A two‐scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity

Abstract

We develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone theory, a statistical thermodynamic theory, to describe irreversible macroscopic plastic deformations due to local rearrangements of the gouge particles. We track the temperature evolution at the grain contacts using a one-dimensional heat diffusion equation. At low temperatures, the strength of the asperities is limited by the flow strength, as predicted by dislocation creep models. At high temperatures, some of the constituents of the grains may melt leading to the degradation of the asperity strength. Our model predicts a logarithmic rate dependence of the steady state shear stress in the quasistatic regime. In the dense flow regime the frictional strength decreases rapidly with increasing slip rate due to thermal softening at the granular interfaces. The transient response following a step in strain rate includes a direct effect and a following evolution effect, both of which depend on the magnitude and direction of the velocity step. In addition to frictional heat, the energy budget includes an additional energy sink representing the fraction of external work consumed in increasing local disorder. The model links low-speed and high-speed frictional response of gouge layers and provides an essential ingredient for multiscale modeling of earthquake ruptures with enhanced coseismic weakening.

Strain localization in dry sheared granular materials: A compactivity-based approach

“…An advantage of the STZ theory in that context is that it is based on the laws of thermodynamics and the state variable evolution is constrained by energy flow and entropy evolution. In the past few years, the STZ framework has been successfully extended to incorporate physical phenomena critical for gouge mechanics such as grain fragmentation [23], flash heating [27], dilation and compaction under combined shear and vibration [19,24,38]. Furthermore, extending STZ theory to higher dimensions (2D and 3D) is possible, enabling investigation of strain localization and inhomogeneous plastic deformation.…”

“…[22,29,34,36,37]). Recently, the theory was extended to model shear flow of granular materials with breakable particles [23], incorporating flash heating effects [27] as well as acoustic fluidization under low normal stresses [38]. Furthermore, the theory has been implemented to investigate conditions for stability of sliding and strain localization in granular layers subjected to shear and vibrations [20,24] and has pointed to the possible effect of vibrations in transition from rapid slip to slow slip and eventually stable sliding; a mechanism that may play a role in tremor-slow slip interaction [24].…”

“…In future work, we plan to expand the model to incorporate more physical processes that enable plastic flow below the stress threshold. This includes for example, creep [27], acoustic vibrations [19,20], and granular fluidity [49,50]. For example, it was shown previously that acoustic vibrations, may tend to fluidize the granular system, analogous to temperature effects in glasses, and enable plastic flow at stresses less than the mechanical minimum flow stress [20,38].…”

Simulating stick‐slip failure in a sheared granular layer using a physics‐based constitutive model

“…This description provides a direct connection between macroscopic friction and the grain-scale physics of deformation; an example of the latter is how grain angularity and surface roughness controls the frictional response of the sheared granular packing [Lieou et al, 2015]. In the past the STZ theory has been applied to physically model constitutive friction laws [Daub and Carlson, 2010;Elbanna and Carlson, 2014], to explain the formation of a refined gouge layer in conjunction with a theory of 10.1002/2016JB013627 grain fragmentation [Lieou et al, 2014a], to show that stick-slip instabilities arise from intergranular frictional interaction [Lieou et al, 2015], and to suggest how seismic waves cause triggered slow slip [Lieou et al, 2016]. In this section we briefly review the theory; the interested reader is referred to the Appendices and, e.g., Lieou et al [2015Lieou et al [ , 2016, for details and derivations from basic physical principles.…”

Dynamic friction in sheared fault gouge: Implications of acoustic vibration on triggering and slow slip

“…This approach directly connects macroscopic dynamics to the grain‐scale physics of deformation, such as the link between frictional properties of grains and their angularity [ Lieou et al , ]. The STZ theory has been successfully invoked to reconstruct and explain constitutive friction laws [ Daub and Carlson , ; Lieou et al , ; Elbanna and Carlson , ] and to show that friction between grains is an essential ingredient for stick‐slip instabilities [ Lieou et al , ]. Here we provide a brief overview of the theoretical elements; for further information, the reader may refer to, e.g., Lieou et al [].…”