An Anisotropic Damage Model For Rock

Abstract

An anisotropic damage model is proposed for the constitutive description of microcracking processes

in brittle rock under a general loading path. Experimental data and micromechanical

models are reviewed to quantify the effect of microcracking on the material stiffness and the

mechanisms of microcrack formation in brittle rocks under compression are discussed. The

sliding crack concept is adopted as the micromechanical basis of the anisotropic damage model.

Undamaged material is represented with a linear elastic constitutive equation. Damage initiation

is defined by a Coulomb friction law, which excludes damage at low deviatoric stress levels.

The formulation of the directional damage extends the arguments of continuum damage models

for tension cracking to general, tension and compression, stress states. This is achieved by the

definition of damage in a subdomain of the total strain and the characterisation of the directional

microcra.cking by a fourth order tensor internal variable, the damaged secant stiffness of

the 'crack' strain subdomain. Induced anisotropy results from the reduction of components of

the initial stiffness tensor in the direction of the positive principal 'crack' strains.

Evolution of the damage magnitude is determined by the principle of maximum damage dissipation

in terms of the undamaged energy norm of the positive part of the 'crack' strain tensor.

Versatile evolution functions, based on the Weibull probability density function, are proposed

for compression and extension damage modes. Unloading and reloading criteria are developed

which are consistent with the sliding crack concept and introduce hysteretic behaviour. A numerical

solution scheme is presented and the model is implemented in a nonlinear finite element

program.

The material constants are determined in a straightforward procedure from standard rock mechanics

test results. The physical interpretation of the material parameters is highlighted in

a sensitivity study. Backpredictions of dilatancy, induced anisotropy and ultimate strengths

of Witwatersrand Quartzite subjected to triaxial stress path tests show good agreement with

experimental data.

The finite element analysis of mining simulation experiments in small Quartzite blocks verified

the applicability of the model for a complex load path involving the sequential removal of

elements. The extent and direction of damage, the predicted strains and the final excavated

span are in good agreement with observations.

The model was applied to Indiana Limestone in diametral compression and three-point tests in a

compression/tension stress field. A quasi-linear constitutive rel~tion was required to account for

stiffening of the highly porous material in compression. Predicted load - deformation response

and damage energy release rates which compare well with experimental data.

A two-dimensional analysis of the Dinorwig power station cavern demonstrates the potential of

the anisotropic damage model to predict the magnitude and direction of damage and the associated

deformation in a full scale engineering problem involving different rock types, geological

features and an excavation and construction sequence.