Previous studies, mostly experimental, have reported conflicting observations on the effect of the initial anisotropic consolidation stress ratio (η<sub>0</sub>) on the stress ratio at the onset of instability (η<sub>f</sub>) for drained and undrained loading that involve static liquefaction. They indicate that as η<sub>0</sub> increases, η<sub>f</sub> could decrease, increase, or remain invariant, albeit without providing potential mechanistic factors. In this study, the anisotropic critical state theory (ACST) is used to investigate potential factors, including compressibility, state, and fabric anisotropy, that can explain the influence of η<sub>0</sub> on η<sub>f</sub> under undrained and drained loading. The assessments consider numerical simulations with the ACST-based SANISAND-F model, insights from SANISAND-F based instability criteria, the instability surface concept, and available experimental observations. Our findings show that compressibility and fabric anisotropy (and its evolution) are key factors in explaining the influence of η<sub>0</sub> on η<sub>f</sub>. In particular, the results show that if fabric evolution is not substantial, an increase in η<sub>0</sub> decreases η<sub>f</sub> for materials with significant compressibility, whereas the effect of η<sub>0</sub> in low compressibility materials is minimal. On the other hand, for materials that promote fabric evolution, the results suggest that the effect of fabric changes counteract compressibility effects, potentially increasing η<sub>f</sub>.
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