Mathematics – Logic
Scientific paper
Jan 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999e%26psl.165..177m&link_type=abstract
Earth and Planetary Science Letters, Volume 165, Issue 2, p. 177-185.
Mathematics
Logic
8
Scientific paper
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 cd and the square of the strain. For geological values, a dimensionless parameter cdη/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.
Agnon Amotz
Lister John R.
Lyakhovsky Vladimir
Mériaux Catherine
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