Simple models to describe time-dependent behavior of geomaterials in 1D and 3D stress conditions are presented. After explaining previous viscoplastic models and the problems these models contain, a new time-dependent model is presented which is formulated not using usual viscoplastic theories but utilizing the subloading surface concept by Hashiguchi . Based on experimental results, it has been shown that the normal consolidation line (NCL) and the critical state line (CSL) on the e — lns plane can shift vertically depending on the strain rate. The model can describe time-dependent behaviors of both normally consolidated unstructured as well as structured soils in the same manner. To describe the behavior of structured soil, a state variable, ?, which represents the influence of density, and another state variable, f, which represents the bonding effect, are introduced. After the formulation is explained in one-dimension to highlight the fundamental concepts of the model, it is extended to three-dimensions using the tij concept .
Most existing viscoplastic models have been formulated based on the over-stress theory or the non-stationary flow surface theory. The over-stress type models are formulated based on the over-stress viscoplastic theory by Perzyna  (e.g., Adachi and Oka ), in which the strain rate effects are described by assuming a Bingham plastic and utilizing the difference in sizes of the static yield surface related to the current plastic strains and the dynamic yield surface related to the current real stresses. However, this type of model is problematic in that the plastic strain rate is related to time alone. Therefore, it is impossible to distinguish whether the stress path is in the loading region or unloading region, because of a lack of loading information. On the other hand, in the nonstationary flow surface models (e.g., Sekiguchi ), the flow surface is a function of time, stress and plastic strain, and a flow rule is assumed on this flow surface, in the same way as elastoplastic models. This type of model is also problematic in that the flow surface contains the arbitrary time variable, t, which is not objective.
In the present study, a unified 1D formulation of timedependent behavior for normally consolidated unstructured soil to structured soil is presented. To describe the behavior of structured soil, a state variable ? which represents the influence of density and another state variable f which represents the bonding effect are introduced.