Analyzing the Impact of Low-Plastic Fines Content on Instability and Critical State of Partially Saturated Sand via the Equivalent State Parameter Concept

Existing literature indicates that limited research has explored the impact of low-plastic fines content on the critical state and instability responses of partially saturated sand–fines mixtures using the concepts of equivalent void ratio ( e *) and equivalent state parameter ( ψ *), especially when compared with studies on fully saturated soils. To address this gap, this study investigates how low-plastic fines content affects the location of the instability line and critical state line (CSL) in partially saturated sands (characterized by a Skempton’s parameter; B ≈ 50%), using both frameworks ( e * and ψ *) and additional factors. The investigation was carried out through two series of standard undrained triaxial tests, covering a range of low-plastic fines contents ( F c = 0%–20%), initial densities ( I D 0 = 0.25–0.8), and confining pressures ( σ 3 ′ = 50–200 kPa). An analysis of the laboratory data shows that the CSL shifts downward in the ( e *–log p ′) plane as the fines content increases. However, when the equivalent granular void ratio e * is employed, all data points are represented by a single, unified line in the ( e *–log p ′) plane, which is applicable to all partially saturated silty sand specimens, irrespective of fines content. Moreover, a clear and consistent correlation is observed between the normalized deviator stress and the initial equivalent state parameter ψ *(0), demonstrating its effectiveness in predicting the mechanical behavior and the onset of instability, regardless of initial conditions or fines content. Based on these observations, new empirical correlations have been established to predict the instability stress ratio, flow potential, and brittleness index based on ψ *(0).