Mechanical Anisotropies of Laminated Sedimentary Rocks

Abstract

Abstract The effects of bedding plane orientation on the elastic constants and the yield strengths of three laminated rocks (one sandstone and two shales) and one isotropic rock (a limestone) were studied. The directional dependence of the elastic properties of these rocks was experimentally evaluated using a triaxial compression cell and auxiliary stress - strain measuring equipment. Symmetry of Poisson's ratios within the bedding plane suggested that horizontal isotropy exists, but the bedding planes do give rise to an appreciable difference between properties in the horizontal and vertical directions. For the three bedded rocks studied, Young's modulus was lower normal to bedding than along bedding. Yield strengths were determined at confining pressures from 0 to 12,000 psi in a triaxial compression cell. The rocks studied showed strength reductions as high as 40 per cent when the test specimen was oriented at 20 degrees 30 degrees to the bedding planes. The mechanical behavior of these rocks suggested that the rock properties of shear strength and/or coefficient of internal friction can vary with direction, depending on the particular rock tested. Tensile strengths were also measured and found to be lowest when failure occurred along bedding. This work shows that bedded formations exhibit sizable directional variations in both their elastic constants and yield strengths. It is suggested that these variations may be accounted for by using the "elastic laminate" model and the "variable coefficients" failure model. Introduction The nature of rock deformation at elevated pressures has been studied by many workers; papers by Handin, and Robinson illustrate the present state of knowledge. Most investigators have either chosen rocks which were as isotropic as possible (in order to avoid complications of data interpretation and analysis) or they have oriented their samples so that the effects of anisotropies (such as bedding planes) have been avoided. Of the studies performed, few were concerned specifically with mechanical anisotropies. Griggs has presented limited data for specimens cut parallel, normal, and 45 to the bedding plane; he relates the strength anisotropy observed to the fabric (bedding) anisotropy. His tests were primarily concerned with large deformations (20 per cent strain); thus, no directional values of the elastic constants were reported. Handin has reported the results of similar experiments. Bott has discussed rock strength anisotropies due to faults, cleavage, or bedding. He was concerned primarily with determining the shear stress on such planes and did not mention the effect of friction. Jaeger later generalized Bott's work by taking friction into account and presented a limited theory for the failure of rocks having a "single plane of weakness", and also for rocks having a constant coefficient of friction, and a shear strength which varies with bedding plane orientation. Donath and Cohen, and Donath have evaluated rock strengths from shale and slate specimens cut normal and parallel to bedding. A dependence of cohesive strength (ro) on the specimen orientation was also shown. Adler has also studied this problem and lists similar results. He assumes that all bedded rocks behave according to Jaeger's single - plane - of - weakness theory. Kalinin and Belorussov list results for strength tests parallel and perpendicular to bedding and use this information as a basis for hole deviation analysis. From the literature it is apparent that sedimentary rocks have been tested under widely varying conditions of stress; however, the assumption of isotropy is generally, but not always, made. Since geologic sedimentation often deposits sediments in very definite layers, it seems that more systematic attention should be given to the possible effects of this natural bedding. Bedding, as used here, refers to visible regularities of grain size or orientation resulting from depositional processes. SPEJ P. 67ˆ