An SBFEM-Based Model for Hydraulic Fracturing in Quasi-Brittle Materials

A numerical model based on the scaled boundary finite element method is developed to simulate the hydraulic fracturing in concrete-like quasi-brittle materials using cohesive interface elements. The shadow domain method developed previously (Yang and Deeks in Eng Fract Mech 143(4):333–354, 2007) is extended to consider crack-width-dependent hydraulic pressure and cohesive traction, so that the stress intensity factors caused by both crack-face forces are semi-analytically calculated separately in the same way. The crack propagation is determined by the criterion of KI⩾0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_\mathrm{I} \geqslant { \mathrm 0}$$\end{document}, and the propagation direction by the linear elastic fracture mechanics criteria. Two examples of concrete structures are modeled, and the results are in good agreement with the experimental data and others numerical results.