| The shape preferred orientation of natural populations of inclusions (or “porphyroclasts”) is
often inconsistent with predictions from established analytical theory for inclusions with
coherent boundaries (e.g., Pennacchioni et al. 2001). A totally incoherent or slipping interface
can explain observed stable back-rotated (or antithetic) orientations but not the observed
cut-off axial ratio, below which inclusions still rotate. However, this behaviour is reproduced
by a rimmed inclusion with a rim viscosity that is not infinitely weak but still weaker
than the matrix (e.g., Schmid and Podladchikov 2005; Johnson et al. 2009). In this
study, finite-element numerical modelling (FEM) is employed to investigate this
system in 2D over a very wide parameter space, from a viscosity ratio (relative to the
matrix) of the inclusion from 106 to 1, the rim from 10-6 to 1, the axial ratio from
1.00025 to 20, and the rim thickness from 5% to 20%. Theoretical consideration of a
concentric elliptical inclusion and ellipse reduces the number of scalar values to be
determined to fully characterize the system to two: one for the rate of stretch of the
inclusion and one for the rate of rotation. From these two values, the rotation and
stretching rate can be calculated for any orientation and 2D background flow field. For
effectively rigid particles, the cut-off axial ratio between rotation and stabilization is
determined by the remaining two parameters, namely the rim viscosity and the thickness,
with low rim viscosity or thick rims promoting stabilization. The shape fabric of a
population of particles in a high strain shear zone, presented as a typical Rf/Ï plot, can
be forward modelled using an initial value Ordinary Differential Equation (ODE)
approach. Because the rim does not remain elliptical to high strain, this method cannot
accurately model the behaviour of individual inclusions. However, a statistical approach,
allowing variation in rim viscosity, which is also a proxy for variation in rim thickness,
reproduces the characteristics of the shape preferred orientation of natural clast
populations remarkably well. Deformable inclusions with a very weak rim show very
similar behaviour to rigid inclusions. As inclusion viscosity is decreased and rim
viscosity is increased toward that of the matrix, there is an increasing tendency for
inclusions to elongate, which promotes back-rotation and development of (quasi-)
stable orientations, rather than the continued rotation of low axial ratio inclusions.
Power-law rheology increases the effective viscosity ratios between inclusion, rim and
matrix: the slowly deforming strong inclusion is stronger and generally nearly rigid,
whereas high strain rate in (parts of) the rim lowers the effective viscosity, tending to
stabilize the inclusion. Because of the range of controlling parameters involved, any
attempt at “vorticity analysis” based on clast shape preferred orientation or on the
“stable” orientation of individual clasts is not really practical. Measurement of
apparently stable back-rotated angles or estimation of the cut-off axial ratio below which
inclusions continuously rotate does not allow a unique determination of the vorticity of
flow.
References:
Johnson, S.E., Lenferink, H.J., Price, N.A., Marsh, J.H., Koons, P.O., West Jr, D.P.,
Beane, R., 2009. Clast-based kinematic vorticity gauges: the effects of slip at matrix/clast
interfaces. Journal of Structural Geology 31, 1322-1339.
Pennacchioni, G., Di Toro, G., Mancktelow, N.S., 2001. Strain-insensitive preferred
orientation of porphyroclasts in Mont Mary mylonites. Journal of Structural Geology 23,
1281-1298.
Schmid, D.W., Podladchikov, Y.Y., 2005. Mantled porphyroclast gauges. Journal of
Structural Geology 27, 571-585. |