## Qfk

Here the subscripts 'd' denote design values (i.e. after partial factors have been applied). When MEd ^ MRd, so AGEO = MRd/MEd ^ 1 and this term can therefore be eliminated from the bottom of the equation.

This equation can be re-written in terms of characteristic parameters as:

k ,i i |
Yg Yc . Y* , |
(Wki +(/Yg),i - \b,)tan |
seca i | ||

. Y* . |
^GEO |

The values of the partial factor grouping in this equation are given on page 269 for each of Eurocode 7's Design Approaches.

Design Approach 1 applies partial factors to actions in Combination 1 and to unfavourable variable actions and material properties in Combination 2.

Design Approach 2 applies partial factors to the effects of actions and to resistances, but not to material properties. Different factors are applied to favourable and unfavourable actions. [en 1997-1 §2.4.7.3.4.2 note 2]

Design Approach 3 applies partial factors to material properties and a small factor to variable actions, but not to other actions or resistances. In Design Approach 3, all actions are treated as 'geotechnical' when designing slopes and embankments. [EN 1997-1 §2.4.7.3.4.4 note 2]

In slip circle analysis, a search is performed to find the critical slip surface and hence the slope's minimum factor of safety. A different critical failure mechanism may be found if partial factors are applied to actions, material properties, or resistances. To avoid this, a traditional slope stability analysis could be carried out first, to establish the critical mechanism, and then a further set of calculations performed on this mechanism, with partial factors from Eurocode 7, to test whether it is stable. However, this complication is probably unnecessary in practice, since the effects of applying partial factors are unlikely to affect the critical mechanism greatly.

The above discussion has focussed on circular mechanisms, whereas it may be more appropriate to consider non-circular or compound mechanisms. For these cases, the same principles apply and the partial factors should be applied in a similar manner to the circular analysis discussed above.

In a traditional analysis it is usual to modify the required factor of safety depending on the perceived level of risk. For example, a very high slope may pose a significantly greater risk than a low height slope, so the required factor of safety would be increased accordingly. In Eurocode 7, one set of partial factors are recommended for all slopes and this may lead engineers to ignore the effects of scale. We therefore recommend that the partial factors should only be used for 'normal' slopes and risk levels. Where the levels of risk to life and property are considered to be large, consideration should be given to using higher partial factors.

### 9.5.5 Design charts for finite slopes

Based on the preceding analysis, we have developed a series of design charts that allow finite slopes to be designed according to Eurocode 7. The charts cover the verification of limit state GEO using Design Approach 1 and are presented in full in Appendix A. An example of one of these charts is shown in Figure 9.8. The slip circle analyses on which the charts are based were performed using commonly available computer software.9

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