Rotation behaviour of rigid inclusions in multiple association: insights from experimental and theoretical models

Abstract

Many rocks are representative of inclusion-matrix systems where rigid inclusions float on a ductile matrix. The geological analogues of such inclusion-matrix systems are theoretically modelled with the help of Jeffery's (1922) theory. In recent years, there have been a number of reinvestigations on the rotational motion of rigid inclusions to account for some geological observations that are not yet predicted in models based on Jeffery's theory. Adding to this effort, this paper investigates the effects of (1) inclusion concentration and (2) the degree of coherence at the inclusion-matrix interface on the rotation behaviour of rigid inclusions in a multiple inclusion system during simple shear deformation. Shear-box experiments were run on models containing multiple, identical elliptic cylinders of wax mimicking rigid inclusion embedded within putty representing ductile matrix. Two sets of experiments were performed, with and without lubrication at the inclusion-matrix interfaces. Each model had an isolated inclusion to reveal the variation of rotations of single and multiple inclusions. Increase in inclusion concentration (a) results in contrasting rotation behaviour of isolated and multiple inclusions initially oriented parallel to the shear direction. When the interfaces were not lubricated, inclusions in multiple association rotated antithetically, whereas the isolated one almost remained stationary. In models wherein the inclusion-matrix interfaces were lubricated with liquid soap, both isolated and multiple inclusions rotated antithetically, but the isolated inclusion rotated at a lower rate. With increasing inclusion concentration, the difference in the rates of antithetic rotation between isolated and multiple inclusions tended to be larger in both lubricated and non-lubricated conditions. The sense of rotation of isolated as well as multiple inclusions, initially oriented perpendicular to the shear direction, was always synthetic irrespective of the nature of the interface (lubricated or non-lubricated); however, the instantaneous rotation rates of inclusions in multiple association were higher than that of the isolated inclusions disposed in the same orientation. Rotation of inclusion in an inclusion-matrix system is basically induced by the traction exerted by the flowing matrix on the surface of the inclusion during deformation. Employing a hydrodynamic model it is shown that mutual mechanical interaction among inclusions, which is a function of inclusion concentration (a), modifies the stresses at the inclusion-matrix interface to a large extent. Moment calculations reveal that inclusions oriented parallel to the shear direction experience an antithetic moment in response to the normal stress components, the magnitude of which increases with increasing inclusion concentration. This implies that rotation of shear-parallel inclusions in antithetic sense is favoured by higher inclusion concentration. On the other hand, inclusions oriented perpendicular to shear direction experience a moment that induces synthetic rotation. The magnitude of the synthetic moment is larger for larger inclusion concentration leading to increase in the rate of synthetic rotation. Using the theoretical model, the moments are calculated as a function of the aspect ratio of inclusions and the inferences based on this moment calculation are complemented with experimental findings.