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  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  and

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 plane (where e is the void ratio at the critical state

p is the normal stress

and p is the standard atmospheric pressure) is utilized to propose a method for determining the initial consolidation pressure p. 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.