Strength criterion based on σ^1/3 spatially mobilized plane of soils and its comparison with conventional criteria

The linear relation between shear strength and normal stress of failure plane shows the essential property of soil shear strength. The Mohr-Coulomb criterion, Drucker-Prager yield criterion and Matsuoka-Nakai criterion respectively respond to the linear relationship between shear stress and normal stress on different shear failure planes including shear failure plane with the angle of 45°+φ/2 relating to the plane of the main principal stress, the octahedral plane in the principal stress space of soil element and the spatially mobilized plane named also σ^1/2 spatially mobilized plane. In this paper, new σ^1/3 spatially mobilized plane is proposed using three points κσ₁^1/3, κσ₂^1/3, κσ₃^1/3 in the soil element in the principal stress axes, named as the σ^1/3 spatially mobilized plane. Furthermore, the new strength criterion is also proposed using the shear stress ratio on theσ^1/3spatial mobilization plane being constant. The strength failure surface depicted in the principal stress space by this criterion is a smooth cone surface with the curved triangle shape on plane. The strength failure surfaces of Mohr-Coulomb criterion, Drucker-Prager yield criterion, Matsuoka-Nakai criterion, Lade-Duncan criterion and σ^1/3 spatially mobilized plane criterion described in the stress space as well as the change laws of Lade-Duncan criterion and σ^1/3 spatially mobilized plane criterion with parameter b on different π planes are comparatively analyzed. It is shown that the Lade-Duncan criterion and σ^1/3 spatially mobilized plane strength criterion are approximate, which reveals the physical essence of Lade-Duncan strength criterion, that is, the former approximately obeys the linear relationship between shear stress and normal stress onσ^1/3 spatially mobilized plane at failure of soils. The