A friction to flow constitutive law and its application to a 2‐D modeling of earthquakes

Abstract

Establishment of a constitutive law from friction to high-temperature plastic flow has long been a challenging task for solving problems such as modeling earthquakes and plate interactions. Here we propose an empirical constitutive law that describes this transitional behavior using only friction and flow parameters, with good agreements with experimental data on halite shear zones. The law predicts steady state and transient behaviors, including the dependence of the shear resistance of fault on slip rate, effective normal stress, and temperature. It also predicts a change in velocity weakening to velocity strengthening with increasing temperature, similar to the changes recognized for quartz and granite gouge under hydrothermal conditions. A slight deviation from the steady state friction law due to the involvement of plastic deformation can cause a large change in the velocity dependence. We solved seismic cycles of a fault across the lithosphere with the law using a 2-D spectral boundary integral equation method, revealing dynamic rupture extending into the aseismic zone and rich evolution of interseismic creep including slow slip prior to earthquakes. Seismic slip followed by creep is consistent with natural pseudotachylytes overprinted with mylonitic deformation. Overall fault behaviors during earthquake cycles are insensitive to transient flow parameters. The friction-to-flow law merges "Christmas tree" strength profiles of the lithosphere and rate dependency fault models used for earthquake modeling on a unified basis. Strength profiles were drawn assuming a strain rate for the flow regime, but we emphasize that stress distribution evolves reflecting the fault behavior. A fault zone model was updated based on the earthquake modeling.

Frictional behavior of talc‐calcite mixtures

“…Moreover, increasing normal stress (from 20 to 50 MPa) and increasing talc content (from 5 to 20%), we observe a switch toward negative values of b , resulting in a transition from a peak evolution of friction to a monotonic evolution of friction upon a velocity step. This behavior can be interpreted as the result of the interplay between brittle and plastic behaviors, possibly framed in a transition from a rate and state friction law, that can explain the peak evolution of pure calcite, to a flow law, that can explain the monotonic evolution of 20% talc gouge at high stress, as suggested from theoretical model by Noda and Shimamoto [] and Shimamoto and Noda []. However, further investigation is required to discriminate the predominant deformation mechanism.…”

Mafic High‐Pressure Rocks Are Preferentially Exhumed From Warm Subduction Settings

“…Figure 7b shows the difference in average of temperature between these new warmer models and the rock record as a function of f arbi . This functional description for shear heating along the fault is a simplification of that obtained by more advanced models that show a more gradual transition between the two mechanisms (Gao & Wang, 2014;Shimamoto & Noda, 2014), but the simpler model is consistent with that used in Wada and Wang (2009) and suffices for the purposes of this paper. Figure 8 shows the PT conditions for 200 random samples pulled from the model OC and are compared to SPD15p.…”

The Brittle‐Ductile Transition Predicted by a Physics‐Based Friction Law

“…The prediction of the BDT of this two‐mechanism model corresponds reasonably well with the depth distribution of earthquakes on continental faults (Sibson, ) as well as the depth of the transition from cataclasite to mylonite associated with the onset of quartz plasticity in fault zones cutting quartzo‐feldspathic rock (Stipp et al, ; Voll, ; S. White et al, ). A smoothed version was developed by Shimamoto and Noda () and was used to explain halite data.…”