The development of delta-clasts in non-linear viscous materials: A numerical approach

Winged porphyroclasts are often used as kinematic or strain indicators in shear zones. In particular, it has been suggested that the geometry of delta-clasts in mylonites can give information about the theological behaviour of the matrix around the clast (Passchier et al., 1993). We tested this hypothesis with a numerical finite element simulation of the flow field of a viscous matrix around a relatively rigid clast. Power-law viscous flow properties of the matrix with stress-exponents of 1 (linear viscous), 3 and 5 were tested, as well as three different sets of approximately simple shear boundary conditions, which are relevant to experimental and/or natural situations, The simulations show that the flow field is primarily determined by the boundary conditions. The stress-exponent is of secondary importance. In general, the different boundary conditions produce two types of flow fields about the rigid clast: an eye-shaped flow field and a bow-tie shaped flow field. The former is produced by boundary conditions that approximate simple shear applied at an infinite distance from the rigid clast, and the latter is produced by boundary conditions which are equivalent to a shear box or ring shear apparatus. Although both the shear-box and ring-shear boundary conditions produce bow-tie flow patterns, the wing geometries which result from the flow patterns for these two cases can be significantly different. The geometry of the wings that develop on a delta-clast is a direct function of the flow field around the clast. For linear and non-linear theologies, only the ring-shear boundary conditions produce wings that show ''stair-stepping'' (i.e. wings that are parallel but not in the same plane). In natural shear zones, delta-clasts both with and without stair-stepping are observed. In comparing geologic observations with experimental or numerical modelling, it is essential to understand which boundary conditions are appropriate.