Stress Analysis of Borehole in Poroelastic Medium

Abstract

A method of analysis based on analytical techniques is presented to determine the axisymmetric response of a cylindrical borehole in a poroelastic medium. The medium is assumed to be fully saturated and governed by the classical Biot's theory. A set of general solutions relevant to the present class of problems are derived through the application of Laplace and Fourier integral transforms with respect to the time and the vertical coordinate, respectively. Boundary‐value problems corresponding to axisymmetric radial tractions or fluid sources applied over a segment of the borehole surface are solved and analytical solutions in the Laplace transform space are presented. Solutions corresponding to ring‐type loads and a fluid source are also presented. These solutions can be used to derive the solutions corresponding to nonuniform distribution of tractions and fluid sources applied over a segment of the borehole surface and a variety of other problems. Time‐domain solutions are obtained by using a numerical technique for the inversion of Laplace transform. Selected numerical results for displacements, stresses, pore pressure, and radial discharge are presented to portray the effects of poroelasticity on the response of the borehole.