Stiffness modulus when using Hardening soil and Undrained B

Question

Hi, 
 I am performing calculations in Plaxis 2D for a deep excavation and am using the Hardening soil model. However i want to set a clay layer to Undrained B as i dont want to overestimate the shear strength of the material. When i change it to undrained B i am aware that the Elastic modulus looses its stress dependency but then im uncertain which stiffness modulus is actually used for the calculation now? 
 Is the calculation for the material performed with Eur for stiffness regardless of strains or load case? 
 Would it then be better to either lower Eur or change model to MC-Undrained B as to not overestimate the stiffness of the material? 
 Kind regards, 
 Johan

Dennis Waterman · Answer

Dear Johan, 
 The HS model does use the Eur directly for the elastic part of the deformation, but does not use E50 as parameters. The model has internal plasticity parameters (not very originally called "alpha" and "beta") that are determined in such a way that when a triaxial test and an oedometer test is is simulated that the E50 and Eoed of those test are exactly the E50 and Eoed that the user specified. And in fact that simulation is made: as soon as you have filled in the parameters and click "ok" in the material set window, a small iterative procedure detemines alpha and beta. Hence, as you can imagine, it's not possible to see exactly what stiffness is used during the calculation. However, we're nnot completely in the dark: if you check the plastic points plot you can see the status of the stress points. If a point is a "Hardening Point" then it has shear hardening, which means that E50 is the main stiffness determining the deformation. For a "cap point" the Eoed is the main stiffness and for a "cap and hardening point" there is both compression and shear hardening, so both E50 and Eoed are the main stiffnesses. Areas without plastic points have elastic behaviour, hence Eur is the stiffness parameter used there. 
 The problem with Undrained B is that this method is mostly suitable for stability analysis and not so much for deformation analysis. Due to the simplification of for instance the HS and HSsmall models the deformations are not so reliable and therefore neither are structural forces. Additional problem is that in HS and HSSmall and also in M-C the user can only fill in 1 undrained shear strength, so which one do you fill in? Under the excavation bottom the stress path resembles the stress path of a triaxial extension test while next to the wall on the side that is not exavated depending on the amount of bending of the wall the stress path may be more like a triaxial compression or a DSS. The problem is that a DSS stress path has an undrained shear strength that is in the order of 50-80% of the undrained shear strength of a triaxial compression stress path and a triaxial extension test gives an undrained shear strength of 15-30% of the undrained shear strength of a triaxial compression test. So with only 1 undrained shear strength to play with, what value should you take? With an undrained shear strength from a triaxial compression test you will use a value that is fine in some parts and overestimated in other - with an undrained shear strength from a triaxial extension test you will be on the safe side, but since undrained shear strength in someareas will be hugely underestimated the design will be expensive. So if overestimating the undrained shear strength is a big issue and it's not possible to do an Undrained A analysis with a check on the results the better way would actually be a total stress analysis (Undrained C) with the NGI-ADP model since this model allows the user to input the 3 undrained shear strengths according to TC, TE and DSS tests and depending on the stress path the right strength is used. 
 With kind regards, 
 Dennis Waterman

Dennis Waterman · Answer

Dear Johan, 
 When using HS model with Undrained B there is still the possibility of mobilized shear. Hence, the stiffness used is a combination of E50ref and Eurref as constant stiffnesses. It's hard to say whether HS or MC with Undrained B overestimates the stiffness. With Mohr-Coulomb the effect of shear plasticity doesn't exist, so the Young's modulus in Mohr-Coulomb should be some weighted average value of E50 and Eur taking into account that those values initially increase with depth and during the calculation decrease with unloading. With the HS model at least E50 and Eur are separated and the model takes into account the correct stiffness for the correct stress path - the only issue is that the 2 stiffness don't change with stress level. The really better solution would be to do an Undrained A analysis with HS or HSSmall and afterwards check if the mobilized strength doesn't exceed the undrained shear strength (for instance by plotting (sig1-sig3)/2 in PLAXIS Output). If it does exceed the undrained shear strength you may for instance want to increase the ratio Eur/Eoed to get a lower resulting undrained shear strength, or lower c and/or phi. But then at least you don't have to worry about stiffness and the settlement prediction will be far better compared to using Undrained B. 
 With kind regards, 
 Dennis Waterman

Stiffness modulus when using Hardening soil and Undrained B

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