Nonlinear Elasticity, Distributed Damage, and Fracture of Rocks
Monday, March 18, 2002 - 11:30am - 12:00pm
Vladimir Lyakhovsky (Geological Survey of Israel)
I present a damage rheology model, which holds a potential for providing a framework for understanding processes of rock deformation such as fracture nucleation, development of process zone at rupture tip, and branching from the main rupture plane. The damage mechanics approach is based on the assumption that the density of micro cracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the linear size of the volume considered. For any system with a sufficiently large number of cracks, one can define a representative volume in which the crack density is uniform and introduce an intensive damage variable for this volume. The present model treats two aspects of the physics of damage: (1) A mechanical aspect - the sensitivity of the macroscopic elastic moduli to distributed cracks and to the sense of loading, and (2) a kinetic aspect - the evolution of damage (degradation-recovery of elasticity) in response to loading. Several numerical results reproduce the main features of rock behavior including damage self- organization and localization into a narrow zones and kink angle of the fracture front breakdown under mixed mode loading. The damage model includes post-failure behavior (healing) that allows simulating a stick-slip motion along a narrow zone with localized damage. Being averaged in space and time this stick-slip motion fits experimentally observed relations between slip velocity, normal and shear stress components (RS friction).