A Nonlinear Rheological Model for Time-dependent Behavior of Geologic Materials

Rheological models are widely accepted as a means of describing the mechanical behavior of geologic materials. It has been found, however, that rheological models developed for a specific stress level on the basis of linear visco-elasticity generally are not satisfactory at other stress levels. It has been suggested that the parameters of such models should be functions of stress level (Hardy, 1965; Kim, 1971). In this paper, continuous functions of stress have been utilized to obtain the required variation of Burgers model parameters with stress level. The model developed using these functions provides a constitutive relation which reflects the real time-dependent behavior of rock materials. The new model is capable of predicting the creep behavior over a wide range of stress levels and also predicts mechanical behavior under different loading condition (e.g. constant stress rate). It is also interesting to note that the mechanical behavior of individual elements in the model appear to reflect the different stages of brittle fracture in rocks (Bieniawski, 1967), namely; crack closure, elastic deformation, stable fracture propagation and unstable fracture propagation.