Simulation of the progressive failure of brittle rock

Sammanfattning: The anisotropic response of a brittle rock due to the formation of cracks under general applied loads has been taken as a continuous phenomenon on a suitable macroscopic scale. The response is described by a continuum field variable called the "damage vector". The damage vector has been taken as an internal state variable and a constitutive relation has been derived using the theory of Internal Variable and the Irrevesible Thermodynamics of Continua. The damage growth occurs in the direction in which a generalised strain on the damage surface attains it's maximum value. In the calculation of the contribution of damage (crack) growth to the overall effective elastic compliance, the effect of crack closure due to compressive stresses is considered. The plane strain case of the constitutive model (called the "damage material model") has been studied. The results show that the peakload in tension as well as in compression occurs at a small value of the damage. Dilatant behaviour (inelastic increase in volume of a specimen) observed in laboratory experiments may be described by the change in effective Poisson's ratio due to the presence of damage (cracks) under compressive loading. The deformation of brittle rocks in the post-peak strain softening range usually localizes to either a single or a small number of discrete localizaton bands. The condition that the second order work becomes zero or negative has been used as the condition for localization in the finite element computer code NFEMP. The material model has been implemented into this finite element code. A finite element size control technique is identified for the case of tensile loading, and this is implemented into the NFEMP code. A number of problems, for example, failure of a specimen loaded under tension, simulation of shear band formation under compressive loading and failure of a rock mass around a tunnel have been studied. The results obtained also illustrates the so-called "snap back" phenomenon in the structure.