On the efficient and reliable numerical solution of rate-and-state friction problems

Pipping, Elias; Kornhuber, Ralf; Rosenau, Matthias; Oncken, Onno

doi:10.1093/gji/ggv512

Cited by 11 publications

(12 citation statements)

References 30 publications

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“…For the spring slider we observe the periodic occurrence of mostly unilateral slip events, similar to related simulations of subduction zones [29]. These slip events are nicely captured by adaptive time stepping, while the number of outer fixed point iterations and inner multigrid iteration remains almost the same for all time steps.…”

Section: Introductionsupporting

confidence: 81%

“…Rate problem with given state. We first consider the rate problem (29) for given state α ∈ L 2 (Γ F ). Following [30], we apply the classical Newmark scheme (36) un…”

Section: Semi-discretization In Timementioning

confidence: 99%

“…In this paper, we extend a variational approach to the simulation of subduction zones [29] to a layered fault system with RSF. More precisely, we consider the deformation of a geological structure with non-intersecting faults that can be represented by I viscoelastic bodies undergoing small viscoelastic deformations and large tangential displacements with RSF contact conditions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of multiscale fault systems with rate- and state-dependent friction

Gräser¹,

Kornhuber²,

Podlesny³

2021

Preprint

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We consider the deformation of a geological structure with non-intersecting faults that can be represented by a layered system of viscoelastic bodies satisfying rate-and state-depending friction conditions along the common interfaces. We derive a mathematical model that contains classical Dieterich-and Ruina-type friction as special cases and accounts for possibly large tangential displacements. Semi-discretization in time by a Newmark scheme leads to a coupled system of non-smooth, convex minimization problems for rate and state to be solved in each time step. Additional spatial discretization by a mortar method and piecewise constant finite elements allows for the decoupling of rate and state by a fixed point iteration and efficient algebraic solution of the rate problem by truncated non-smooth Newton methods. Numerical experiments with a spring slider and a layered multiscale system illustrate the behavior of our model as well as the efficiency and reliability of the numerical solver.This research has been funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 "Scaling Cascades in Complex Systems", Project Number 235221301, Project B01 "Fault networks and scaling properties of deformation accumulation".

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Section: Introductionsupporting

confidence: 81%

“…Rate problem with given state. We first consider the rate problem (29) for given state α ∈ L 2 (Γ F ). Following [30], we apply the classical Newmark scheme (36) un…”

Section: Semi-discretization In Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of multiscale fault systems with rate- and state-dependent friction

Gräser¹,

Kornhuber²,

Podlesny³

2021

Preprint

Self Cite

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“…The experimental setup used in this study is a development from an earlier quasi‐two‐dimensional setup used for seismotectonic scale modeling by Rosenau et al (, ) where the method has been explained in detail. The setup used in the current study is six times wider with respect to previous experiments and therefore truly 3‐D and allows simulating along‐strike analogue earthquake ruptures (e.g., Pipping et al, ). The experimental device consists of a glass‐sided box (100 cm across‐strike, 60 cm along‐strike, and 50 cm deep) with a 15° dipping basal conveyer plate equipped with blades to ensure the transfer of basal stresses into the overlying material.…”

Section: Modeling and Analysis Methodsmentioning

confidence: 99%

Synchronization of Great Subduction Megathrust Earthquakes: Insights From Scale Model Analysis

et al. 2019

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The magnitude of great subduction megathrust earthquakes is controlled mainly by the number of adjacent asperities failing synchronously and the resulting rupture length. Here we investigate experimentally the long-term recurrence behavior of a pair of asperities coupled by static stress transfer over hundreds of seismic cycles. We statistically analyze long (c. 500 ka) time series of M8-9 analogue earthquakes simulated using a seismotectonic scale model approach with two aims: First, to constrain probabilistic measures (frequency-size distribution, variability) useful for hazard assessment and, second, to relate them with geometric observables (coseismic slip pattern, locking pattern). We find that the number of synchronized asperity failures relative to the number of individual asperity failures as well as the coefficients of variation of recurrence intervals and seismic moment scale with the logarithm of stress coupling between the asperities. Accordingly, tighter packed asperities tend to recur more periodically and with a more characteristic magnitude while more distant asperities show clustering of more variable sized events. The probability of synchronized failures seems to be controlled to first order by geometrical relations (i.e., spacing and offset of asperities). The effects of rheological properties are evident but it remains to be explored to which extent they vary in nature and how sensitive the system is to those.

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“…Elastic deformation in the solid surrounding the crack is usually described by elastic dislocation theory (e.g. Pollard and Segall, 1987). Since the Earth's surface is considered mechanically a free surface, i.e.…”

Section: Analogue Rock Rheologymentioning

confidence: 99%

Reply to Review by Anonymous

Rosenau¹

2017

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Earth deformation is a multi-scale process ranging from seconds (seismic deformation) to millions of years (tectonic deformation). Bridging short-and long-term deformation and developing seismotectonic models has been a challenge in experimental tectonics for more than a century. Since the formulation of Reid's elastic rebound theory 100 years ago, laboratory mechanical models combining frictional and elastic elements have been used to study the dynamics of earthquakes. In the last decade, with the advent of high-resolution monitoring techniques and new rock analogue materials, laboratory earthquake experiments have evolved from simple spring-slider models to scaled analogue models. This evolution was accomplished by advances in seismology and geodesy along with relatively frequent occurrences of large earthquakes in the past decade. This coincidence has significantly increased the quality and quantity of relevant observations in nature and triggered a new understanding of earthquake dynamics. We review here the developments in analogue earthquake modelling with a focus on those seismotectonic scale models that are directly comparable to observational data on short to long timescales. We lay out the basics of analogue modelling, namely scaling, materials and monitoring, as applied in seismotectonic modelling. An overview of applications highlights the contributions of analogue earthquake models in bridging timescales of observations including earthquake statistics, rupture dynamics, ground motion, and seismic-cycle deformation up to seismotectonic evolution.

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On the efficient and reliable numerical solution of rate-and-state friction problems

Cited by 11 publications

References 30 publications

Numerical simulation of multiscale fault systems with rate- and state-dependent friction

Numerical simulation of multiscale fault systems with rate- and state-dependent friction

Synchronization of Great Subduction Megathrust Earthquakes: Insights From Scale Model Analysis

Reply to Review by Anonymous

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