# 2.4.7.3 Verification of resistance for structural and ground limit states in persistent and transient situations

2.4.7.3.1 General

(1)P When considering a limit state of rupture or excessive deformation of a structural element or section of the ground (STR and GEO), it shall be verified that:

*E*

_{d}≤

*R*

_{d}

2.4.7.3.2 Design effects of actions

(1) Partial factors on actions may be applied either to the actions themselves (*F*_{rep}) or to their effects (*E*):

*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}}

(2) In some design situations, the application of partial factors to actions coming from or through the soil (such as earth or water pressures) could lead to design values, which are unreasonable or even physically impossible. In these situations, the factors may be applied directly to the effects of actions derived from representative values of the actions.

(3)P The partial factors defined in A.3.1 (1)P and A.3.2 (1)P shall be used in equations (2.6a) and (2.6b).

NOTE The values of the partial factors may be set by the National annex. Tables A.3 and A.4 give the recommended values.

2.4.7.3.3 Design resistances

(1) Partial factors may be applied either to ground properties (*X*) or resistances (*R*) or to both, as follows:

*R*

_{d}=

*R*{γ

_{F}

*F*

_{rep};

*X*

_{k}/γ

_{M};

*a*

_{d}}

or

*R*

_{d}=

*R*{γ

_{F}

*F*

_{rep};

*X*

_{k};

*a*

_{d}}/γ

_{R}

or

*R*

_{d}=

*R*{γ

_{F}

*F*

_{rep};

*X*

_{k}/γ

_{M};

*a*

_{d}}/γ

_{R}

NOTE In design procedures where the effects of actions are factored, the partial factor for actions γ_{F} = 1,0. (See also B.3 (6))

(2)P The partial factors, defined in A.3.3.1 (1)P, A.3.3.2 (1)P, A.3.3.4 (1)P, A.3.3.5 (1)P and A.3.3.6 (1)P shall be used in equations (2.7 a, b, and c).

NOTE The values of the partial factors may be set by the National annex. Tables A.5, A.6, A.7, A.8, A.12, A.13 and A.14 give the recommended values.

2.4.7.3.4 Design Approaches

2.4.7.3.4.1 General

(1)P The manner in which equations (2.6) and (2.7) are applied shall be determined using one of three Design Approaches.

NOTE 1 The way to use equations (2.6) and (2.7) and the particular Design Approach to be used may be given in the National annex.

NOTE 2 Further clarification of the Design Approaches is provided in Annex B.

NOTE 3 The partial factors in Annex A to be used in equations (2.6) and (2.7) are grouped in sets denoted by *A* (for actions or effects of actions), *M* (for soil parameters) and *R* (for resistances). They are selected according to the Design Approach used.

2.4.7.3.4.2 Design Approach 1

(1)P Except for the design of axially loaded piles and anchors, it shall be verified that a limit state of rupture or excessive deformation will not occur with either of the following combinations of sets of partial factors:

- Combination 1:
*A1*“+”*M1*“+”*R1* - Combination 2:
*A2*“+”*M2*“+”*R1*

where “+” implies: “to be combined with”.

NOTE In Combinations 1 and 2, partial factors are applied to actions and to ground strength parameters.

(2)P For the design of axially loaded piles and anchors, it shall be verified that a limit state of rupture or excessive deformation will not occur with either of the following combinations of sets of partial factors:

- Combination 1:
*A1*“+”*M1*“+”*R1* - Combination 2:
*A2*“+” (*M1*or*M2*) “+”*R4*

NOTE 1 In Combination 1, partial factors are applied to actions and to ground strength parameters. In Combination 2, partial factors are applied to actions, to ground resistances and sometimes to ground strength parameters.

NOTE 2 In Combination 2, set *M1* is used for calculating resistances of piles or anchors and set *M2* for calculating unfavourable actions on piles owing e.g. to negative skin friction or transverse loading.

(3) If it is obvious that one of the two combinations governs the design, calculations for the other combination need not be carried out. However, different combinations may be critical to different aspects of the same design.

2.4.7.3.4.3 Design Approach 2

(1)P It shall be verified that a limit state of rupture or excessive deformation will not occur with the following combination of sets of partial factors:

- Combination:
*A1*“+”*M1*“+”*R2*

NOTE 1 In this approach, partial factors are applied to actions or to the effects of actions and to ground resistances.

NOTE 2 If this approach is used for slope and overall stability analyses the resulting effect of the actions on the failure surface is multiplied by γ_{E} and the shear resistance along the failure surface is divided by γ_{R;e}.

2.4.7.3.4.4 Design Approach 3

(1)P It shall be verified that a limit state of rupture or excessive deformation will not occur with the following combination of sets of partial factors:

- Combination: (
*A1** or*A2*^{†}) “+”*M2*“+”*R3*

* on structural actions

^{†} on geotechnical actions

NOTE 1 In this approach, partial factors are applied to actions or the effects of actions from the structure and to ground strength parameters.

NOTE 2 For slope and overall stability analyses, actions on the soil (e.g. structural actions, traffic load) are treated as geotechnical actions by using the set of load factors *A2*.