Microplane Constitutive Model for Porous Isotropic Rocks

This project deals with constitutive modeling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane constitutive model for hardening and softening non-linear triaxial behavior 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, this model is similar to the 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
  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 have been demonstrated. Although these data do not cover the entire range of behavior, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete, an artificial rock. The model is developed for large explicit finite-element programs at US Army Corps of Engineers, Vicksburg, Mississippi.

Kinematically constrained microplane model:

  • A) Microstructure and microplanes in a representative volume of a cohesive granular material
  • B) Icosahedron where the circled points represent the directions of microplane normals in a 21-point optimal Gaussian integration formula for a hemisphere
  • C) Strain projections on each microplane (kinematical constraint)