Although the mechanism of finite strain consolidation (FSC) theory is rigorous

its inherent complexity and non-linearity lead to the present controversy on the difference between foundation settlements predicted by FSC theory and by small strain (SS) theory. Based on fundamentals of continuum mechanics

the FSC incremental finite element (FE) equations with total Lagrangian (TL) description are formulated using soil mechanics sign convention; and the corresponding reduced FE equations for total stress analysis are also obtained. Through a case study

the influence of material linearization method and material geometrical bi-linearization method on the results of FSC theory is analyzed with the discussion of the appropriate length of sub-load step

and the difference between the ultimate settlements by FSC theory and SS theory are probed. The results show that the predicted settlements by linearization methods are sensitive to the length of sub-load step; the settlement by FSC theory is larger than that by SS theory

due to the effect of different stiffnesses under tensile and compressed state in geometrically nonlinearty problems; the initial stress matrix plays an important role in calculating the ultimate settlement by FSC theory

etc.