Stability analysis of tailings dams using NorSand

Question

Hi Plaxis, 
 I would like to run a fully coupled stress-flow analysis of the staged construction of a tailings dam using NorSand model for the mine tailings. 
 After the consolidation stage, how can calculate the factor of safety for the tailings dam? can I just add a safety calculation phase to calculate the Factor of Safety? If yes, which material parameter (strength) will be reduced by the strength reduction factor. I understand that it might be not possible to use NorSand with the strength reduction factor method in which the material parameter (strength) will be reduced. 
 Thanks 
 JZ

Dennis Waterman · Answer

Dear Jian Zheng, 
 It's not possible to do a Safety analysis for the Norsand model - Safety analysis only works for soil models that have a failure surface that is also a yield surface, like Mohr-Coulomb or Hardening Soil but also Hoek-Brown. 
 Critical State models do not have a yield surface as failure surface: the stress state can be beyond the critical state (the dry side), so reducing the critical state line would have no effect. Hence, in this case the Safety analysis would give an almost infinite factor of safety. 
 There is no uniform way to do a Safety analysis for a critical state model. Some people have suggested to reduce simultaneously the critical state line and the normally consolidated state line, but this is not a procedure we have implemented. Others suggest to change from for instance the NorSand model to Mohr-Coulomb just for the safety analysis. However, when doing so any stress state on the dry side would then be outside the M-C criterion and will first be projected down to the M-C criterion - this may lead to a very low factor of safety as in this process a heavily overconsolidated material all the points on the dry side would suddenly become failure points. However, for mildly overconsolidated materia this may work though. 
 With kind regards, 
 Dennis Waterman

Dennis Waterman · Answer

Dear Jian, 
 We have no method implemented in PLAXIS because there is no clear single method for safety analysis with critical state models. That is also why we don't have a recommendation. The different methods used in practice will give different safety factors. 
 When using M-C model one can calculate cohesion and friction angle from the critical state line used in NorSand, which means drained parameters should be used. Technically it's possible to change to Shansep, however how would one determine the undrained shear strength for stress points on the dry side and would one set of Shansep parameters properly predict the undrained shear strength for both stress states on the wet and the dry side? So this may not be so straight forward. Most advanced models that have some kind of Cam-Clay like cap will reduce to a Mohr-Coulomb like model when using undrained shear strength as the cap is undefined for phi = 0. Therefore Shansep version of any advanced model will practically reduce to Mohr-Coulomb with Shansep. This is the resason why this is the only Shansep model available. The only model that can actually properly handle elasto-plastic loading behaviour combined with undrained shear strength is the NGI-ADP model - therefore we also have a Shansep model coupled to the NGI-ADP model, it's called "NGI-ADP-S" 
 With kind regards, 
 Dennis Waterman