Details

Autor(en) / Beteiligte

• Pranger, Casper
• Sanan, Patrick
• May, Dave A.
• Le Pourhiet, Laetitia
• Gabriel, Alice‐Agnes

Titel

Rate and State Friction as a Spatially Regularized Transient Viscous Flow Law

Ist Teil von

• Journal of geophysical research. Solid earth, 2022-06, Vol.127 (6), p.n/a

Ort / Verlag

Washington: Blackwell Publishing Ltd

Erscheinungsjahr

2022

Link zum Volltext

Quelle

Wiley Blackwell Single Titles

Beschreibungen/Notizen

• The theory of rate and state friction unifies field, laboratory, and theoretical analysis of the evolution of slip on natural faults. While the observational study of earthquakes and aseismic fault slip is hampered by its strong multi‐scale character in space and time, numerical simulations are well‐positioned to link the laboratory study of grain‐scale processes to the scale at which rock masses move. However, challenges remain in accurately representing the complex and permanently evolving sub‐surface fault networks that exist in nature. Additionally, the common representation of faults as interfaces may miss important physical aspects governing volumetric fault system behavior. In response, we propose a transient viscous rheology that produces shear bands that closely mimic the rate‐ and state‐dependent sliding behavior of equivalent fault interfaces. Critically, we show that the expected tendency of the continuum rheology for runaway localization and mesh dependence can be halted by including an artificial diffusion‐type regularization of anelastic strain rate in the softening law. We demonstrate analytically and numerically using a simplified fault transect that important aspects of the frictional behavior are not significantly affected by the introduced regularization. Any discrepancies with respect to the interfacial description of fault behavior are critically evaluated using one dimensional numerical velocity stepping and spring‐slider experiments. Since no new physical parameters are introduced, our model may be straightforwardly used to extend the existing modeling techniques. The model predicts the emergence of complex patterns of shear localization and delocalization that may inform the interpretation of complex damage distributions observed around faults in nature. Plain Language Summary How, where, and when earthquakes nucleate is one of the great questions in science and society that, despite steady progress, has hardly been answered to any practical degree. Based on field observations, laboratory experiments, and theoretical work it is believed that a cocktail of escalating mechanical, chemical, and thermal grain‐scale processes cause the sudden and rapid onset of earthquakes. The net effect of these processes are characterized by an immediate strengthening and a gradual weakening response to deformation and are unified in simplified form in the theory of "rate and state friction.” This theory is commonly used in computer simulations of earthquake sequences. We point out that rate and state friction, unlike some physical theories of earthquake rupture, does not incorporate a diffusion process such as for example heat conduction. We show the introduction of an artificial diffusion process can prevent the mathematical reduction of a fault zone to a two‐dimensional interface while retaining the properties of the original friction law. This in turn enables simulation techniques that rely on an interface‐free description of the earth and promise to provide new insights into the spontaneous organization of seismic and aseismic phenomena in developing fault zones. Key Points We reformulate the empirical rate and state friction law as a bulk viscous flow law in terms of anelastic shear strain rate We show how mesh independence is achieved by including a gradient‐like nonlocal anelastic shear strain rate equivalent We show analytically and numerically that the proposed continuum model closely reproduces existing results of rate and state friction