State parameter from CPT under high overburden stress: a nonlinear critical state approach

The state parameter ( ψ), representing the difference between a soil’s current and critical void ratios at the same mean effective stress, is a key indicator of soil behaviour. However, traditional methods for estimating ψ from cone penetration test (CPT) data often assume a linear critical state line (CSL), which becomes inaccurate under high overburden stress due to the pronounced nonlinearity of the CSL reflecting the onset of significant particle crushing. This study introduces a refined framework based on Bolton’s relative dilatancy index ( I R ), which inherently accounts for a nonlinear CSL and the stress-dependent behaviour of soils. The proposed method integrates relative density derived from CPT data with the soil behaviour type index ( I c ), enabling incorporation of sleeve friction data into the analysis for differentiating between soil types. For clean sands ( I c < 1.64), the framework is further enhanced by accounting for compressibility using readily available index properties. Preliminary validation using calibration chamber data and an example application to a field CPT in deep mine tailings indicates the proposed I R -based method provides an improved method for estimating ψ, particularly under high-stress conditions. Importantly, it is stressed that while ψ offers insight into in situ soil state, it should not be interpreted as a direct measure of liquefaction potential or liquefied strength at high stresses, where soils also tend to become more ductile.