Reactivation tendency analysis: A theory for predicting the temporal evolution of preexisting weakness under uniform stress state

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Understanding the mechanical controls on reactivation of preexisting weakness is a fundamental problem in tectonic studies. In this study, we develop a theoretical framework for evaluating the likelihood of seismicity on active faults and the sequence of reactivation of multiple sets of preexisting weakness. Our analysis overcomes the restrictions of the early work that assumes uniform coefficient of friction across all preexisting planes with negligible cohesive strength and vertical or horizontal orientations of principal stresses. Using a coordinate-system transformation, we developed a new graphical technique that can express the reactivation problem in the Mohr space with the principal stresses oriented neither vertically nor horizontally. We verified the predicted sequence of reactivation on preexisting weakness and initiation of new fractures, according to the Byerlee law and the Coulomb fracture criterion, by conducting a simple sandbox experiment. Our proposed reactivation-tendency analysis can be expanded to evaluate the likelihood of seismicity on a single fault with curvi-planar geometry (e.g., listric normal faults, ramp-flat thrusts, and strike-slip faults with restraining- and releasing-bend geometry). Our analysis also provides a new insight into the mechanical cause of temporal evolution of pre-existing weakness in geologic records. Finally, our work implies that the sequence of faulting reactivated from preexisting weakness provides critical information on the mechanical properties of the deforming lithosphere.