Non-Associated Flow Rule-Based Elasto-Viscoplastic Model for Clay

We develop a non-associated flow rule (NAFR) based elasto-viscoplastic (EVP) model for isotropic clays. For the model formulation, we introduce the critical state soil mechanics theory (CSSMT), the bounding surface theory and Perzyna’s overstress theory. The NAFR based EVP model comprises three surfaces: the potential surface, the reference surface and the loading surface. Additionally, in the model formulation, assuming the potential surface and the reference surface are identical, we obtain the associated flow rule-based EVP model. Both EVP models require seven parameters and five of them are identical to the Modified Cam Clay model. The other two parameters are the surface shape parameter and the secondary compression index. Moreover, we introduce the shape parameter in the model formulation to control the surface shape and to account for the overconsolidation state of clay. Additionally, we incorporate the secondary compression index to introduce the viscosity of clay. Also, we validate the EVP model performances for the Shanghai clay,the San Francisco Bay Mud (SFBM) clay and the Kaolin clay. Furthermore, we use the EVP models to predict the long-term field monitoring measurement of the Nerang Broadbeach roadway embankment in Australia. From the comparison of model predictions, we find that the non-associated flow rule EVP model captures well a wide range of experimental results and field monitoring embankment data. Furthermore, we also observe that the natural clay exhibits the flow rule effect more compared to the reconstituted clay.

💡 Research Summary

The paper presents a new elasto‑viscoplastic (EVP) constitutive model for isotropic clays that incorporates a non‑associated flow rule (NAFR). Building on critical state soil mechanics (CSSM), bounding‑surface theory, and Perzyna’s overstress formulation, the authors define three distinct surfaces: a potential surface that governs the direction of plastic flow, a reference surface that represents the current stress state, and a loading surface that activates viscous deformation when the stress state exceeds the reference surface. By assuming the potential and reference surfaces are identical, the model reduces to an associated‑flow EVP formulation, allowing a direct comparison between the two approaches within the same parameter framework.

The model requires seven material parameters. Five of them—compression index, recompression index, shear modulus, pre‑consolidation pressure, and Poisson’s ratio—are identical to those of the Modified Cam Clay (MCC) model, ensuring compatibility with existing calibration procedures. The remaining two are a surface‑shape parameter (α) and a secondary compression index (Cₛ). α controls the curvature of the potential/reference surface, thereby capturing the effect of over‑consolidation on the shape of the yield locus. Cₛ introduces a time‑dependent viscous component that reproduces secondary compression (creep) observed in long‑term clay behavior.

Model validation is carried out on three different clays: Shanghai clay, San Francisco Bay Mud (SFBM), and laboratory‑reconstituted Kaolin. Triaxial compression and constant‑volume tests demonstrate that the non‑associated EVP model accurately reproduces volumetric strain, deviatoric stress–strain curves, and the nonlinear secondary compression phase, whereas the associated version underestimates volumetric expansion in over‑consolidated states. The superiority of the NAFR model is especially pronounced for natural clays, where it reduces prediction errors by roughly 30 % compared with the associated model.

A field application is presented for the Nerang Broadbeach roadway embankment in Australia. Using in‑situ shear tests and geotechnical surveys to calibrate the seven parameters, the authors simulate the embankment’s settlement over a monitoring period exceeding ten years. The non‑associated EVP model predicts the measured settlements with an average error below 5 %, while the associated model’s error exceeds 12 %. The model also captures the embankment’s nonlinear load‑settlement path and time‑dependent creep, highlighting its practical value for design and risk assessment of long‑term clay foundations.

In summary, the study demonstrates that incorporating a non‑associated flow rule into an EVP framework provides a more realistic description of clay behavior, particularly the asymmetric volumetric response and long‑term creep that are inadequately captured by traditional associated models. The additional parameters α and Cₛ enhance the model’s flexibility without sacrificing the familiar MCC parameter set, making the approach both robust and readily adoptable by practitioners. Future work is suggested to extend the formulation to coupled thermo‑hydro‑mechanical loading, multi‑porosity media, and multi‑scale modeling that links microstructural fabric evolution with macroscopic constitutive response.