Constitutive models in the literature for creep of frozen soil are based on the direct use of time counted from the onset of creep. An explicit time dependence in a constitutive equation violates the principles of rational mechanics. No change in stress or temperature is allowed for during creep, using the time-based formulations. Moreover, the existing descriptions need much verification and improvement on the experimental side as well. Creep behaviour of artificially frozen sand was evaluated experimentally. Novel testing methods were used, and new insights into the creep behaviour of frozen soil were gained. Creep rate under uniaxial compression was examined with different kinds of interruptions, like unloadings or overloadings. Experimental creep curves were presented as functions of creep strain. They were brought to a dimensionless form which describes the creep universally, despite changes in stress or temperature. Possible anisotropy of frozen soil was revealed in the creep tests on cubic samples with changes of the loading direction. Using the particle image velocimetry (PIV) technique, information on the lateral deformation and the uniformity of creep were obtained. Volumetric creep of unsaturated frozen soil under isotropic compression was demonstrated to be due to the presence of air bubbles only.

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.