A Strength Criterion for Anisotropic Rocks Based Upon Experimental Observations
Authors: McLamore R.T. , Gray K.E. 
Published: December 2007

This paper was prepared for the 96th Annual AIME Meeting to be held in Los Angeles, Calif., Feb. 19 through 23, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made.
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Abstract
Compressive strengths as a function of confining pressure and sample orientation were determined for three anisotropic rocks that possessed two distinctive types of anisotropic features:cleavage planes (slate);bedding planes (two types of Green River shale).
The samples were tested over a confining pressure range of 1000 to 40,000 psi, with pore pressure held constant at atmospheric pressure. The orientation of the plane of anisotropy (bedding or cleavage plane) was varied between 0 deg. and 90 deg. relative to the axial stress. The compressive strength of all three rocks was found to be highly anisotropic. Maximum values of strength occurred at orientations of 0 deg. and 90 deg., while minimum value occurred at an orientation of 30 deg. for the Green River shale. The orientation of the minimum compressive strength for slate was found to be dependent upon the initial stress state.
The test results indicate that anisotropic rocks fail or deform by one of three mechanisms:shear faulting (across or parallel to the bedding or cleavage plane);plastic slip along the bedding or cleavage plane;internal buckling (kinking).
It was found that the failure mechanism was a function of both the initial stress state and the orientation of the plane of anisotropy relative to the axial stress.
Three current failure theories for anisotropic rocks—(1) the Walsh-Brace modification of Griffith's tensile failure theory; (2) Jaeger's single plane of weakness theory based on the Mohr-Coulomb theory; (3) Jaeger's continuously variable shear strength theory, also based on the Mohr-Coulomb theory—were analyzed and compared to the experimental strength data. It was found that the Walsh-Brace and the single plane of weakness theories predict identical failure criteria and could only be used successfully to describe the compressive strength behavior of the Green River shale. Jaeger's continuously variable shear strength theory could only be used to describe the compressive strength characteristics of the slate over a limited range of orientations.
The experimental data indicated that both the cohesive strength, , and the coefficient of internal friction, , may vary with respect to orientation for a given anisotropic rock.