Fractional stress-dilatancy equation based on critical state lines with arbitrary form

Abstract

The original state-dependent fractional stress-dilatancy (FSD) equation for soils is developed based on the critical state lines (CSLs) with linear form. However, experimental evidences showed that the CSLs of soil in the $p^{\prime}$–$q$ and $e$–$p^{\prime}$ planes could be both nonlinear as well due to significant material degradation. This note aims to propose a unified FSD equation for soils with arbitrary types of CSLs. Detailed derivations are provided. To validate the proposed FSD equation, a series of triaxial test results of ballast and rockfill are simulated.

Keywords

• Fractional derivative
• Fractional plasticity
• Stress-dilatancy
• Sand
• Rockfill
• State dependence