2D model for development of steady-state and oblique foliations in simple shear and more general deformations

Despite the common occurrence of steady state and oblique foliations in natural shear zones, their quantitative interpretation is somewhat lacking. We present a mathematical model for the development of steady state and oblique foliations. Foliation forming processes are usually due to deformation which tends to elongate grains that are counterbalanced by foliation destroying processes tending to make grains more equant. Foliation-destroying processes are assumed (1) to reduce the elongation of grains, (2) no longer operate when grain shapes are equant, (3) are independent of grain orientation and (4) tend to become more effective the more elongate the grain. The resulting mathematical model is readily analysed both qualitatively and quantitatively. Equations are derived for calculation of the relative importance of foliation destroying processes (the parameter α) and also the type of deformation (β) or kinematic vorticity number (Wk) assuming a passive response by grains to deformation. If the kinematics of deformation can be con.dently assumed it is possible to estimate the relative strength of the foliation destroying processes (α) and the relative competency (μr) of the grains. Application of the model to both experimental and natural data lends qualitative support to the applicability of the model.