An analytical approach to the stress distribution around a cased borehole in an anisotropic formation

• Published in: Applied Mathematical Modelling Vol. 107; pp. 316 - 331
• Main Authors: Wang, Hongwei, Miao, Miao, Zhou, Tao
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2022; Elsevier BV
• Subjects: Anisotropic formation; Boreholes; Cased borehole; Contact stresses; Elastic anisotropy; Modulus of elasticity; Nonwelded; Plane strain; Robustness (mathematics); Stress distribution; Cased borehole; Stress distribution; Anisotropic formation; Nonwelded
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2022.02.040

•An analytical solution is provided to calculate the stress distribution of a borehole.•The formulae can meet complex geological conditions, including arbitrary medium, in situ stress and contact stiffness.•The derived formulae can be applied to the drilling and the Anchoring in tunnel engineering. We present an explicit analytical approach for calculating the distribution of stress around a circular cased borehole in a discontinuous anisotropic formation. The borehole model is built on a pure elastic model with the assumption of the generalized plane strain, in which casing and cement rings are assumed to be isotropic, while formation is anisotropic. Also the borehole model is subject to arbitrary far-field stress, whose inner boundary between cement and formation is nonwelded. The accuracy and robustness of the approach is validated through comparing its results with those calculated from the existing classical solution, such as the Amadei solution for an isotropic example and the solution for an anisotropic cased borehole example based on the welded contact. The numerical examples show that within a certain range of the contact compliance, the formation's stress changes obviously.