Microplane constitutive model for porous isotropic rocks

Zdeněk P. Bažant, Goangseup Zi

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane-type constitutive model for hardening and softening non-linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shear-enhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress-strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete-an artificial rock. The model is intended for large explicit finite-element programs.

Original languageEnglish
Pages (from-to)25-47
Number of pages23
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number1
Publication statusPublished - 2003 Jan
Externally publishedYes


  • Finite elements
  • Fracturing
  • Material modelling
  • Microplane model
  • Plasticity
  • Porous rock

ASJC Scopus subject areas

  • Computational Mechanics
  • Materials Science(all)
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials


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