SUMMARY Based on experimental observations and theoretical analyses, the author introduces an ideal microcrack model in which an array of cracks with the same shape and initial size is distributed evenly in rocks. The mechanism of creep dilatancy for rocks is analysed theoretically. Initiation, propagation and linkage of pre‐existing microcracks during creep are well described. Also, the relationship between the velocity of microcrack growth and the duration of the creep process is derived numerically. The relationship agrees well with the character of typical experimental creep curves, and includes three stages of creep. Then the damage constitutive equations and damage evolution equations, which describe the dilatant behaviour of rocks, are presented. Because the dilatant estimated value is taken as the damage variable, the relationship between the microscopic model and the macroscopic constitutive equations is established. In this way the mechanical behaviour of rocks can be predicted.

SUMMARY We present a perturbation method to investigate the steady‐state propagation of a dyke from an over pressured source (e.g. a magma chamber) into a semi‐infinite elastic solid with graded mass density. The non‐linear dyke propagation/magma transport problem is reduced to a series of linear problems using a perturbation technique with the small non‐dimensional parameter ɛ= 12ηV/(H2Δρ0g), where η is the magma viscosity, V the propagation velocity, Δρ0 the difference between the densities of the host rock and magma at the dyke tail, g the gravitational acceleration and H a parameter on the order of maximum dyke thickness. In general, the perturbation method is applicable to mafic dyke propagation at a relatively low propagation velocity wherein ɛ remains small (e.g. less than 0.1). We describe an integral equation approach to obtain the stress intensity factor at the dyke tip and the separation displacement of the two dyke surfaces. Numerical examples are presented to examine the effects of various physical parameters, for example, buoyancy, density gradation, propagation velocity and overpressure on the dyke propagation behaviour. It is found that dyke propagation could reach a steady‐state in some specific ranges of growth for a given density gradient of the host rock. The propagation tends to decelerate when the dyke tip approaches the level of neutral buoyancy.

[1] The purpose of this paper is to explore a viscoelastic energy dissipation theory for subcritical dike growth from a magma chamber. The theoretical relationship between the dike growth velocity and dike length is established using the viscoelastic subcritical crack growth theory proposed by the first author and the solutions of stress intensity factor at the crack tip derived by a perturbation method. Effects of magma chamber over-pressure, buoyancy and viscoelastic properties of the host rock on the subcritical growth rate are included in the model. The numerical results indicate that the viscous energy dissipation of the host rock could allow a short dike to slowly grow on the order of 10 À7 -10 À5 m/s under modest over-pressure and to accelerate when the stress intensity factor increases close to the fracture toughness, followed by the unstable dike propagation. The proposed theory provides a reasonable understanding of dike initiation process from a magma chamber.Citation: Chen, Z., and Z.-H. Jin (2006), Magma-driven subcritical crack growth and implications for dike initiation from a magma chamber, Geophys.