The concept of residual stress in rock

Abstract

The purpose of this paper is to clarify the concept of residual stress in rock. Residual stress is stress near a point in a body subjected to zero external tractions and to zero temperature gradients, excluding body forces. Thus, residual stresses can develop in rock if there are local phase transformations, inelastic strains, or differences in thermal or elastic properties. In these cases, residual stresses can result from changes in temperature, applied stress or configuration of the body. Analysis of residual stresses at the scale of mineral grains within a polycrystalline aggregate such as rock is virtually intractable. One can, however, obtain important insights into residual stresses within bodies with widely spaced sources of residual stress, such as inclusions, and within bodies comprised of multilayers. The analyses indicate that patterns of residual stress in rock can be expected to be extremely complicated. For example, study of residual stresses in a body containing a circular inclusion indicates that: 1. (1) There is a single state of residual stress within an inclusion but the state within the surrounding medium is variable. Thus, values of residual stress within rocks reported in the literature generally are of minor value because the sizes and shapes of the sources and the positions of the measurements relative to the positions of sources of residual stresses in the bodies have not been determined. 2. (2) Residual stresses within an inclusion can be tensile or compressive, even though the applied stresses were compressive, depending upon the source of residual stress. 3. (3) The magnitudes and orientations of residual stresses in an isolated body of rock containing one or more inclusions depends upon the size and shape of the body. The same general conclusions are derived from an analysis of residual stresses in a simple multilayered body. 4. (4) In addition, however, the anisotropy of a multilayered body tends to cause principal residual stresses to parallel the layers rather than to parallel the applied stresses that were responsible for inducing the residual stresses. Thus, without identifying the sources of residual stresses in a body, one cannot infer the directions of principal tectonic stresses that might have been responsible for the residual stresses. Comparison of the theoretical results with measurements of change of residual stress in blocks of granite, with maximum dimensions of 2.5 m in the field and 0.2 m in the lab oratory, suggests that sources of residual stress are inhomogeneous elements or elements of inelastic deformation within the blocks that are smaller than the blocks themselves, but larger than individual mineral grains. The sources of residual stress are unknown in these granites.