KINEMATIC VORTICITY, POLAR MOHR CIRCLE AND THIER APPLICATION IN QUANTITATIVE ANALYSIS OF GENERAL SHEAR ZONES

Most of shear zones in nature are results of co-actions of simple and pure shears and called general shear zones.A general shear zone can be narrowed or broadened. The relationship between simple and pure shears, and the change of shear zones in thickness can be analysed quantitatively by the method of kinematic vorticity (W_K) and polar Mohr circle. The kinematic vorticity is a measure of the non-coaxiality in progressive deformation history and, therefore, is the ratio of the pure shear to simple shear of a general shear zone.
W_K=cos (v), where v is the angle between the two eigenvectors in a shear zone. For a pure shear, v=90°, W_K=0;for a simple shear, v=0°, W_K=1;and for a general shear, 0° < v < 90°, 0 < W_K < 1. A polar Mohr circle, which can be constructed with some more practical methods presented by this paper f provides a convenient and feasible method for measuring v.
Once a polar Mohr circle is constructed, the angle (v), kinematic vorticity (W_K), ratio of the strain-rates (ε/γ)and the change of thickness of a shear zone can be obtained.