Finite element analysis and Eurocode 7
In spite of the use of numerical methods being encouraged by EC7, there is a notable lack of guidance on this in the design code. In order to address this, and a number of other issues, 13 Evolution Groups were formed to advise the EC7 Committee on the changes and additions required to the code. Evolution Group 4 is studying the issues associated with using numerical methods for design in accordance with EC7, which will lead to the publication of an advice document and, ultimately, to a revised Eurocode 7 incorporating changes from all the evolution areas.
This page provides a summary of some of these issues and current advice as they relate to finite element analysis. To be kept informed on developments, follow us @GeotechFEA. To voice your opinion, please join the discussion forum. A broader summary of the issues can be found in this book chapter.
No significant issues have been identified with serviceability limit state (SLS) analysis since FEA is particularly suited to this. Remember, however, that the derived parameters should be appropriate for the limit state to be analysed. For instance, peak soil strength may be adopted for more accurate deformation prediction in SLS analysis, while a more conservative post-peak strength may be selected for ultimate limit state (ULS) analysis.
ULS Design Approaches
DA1/2 and DA3: essentially two methods of applying partial factors have been considered: duration factoring, where design values of actions and parameters are imposed from the start and throughout all the construction stages of an analysis, and staged factoring, where characteristic values are used throughout and design values are only imposed in separate, dedicated ULS checks at critical construction stages.
Duration factoring is easier to apply and is possible in all software packages, but is likely to lead to less accurate predictions because, intentionally, design parameters are unrealistic. It is also often unclear whether design values imposed at the start have a favourable or unfavourable effect later in the analysis. Therefore, staged factoring is falling more into favour. Staged factoring is undertaken by increasing actions to their design values and reducing soil strength to its design value to obtain design values of structural forces and to check for soil failure. Stepwise reduction of soil strength can also be performed to failure, if desired, in order to identify the critical failure form. There is no standard method of reducing soil strength in an analysis, so users should be well versed in the particular method employed in their software, and its limitations.
DA1/2 and DA3 are load and material factoring approaches which, in some situations, can lead to an inconsistent level of conservatism in design values of structural forces. For example, a stiff soil without yield, such as around a multi-propped retaining wall, is likely to give design values of structural forces similar to characteristic values. An advantage of DA1 for FEA is that the DA1/1 partial factors ensure appropriate design values of structural forces are obtained even when the soil is not yielding. In some cases while using FEA, when DA3 is a requirement, engineers may choose also to perform a DA1/1 (or DA2*, see below) check for the structural forces.
DA2 introduces resistance factoring which requires that adequate safety against specific failure forms (e.g. bearing, sliding, passive) is checked. This is relatively straightforward in FEA for externally-loaded structures (e.g. spread foundations) where, following load factoring, simple combinations of applied loads can be further increased stepwise until particular failure forms are reproduced and the margin between load at failure and design applied load checked against the resistance partial factor for that failure form. However, for structures loaded by geotechnical actions (e.g. retaining walls), this is less straightforward. Typically, a check on geotechnical failure (e.g. embedment depth of a retaining wall) is performed using traditional methods (e.g. limit equilibrium analysis) and the required embedment depth is then adopted in the numerical analysis to determine structural forces. For statically indeterminate structures, FEA outputs of horizontal stress can be compared with limiting passive values to check for adequate resistance, but this may not be possible for ground with raised K0 whose FEA outputs of horizontal stress may exceed factored passive earth resistance.
Overall, the requirement to check adequate safety against particular failure forms is not well suited to FEA where analyses are free to calculate a single critical case from all failure forms, hence why some countries adopting DA2 have allowed the use of DA3 with numerical methods in their national annexes.
To overcome the difficulty of factoring geotechnical actions in the determination of design values of structural forces (e.g. retaining wall bending moment), a modified DA2 (called DA2*) is often used which involves factoring the “effects” of actions, i.e. outputs of structural forces obtained using characteristic values are multiplied by the load factors to obtain the design values of structural forces, which is the same method used for DA1/1 with FEA. Where national annexes allow, and in some other cases for peace of mind, engineers may choose to combine DA2* and DA3 checks when using FEA, which is more or less the same as DA1, to benefit from the advantages of each approach.
Factoring soil stiffness.
Some design guidance, e.g. CIRIA Report C580, recommend reducing ground stiffness in ULS analyses to take account of the lower soil stiffness at high strains and this can have an effect on outputs of structural forces. However, throughout the Eurocodes, mean values of stiffness are used and this is likely to remain the same in EC7. The best current advice is to investigate the sensitivity of ULS to variation of soil stiffness.
Factors on undrained shear strength
It is unclear what value of partial factor to apply to soil strength in undrained and consolidation analyses when effective stress parameters are used. Even with advanced models, undrained strength prediction can be uncertain and using a low material factor (e.g. 1.25) may be inadequately conservative. Check outputs carefully and ensure that shear stress does not substantially exceed the design value of undrained shear strength. Model factors can be used to increase factoring where necessary.
The way forward
At the end of the evolution process, work should begin on redrafting clauses in Eurocode 7. The process takes time, there’s a review process and then all the countries vote, but the current aim is to have the second generation of codes published towards the end of 2019.
To cover numerical methods, the second generation Eurocode 7 should include clauses covering areas such as:
- Definition of "numerical methods".
- Competency of users of numerical methods software
- Validation and verification of software and analyses.
- Numerical methods (elasto-plastic) particularly suited to SLS.
- Summary of issues concerning numerical methods and ULS verification.
- ULS GEO/STR verification: as described above, no single design approach is adequate for numerical methods so a dual factoring approach (load effect factoring + material strength factoring) would be more appropriate and used by all countries adopting Eurocode 7.
- Partial factor values: appropriate values for numerical methods, for advanced models and for additional parameters such as stiffness, dilatancy, etc.
Do you agree or disagree? Voice your opinions on the discussion forum.