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In sand constitutive models, it is of cardinal importance to consider a state parameter to distinguish the real dilatancy for cohesionless soils (sand), which is different from cohesive soils (clay). Thus, one of the key issues in simulating the sand behaviour is the better representation and parameter calibration of critical state line (CSL) for estimating contraction in loose state and dilatancy in dense state, respectively. For this purpose, a new exponential form for CSL with two model constants a and <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">b</mi> </semantics> </math> </inline-formula> has been presented in the literature. This paper provides a valuable insight into the two model constants, controlling the shape of the critical state line by simulating a uniform quartz reference sand (Hostun RF) in loose and dense states under undrained triaxial conditions. It can be concluded that the liquefaction behaviour in loose state is fundamentally affected by even a minor variation in model constant <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">a</mi> </semantics> </math> </inline-formula>, but insensitive to model constant <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">b</mi> </semantics> </math> </inline-formula>. Moreover, the linear fitting calibration of CSL recommended in the literature is complicated in consideration of the non-unified critical state line. Thus, the maximum void ratio in the natural state could be considered as a comparison basis on which to evaluate the liquefaction potential as an alternative. The numerical results showed good agreement with real experimental data. However, in dense state, the dilatant behaviour of sand was found to be mainly controlled by model parameter <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">b</mi> </semantics> </math> </inline-formula>. In addition, the influence of a non-unified critical state under various confining pressures on the determination of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">b</mi> </semantics> </math> </inline-formula> should not be neglected. With the correction of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">b</mi> </semantics> </math> </inline-formula>, the numerical results were found to be consistent with the experimental data concerning Hostun RF sand.