x 1.0

Curve 1 on each graph shows the results obtained for a serviceability limit state calculation, with all partial factors set to 1.0 - i.e. with all parameters at their characteristic values. The depths of embedment needed to ensure stability for this situation are 9.63m and 7.00m respectively for the two walls.

Curve 2 shows the results obtained when passive earth pressures are treated as an unfavourable action, as allowed by the Single-Source Principle discussed in Chapter 3. A single partial factor yg = 1.35 is applied to active and passive earth pressures. The depths of embedment needed to ensure stability for this situation are identical to those obtained for the serviceability limit state (SLS) calculation and the structural effects (bending moments, shear forces, and prop force) are 35% higher. Hence this result could have been obtained directly from the SLS calculation by applying the factor yg = 1.35 to the effects of actions, rather than to the actions themselves (as suggested previously27).

Curve 3 shows the results obtained when passive earth pressures are treated as a favourable action. The partial factor yg = 1.35 is applied solely to active earth pressures and YG,fav = 1.0 to passive. With this assumption, both forms of earth pressure are treated consistently (as actions), but their effects are taken into account when deciding which load factor to apply. The embedments needed to ensure stability (10.67m and 7.52m) are larger than before and, as a consequence, so too are the structural effects.

Curve 4 shows the results obtained when passive earth pressures are treated as a resistance, using partial factors from Design Approach 2. Active earth pressures are multiplied by yg = 1.35, but passive pressures are divided by YRe = 1.4. This is the most 'natural' way in which to apply partial factors in embedded retaining wall design28 - intuitively, most engineers would regard passive earth pressures as a resistance. However, the depths of embedment needed to ensure stability are greatest with this assumption (12.32m and 8.36m) and so too are structural effects. (Note that, if the partial factors from Design Approaches 1 or 3 had been used, then Curve 4 would have coincided with curve 3, since YRe = 1.0.)

A variation on Case 4 is to treat the passive earth pressures as both an unfavourable action and a resistance at the same time. Hence, they would be multiplied by yg = 1.35 and divided by YRe = 1.4, i.e. multiplied by a net value YG/ YRe = 0.96. The resulting action effects would be very similar to Curve 3.

Finally, Curve 5 shows the results obtained when partial factors from Design Approach 1, Combination 2 are used, i.e. earth pressures are unfactored but a material factor y9 = 1.25 is applied to the soil's shearing resistance on both sides of the wall. The effect is to increase active earth pressures and simultaneously to decrease passive. The embedments needed to ensure stability with this assumption (11.14m and 7.76m) are similar to those for Curve 3, as are the structural effects.

Our conclusion from the above analysis is that, for consistent results to be obtained regardless of the calculation model assumed, passive earth pressures should be treated as both an unfavourable action and a resistance simultaneously. Adopting this philosophy ensures that all three Design Approaches yield similar results.

12.4.6 Net pressures

Figure 12.11 shows another inconsistency that arises when passive earth pressures against embedded walls are treated as a resistance.

The top diagram shows gross values of active and passive pressures, to which the partial factors yg and YRe are applied. (The discussion in Section 12.4.5 implicitly assumes factors are applied to gross pressures.)

The middle diagram shows net pressures for the same situation, i.e. the difference between the active and passive pressures at each point along the wall. The active earth pressures that are ignored are equal in magnitude to the ignored passive pressures, before partial factors are applied. The only way for bending moments and shear forces for these two situations to be identical is if the same factor is applied to pressures on both sides of the wall. This is only true if passive earth pressures are treated as unfavourable actions (or all the factors are 1.0, as they are in Design Approach 1, Combination 2 and Design Approach 3).

The same argument applies — but to a lesser extent — with the use of revised net earth pressures, shown at the bottom of Figure 12.11.

Revised net pressures (which are promoted in CIRIA 10429) are obtained by deducting, from the active and passive earth pressures below formation level, the increase in active earth pressure that occurs below that level.

This discussion highlights the complications involved in applying partial factors to established design methods that were not originally developed with partial factors in mind. It is uncertain whether net pressure methods, in particular, can be used reliably with Eurocode 7 and hence the considerable experience that has been acquired from their use may be lost.

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