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

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 CSLs of soil in p ′ –q and e–p planes could be both nonlinear as well due to significant material degradation. This note aims propose a unified FSD arbitrary types CSLs. Detailed derivations are provided. To validate proposed equation, series triaxial test results ballast rockfill simulated.