2.4.7 Ultimate Limit States

2.4.7.1 General

(1)P Where relevant, it shall be verified that the following limit states are not exceeded:

  • loss of equilibrium of the structure or the ground, considered as a rigid body, in which the strengths of structural materials and the ground are insignificant in providing resistance (EQU);
  • internal failure or excessive deformation of the structure or structural elements, including e.g. footings, piles or basement walls, in which the strength of structural materials is significant in providing resistance (STR);
  • failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance (GEO);
  • loss of equilibrium of the structure or the ground due to uplift by water pressure (buoyancy) or other vertical actions (UPL);
  • hydraulic heave, internal erosion and piping in the ground caused by hydraulic gradients (HYD).

NOTE Limit state GEO is often critical to the sizing of structural elements involved in foundations or retaining structures and sometimes to the strength of structural elements.

(2)P The partial factors in persistent and transient situations defined in Annex A shall be used.

NOTE The values of the partial factors may be set by the National annex. The tables in Annex A give the recommended values.

(3) All values of partial factors for actions or the effects of actions in accidental situations should normally be taken equal to 1,0. All values of partial factors for resistances should then be selected according to the particular circumstances of the accidental situation.

NOTE The values of the partial factors may be set by the National annex.

(4) More severe values than those recommended in Annex A should be used in cases of abnormal risk or unusual or exceptionally difficult ground or loading conditions.

(5) Less severe values than those recommended in Annex A may be used for temporary structures or transient design situations, where the likely consequences justify it.

(6) When calculating the design value of the resistance, (Rd), or the design value of the effect of actions, (Ed), model factors, (γR;d) or (γS;d) respectively, may be introduced to ensure that the results of the design calculation model are either accurate or err on the safe side.

2.4.7.2 Verification of static equilibrium

(1)P When considering a limit state of static equilibrium or of overall displacements of the structure or ground (EQU), it shall be verified that:

Edst;d ≤ Estb;d
(2.4)

with

Edst;d = E{γFFrep ; Xk/γM ; ad}dst
(2.4a)

and

Estb;d = E{γFFrep ; Xk/γM ; ad}stb
(2.4b)

(2)P The partial factors for persistent and transient situations defined in A.2 (1)P and A.2 (2)P shall be used in equation (2.4).

NOTE 1 Static equilibrium EQU is mainly relevant in structural design. In geotechnical design, EQU verification will be limited to rare cases, such as a rigid foundation bearing on rock, and is, in principle, distinct from overall stability or buoyancy problems.

NOTE 2 The values of the partial factors may be set by the National annex. Tables A.1 and A.2 give the recommended values.

Eurocode 7 Geotechnical design Part 1 : General rules