Models for normal fracture deformation under compressive loading

B. Malama, P. H.S.W. Kulatilake

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


A new semi-empirical model that can be used to predict fracture deformation behavior under normal compressive loading is presented. The development of a simple exponential model is presented first after which a modified and more general exponential model, with an additional degree of freedom in the model parameters, is obtained. The simple and the modified exponential models are then compared to available fracture closure models, namely the empirical Barton-Bandis hyperbolic model, and a power-law model based on Hertzian contact theory, to determine how good they fit the results of fracture closure experiments under monotonically increasing normal compressive loading. A new parameter called the half-closure stress, σ1/2, is introduced and is used, in addition to the maximum fracture closure, Δvm, in the model fitting procedures for the Barton-Bandis and the simple exponential model. The half-closure stress is shown to be related to the initial normal stiffness, Kni, used in the original Barton-Bandis model. An additional parameter, n, is used in fitting the modified exponential model to the experimental data. Of the models presented herein, the modified exponential model was found to provide the best fit to the experimental data, for the same values of σ1/2 and Δvm, over the entire range of compressive stresses. The power-law model based on Hertzian contact theory was found to be unsuitable for predicting normal fracture deformation behavior.

Original languageEnglish (US)
Pages (from-to)893-901
Number of pages9
JournalInternational Journal of Rock Mechanics and Mining Sciences
Issue number6
StatePublished - Sep 2003


  • Deformability
  • Empirical
  • Experimental
  • Normal stress
  • Single fractures
  • Theoretical

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology


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