Some Constitutive Equations For Rock Materials

In engineering analyses, rock is frequently treated as a homogeneous, isotropic, and linearly elastic medium. However, rock material exhibits, in most cases, physical nonlinearity, time-dependency, and anisotropy. In some instances, anelasticity due to nonmechanical effects, such as density and temperature changes, must also be taken into account. The influence of these different anomalies in the physical behavior of a rock material is often neglected. An estimate of the discrepancies which are introduced when classical theory of elasticity is used is consequently required. The easiest theoretical path by which these discrepancies can be analyzed is to vary the constitutive equations of the rock material. The constitutive equations, representing various physical experiences with different types of media, define a class of ideal substances. Assuming different constitutive equations for the description of the rock physical behavior, one can establish a sensitivity analysis to determine how much information is contained in elastic theory for reliable design purposes. The method may be applied also using numerical techniques (e.g., finite element or finite differences) which, because of the nature of the formulation, require one to assume in each case the rock constitutive equations. Theoretical and experimental work is needed to be able to perform such analyses with confidence. Adequate and practical procedures for the determination of the material functions which enter the various constitutive equations must be established. This paper presents such an attempt with respect to the simulation of some behavior patterns of rock material. It is felt worthwhile to stimulate activity in this field and it is hoped to contribute to this objective.