Distortion measurement between photographic images : a new rock-mechanics tool

Abstract

Although a qualitative understanding of the fracture of rocks has been acquired, quantitative models are still inadequate. The construction of a predictive model of the brittle deformation of crystalline rocks requires knowledge of the local stress needed for microcrack initiation and propagation. The principal result of this study is the development of a technique for determining the local microscopic stresses with sufficient accuracy to determine these cracking stresses quantitatively. Photomicrographs of a thin rock wafer at sequential increments of load are digitized, and the strain and displacement fields for each increment of load are computed from numerical comparison of the photos. From knowledge of the strain variation within a grain and its anisotropic elastic stiffness, the stress field can be determined. The accuracy with which the strains and displacements can be determined depends on the quality of the photographic image and its spatial frequency content; the greater the high frequency content, the higher the accuracy. The technique was tested on optical, transmitted -light photomicrographs of Westerly granite. The displacements were determined to better than 1/50 of the sampling interval and the strains to better than 2x10⁻⁴ when the photographs, which had a large high-frequency content, were digitized with a sampling interval of 50 pm. These error values are actually measures of the scatter in the deformation parameters, much of which is due to heterogeneity in the strain field. Therefore, these values are upper bounds on the error that is intrinsic to the displacement and strain-determination method. More accurate results would be expected if the photographs were digitized with a finer sampling interval and if the effective heterogeneity of the strain field were reduced by treating smaller sections of the photograph.