Poroelastic solutions for borehole and cylinder

Abstract

This dissertation presents a theoretical study of poromechanical responses of a finite cylinder, and an infinite borehole under axisymmetric loading. The disturbed zone due to borehole drilling process is taken into account in the analysis of borehole problems, in which shear modulus and permeability coefficient are changed from their original values. There are three problems presented in this study, i.e. quasi-static responses of a cylinder and a borehole, and dynamic response of a borehole. The solutions to these problems are useful for theoretical modeling of several laboratory and in-situ tests in civil engineering. A new set of analytical solutions to all problems are derived based on Biot’s theory of poroelasticity by employing integral transform techniques. The general solutions to the coupled governing equations are obtained by applying the Laplace transform with respect to time for quasi-static problems, and applying the Fourier transform with respect to the vertical coordinate for the borehole problems. They are then numerically inverted by applying an accurate numerical scheme for the Laplace inversion, and applying an adaptive quadrature scheme for the Fourier inversion. Accuracy of numerical solutions is confirmed by comparing with independent existing solutions for the limiting cases. Several boundary-value problems are solved to demonstrate the applications of the general solutions to practical situations involving cylinders and boreholes. Selected numerical results are presented for displacements, stresses, pore pressure and fluid discharge to demonstrate the influence of poroelastic material properties and other governing parameters, and the salient features of the coupled poroelastic response.