Transient behavior and stability analyses of halite shear zones with an empirical rate-and-state friction to flow law

Generation of large earthquakes involves with behaviors of whole plate boundaries or faults from brittle to ductile regimes. This paper reports stability analyses of halite shear zones using a recently developed rate-and-state friction to flow law with an emphasis on the behaviors across the brittle–ductile transition. The law smoothly connects the friction law with pressure-insensitive flow law without any additional constitutive parameter. Behavior upon a velocity step is characterized by an instantaneous change in shear resistance followed by transient behavior toward a steady-state. These transient behaviors are in opposite directions between friction and flow regimes, resulting in variable transient behaviors across the brittle–ductile transition. Linear stability analyses of a spring-slider system around steady-state solutions predict pressure and temperature conditions for unstable fault motion that are consistent with experimental results. The condition for potential instability is not equal to, but includes that for rate-weakening. A nonlinear analysis at the stable-unstable boundary has revealed that a sub-critical Hopf bifurcation takes place and thus a permanently sustained oscillation around a destabilized steady-state solution does not exist although experimental results suggest it. This issue deserves further study including the investigation of the friction law and construction of a physical model for brittle–ductile transition.