Tertiary creep behavior for various rate- and state-dependent friction laws
Hiroyuki Noda, Chengrui Chang
Abstract
Forecasting the acceleration of slow landslides to the point of catastrophic failure is crucial. It follows the Voight power-law model with the power exponent α, which is typically close to 2 but can be significantly smaller. Understanding the underlying mechanisms may improve landslide warnings. A previous study 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, 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 law. We showed that the acceleration is expressed in terms of the slip rate using the state-evolution equation. As the slip rate increases, α decays to 2, regardless of the frictional parameters, following a power law for the aging and Nagata laws and logarithmically for the slip and the composite laws. For 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 friction coefficient or normalized shear stress f minus frictional strength Θ. The logarithmic direct effect and a linear increase with slip in f−Θ independent of the slip rate, which is a characteristic of aging and Nagata laws under constant stress conditions, leads to α=2. By contrast, 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 laboratory experiments of investigation of RSF law, constant-load creep tests in the tertiary-creep stage have been rarely conducted, but they could provide new insights on the form of the state-evolution equation and deserve future study.