This study aims to explore the undrained shear behavior and static liquefaction potential of sand in both overconsolidated and normally consolidated states. Based on the uncertainty associated with the Critical State Line (CSL) and the state parameter (\(\psi\)) of the samples defined as the current void ratio (es) and the critical void ratio (ec) at the same mean effective stress (p'), the samples were classified into four states: heavily overconsolidation state (HO), intermediate overconsolidation state (IO), lightly overconsolidation state (LO), and normally consolidation state (NC). The latter corresponds to a very loose sand with initial relative density (Dr) of about − 20%. The study findings revealed significant differences in the undrained shear behavior among samples in different consolidation states. Samples in heavily (HO) and intermediate (IO) overconsolidation states exhibited a tendency of initial contraction followed by dilation, with the main difference lying in the presence of a distinct peak strength (qpeak). In contrast, samples lightly overconsolidated (LO) and normally consolidated (NC) only showed a contraction tendency, with the main difference being in residual strength (qresidual). Finally, exploration was conducted into the potential for static liquefaction under different consolidation states. The study found that for overconsolidated samples, their liquefaction potential is mainly controlled by the state parameter (\(\psi\)). As the state parameter increases, the sample's liquefaction potential also increases. Conversely, for normally consolidated samples, their liquefaction potential is determined by the initial mean effective stress (p'0), with the potential decreasing as the initial mean effective stress (p'0) increases.