Time occurrence of earthquake instabilities in rate– and state–dependent friction models

Since the latter half of last century many studies and laboratory experiments have focused on the understanding of the evolution of frictional strength during sliding events on active faults. Such events may occur through aseismic fault creep, high-velocity slip and, in some cases, as a combination of both.
According to the concept that earthquakes are frictional instabilities, their time occurrence may show a periodical pattern (the seismic cycle) whose behavior can be referred to the stick-slip dynamic. The dynamic evolution of a fault is often modeled considering its formal analogy with a physical system known as the spring-slider model (namely, a damped harmonic oscillator). Many experimental studies have been conducted using the spring-slider model, most of them simulating the interaction between slip surfaces with the surrounding elastic medium with a single-degree-of-freedom system. Despite its obvious limitations, such a model has provided important insights on dynamics of stick-slip cycle [Gu et al., 1984; Carlson et al., 1994], nucleation of earthquakes and triggered earthquake phenomena [e.g. Belardinelli et al., 2003].
On the basis of several experimental results on rock friction, Dieterich (1979) and Ruina (1983) formulated rate- and state-dependent friction laws, in which the frictional resistance is expressed through the evolution of the sliding rate and its history. Afterwards, Chester and Higgs (1992) figured out that also the temperature variation, produced by frictional heating, can affect the duration of the seismic cycle and the evolution of the frictional strength as well and consequently they incorporate such a thermal effect, improving the previous Ruina’s constitutive law.
The present study is aimed to:

1. investigate the spring-slider physical response depending on the adopted constitutive law;

2. show the influence that the constitutive laws can exert on the time occurrence of a seismic instability and on the seismic cycle duration;

3. compare the constitutive laws in order to show their different features in simulating the evolution of slip velocity, stress drop and seismic cycle.