A phenomenological numerical approach for investigating grain size evolution in ductiley deforming rocks

The sizes of recrystallised grains in exhumed ductile shear zones are often used to infer conditions of deformation (i.e. stress, strain rate and temperature). Here we present a simple numerical method of calculating the dynamic evolution of grain size during ductile deformation. Our phenomenological method is based on the fact that the dynamic competition between grain growth and recrystallisation will drive grains towards a steady-state size. At each time increment, grain growth and reduction contributions are calculated, with magnitudes which depend on the difference between the current grain size and a desired steady-state grain size. In our models we use a recrystallised grain size piezometer to calculate the steady-state grain size for a given stress. Our numerical routine is incorporated into the SULEC finite element package, allowing us to explore spatial and temporal changes in grain size.As a test, we compare model results to measured grain sizes in quartz layers thinned and recrystallised around rigid garnet porphyroclasts under simple shear dominated deformation in the Alpine Fault Zone of New Zealand. Numerical models are able to replicate observed grain size variations, with boundary conditions consistent with those constrained for the central Alpine Fault Zone.