When a very stiff, saturated, clay is sheared quickly, it wants to dilate, but cannot because there is no volume change. No volume change because porewater is taking the load and porewater is incompressible. The result is the pore water pressure goes negative, increasing the effective stress and thereby the soil shear strength.
Given enough time (slow loading), the pore water will drain and you lose negative pore pressure, and reduce shear strength. This is suitable for analysis of a long term condition...years maybe, depending on the permeability of the clay.
A soft clay contracts under shear and causes pore pressure to increase, thereby decreasing effective stress and shear strength of the soil. This analysis is suitable to analyze a short term condition...months maybe, depending on the permeability of the clay.
A phi=0 analysis is fine for soft, contractive clay soils, but not for very stiff clay, particularly high plasticity clay. You need to look at an effective stress analysis for very stiff clay.
You can find this discussion in any good soil mechanics book-Holtz & Kovacs, Terzaghi&Peck, Lam and Whitman, etc. Also, look for papers by Stark and Mesri who have done a lot of work with shear strength of very stiff clay.
The analysis you choose to perform (drained or undrained) should be determined by what the critical condition will be as discussed above. The drained analysis uses effective stress strengths, and the undrained annalysis uses total stress strength. Saturation should be at least 85-90% for an undrained analysis.
I think I'm done.