Self-organisation and fracture connectivity in rapidly heated continental crust

Volume expansion (∼1–5% volume strain with ΔVmelting positive) and fluid-absent partial melting, in which ΔVmelting is positive, of continental crust by intruding basaltic magma is a strongly irreversible process involving the dissipation of both thermal energy and matter (partial melt). Using a simple random graph model we show by analogy how isolated fractures that form during rapid thermal perturbation in the source region can combine to form a single, interconnected structure with high permeability. Once connected, the fracture network may be thought of as a single structure or pattern that will remain stable so long as a strong temperature gradient is maintained in the source region. Estimates of fracture permeability that take into account changes in connectivity and fracture spacing range from approximately 10−10 to 10−5 m2, many orders of magnitude greater than values considered typical during large-scale crustal deformation and prograde regional metamorphism. The ability of the isotropic fracture network to develop a top–bottom directionality is crucial for buoyancy-driven melt transport. A physical model based on non-linear evolution rules during thermal expansion is given that predicts the emergence of directionality (vertical fracture alignment) on a time scale of the order of 105 y. The necessary ingredients are a deviatoric strain path, a heterogeneous medium and a stiffness that evolves as a function of the local strain.