# [SSS15-08] A fault constitutive law in a brittle-plastic transitional regime accounting for geometry of deformation in a shear zone

Keywords:Fault constitutive law, Brittle plastic transition

A fault constitutive law in a brittle-plastic transitional regime is of great importance in considering generation processes of large earthquakes that are nucleated around the deeper limit of a seismogenic layer [Sibson, 1982]. There are several published models such as a two-mechanisms model [Reinen et al., 1992], a phenomenological connection between brittle (frictional) and plastic (flow) laws [e.g., Shimamoto and Noda, 2014], and microphysics-based homogenized granular models [e.g., CNS model by Chen and Spiers. 2016].

CNS model is one of the most involved one among them, and can explain many characteristics in the fault property such as switching between rate-strengthening and rate-weakening at the onset of dilatant deformation and dependency of so-called

In the two-mechanism model, two deformation mechanisms share the stress and contribute to the net deformation. The previous model by Reinen et al. [1992] treats the deformation as a vector (relative motion across the fault), and results in a discontinuous transition between rate-strengthening and rate-weakening behavior with a metastable stronger steady-state strength than frictional resistance. In experiments, the transition is usually accompanied by smaller shear strength than both frictional and flow resistances, and thus the model by Reinen et al. [1992] is not realistic as pointed out by Shimamoto and Noda [2014].

Internal deformation of the shear zone has four displacement gradient components and three strain components (e.g., fault-normal extension, fault parallel extension, and simple-shear strain) if the problem is idealized as a 2-D in-plane problem. In the present model, frictional and flow deformation mechanisms share a stress tensor and contribute to the net deformation in the tensorial form. A rate- and state-dependent logarithmic law is assumed the brittle deformation with a slip plane which maximizes the shear traction per the normal compressional traction on it. A power-law is assumed for the flow law in which the flow strain rate is parallel to the deviatoric stress tensor. In addition, a geometrical constraint is given by the condition that the length and thickness of the shear zone does not evolve at a steady state. These set of equations can be solved numerically to obtain, for example, shear traction and fault-parallel normal traction on the fault as a function of applied fault-normal traction, slip rate, and temperature.

The present model yields a continuous transition consistently with experimental data and the empirical connection by Shimamoto and Noda [2014]. Localized shear planes of brittle deformation are expected to develop in a shallow angle from the shear zone. The angle is about zero (Y-plane) for almost purely frictional case and increase towards the transition up to about 15°. This range is consistent with previously reported internal structure of experimental shear zones [Hiraga and Shimamoto, 1987], although rotation of those planes is not considered in the present model.

CNS model is one of the most involved one among them, and can explain many characteristics in the fault property such as switching between rate-strengthening and rate-weakening at the onset of dilatant deformation and dependency of so-called

*a*-,*b*-, and*d*-values on slip rate [e.g., Chen et al., 2017]. However, the assumed granular structure of the shear zone may not be a good approximation to ductile shear zones, and it is difficult to interpret typically observed composite surface structures as model parameters. In addition, existence of fault-parallel normal stress is ignored in this model. In the present study, the two-mechanisms model is extended to tensorial deformation expression and demonstrate the smooth connection between the frictional and flow laws in the transitional regime._{c}In the two-mechanism model, two deformation mechanisms share the stress and contribute to the net deformation. The previous model by Reinen et al. [1992] treats the deformation as a vector (relative motion across the fault), and results in a discontinuous transition between rate-strengthening and rate-weakening behavior with a metastable stronger steady-state strength than frictional resistance. In experiments, the transition is usually accompanied by smaller shear strength than both frictional and flow resistances, and thus the model by Reinen et al. [1992] is not realistic as pointed out by Shimamoto and Noda [2014].

Internal deformation of the shear zone has four displacement gradient components and three strain components (e.g., fault-normal extension, fault parallel extension, and simple-shear strain) if the problem is idealized as a 2-D in-plane problem. In the present model, frictional and flow deformation mechanisms share a stress tensor and contribute to the net deformation in the tensorial form. A rate- and state-dependent logarithmic law is assumed the brittle deformation with a slip plane which maximizes the shear traction per the normal compressional traction on it. A power-law is assumed for the flow law in which the flow strain rate is parallel to the deviatoric stress tensor. In addition, a geometrical constraint is given by the condition that the length and thickness of the shear zone does not evolve at a steady state. These set of equations can be solved numerically to obtain, for example, shear traction and fault-parallel normal traction on the fault as a function of applied fault-normal traction, slip rate, and temperature.

The present model yields a continuous transition consistently with experimental data and the empirical connection by Shimamoto and Noda [2014]. Localized shear planes of brittle deformation are expected to develop in a shallow angle from the shear zone. The angle is about zero (Y-plane) for almost purely frictional case and increase towards the transition up to about 15°. This range is consistent with previously reported internal structure of experimental shear zones [Hiraga and Shimamoto, 1987], although rotation of those planes is not considered in the present model.