On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture

TL;DR

This paper introduces a 2D hydro-mechanical lattice model for hydraulic fracturing that accurately captures fluid-structure interactions and size effects, validated against analytical solutions and demonstrating mesh independence.

Contribution

The novel lattice approach effectively models hydraulic fracturing with size-dependent strength effects, incorporating Biot's theory for fluid-structure interaction.

Findings

Lattice results agree with analytical elastic solutions.

Model results are mesh size independent.

Size effect on strength decreases with higher Biot's coefficient.

Abstract

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biot's coefficient.