Because the three-dimensional strength of soil, rock, and concrete is influenced nonlinearly by the hydrostatic pressure and Lode's angle, the failure surface is irregular in stress space, especially in the large stress range. Based on Lade's criterion, exponential failure function in coordinate p-q, and the concept of original transformed stress space, an extended transformed stress space and its corresponding transformed stress tensors are proposed in this paper. Compared with original transformed stress space, the extended one would be suitable to the large stress range. Processing test results in extended transformed stress space, the unified stress-strain relationship for a certain geomaterial can be easily obtained from the test results. The validity of extended transformed stress space is confirmed by test results of soil, rock, and concrete. Based on extended transformed stress space and the Modified Cam-Clay Model, a new constitutive model is also proposed in this paper, which can be used to predict three-dimensional stress-strain relationship for soils in the large stress range. The capacity of this model is demonstrated using triaxial test results of Toyoura sand with different stress paths in the large stress range.

Based on the relationships between the Hvorslev envelope, the current yield surface and the reference yield surface, a new constitutive model for overconsolidated clays is proposed. It adopts the unified hardening parameter, to which the potential failure stress ratio and the characteristic state stress ratio are introduced. The model can describe many characteristics of overconsolidated clays, including stress-strain relationships, strain hardening and softening, stress dilatancy, and stress path dependency. Compared with the Cam-clay model, the model only requires one additional soil parameter which is the slope of the Hvorslev envelope. Comparisons with data from triaxial drained compression tests for Fujinomori clay show that the proposed model can rationally describe overconsolidated properties. In addition, the model is also used to predict the stress-strain relationship in the isotropic consolidation condition and the stress paths in the undrained triaxial compression tests.

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.

Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.