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 γf 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 γS;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 γS;d and γf to be combined into one factor multiplying Fk:

γF = γS;dγf
(B.1)

(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 γS;d for actions from the ground will remain exceptional and is therefore left to national determination, γF is used throughout for simplicity for actions and γE 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 γS;d×γf

(4) Equation (2.6) includes XkM 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 γF ≠ 1 and γE = 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 γF ≠ 1 (example: tank with fixed fluid level), then γF = 1 and γE ≠ 1 are used.

In Combination 2, γE = 1 is always used, with γF ≠ 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

Ed = EFFrep ; XkM ; ad}
(B.2).

(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 γE ≠ 1 and γF = 1, or γF ≠ 1 and γE = 1 are applied. Since γM = 1 is used, equation (2.6) reduces to:

Ed = γE · E{Frep ; Xk ; ad}, or
(B.3.1)
Ed = EFFrep ; Xk ; ad}
(B.3.2)

(7) In Design Approach 3, a single calculation is required. However, in this Design Approach a difference is made between actions Frep from the structure and actions from or through the ground calculated from Xk. Either γE ≠ 1 and γF = 1 or γE = 1 and γF ≠ 1 are applied. Thus equation (2.6) remains:

Ed = EFFrep ; XkM ; ad}, or
(B.4.1)
Ed = γEE{Frep ; XkM ; ad}
(B.4.2)

Eurocode 7 Geotechnical design Part 1 : General rules