F6. Normative aspects: Principles of the Eurocode 7
F6. Normative aspects: Principles of the Eurocode 7
Numerical modeling always had a particular relationship with calculation standards, which essentially focus on the verification of ultimate limit states by calculating safety coefficients or the equilibrium of forces integrating partial coefficients. Indeed, numerical modeling provides first and foremost values of displacements and deformations and is therefore a tool very well suited to the verification of serviceability limit states (SLS) for which the partial coefficients are equal to 1 Its use for the verification of ultimate limit states (ULS) therefore initially appeared to be limited. From now on, particularly with procedures aiming to reduce the shear properties of soils (for example, the "c-phi reduction" procedure), it is easy to calculate a safety coefficient. It is also possible, through the procedures suggested by certain calculation standards, in particular Eurocode 7, to consider the results of numerical modeling both for the verification of the ultimate limit states and for that of the serviceability limit states.
However, Eurocode 7 in its current version is not very clear about how the analysis and processing of the results using numerical modeling should be conducted. Indeed, the three calculation approaches proposed by Eurocode 7, which allow applying partial coefficients on the actions, the effects of the actions (bending moments and shear forces in a retaining wall, axial force in a pile, etc.), the properties of the soils (c and or cU), and the geotechnical resistances, have been designed to be used with limit equilibrium methods. The verifications related to the application of the Eurocodes are mainly transcribed in the form of comparisons between actions or effects of actions and resistances. Nevertheless, several publications (Potts and Zdravkovic, 2012, Tschuchnigg et al., 2015, etc.) and reports of different working groups convened for the development of the second generation of the Eurocodes make it possible to outline verification procedures. First of all, it is important to underline that the weighting "at the source" of the soil or rock properties, i.e. the possibility of reducing the cohesion and the angle of friction before carrying out the calculation, is not allowed because it leads to results that cannot be interpreted. Different procedures can however be used and are summarized in the table below.
Synthesis of the different types of ULS verifications
Type of ULS verifications |
1 - Structural ULS |
2 - Geotechnical (and structural) ULS |
3 - Geotechnical ULS |
4 - Structural (and geotechnical) ULS |
Type of procedures |
Multiplication of the effects of the actions by 1.35 |
Reduction of the shear properties of the soils |
Estimation of the resistance centered around a specific geotechnical structure (pile, tie rod, etc.) |
Increase of the loads applied to the geotechnical structure |
Comments |
Must be combined with the verification of geotechnical ULS |
Must be combined with the verification of structural ULS |
Must be combined with the verification of structural ULS |
A priori, this approach is sufficient on its own |
The approach that tends to be used is to carry out a calculation with characteristic values for both the loads and the properties of the soil to reach the first state of equilibrium. Concerning this state of equilibrium, two types of verifications must be carried out. The first verification, namely type 1, is relative to the structural ULS and consists of multiplying the effects of the calculated actions by 1.35 (i.e. the coefficient usually considered in the Eurocodes for unfavorable permanent loads). The second verification, type 2, is related to geotechnical ULS and consists of progressively reducing the shear resistance properties of the modeled soil to reveal a failure mechanism. The reduction factor applied can be considered as a safety factor, but its interpretation can be subjected to a discussion. Indeed, during the reduction of shear properties, different elements may interact such as strain-hardening functions or flow rules. In the case of calculations associating volumetric elements and structural elements such as "bar" or "beam" type elements, this verification can also be used to check structural ULS. The displacements accumulated during the procedure of reduction of the shear resistance properties generate forces in the structural elements whose interpretation is a matter of debate among the engineering researcher’s community. Therefore, the user must be extremely careful about the way to implement this type of procedure. Figure 7.1 shows the sequence of type 1 and 3 verifications in the case of a phased calculation.
Geotechnical ULS can also be specifically apprehended by considering the resistance centered around the geotechnical structure to be dimensioned, a pile, an anchor, etc. and comparing it to the mobilized resistance provided by the standards, for instance, the pressuremeter norms for the calculation of the bearing capacity of piles: this is the type 3 procedure and it must be associated with the type 1 for structural ULS.
In certain configurations, specifically for piles or footings, it is also possible to increase the actions applied to the geotechnical structure to be dimensioned to directly obtain the maximum applicable force and to deduce the safety coefficient: this is the object of the type 4 approach.
More generally, the methods used to justify geotechnical ULS must allow either to identify the failure mechanism and verify that there is a sufficient margin to trigger the mechanism (this is the object of types 2 and 4 verifications) or to compare the mobilized resistance with a mobilizable resistance that can be calculated elsewhere (this is the purpose of type 3 verifications).
Sequencing of the ULS verifications in a phased computation
When the failure mechanism is associated with the action of water special precautions must be taken. Indeed, the procedures described above do not enable us to correctly compute the safety coefficient if the failure mechanism results exclusively from the action of water. Firstly, it is necessary to define whether the failure mechanism is related to a mechanical equilibrium defect (for example, water rising too high behind a retaining wall), or to a hydraulic problem (for example, a hydraulic gradient being too high). In the case of a mechanical equilibrium defect, it is necessary to carry out a parametric study relative to the level of the water table to estimate its effect by implementing the ULS verifications presented in the previous table. In the case of a hydraulic problem, it is possible to compare the calculated gradient with a critical gradient calculated elsewhere and to verify that the effective stresses remain positive at any point of the solid (because the condition on the critical gradient is more conservative than the condition on the effective stress).
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