[S-CG50] Rheology, fracture and friction in Earth and planetary sciences

[SCG50-03] New evolution laws for rate- and state- dependent friction

★Invited Papers

*Takahiro Hatano¹, Ryo Mizushima¹ (1.Department of Earth and Space Science, Osaka University)

Keywords:friction, rate- and state-dependent friction, limit cycle

Friction laws are fundamental to the process of earthquake generation and play an important role in various geological phenomena involving flow and large deformation: e.g., landslides and glacier flows. However, friction laws governing such large-scale flow phenomena are still not well understood. At least, it is known that the frictional force for slow slip in laboratory-scale is well described by an empirical law, which is referred to as the rate- and state-dependent friction law. This law describes the friction force as a function of slip velocity and state variable(s). Supposedly, the state variable expresses the physicochemical state of the sliding surface. However, there is no theory that can derive evolution equations for state variables. Namely, the evolution laws are just empirical. Recently, many substances have been discovered that cannot be described by simple evolution laws, and therefore evolution laws must be scrutinized on the firm physical basis.
Here we propose two novel evolution laws, both of which are based on the aging law and include the effect of aging of the static interface. By choosing parameters in an appropriate range, an evolution law can represent non-monotonic rate dependence.
A merit of these new evolution laws is stability. The aging law and the slip law are highly unstable, and their numerical solutions usually diverge without radiation damping. Contrastingly, the new evolutionary laws proposed here can realize a limit cycle (slow periodic oscillatory solutions) without introducing radiation damping. The microscopic origin of these new evolution laws is also discussed.