Fracture toughness evaluation based on tension-softening model and its application to hydraulic fracturing

Kazushi Sato, Toshiyuki Hashida

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


This paper discusses the applicability of the tension-softening model in the determination of the fracture toughness of rocks, where the fracture toughness evaluated based on the tension-softening model is compared with the crack growth resistance deduced from laboratory-scale hydraulic fracturing tests. It is generally accepted that the fracture process is dominated by the growth of a fracture process zone for most types of rocks. In this study, the J-integral based technique is employed to determine the fracture toughness of Iidate granite on the basis of the tension-softening model, where compact tension specimens of different dimensions were tested in order to examine the specimen size effect on the measured fracture toughness. It was shown that the tension-softening relation deduced from the J-integral based technique allowed us to determine the specimen size independent fracture toughness Kc of Iidate granite. Laboratory-scale hydraulic fracturing tests were performed on cubic specimens (up to a 10 m sized specimen), where cyclic pressurization was conducted using a rubber-made straddle packer to observe the extent of the hydraulically induced crack. The experimental results of pressure and crack length were then used to construct the crack growth resistance curve based on the stress intensity factor K. The crack growth resistance obtained from the hydraulic fracturing tests was observed to initially increase and then level off, giving a constant K value for a long crack extension stage. The plateau K value in the crack growth resistance curve was found to be in reasonable agreement with the fracture toughness Kc deduced from the tension-softening relation. It was demonstrated that the tension-softening model provides a useful tool to determine the appropriate fracture toughness of rocks, which may be applicable for the analysis of the process of large-scale crack extension in rock masses.

Original languageEnglish
Pages (from-to)1073-1089
Number of pages17
JournalPure and Applied Geophysics
Issue number5-6
Publication statusPublished - 2006 Jun


  • Fracture toughness
  • Hydraulic fracturing
  • J-based technique
  • Rock
  • Tension-softening model

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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