Residual elastic strain in rocks

Abstract

Residual elastic strains (stresses) consist of locked-in strains, reflecting crystal distortions related to past external loads, and those that constrain them, the locking strains. The forces or stresses giving rise to locked-in and locking strains exist in rocks with no external loads across their boundaries and satisfy internal equilibrium conditions i.e., their sum is zero. The strains are stored by cementation and physical and chemical interactions between anisotropic grains while under load. The measure of residual strain provided by strain relief or X-ray methods consists of some unknown combination of locking and locked-in strains that depends on the distribution, relative magnitudes, and degrees of relaxation (strain relief method) of these components and the special bias of the measuring technique. With the X-ray technique, the bias is toward detection of strains in the most voluminous rock elements satisfying the Bragg condition for diffraction. In sandstone, therefore, the residual strains in the grains are sampled preferentially to those in the cement. The special view of residual stresses obtained from X-ray diffraction studies and supported by data from strain relief techniques has yielded significant information as follows: 1. (1) Magnitudes can be large; differential stresses between 300 and 400 bar have been measured in quartzites, sandstones, and granites. 2. (2) Residual stresses relating to Mesozoic and possibly even to Precambrian geologic events have been mapped. 3. (3) Principal axes correlate with the geometry of large-scale folds and to stresses inferred from nearby fractures and calcite twin lamellae. 4. (4) Residual stresses have been found to vary systematically along fault surfaces in such a manner as to be related to the process of sliding. Items 1–4 suggest that rocks have long-term fundamental strength; volumetric stored strain energy is commonly of the order of 10 4 erg/cm 3. 5. (5) Stored stresses relax when grains are freed from constraints of nearest neighbors. 6. (6) They relax within 5 mm of an induced tensile fracture in sandstone probably because movements along grain boundaries occur that far from the fracture surface. 7. (7) Residual stresses influence the orientations of tensile and shear fractures induced experimentally under certain conditions of loading. 8. (8) Observed residual stresses can contribute to strength anisotropy. Items 7 and 8 are explicable from superposition of applied loads on the observed residual stresses. 9. (9) In the Barre Granite the principal axes of residual strain are subparallel to the principal directions of ultrasonic attenuation and velocity fields.