[S-CG45] Science of slow-to-fast earthquakes

[SCG45-38] Tertiary creep behavior and Voight model for failure prediction expected from various rate-and-state friction laws

*Hiroyuki Noda¹, Chengrui Chang² (1.Kyoto University, Disaster Prevention Research Institute, 2.The University of Tokyo, Graduate School of Agricultural and Life Sciences)

Keywords:Rate- and state-dependent friction, Creep test, Failure-time forecast, Landslides

Forecasting the acceleration of slow slip to the point of catastrophic failure is crucial in disaster mitigation of earthquake and landslide. In observation of landslides, the process follows the Voight power-law model (Fukuzono, 1985; Voight, 1988) with the power exponent α, which is typically close to 2 but can be significantly smaller (e.g., Segalini et al., 2018; Intrieri et al., 2019; Bozzano et al., 2014). Understanding the underlying mechanisms may improve landslide warnings and leads to examination of applicability to earthquake phenomena. Helmstetter et al. (2004) applied a rate- and state-dependent friction (RSF) law in the form of the aging law to the creep behavior of an underlying shear zone of landslides subjected to a constant loading condition and showed an α value of 2. The aging law is one of the conventional forms of RSF law, and we extended the analysis to other representative laws: the slip law, Perrin-Rice-Zheng (PRZ) law, composite law, and Nagata’s law. We showed that the acceleration was expressed in terms of the slip rate using the state-evolution equation. As the slip rate increases, α decays to 2 more rapidly with the aging and Nagata’s laws than the slip and the composite laws, regardless of the frictional parameters. Using the PRZ law, the asymptotic value of α is between 2 and 3 and depends on frictional parameters.
In typical RSF laws, the logarithm of the slip rate is proportional to the level of applied shear stress f minus frictional strength Θ. The logarithmic direct effect and a rate-independent linear increase in f-Θ as a function of slip, which is a characteristic of aging and Nagata’s laws (Nakatani, 2001; Bhattacharya and Rubin, 2014) under constant stress conditions, leads to α=2. On the other hand , a purely time-dependent increase in f-Θ would lead to α=1. If these two effects coexist, α increases from 1 to 2 with acceleration. In order to obtain α<1, the logarithmic form of the direct effect have to be modified, or the RSF parameters may have to evolve with slip caused by structural evolution of the shear zone. In laboratory experiments of investigation of RSF law in the community of fault mechanics, creep tests have been rarely conducted partly because of scarcity of observed counterpart natural phenomena. They could provide new insights on the form of the state-evolution equation and deserve future study.