Incorporating damage mechanics into explosion simulation models

The source region of an underground explosion is commonly modeled as a nested series of shells. In the innermost open-quotes hydrodynamic regimeclose quotes pressures and temperatures are sufficiently high that the rock deforms as a fluid and may be described using a PVT equation of state. Just beyond the hydrodynamic regime, is the open-quotes non-linear regimeclose quotes in which the rock has shear strength but the deformation is nonlinear. This regime extends out to the open-quotes elastic radiusclose quotes beyond which the deformation is linear. In this paper, we develop a model for the non-linear regime in crystalline source rock where the nonlinearity is mostly due to fractures. We divide the non-linear regime into a open-quotes damage regimeclose quotes in which the stresses are sufficiently high to nucleate new fractures from preexisting ones and a open-quotes crack-slidingclose quotes regime where motion on preexisting cracks produces amplitude dependent attenuation and other non-linear effects, but no new cracks are nucleated. The boundary between these two regimes is called the open-quotes damage radius.close quotes The micromechanical damage mechanics recently developed by Ashby and Sammis (1990) is used to write an analytic expression for the damage radius in terms of the initial fracture spectrum of the source rock, and to develop an algorithm which may be used to incorporate damage mechanics into computer source models for the damage regime. Effects of water saturation and loading rate are also discussed