Kinematics and dynamics of fault reactivation: The Cosserat approach

In the theory of Cosserat continuum, the faulting-related deformation of rocks is described using translational and rotational degrees of freedom, producing definitions for a symmetric macrostrain tensor and a skew-symmetric relative microrotation tensor. The macrostrain tensor describes the large-scale deformation of the region, whilst the relative microrotation tensor describes the difference between the large-scale regional rotation and local systematic microrotations of blocks between faults. Faults are activated when the resolved shear stress in the direction of movement exceeds frictional resistance for sliding, according to Amontonsʹs Law of Friction. The direction of slip along the faults depends on the Cosserat strain tensor, which is defined as the sum of the macrostrain tensor and the relative microrotation tensor. We develop a constitutive relation for the faulting-related strain of rocks (cataclastic flow) based on the J-2 plasticity model for the Cosserat continuum, from which we derive the generally asymmetric stress tensor. We also develop the Cosserat stress–strain inverse method for fault-slip data analysis. We show that the geometry of fault systems is controlled by both the Cosserat strain tensor and the stress tensor, and present a field example of a fault system that conforms to the predictions of the Cosserat theory.