In the design of foundations for large structures and of safe mine openings in rock, the results of laboratory and small-scale in-situ tests are often used to predict the behavior of the material as a whole. For reasons of simplicity in these analyses, the rock is usually treated as an ideally elastic, isotropic material. It has been observed, however, that most rocks are neither isotropic nor ideally elastic. This observation is particularly true for rocks subjected to low confining pressures. It is therefore necessary to investigate further the effects of anisotropy and nonlinearity on the mechanical behavior of rocks.
When small differences in stress and strain only are involved, the rock may be treated as an elastic material. The elastic constants for such a material subjected to a particular confining pressure can be calculated from the classical theory of elasticity for different degrees of anisotropy. There are two experimental methods by which this can be done: first, from measurements of static stress-strain relationships; second, from elastic wave velocities measured in the rock. The former yields the static elastic constants, and the latter, the dynamic constants. The static constants will be equal in magnitude to the corresponding dynamic constants only if the rock is ideally elastic.
Walsh and Brace1 have reviewed theoretical studies of the elasticity of rock considered as a material containing pores and cracks. They reported that the presence of sharp, narrow cavities at low confining pressures strongly influences the mechanical properties of a rock. A considerable reduction in magnitude of elastic moduli is associated with the presence of inhomogeneities such as cracks or joints. The elastic properties appear to approach those of the uncracked material in magnitude as the cavities are closed by higher pressures. Walsh and Brace1 also reported that the presence of cracks apparently affects the static and dynamic properties of rocks differently. Simmons and Brace2 found experimentally that at low confining pressures the dynamic elastic moduli were considerably higher than the static values. Both Walsh3 and Cook and Hodgson4, have shown theoretically that these differences are predicted by a material containing cracks. At hydrostatic confining pressures in excess of 30,000 psi, Simmons and Brace2' found the static and dynamic moduli closely in agreement. This suggests that any cracks present at lower confining pressures had been closed by the increase in pressure.
Based on the results of earlier measurements of ultrasonic wave velocity measurements on several sandstones5, an isotropic sandstone (Boise) was chosen on which to compare the static and dynamic elastic constants. Measurements of static stress-strain relations and ultrasonic wave velocities were made concurrently on the same specimen of dry Boise sandstone when it was subjected to different confining pressures. Preliminary results6 indicated that, whereas the dynamic moduli are always higher than the static moduli, they approach each other in magnitude as the confining pressure is increased to 6000 psi. This behavior is in agreement with that predicted for a cracked material.
In this chapter are presented the results of similar tests on a second dry sandstone (Berea), which had previously been found5 to exhibit transverse isotropy.
