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 (Bienlawski, 1967), namely; crack closure, elastic deformation, stable fracture propagation and unstable fracture propagation.
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The subject of time-dependent behavior of rocks has been studied now for over sixty years, and a wide range of methods for such studies have been developed. The study of time-dependent behavior of rocks have been undertaken in many areas such as mining, civil engineering, geology and seismology; and has involved various loading forms including tension, compression, torsion and bending both in the laboratory and in the field. Generally, the methods can roughly be divided into three categories, namely:
empirical method,
physical theory method and,
theological (or mechanical model) method.
The empirical method involves selection of a curve to fit a set of experimental data. Fitting curves to a set of data can assist in establishing certain relationships between the data. This is useful especially when the mechanism of the physical process is vague or unknown. Because this approach is based on interpolation, extrapolation from the laws developed using this method is hazardous (Price, 1969), especially where the deformation mode changes. The physical theory method starts from the analysis of the microscopic structural variation of the material observed under loading, and produces a theoretical explanation of the basis of the time-dependent behavior. The method originated in metallurgy and was later introduced into rock mechanics. Rock, however, is a much more complex material than a metal. For example, the atomic bond in natural rock is always a chemical bond rather than a metallic bond; furthermore most rocks are multigranular-structured in contrast to the relatively homogeneous structure of metals. These factors make the microscopic characteristics of rocks, such as dislocations (Mott, 1956; Cotttell, 1963), activation energy (Cruden, 1971), etc., different from those of metals. Since there is still a lot of work required in order to understand the microscopic characteristics of rock, physical theories are not widely used in rock mechanics.
In the theological or mechanical model method the actual mechanism of deformation is ignored. When materials are deformed, two basic characteristics are clearly observed, namely: elasticity and viscosity.
