5:15 PM - 7:15 PM
[SCG45-P43] Multi-Scale Rate- and Roughness-Dependent Fault Constitutive Law and Dynamic Earthquake Sequence Simulation
Keywords:Multi-scale rate- and roughness-dependent fault constitutive law, Dynamic earthquake sequence simulation, Fracture energy scaling, Expansion of conventional rate- and state-dependent friction law
What physics governs the multi-scale source property of earthquakes, such as fracture energy scaling, is an interesting, long-lasting question. The fracture energy scaling indicates that energy dissipation during the dynamic event has a power law relationship with the coseismic displacement. Although many studies adopted rate- and state-dependent friction (RSF) law to simulate earthquake sequences, and various aspects of them can be expressed by the RSF framework, such a multi-scale property is absent in the conventional RSFs. Therefore, in this study, we pursue a way to properly incorporate the multi-scale source properties of earthquakes into the RSF framework.
We utilize the previously proposed slip- and time-dependent fault constitutive (STF) law. It accounts for the evolution of fault surface roughness by abrasion (flattening) and adhesion (healing), whose characteristic slip and time, respectively, depend on the wavelength. After defining an elemental length scale to coarse-grain the surface roughness, the Fourier components of surface roughness serve as the state variable. The shear strength is expressed by the sum of contributions from the roughness of different wavelengths. Particularly, the roughness of a larger wavelength evolves more slowly but has a larger contribution than that of a smaller wavelength. This property potentially replicates the fracture energy scaling. However, STF has no rate dependency (direct effect) which is crucial to modernizing the friction law, allowing us to treat diverse fault behaviors in a single framework (e.g., dynamic rupture, slow nucleation, slow slip, etc.). Thus, we modify the STF law by adding the direct rate dependency and treat it as a form of RSF law, named rate- and roughness-dependent fault constitutive (RRF) law. The rate dependency and Fourier roughness (state) dependency express the fault shear stress in the RRF framework.
We perform the dynamic earthquake sequence simulation with RRF law and find that the fracture energy scaling is reproduced on the uniform fault. However, due to the steady-state property of RRF law, the significant afterslip is produced in the area of coseismic slip, unlike the natural earthquake sequences. Therefore, we further modify the friction law by, for example, adding saturation of the direct rate dependency or testing a multi-scale extension of conventional state-evolution law to obtain the comparable earthquake sequence while keeping the property of the fracture energy scaling. This result will add another line to replicate the multi-scale source property of earthquakes and offer insight into how we incorporate such multi-scales into the constitutive law to explain the general earthquake behavior.
We utilize the previously proposed slip- and time-dependent fault constitutive (STF) law. It accounts for the evolution of fault surface roughness by abrasion (flattening) and adhesion (healing), whose characteristic slip and time, respectively, depend on the wavelength. After defining an elemental length scale to coarse-grain the surface roughness, the Fourier components of surface roughness serve as the state variable. The shear strength is expressed by the sum of contributions from the roughness of different wavelengths. Particularly, the roughness of a larger wavelength evolves more slowly but has a larger contribution than that of a smaller wavelength. This property potentially replicates the fracture energy scaling. However, STF has no rate dependency (direct effect) which is crucial to modernizing the friction law, allowing us to treat diverse fault behaviors in a single framework (e.g., dynamic rupture, slow nucleation, slow slip, etc.). Thus, we modify the STF law by adding the direct rate dependency and treat it as a form of RSF law, named rate- and roughness-dependent fault constitutive (RRF) law. The rate dependency and Fourier roughness (state) dependency express the fault shear stress in the RRF framework.
We perform the dynamic earthquake sequence simulation with RRF law and find that the fracture energy scaling is reproduced on the uniform fault. However, due to the steady-state property of RRF law, the significant afterslip is produced in the area of coseismic slip, unlike the natural earthquake sequences. Therefore, we further modify the friction law by, for example, adding saturation of the direct rate dependency or testing a multi-scale extension of conventional state-evolution law to obtain the comparable earthquake sequence while keeping the property of the fracture energy scaling. This result will add another line to replicate the multi-scale source property of earthquakes and offer insight into how we incorporate such multi-scales into the constitutive law to explain the general earthquake behavior.