A two-parameter expression for failure surfaces

The Mohr–Coulomb, Tresca and Von Mises criteria are classical failure criteria, widely accepted and used for various materials. To take into account the influence of intermediate principal stress on the strength of soil, Bishop, Lade–Duncan and Matsuoka proposed criteria in terms of three principal stresses or three stress invariants. This note describes an expression with two parameters for modeling the shape of the failure surface in the octahedral plane. By studying the roles of these two parameters and comparing the new criterion with the aforementioned criteria, the advantage and flexibility of the proposed function is explored. Application of the function is demonstrated by fitting the new surface to experimental data for various soils.