Abstract
We investigated the constitutive parameters in the rate- and state-dependent friction (RSF) law by conducting numerical simulations, using the friction data from large-scale biaxial rock friction experiments for Indian metagabbro. The sliding surface area was 1.5 m long and 0.5 m wide, slid for 400 s under a normal stress of 1.33 MPa at a loading velocity of either 0.1 or 1.0 mm/s. During the experiments, many stick–slips were observed and those features were as follows. (1) The friction drop and recurrence time of the stick–slip events increased with cumulative slip displacement in an experiment before which the gouges on the surface were removed, but they became almost constant throughout an experiment conducted after several experiments without gouge removal. (2) The friction drop was larger and the recurrence time was shorter in the experiments with faster loading velocity. We applied a one-degree-of-freedom spring-slider model with mass to estimate the RSF parameters by fitting the stick–slip intervals and slip-weakening curves measured based on spring force and acceleration of the specimens. We developed an efficient algorithm for the numerical time integration, and we conducted forward modeling for evolution parameters (b) and the state-evolution distances (L_{text{c}}), keeping the direct effect parameter (a) constant. We then identified the confident range of b and L_{text{c}} values. Comparison between the results of the experiments and our simulations suggests that both b and L_{text{c}} increase as the cumulative slip displacement increases, and b increases and L_{text{c}} decreases as the loading velocity increases. Conventional RSF laws could not explain the large-scale friction data, and more complex state evolution laws are needed.
Highlights
An earthquake cycle involves a very wide range of slip velocities, from orders of magnitude slower than a plate motion to as fast as a slip velocity at a rupture front during an earthquake
Comparison between the results of the experiments and our simulations suggests that both b and Lc increase as the cumulative slip displacement increases, and b increases and Lc decreases as the loading velocity increases
A rotary shear apparatus enables the investigation of rock friction properties with a wide range of slip velocities and large displacement as described above, the apparatus would not be suitable to investigate stick–slip behavior, which could be considered analogous to a sequence of earthquakes on natural faults (Brace and Byerlee 1966)
Summary
An earthquake cycle involves a very wide range of slip velocities, from orders of magnitude slower than a plate motion to as fast as a slip velocity at a rupture front during an earthquake. The rate- and state-dependent friction (RSF) laws have been widely used to simulate earthquake sequences (e.g., Hori et al 2004; Lapusta and Liu 2009; Noda and Lapusta 2013) These laws were originally proposed to model laboratory experimental data (Dieterich 1978, 1979; Ruina 1983), and the RSF parameters have been investigated using biaxial loading apparatuses at the low slip velocity from *0.01 lm/s to *1 cm/s, in which the cumulative displacement was of the order of cm at most (e.g., Mair and Marone 1999). A rotary shear apparatus enables the investigation of rock friction properties with a wide range of slip velocities and large displacement as described above, the apparatus would not be suitable to investigate stick–slip behavior, which could be considered analogous to a sequence of earthquakes on natural faults (Brace and Byerlee 1966). Since the evolution of the internal structure causes evolution in the parameters in RSF (e.g., Beeler et al 1996), it is important to study them in experiments with stick–slips to better understand behavior of seismogenic faults
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