Assuming running the undrained effective stress analysis in FLAC3D via Config FLUID using the effective stiffness and strength parameters, are we expecting the constant effective stresses in the model?
During undrained analysis, the effective stress remains constant because the increment in the total stress equals the increment in pore water pressure.
In the paper below, it was mentioned that "This finding is potentially useful for undrained effective stress analysis where p′ may change during loading, and ...".
Yniesta S, Brandenberg SJ. Stress-ratio-based interpretation of modulus reduction and damping curves. Journal of Geotechnical and Geoenvironmental Engineering. 2016 Jul 29;143(1):06016021.
According to Biot's theory of consolidation, the excess pore water pressure may rise above the the increase in the total vertical stress, so that the effective stress changes. This phenomenon is called Mandel - Cryer effect.