A proposal of the simplest convex-conical surface for soils

The simplest convex conical surface in the principal stress space is proposed in this article, relaxing the requirement that the frictional angles in the triaxial compression and extension states coincide with each other. It could be adopted as the equation of the critical state surface which is incorporated into the yield/loading surface in elastoplastic constitutive equations of soils. Also, it could roughly describe the failure surface of soils although the failure surface is not a material property, depending on loading conditions, i.e. the drained (volume change) or the undrained (constant volume), the constant lateral stress or the constant mean stress, etc.