Borehole Cross-Sectional Shape Analysis under in Situ Stress

Abstract

The stress relief method is currently one of the most commonly used in situ stress measurement methods, and its basic measurement principle is the relationship between borehole deformation and in situ stress. The research object of this paper is a circular hole in an infinite elastic plate under plane stress conditions. Based on the elasticity theory, the shape of a circular hole in an infinite elastic plate under plane stress conditions is an ellipse. The formula to convert the ellipse shape parameters to stress is given. A new method for calculating the ellipse shape parameters is proposed, in which any three points on the original circular hole are used to describe the ellipse shape and the corresponding formulas are derived. The feasibility of the method and the formulas are verified by analyzing a specific example. By developing the relationship between borehole geometry and stress, a stress calculation method based on a borehole cross-sectional shape is constructed, which is significant for guiding in situ stress measurements.