Annex B

(informative)

# Background information on partial factors for Design Approaches 1, 2 and 3

## B.1 General

(1) For limit state types STR and GEO in persistent and transient situations, three Design Approaches are outlined in 2.4.7.3.4. They differ in the way they distribute partial factors between actions, the effects of actions, material properties and resistances. In part, this is due to differing approaches to the way in which allowance is made for uncertainties in modelling the effects of actions and resistances.

(2) In Design Approach 1, for all designs, checks are, in principle, required for two sets of factors, applied in two separate calculations. Where it is obvious that one of these sets governs the design, it will not be necessary to carry out calculations for the other set.

Generally, factors are applied to actions, rather than to the effects of actions, though with one noted exception (2.4.7.3.4.2 (2)). In many cases, factors are applied to ground parameters, but for the design of piles and anchors they are applied to resistances.

(3) In Design Approaches 2 and 3, a single calculation is required for each part of a design, and the way in which the factors are applied is varied according to the calculation considered.

(4) In Design Approach 2, factors are applied either to actions or the effects of actions and to resistances.

(5) In Design Approach 3, factors are applied to actions or the effects of actions from the structure and to ground strength (material) parameters.

## B.2 Factors on actions and the effects of actions

(1) EN 1990:2002 states that γ_{f} is a partial factor for an action and takes account of the possibility of unfavourable deviations of the action value from its characteristic value. Likewise γ_{S;d} is a partial factor taking account of uncertainties in modelling the actions and in modelling the effects of actions.

(2) EN 1990:2002 allows γ_{S;d} and γ_{f} to be combined into one factor multiplying *F*_{k}:

_{F}= γ

_{S;d}γ

_{f}

(3) The various approaches in EN 1997-1 require that factors be applied either to actions or the effects of actions. Since the use of model factors γ_{S;d} for actions from the ground will remain exceptional and is therefore left to national determination, γ_{F} is used throughout for simplicity for actions and γ_{E} for the effects of actions in geotechnical design (see Annex A, Tables A.1 and A.3).

This enables national authorities to select alternative values of the combination γ_{S;d}×γ_{f}

(4) Equation (2.6) includes *X*_{k}/γ_{M} in the calculation of actions because ground material properties may affect the values of geotechnical actions in some cases.

(5) In Design Approach 1, checks are required for two combinations of sets of factors, applied in two separate calculations.

In Combination 1, factors unequal to 1 are generally applied to actions, with factors equal to 1 on the effects of actions. Thus γ_{F} ≠ 1 and γ_{E} = 1 are applied in equation (2.6).

An exception to this is noted in 2.4.7.3.2 (2): in cases where it would be physically unreasonable to apply γ_{F} ≠ 1 (example: tank with fixed fluid level), then γ_{F} = 1 and γ_{E} ≠ 1 are used.

In Combination 2, γ_{E} = 1 is always used, with γ_{F} ≠ 1 only for variable actions.

Thus, except as noted in 2.4.7.3.2 (2), for Design Approach 1 equation (2.6) reduces to

*E*

_{d}=

*E*{γ

_{F}

*F*

_{rep};

*X*

_{k}/γ

_{M};

*a*

_{d}}

(6) In Design Approach 2, a single calculation is required for each part of a design, and the way in which the factors are applied either to actions or the effects of actions is varied according to the calculation considered and chosen according to national determination.

Either γ_{E} ≠ 1 and γ_{F} = 1, or γ_{F} ≠ 1 and γ_{E} = 1 are applied. Since γ_{M} = 1 is used, equation (2.6) reduces to:

*E*

_{d}= γ

_{E}·

*E*{

*F*

_{rep};

*X*

_{k};

*a*

_{d}}, or

*E*

_{d}=

*E*{γ

_{F}

*F*

_{rep};

*X*

_{k};

*a*

_{d}}

(7) In Design Approach 3, a single calculation is required. However, in this Design Approach a difference is made between actions *F*_{rep} from the structure and actions from or through the ground calculated from *X*_{k}. Either γ_{E} ≠ 1 and γ_{F} = 1 or γ_{E} = 1 and γ_{F} ≠ 1 are applied. Thus equation (2.6) remains:

*E*

_{d}=

*E*{γ

_{F}

*F*

_{rep};

*X*

_{k}/γ

_{M};

*a*

_{d}}, or

*E*

_{d}= γ

_{E}

*E*{

*F*

_{rep};

*X*

_{k}/γ

_{M};

*a*

_{d}}