An anisotropic damage model for rock
Doctoral Thesis
1994
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University of Cape Town
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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 microcracking 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.
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Bibliography: pages 146-155.
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Reference:
Sellers, E. 1994. An anisotropic damage model for rock. University of Cape Town.