Rock Mechanics - Method of Determining In-Situ Stress in Anisotropic Rock

The evaluation of in-situ rock stresses from measurements of the change in diameter of a borehole that is stress-relieved by overcoring has become a common practice. Generally the stress evaluation has been based on isotropic relations whereas rock in varying degrees is aniso tropic. A plane elasticity solution fora circular hole along one axis of an orthotropic medium has been adapted to evaluation of in situ stress. The necessary elastic parameters for this evaluation may conveniently be obtained from static tests on the overcore in conjunction with a consistent orthotropic thick-wall cylinder solution. The method and equations for the laboratory and field evaluations are summarized and illustrated. The determination of in-situ rock stresses from boreholc deformation measurements has gained widespread acceptance. Hastl measured the change in diameter of a borehole that was stress-relieved by drilling a larger concentric core; this overcoring method has produced a major portion of the field data for recent stress evaluations in rock. These evaluations are based on the elastic properties of the rock, which are conveniently determined by testing the overcore.6-8 The stress evaluation and the overcore testing procedures generally assume isotropic relations whereas rock is anisotropic in varying degrees. Recently, an anisotropic plane stress solution was adapted for evaluation of in-situ stress9 and a related plane strain solution was developed for the testing of stress-relief core. 10 The present paper unifies the stress evaluation and overcore testing procedures for a general class of anisotropic rock. Equations are presented for calculating the state of stress in a plane normal to the borehole, and a consistent thick-wall cylinder solution is given for determining the necessary elastic properties. In addition, a complete example of stress evaluation from laboratory and field data is presented, and the order of error in computing the state of stress from isotropic relations is illustrated. Several limitations of the results should be emphasized. All results assume small linearly elastic deformations of a homogeneous medium. Rock characterized by orthotropic, transversely isotropic, and isotropic elasticity is considered; however, the anisotropic results assume a special relation among certain elastic constants in addition to geometric orientation with respect to a plane of elastic symmetry. For some stress determinations in rock, these may be severe limitations. On the other hand, the anisotropic evaluation procedure involves little additional effort and is much more flexible than the corresponding isotropic evaluation procedure. The collection of field data is identical. The laboratory determination of elastic parameters is no more difficult and time-consuming for the anisotropic than for the isotropic model. Only the calculations require some additional effort for the anisotropic evaluation, and this additional effort is eliminated by use of a small computer. The flexibility of the anisotropic procedure is greater because more than two independent elastic constants are available in fitting rock data. For the special relationship assumed among orthotropic constants, five independent elastic constants are available for the determination of in-situ secondary principal stresses as compared with two independent elastic constants for the isotropic model. Much of the material presented is either directly from the literature or adapted from the literature through superposition or the usual transformations. Consequently, only enough detail for clarity of presentation is included. RELATIONS FROM ANISOTROPIC ELASTICITY Materials that have three mutually orthogonal planes of elastic symmetry are called orthotropic. By directing the axes of the coordinates perpendicular to these planes, Hooke's law for an orthotropic solid 11 is