Application of Lade's Criterion to Cam-Clay Model

Abstract

Lade's criterion is one of the best criteria for describing the shear yield and failure behavior of soils in 3D stresses, and the original Cam-clay model is the most popular and fundamental elastoplastic model for normally consolidated clays. In this paper, a transformed stress tensor is proposed for combining Lade's criterion and the Cam-clay model. The transformed stress is deduced from what makes the curved surface of Lade's criterion become a cone with the axis being the space diagonal, i.e., Lade's criterion becomes the extended Mises type criterion in the transformed principal stress space. The Cam-clay model revised by Lade's criterion is capable of describing the mechanical behavior of soils in general stresses. It is presented that the revised model can simulate well the drained and undrained behavior of soils, not only under triaxial compression conditions, but also under plane strain, true triaxial, and hollow cylinder conditions. The elastoplastic models for soils, in which only the first and second stress invariants are used, can be extended simply to the model, including the third stress invariant by adopting Lade's criterion. where sij = deviator stress tensor; and dij = Kronecker's delta. Therefore, the Cam-clay model is generalized by assuming a section of the yield surface to be circular in the p-plane. That is to say, the extended von Mises criterion (q/p = const) was adopted for the shear yield and the shear failure of clay in the Cam-clay model. However, as experimental evidence shows, the extended Mises criterion grossly overestimates strength in triaxial extension, and also results in incorrect intermediate stress ratios in plane strain (Wroth and Houlsby 1985). It is well known that the failure of soils can be explained by the Lade's criterion (Lade and Duncan 1975; Lade 1977; Lade and Musante 1978), and others (Matsuoka and Nakai 1974), which incorporate the third stress invariant. Taking the consistency in the shear deformation and the shear failure into considera- tion, it is reasonable to introduce Lade's criterion or other cri- teria for the shear yield as well as the shear failure of soils. Based on such ideas, some researchers attempted to improve the Cam-clay model to a 3D model for soils (Zienkiewicz and Pande 1977; Randolph 1982). However, Wroth and Houlsby (1985) commented that further study is necessary to improve the Cam-clay model by combining the idea of critical state theory with such failure criteria as Lade and Duncan's (1975)