D.5 Ultimate limit state design
D.5.1 Principles and requirements
Each anchored structure should be checked at the ultimate limit state using the design actions and design situations appropriate to that state, as specified in clause D.3. All ultimate limit states which apply to the anchored structure should be considered.
When considering a limit state of static equilibrium or gross displacements of the structure as a rigid body (overall stability), it should be verified that:
Ed,dst ≤ Ed,stb
where
Ed,dst is the design value of the effect of destabilising actions;
Ed,stb is the design value of the effect of stabilising actions.
When considering a limit state of rupture or excessive deformation of a section, anchor or connection, it should be verified that:
Ed ≤ Rd
where
Ed is the design value of the effect of actions, such as anchor force;
Rd is the corresponding design resistance, associating all structural properties with the respective design values.
The design value of the effect of stabilising actions Ed,stb and the design resistance of the anchored structure Rd should be calculated using the design strengths for the ground as specified in clause 2.4.3 of ENV 1997-1:1994, together with design strengths for structural materials as specified in ENV 1992-1-1 and ENV 1993-1-1.
The assessment of design strengths of different materials should take into account the compatibility of their stress-strain behaviour when they are considered together in a design.
Upper or lower design values should be used for the strength of the ground, whichever is more adverse.
The design resistance Rd of the anchor depends on the manner in which the anchor is being stressed in the limit mode under consideration.
If the anchor is stressed only by tension:
Rd = Rk/γR
where
Rk is the lower value of the characteristic internal or external anchor resistance;
γR is the partial factor for anchor resistance.
The partial factor for anchor resistance γr takes into account:
- the variations of ground properties within a distinct ground area;
- the variations of dimensions and properties of the components of the anchors;
- the variations in the execution of the anchor works.
If the anchor is not only subjected to tension, but also to shear and bending:
Rd = γqP0
where
γq is the variation factor for the anchor load.
The variation factor for anchor load γq considers the changes of the anchor load during the time between the initial lock-off of the anchor and the occurrence of the considered limit mode due to:
- relaxation of the tendon;
- creep of fixed anchor length;
- displacements of the structure at the anchor head;
- displacements of the structure as a rigid body in the limit mode considered.
The factor for anchor load γq usually varies between the following limits:
0,8 ≤ γq ≤ 1,1
but can take higher values.
For all anchors the partial factor γR should be:
γR ≥ 1,35
NOTE Typical examples of limit modes where anchors are not directly pulled out are shown in Figures D.1a) and D.1b). Considering the limit mode shown in Figure D.1a), the design resistance of the anchor cannot be higher than the actual anchor force, because pull-out failure of the anchor occurs only after a gross displacement of the structure.
D.5.2 Characteristic internal anchor resistance
The characteristic internal anchor resistance, Rik is the characteristic load capacity of the tendon:
Rik = Ptk = Atftk
where
At is the cross sectional area of tendon;
ftk is the characteristic tensile strength of tendon.
The design, construction and execution of anchors should ensure that the failure resistance of the anchor head and the failure resistance of bond at internal interfaces (tendon-grout and, where relevant, grout-encapsulation) are equal to or higher than Ptk. (see 6.3).
D.5.3 Characteristic external anchor resistance
The external anchor resistance Ra is the failure resistance of the anchor at the grout-ground interface. Ra is equal to the load at which there is continuous displacement of the fixed anchor length, and at which after a period of time pull-out of the fixed anchor length will occur.
The characteristic external anchor resistance Rak is derived from values of Ra which should be evaluated from the results of load tests (see clause 9).
NOTE 1 For practical purposes the external anchor resistance Ra is defined as the load causing a creep displacement rate ks, α or load loss k1. (See annex E).
When deriving the characteristic anchor resistance Rak from values of Ra measured in the Investigation Tests, Rak should be not greater than the lowest value of Ra.
NOTE 2 If a value of Rak is adopted which is greater than the lowest measured value of Ra, then this shall be justified. It may be necessary to provide further evidence by undertaking additional Investigation Tests.
The characteristic external anchor resistance is normally taken is be equal to or higher than the characteristic internal anchor resistance:
Rak ≥ Rik
