Abstract: The unified critical state parameter model (clay and sand model with subloading surface, CASM-S) effectively describes the mechanical behavior of sand and overconsolidated clay. However, the model does not include the nonlinear critical state line of sand. This study investigates the soil’s compression characteristics and its nonlinear critical state line in the e-lnp plane. The CASM-S introduces a power function form of the critical state line and reference compression line (RCC) suitable for sandy soil. With additional parameters ξ  and λ_r, yield surface and subsequent loading surface functions are proposed to describe the shear characteristics of the sand. The linear relationship of the reference compression curve in the e-(p/p)^ξ  plane (where e is the void ratio at the critical state, p is the normal stress, and p_a is the standard atmospheric pressure) is utilized to propose a method for determining the initial consolidation pressure p_c0. All 11 parameters required for this model can be obtained through conventional geotechnical tests or empirical methods. Finally, by comparing the model’s predictions with triaxial drained and undrained shear test results for four types of sand, the refined CASM-S effectively considers the effect of nonlinear critical state line and describes the triaxial shear characteristics of saturated sand under varying void ratios and confining pressures.

Key words: critical state, saturated sand, subloading surface, elasto-plastic model