Relationship between fractal dimension of multiple microcracks and fracture energy in rocks

Kazushi Sato, Toshiyuki Hashida, Hideaki Takahashi, Toru Takahashi, Kazuo Hayashi

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


This paper presents a relation between the fracture energy of rocks and the fractal dimension of multiple crack distributions. Firstly, we have developed a method for determining the grain scale strength distribution in order to characterize the inhomogeneity in rocks. The method has shown that the microscopic strength distribution can be described by the Weibull function. Secondly, numerical analyses using a network model were carried out to simulate the multiple cracking behavior in fracture toughness specimens. It is demonstrated that the multiple crack pattern formed in the fracture toughness specimens exhibits a fractal distribution and the fractal dimension of crack length-frequency distributions depends on the microscopic strength distribution. Fracture toughness tests conducted on lidate granite and Tohoku marble confirm the above numerical results. The network model reveals that the fracture energy consumed in the microcrack region correlates positively with the fractal dimension.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalGeothermal Science and Technology
Issue number1-4
Publication statusPublished - 1999


  • Acoustic emission
  • Fractal dimension
  • Fracture
  • Microcrack
  • Network model
  • Rock


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