Formulation of a three-dimensional rate-dependent constitutive model for chalk and porous rocks

Rate-dependent behaviour of chalk and other porous rocks has undergone widespread study in geomechanics due to its implications on the performance of engineering structures. We present a rate-dependent constitutive model for chalk and other porous rocks with several new features. The model formulation is based on a viscoplastic rate-lines approach in which the axial strain rate depends on the proximity of the stress point to an elliptical reference surface. A non-associated viscoplastic potential surface and an axial scaling algorithm are used to determine the viscoplastic strain components. The model predicts that axial yields stress varies as a power function of applied axial strain rate, as shown by published laboratory data. Comparisons with published experimental data indicate that the model is capable of reproducing observed rate-dependent behaviour of chalk under a variety of loading conditions. Copyright (c) 2006 John Wiley & Sons, Ltd.