After a year of evolution studies for Eurocode 7, the group studying the use of numerical methods has made good progress. Andrew Lees reports.
In response to a European Commission mandate for further evolution of the Structural Eurocodes, which includes reducing the number of nationally determined parameters, incorporating recent research and responding to feedback from stakeholders, the sub-committee (TC250/SC7) of Eurocode 7 (EC7) last year formed “Evolution Groups” to begin the work of evolving Eurocode 7.
Using background research and thinking, as well as feedback from code users, each pan-European group of specialists is tasked with identifying where issues exist in the implementation of designs in accordance with EC7, and to propose solutions. This initial stage should be complete by March 2013, with the process of redrafting EC7 clauses beginning thereafter. Work is currently at the half-way stage where Evolution Group convenors are reporting progress to the annual SC7 meeting, taking place this year in The Hague.
One of the areas in most need of evolution, as identified from surveys of code stakeholders, is a lack of guidance on the use of numerical methods (NM) in accordance with EC7, in spite of their use being encouraged by the code. Evolution Group 4 (EG4) was tasked with addressing this issue. NM was taken to include finite element, finite difference and boundary element analysis, as well as beam-spring approaches and computational limit analysis, which covers a large proportion of geotechnical design software.
Progress to date has been swift, with a large number of specific issues being identified. Work is ongoing to investigate these issues and to identify possible solutions, or at least to flag them up to users of EC7. No significant issues have been identified with serviceability limit state (SLS) analysis since NM are particularly suited to this, not forgetting, though, 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.
“One of the areas in most need of evolution, as identified from surveys of code stakeholders, is a lack of guidance on the use of numerical methods (NM) in accordance with EC7.”
Many more issues have been identified for ULS analysis, in particular concerning the application of partial factors. Although more time-consuming than traditional design methods and requiring specific competencies, there are several benefits in the verification of ULS by numerical analysis. These include the simultaneous checking of multiple failure forms which are not pre-determined in the analysis and, when properly implemented, higher accuracy.
As far as Design Approach 1 Combination 2 (DA1/2) is concerned, 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, which has the additional advantages that load factoring (in DA1/1) with characteristic parameters can be undertaken in the same analysis as the material factoring check(DA1/2), whereas duration factoring requires two complete analyses.
The DA1/2 ULS check in staged factoring is undertaken by increasing the variable actions to their design values and then invoking a stepwise reduction of soil strength, as far as the material partial factor requires to obtain design values of structural forces and to check for soil failure. The reduction can then be continued all the way to failure, if desired, 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.
DA3 is a load and material factoring approach and is the same as DA1/2 (except that factors are applied essentially to all structural actions), so the staged factoring method is also favoured here and the design values of structural forces will be the greater of those obtained using characteristic values or during each ULS check. Note, however, that 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 NM 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 NM, when DA3 is a requirement, engineers might also perform a DA1/1 check for the structural forces.
DA2 introduces resistance factoring which requires that adequate safety against specific failure forms, such as bearing, sliding or passive, is checked. This is relatively straightforward in NM for externally-loaded structures, such as spread foundations, where, following load factoring, 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, retaining walls for example, this is less straightforward. Typically, a check on geotechnical failure for an embedment depth of a retaining wall is performed using traditional methods, such as limit equilibrium analysis and the required embedment depth is then adopted in the numerical analysis to determine structural forces. Alternatively, artificial “perturbing” forces can be applied in an analysis to cause particular failure forms, as reported in the technical papers in the October and November 2011 issues of GE, but this has yet to be applied in practice.
Overall, the requirement to check adequate safety against particular failure forms is not well suited to NM 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 NM in their national annexes.
To overcome the difficulty of factoring geotechnical actions in the determination of design values of structural forces, for example retaining wall bending moment, a modified DA2 (called DA2*) is often used which involves factoring the “effects” of actions, ie 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 NM. Where national annexes allow, and in some other cases for peace of mind, engineers may choose to combine DA2* and DA3 checks when using NM, which is more or less the same as DA1, to benefit from the advantages of each approach.
Among the other issues being considered by EG4 is the factoring of soil stiffness. CIRIA Report C580 recommends reducing ground stiffness by a factor of two 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.
It is also 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 (eg 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. Another issue is that some models may fail with factored undrained strength just from overburden stress.
“Overall, the requirement to check adequate safety against particular failure forms is not well suited to NM where analyses are free to calculate a single critical case from all failure forms.”
The current partial factors given in EC7 and its national annexes are calibrated generally against traditional design methods, but are they appropriate for NM? A well executed analysis should have less uncertainty and therefore lower partial factors, but on the other hand NM are normally less conservative than traditional methods and perhaps need higher partial factors to obtain the same well-established degrees of conservatism. For the time being, analysis results should be compared with more traditional design methods where possible and model factors applied to manage the degree of conservatism if necessary.
These and several other issues are subjects of ongoing study by EG4. More comprehensive advice should be available once the work is completed. A central aim of EC7 evolution is to engage users of the code in this process. Therefore, any views expressed by stakeholders in EC7 on these or any other issues concerning the code would be very welcome.