An Invariant Rate‐ and State‐Dependent Friction Formulation for Viscoeastoplastic Earthquake Cycle Simulations

Herrendörfer, Robert; Gerya, Taras; Dinther, Ylona van

doi:10.1029/2017jb015225

Cited by 81 publications

(126 citation statements)

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“…We present the main ingredients of the applied STM‐RSF modeling approach (Herrendörfer et al, ) in section . We introduce the model setup and parameters in section .…”

Section: Methodsmentioning

confidence: 99%

“…The invariant quantities μ l , P , τ II , and σ yield are scalars that are independent of the coordinate system and can vary both in space and time. As local stresses are increased toward the yield criterion, plastic strain rates become noticeable once the local strength of the material is overcome (Herrendörfer et al, ; Nakatani, ) and plastic deformation slowly starts to localize. In our continuum mechanics approach fault slip is represented by plastic strain occurring in a shear band or fault zone of finite width, which can occur at every marker.…”

Section: Methodsmentioning

confidence: 99%

“…We further assume that σ yield = τ II and thus, F =0. The invariant reformulation of the classical rate‐ and state‐dependent friction formalism according to Herrendörfer et al () reads as

τ_{I I} = σ_{yield} = μ_{l} false(1 - λ false) P = a P arcsinh ([], \frac{V_{p}}{2 V_{0}} \exp ((), \frac{μ_{0} + b \ln \frac{θ V_{0}}{L}}{a})) false(1 - λ false),

where a and b are laboratory‐based, empirical rate‐ and state‐dependent friction values, L is the rate‐ and state‐dependent friction characteristic slip distance, and V 0 is an arbitrary reference slip velocity (Lapusta & Barbot, ). The parameter μ 0 is the reference static friction coefficient, θ denotes the evolving state variable with the aging evolution law

\frac{normald θ}{normald t} = 1 - \frac{V_{p} θ}{L},

and V p is the plastic slip rate defined by

V_{p} = 2 {\overset{ε}{true}}_{II false(p false)}^{'} W,

where W denotes the thickness or width of the fault zone in the continuous host rock.…”

Section: Methodsmentioning

confidence: 99%

“…The parameter μ 0 is the reference static friction coefficient, θ denotes the evolving state variable with the aging evolution law

\frac{normald θ}{normald t} = 1 - \frac{V_{p} θ}{L},

and V p is the plastic slip rate defined by

V_{p} = 2 {\overset{ε}{true}}_{II false(p false)}^{'} W,

where W denotes the thickness or width of the fault zone in the continuous host rock. Following van Dinther, Gerya, Dalguer, Mai, et al () and Herrendörfer et al () we define W =Δ x , where Δ x is the numerical grid size. We use this approximation because in classical applications of plasticity the deformation localizes to within 1–2 grid cells (e.g., Lavier et al, ; van Dinther, Gerya, Dalguer, Corbi, et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…The recently developed seismo‐thermomechanical modeling framework (van Dinther, Gerya, Dalguer, Mai, et al, , van Dinther, Gerya, Dalguer, Corbi, et al, ) with adaptive time stepping and an invariant continuum‐based rate‐ and state‐dependent friction formulation (STM‐RSF) offers the full combined spectrum of the needed ingredients (Herrendörfer et al, ). This 2‐D STM‐RSF code is in line with the geodynamic modeling approach as it allows for large deformation simulations of self‐consistently evolving fault zones on geological timescales (Gerya & Yuen, ; van Dinther et al, ).…”

Section: Introductionmentioning

confidence: 99%

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Seismic and Aseismic Fault Growth Lead to Different Fault Orientations

et al. 2019

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Orientations of natural fault systems are subject to large variations. They often contradict classical Coulomb failure theory as they are misoriented relative to the regional Andersonian stress field. This is ascribed to local effects of structural or stress heterogeneities and reorientations of structures or stresses on the long term. To better understand the relation between fault orientation and regional stresses, we simulate spontaneous fault growth and its effect on the stress field. Our approach incorporates earthquake rupture dynamics, viscoelastoplastic brittle deformation and a rate‐ and state‐dependent friction formulation in a continuum mechanics framework. We investigate how strike‐slip faults orient according to local and far‐field stresses during their growth. We identify two modes of fault growth, seismic and aseismic, distinguished by different fault angles and slip velocities. Seismic fault growth causes a significant elevation of dynamic stresses and friction values ahead of the propagating fault tip. These elevated quantities result in a greater strike angle relative to the maximum principal regional stress than that of a fault segment formed aseismically. When compared to the near‐tip time‐dependent stress field the fault orientations produced by both growth modes follow the classical failure theory. We demonstrate how the two types of fault growth may be distinguished in natural faults by comparing their angles relative to the original regional maximum principal stress. A stress field analysis of the Landers‐Kickapoo fault suggests that an angle greater than ∼25° between two faults indicates seismic fault growth.

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“…We present the main ingredients of the applied STM‐RSF modeling approach (Herrendörfer et al, ) in section . We introduce the model setup and parameters in section .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

τ_{I I} = σ_{yield} = μ_{l} false(1 - λ false) P = a P arcsinh ([], \frac{V_{p}}{2 V_{0}} \exp ((), \frac{μ_{0} + b \ln \frac{θ V_{0}}{L}}{a})) false(1 - λ false),

\frac{normald θ}{normald t} = 1 - \frac{V_{p} θ}{L},

and V p is the plastic slip rate defined by

V_{p} = 2 {\overset{ε}{true}}_{II false(p false)}^{'} W,

where W denotes the thickness or width of the fault zone in the continuous host rock.…”

Section: Methodsmentioning

confidence: 99%

“…The parameter μ 0 is the reference static friction coefficient, θ denotes the evolving state variable with the aging evolution law

\frac{normald θ}{normald t} = 1 - \frac{V_{p} θ}{L},

and V p is the plastic slip rate defined by

V_{p} = 2 {\overset{ε}{true}}_{II false(p false)}^{'} W,

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Seismic and Aseismic Fault Growth Lead to Different Fault Orientations

et al. 2019

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Seismic and Episodic Slip Characteristics of Frictional-Viscous Subduction Megathrust Shear Zones

Gerya

Cannizzaro

Blass

2021

Preprint

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The deep roots of subduction megathrusts exhibit aseismic slow slip events, commonly accompanied by tectonic tremor. Observations from exhumed rocks suggest this region of the subduction interface is a shear zone with frictional lenses embedded in a viscous matrix. Here we use numerical models to explore the transient slip characteristics of finite-width frictional-viscous megathrust shear zones. Our model utilizes an invariant, continuum-based, regularized form of rate-and state-dependent friction (RSF) and simulates earthquakes along spontaneously evolving faults embedded in a 2D heterogeneous continuum. The setup includes two elastic plates bounding a viscoelastoplastic shear zone (subduction interface melange) with inclusions (clasts) of varying distributions and viscosity contrasts with respect to the surrounding weaker matrix. The entire shear zone exhibits the same velocity-weakening RSF parameters, but the lower viscosity matrix has the capacity to switch between RSF and viscous creep as a function of local stress state. Results show that for a range of matrix viscosities near the frictional-viscous transition, viscous damping and stress heterogeneity in these shear zones both 1) sets the 'speed limit' for earthquake ruptures that nucleate in clasts such that they propagate at slow velocities; and 2) permits the transmission of slow slip from clast to clast, allowing slow ruptures to propagate substantial distances over the model domain. For reasonable input parameters, modeled events have moment-duration statistics, stress drops, and rupture propagation rates that match natural slow slip events. These results provide new insights into how geologic observations from ancient analogs of the slow slip source may scale up to match geophysical constraints on modern slow slip phenomena.

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

Pranger

Sanan

May

et al. 2021

Preprint

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10• We reformulate the empirical rate and state friction law as a bulk viscous flow law 11 in terms of anelastic shear strain rate. 12• We show how mesh independence is achieved by including a gradient-like non-local 13 anelastic shear strain rate equivalent. 14 • We show analytically and numerically that the proposed continuum model closely 15 reproduces existing results of rate and state friction.

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An Invariant Rate‐ and State‐Dependent Friction Formulation for Viscoeastoplastic Earthquake Cycle Simulations

Cited by 81 publications

References 82 publications

Seismic and Aseismic Fault Growth Lead to Different Fault Orientations

Seismic and Aseismic Fault Growth Lead to Different Fault Orientations

Seismic and Episodic Slip Characteristics of Frictional-Viscous Subduction Megathrust Shear Zones

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

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