Cavitation Stress

Question

Hi 
 
 I was modelling a deep excavation in clay (modeled as undrained B), and upon inspecting the results, I noticed the generation of high positive porewater pressure (pexcess is large and positive, psteady is negative as it should be, and the resulting pactive is large and positive ) at the bottom of excavation. To address this, I capped the pactive at the default Patmospheric, and the problem stopped converging after a certain depth of excavation. The same problem was converging when the cavitation cap was not applied. This was surprising especially when using undrained B, since the strength is independent on the effective stress (and hence the pwp) and the shear stress should be similarly independent on the pwp (total shear stress = effective shear stress). 
 I referred to the reference manual to check the way the cavitation cap is applied, and found no mentioning of how this cap is reflected back on stresses and the equilibrium of the problem. I also compared the TOTAL stresses with and without the cavitation cap, and they are certainly different which is also confusing. 
 I would appreciate some insight on this issue, because i am not sure now whether this "soil body seems to collapse" after i apply the cavitation cap is indicating a real basal stability problem or it is just an error or limitation in the implementation of this feature. 
 
 Thank you 
 
 (Software = Plaxis 3D; Soil Models: HS and HS small)

Dennis Waterman · Answer

Dear Omar, 
 Some of the assumptions you make are indeed true, but unfortunately only for a 1D loading case on elastic soil. For 2D or 3D loading on elasto-plastic soil things are a bit more complicated. 
 When cavitation cut-off is used, the criterion for the cut-off is the active pore tension. When that is exceeded, the program will reduce the excess pore tension to fullfil the cut-off conditions. Excess pore tension leads to increased effective stresses, so by reducing the excess pore tension we reduce the effective stresses. Water pressures are the same in any direction, so if the cavitation is limited to let's say 50 kPa and I have 100 kPa, we go from horizontal and vertical water pressures (or any other direction) of 100 kPa to 50 kPa. However, if effective stresses reduce this will not be the same in any direction. To start with, the chance that the effective stresses are the same in horizontal and vertical direction are the same is quite small, and then when they're being reduced they will not be reduced in equal amount - the ratio of stress reduction in horizontal and vertical direction depends on the Poisson's ratio for elastic behaviour and on K0nc for elasto-plastic behaviour. So the results is that horizontal and vertical stresses change differently, and in fact the difference between horizontal and vertical stresses will increase, which means the Mohr-Circle will become larger which means the maximum shear stress will become larger - and possibly even larger than the undrained shear strength you specified. Hence, the shear stress is not independent on the pore water pressure... That is, the shear stress is independent from the steady-state pore pressures, but not independent from the excess pore pressures: a reduction on excess pore water pressure will lead to an increase of difference in normal stress components, which results in a higher deviatoric stress and shear stress. On top of that, if excess pore pressures in certain parts of your model are being effected by the cavitation cut-off more than in other parts then there will be a redistribution of strresses, which results in the total stresses changing. We won't see this in a soil test since in soil tests we typically have a 1D loading case and/or homogeneous stress state. But in plane strain 2D or 3D stress state this redisribution will take place and total stresses will change. 
 For the final part....about deformations. With the cavitation cut off activated the calculation can't finish - hence whatever change you wanted to apply has not been fully applied and maybe even only a small part of it. So that that would give you less deformation is not a surprise. Compare it to doing an excavation, in 1 case you can excavate 10m without a problem and in the other case after excavating only 2 meters it fails - it's very well possible that having excavated 10m gives larger deformations than having only excavated 2m, in spite of the failure in the latter case. 
 With kind regards, 
 Dennis Waterman