Initiation of fluid-induced fracture in a thick-walled hollow permeable sphere

TL;DR

This study analyzes how Biot's coefficient and size influence fluid-induced fracture initiation in a thick-walled permeable sphere, using numerical methods validated against analytical solutions.

Contribution

It introduces a coupled fluid-solid model for fracture initiation in permeable spheres, highlighting the effects of Biot's coefficient and size on fracture strength.

Findings

Nominal strength increases with Biot's coefficient.

Nominal strength decreases with sphere size.

Numerical model validated against analytical solutions.

Abstract

The initiation of fluid-induced fracture in formations of permeable geomaterials subjected to quasi-stationary flow processes (drained response) can be strongly affected by Biot's coefficient and the size of the formation. The aim of this paper is to analyse the influence of these parameters on the initial fracture process of a thick-walled hollow permeable sphere subjected to fluid injection in the hole. Assuming that fracture patterns are distributed uniformly during the hardening stage of the fracture initiation process, the coupled fluid-solid problem is described by a nonlinear ordinary differential equation, which is solved numerically by means of finite differences combined with shooting and Newton methods. The finite difference code has also been validated in the elastic range, i.e., before initiation of fracture, against an original closed-form analytical solution of the above differential equation. The results show that the nominal strength of the sphere increases with increasing Biot's coefficient and decreases with increasing size.