Critical State Response of Granular Soils: Probabilistic Predictive Models Incorporating Grain Size, Distribution and Shape Effects

The critical state locus (CSL), expressed in the void ratio (e) – natural logarithmic mean effective stress (ln⁡p') space, is typically defined by slope (λ_e) and intercept parameters (Γ_1), the latter corresponding to the void ratio at a reference mean effective stress of unity. The angle of shearing resistance at the critical state (ϕ_cs^') relates the shear strength to effective normal stresses. These parameters are fundamentally governed by intrinsic properties of granular soils. This study examines their dependence on particle-scale descriptors, namely median grain size (D_50), coefficient of uniformity (C_u), particle roundness (R), and sphericity (S). A database containing critical state parameters (CSP), and grain size, gradation, and shape descriptors for over two hundred sandy and silty non-plastic soils was compiled from available literature, supplemented with laboratory tests performed on Cine, Sile, Tekirdag, and Iskenderun silica sands from Turkiye, and Sabratha silt from Libya. Their CSPs were evaluated following the procedures outlined by Santamarina and Cho [1], modified by benefiting from photogrammetric techniques for monitoring the specimen volume. Particle roundness and sphericity were quantified from microscopic imaging using the method defined by Cho et al. [2]. Semi-empirical probabilistic predictive models were developed using a maximum-likelihood estimation framework. They suggest that ϕ_cs^' decreases with increasing R, decreasing C_u, but log-linearly increases with increasing D_50. The intercept Γ_1 decreases linearly with increasing R and decreasing S and C_u, and exhibits a log-linear decrease with increasing D_50. The compressibility λ_e increases with increasing D_50, whereas it decreases with better grading. It exhibits a log-linear decrease with increasing R and S. The model performances, evaluated through analyses of residuals, indicate unbiased predictions with well-quantified levels of model precision. The resulting models provide quantitative insight into the relationships between micro-scale particle characteristics and macro-scale critical state behavior. They offer practical means for preliminary estimation of CSPs by explicitly incorporating variability in grain size, gradation, and shape metrics of granular soils.