## Bnc

1. Multiply variable actions yq/ Yg 1.11 by ratio Yq/Yg

Ycu 1.0

3. Perform soil structure interaction analysis

4. Check ratio of restoring yg x YRe 1.35 to overturning moment Mr/Mo \$ Yg x YRe

5. Apply partial factor to action effects tPartial factors from Set A2 for geotechnical actions

First, variable actions are 'pre-factored' by the ratio yq/yG > 1 so that subsequent parts of the calculation can treat them as permanent actions. Second, soil strengths are factored down by ym \$ 1. The resulting design values of surcharge and material properties are entered into the computer program and the soil structure interaction analysis is performed (Step 3).

fThis method implicitly treats passive earth pressure as both an unfavourable action and a resistance.

For cantilever and single-propped walls, toe embedment is then verified (in Step 4), by checking that the ratio of the restoring moment about the point of fixity Mr to the overturning moment MO about the same point is at least equal to the product of yg (the partial factor on unfavourable actions) and YRe (the partial factor on passive resistance). If the wall passes this check, then design bending moments and shear forces in the wall (and design forces in any props or anchors) may be obtained from the calculated action effects by multiplying by yg.

### 12.5.2 Numerical methods

Embedded walls may also be designed to Eurocode 7 using numerical methods based on finite elements (for example, see Figure 12.13, left), boundary elements, or finite difference techniques. Some of the issues that arise when using numerical methods for Eurocode 7 designs are similar to those discussed in Section 12.5.1 for sub-grade reaction models.

Figure 12.13. (Left) Finite element model of embedded retaining wall; (right) c-q reduction

Verification of ultimate limit states using numerical methods can be achieved most easily by using the material factor approach, which is embodied in Design Approach 1, Combination 2 and Design Approach 3 (as discussed in Chapter 6).33

There are two main ways of introducing material factors into numerical models. In the first, partial factors ym \$ 1 are applied to material properties before they are entered into the computer program. The analysis is then performed and the resulting action effects (i.e. bending moments and shear forces in the wall and forces in any props or anchors) are regarded as design values for verification of structural strength. A potential problem with this method is that premature yielding of soil in highly stressed regions may lead to the wrong failure mechanism being predicted.

Figure 12.13. (Left) Finite element model of embedded retaining wall; (right) c-q reduction

In the second (so-called 'c-9 reduction') method, the analysis is performed using unfactored (i.e. characteristic) values of material properties and is saved at various points up to failure (points 1, 2, and 3 on Figure 12.13, right). At each of these points, a separate analysis is undertaken, starting from the saved conditions but with material strengths reduced by the appropriate partial factor y^ Yc or Ycu. The additional movement caused by the reduction in soil strength (with the same external loads) defines the load vs displacement curve for ultimate conditions (points 1a, 2a, and 3a on Figure 12.13, right). The ultimate load is given by the peak of this curve. An advantage of this method is that the introduction of partial factors, per se, is unlikely to trigger a wrong failure mechanism. On the downside, analyses based on c-9 reduction do take considerably longer to complete.

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