A 3D Elasto-plastic Constitutive Model for Clay Based on the Unified Hardening Model with Insights into the Coupling Effect of Small-Strain Stiffness and Over-Consolidation Ratio

The deformation or failure strength of soils in practical projects is usually misestimated. This is because the effects of small-strain stiffness, over-consolidation state, and stress-induced anisotropy are neglected in most existing constitutive models, especially the influence of over-consolidation ratio on the small-strain stiffness. A proper constitutive is critical to ensure the accuracy of numerical calculations, and there is the lack of a comprehensive constitutive model considering the above-mentioned complex natures. In this regard, an elasto-plastic constitutive model for clay considering the over-consolidation state and the nonlinear small-strain characteristic within the critical state concept framework was proposed. The unified hardening parameter and the sub-loading surface concepts were combined. In addition, the influence of over-consolidation ratio on the small-strain stiffness was considered. Motivated by true triaxial test observations, the developed constitutive model was combined with the generalized nonlinear strength theory (GNST), so that the stress-induced anisotropy (i.e., the effects of the stress in the second principal direction on soil's strength) could be captured by this constitutive model. Then, the model was incorporated into the ABAQUS program by the FORTRAN programming language. The application of the proposed constitutive model for true triaxial test and shield tunneling engineering was tested to verify its practicability. The results indicated that the model can describe the clay's mechanical properties from a hardening state to a softening state, and from a shrinkage state to a dilatancy state, with an increasing over-consolidation ratio (OCR). In addition, the transition OCR of the soil in this study was 2. Furthermore, the phenomena of strength attenuation with Lode angle and also failure envelopes extension with OCR could be described well. The results showed that when Lode angle is 60 degrees (i.e., b = 1), the strengths was overestimated 42.6%, 43.9%, 44.9%, 49.7%, and 60.4% by Mises criterion for over-consolidated clay with OCR = 1, 1.5, 2, 4, and 8. By considering the influence of small strain behavior and intermediate principal stress, the finite element's applicability in excavation analysis was improved. Overall, the conducted study could provide a helpful reference for the description of clay's mechanical properties.