Bounding Surface Elasto-Viscoplasticity: A General Constitutive Framework for Rate-Dependent Geomaterials

Abstract

A general framework is proposed to incorporate rate and time effects into bounding surface (BS) plasticity models. For this purpose, the elasto-viscoplasticity (EVP) overstress theory is combined with bounding surface modeling techniques. The resulting constitutive framework simply requires the definition of an overstress function through which BS models can be augmented without additional constitutive hypotheses. The new formulation differs from existing rate-dependent bounding surface frameworks in that the strain rate is additively decomposed into elastic and viscoplastic parts, much like classical viscoplasticity. Accordingly, the proposed bounding surface elasto-viscoplasticity (BS-EVP) framework is characterized by two attractive features: (1) the rate-independent limit is naturally recovered at low strain rates; and (2) the inelastic strain rate depends exclusively on the current state. To illustrate the advantages of the new framework, a particular BS-EVP constitutive law is formulated by enhancing the modified Cam-clay model through the proposed theory. From a qualitative standpoint, this simple model shows that the new framework is able to replicate a wide range of time/rate effects occurring at stress levels located strictly inside the bounding surface. From a quantitative standpoint, the calibration of the model for overconsolidated Hong Kong marine clays shows that, despite the use of only six constitutive parameters, the resulting model is able to realistically replicate the undrained shear behavior of clay samples with OCR ranging from 1 to 8, and subjected to axial strain rates spanning 0.15%/h to 15%/h. These promising features demonstrate that the proposed BS-EVP framework represents an ideal platform to model geomaterials characterized by complex past stress history and cyclic stress fluctuations applied at rapidly varying rates.