Transformed Stress Method for Generalizing Soil Constitutive Models

It is important to generalize constitutive models from the triaxial compression state to the three-dimensional stress state for soils. However, there are some deficiencies in the existing methods, e.g., the using failure criteria method, the generalized shear stress ratio method, and the shape function approach using Lode’s angle or reduced Lode’s angle, for generalizing either isotropic or anisotropic constitutive models. For example, the critical state curve may be misshapen and the yield surface will appear to be curvature discontinuous if the constitutive model is generalized with the shape function approach using reduced Lode’s angle. The transformed stress (TS) space has been proposed in the authors’ former work based on the spatially mobilized plane (SMP), the Lade’s, and the generalized nonlinear strength criterion. In this paper, the TS method based on an arbitrary failure criterion is proposed. It is a simple approach to generalize constitutive models without introducing any extra parameters. Another important work in this paper is using the TS method to generalize anisotropic models. It was found that (1) the processes for generalizing anisotropic models and isotropic models are the same, i.e., the proposed method can be directly used to generalize anisotropic models without any modification; (2) the deficiencies of other methods for generalizing constitutive models can be eliminated with the TS method (for instance, the yield surfaces appear to be curvature continuous after generalization, and the critical state curves of the generalized models are consistent with the adopted failure criteria); and (3) it is demonstrated by the comparison between the predictions and test results that the TS method is better than the shape function approach using Lode’s angle in describing the soil behaviors in the general stress state. In this paper, the modified Cam clay model is taken as an example for the discussion.