1.