The XFEM for a simplified model in hydraulic fracturing

Markus Schätzer, Thomas Peter Fries

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


Hydraulic fracturing is an important branch in geomechanics, where a fracture initiates and propagates in the host rock due to the induced hydraulic loading. The pressure exerted by the fracking fluid onto the surrounding solid, typically is obtained by a Reynolds equation which relates the crack width with the pressure. This poses severe difficulties for the numerical treatment, also in terms of robustness. In the presented work, the Reynolds equation is replaced by pre-defined pressure distributions which leads to a much simpler and robust coupled problem. For each assumed distribution, the critical pressure is determined where the critical energy release rate Gc is exceeded. The influence of the different distributions is investigated in a separate example. The energy release rates are determined based on stress intensity factors with the XFEM by using crack opening displacements. This happens by a comparison of an approximated state which represents the computed displacements in the solid, and a reference state which represents the expected openings for a pure mode I, II and III. This method is intuitive, computationally cheap and has the advantage that only displacements are fitted, wherefore no additional consideration of pressurized crack surfaces is required. The critical pressure is determined based on the superposition principle in linear elastic fracture mechanics. Herein, a separate observation of the external loadings by means of volume forces and tractions at the boundary, and the internal loadings by means of the pressure exerted by the fracking fluid is done. Based on a scaling factor of the internal state, the critical pressure is extracted from the energy release rate.

Original languageEnglish
Title of host publicationECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
PublisherNational Technical University of Athens
Number of pages10
ISBN (Electronic)9786188284401
Publication statusPublished - 2016
Event7th European Congress on Computational Methods in Applied Sciences and Engineering: ECCOMAS 2016 - Crete, Greece
Duration: 5 Jun 201610 Jun 2016


Conference7th European Congress on Computational Methods in Applied Sciences and Engineering
Abbreviated titleECCM 2016
Internet address


  • Crack opening displacements
  • Energy release rate
  • Stress intensity factors
  • Superposition

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics


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