Observations of off-plane inelastic deformation around dykes motivate consideration of models of fluid-driven crack propagation in a solid which can undergo material degradation, or damage. The application to dyke propagation of a recently proposed damage rheology [Lyakhovsky et al., J. Geophys. Res. 102 (1997) 27635-27649] based on thermodynamical principles and experimental measurements is discussed. The rate of accumulation of damage in this rheology is the product of a material-dependent parameter c(d) and the square of the strain. For geological values, a dimensionless parameter c(d)η/ΔP characterizing the ratio of a damage timescale to a flow timescale is very small, where η is the magmatic viscosity and ΔP the driving pressure. As a result, significant rates of damage are confined to a small region near the dyke tip, where the strain is large. Consideration of possible singularities in near-tip solutions, shows that the rate of propagation is governed by the viscous fluid mechanics. To a good approximation, the rate has a value equal to that given by the zero-stress-intensity solutions of previous models based on linear elastic fracture mechanics. Predictions from the damage rheology both of a narrow damage zone and of the rate of propagation are in good agreement with observations.
Bibliographical noteFunding Information:
This study was made possible by generous grants from the Lady Davis Fellowship programme, the US–Israel Binational Science foundation and a TMR/Marie Curie Research Fellowship. We are very grateful to P. Delaney, R. Kerr and A. Rubin for thoughtful and constructive reviews of this manuscript and to G. Pijaudier-Cabot for useful discussions. [FA]
- Flow mechanism