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High‐resolution three‐dimensional discrete element method (DEM) simulations of sandbox‐scale models of accretionary wedges suggest thrusts follow a variety of propagation processes and orientations depending on a number of factors. These include the stage of development of the wedge (precritical vs. critical), basal friction, and type of thrust (forward vs. backward‐vergent). In terms of propagation processes, two clear mechanisms are identified. The first involves propagation from the décollement to the wedge top, similar to the standard model of thrust propagation seen in many kinematic models, and in the second, thrusts grow downward from an initial nucleation point just below the top surface of the wedge as well as upward from the décollement joining in the middle. In terms of orientation, forward‐vergent thrusts initially form at Roscoe (θ_R = 45° − Ψ/2) or Arthur orientations (θ_A = 45° − (ϕ + Ψ)/4), and over greater shortening, rotate into Coulomb orientations (θ_C = 45° − ϕ/2). To arrive at these results, a wide array of continuum parameters and fields were extracted from the DEM simulations, including stress, strain, strain rate, kinetic energy, Mohr‐Coulomb parameters, and proximity to yielding using the Drucker‐Prager criterion to visualize thrust nucleation and propagation. Lastly, the advantages and disadvantages of these continuum proxies for discerning failure in the granular assembly are considered, and the spatial and temporal relationship between proximity to yielding and strain localization (both pre‐peak and subsequent persistent shear banding) in the granular model of an accretionary wedge is explored.

 

Nearly all frictional interfaces strengthen as the logarithm of time when sliding at ultra-low speeds. Observations of also logarithmic-in-time growth of interfacial contact area under such conditions have led to constitutive models that assume that this frictional strengthening results from purely time-dependent, and slip-insensitive, contact-area growth. The main laboratory support for such strengthening has traditionally been derived from increases in friction during “load-point hold” experiments, wherein a sliding interface is allowed to gradually self-relax down to subnanometric slip rates. In contrast, following step decreases in the shear loading rate, friction is widely reported to increase over a characteristic slip scale, independent of the magnitude of the slip-rate decrease—a signature of slip-dependent strengthening. To investigate this apparent contradiction, we subjected granite samples to a series of step decreases in shear rate of up to 3.5 orders of magnitude and load-point holds of up to 10,000 s, such that both protocols accessed the phenomenological regime traditionally inferred to demonstrate time-dependent frictional strengthening. When modeling the resultant data, which probe interfacial slip rates ranging from 3 . μ m · s − 1 . to less than 10 − 5 μ m · s − 1 , we found that constitutive models where low slip-rate friction evolution mimics log-time contact-area growth require parameters that differ by orders of magnitude across the different experiments. In contrast, an alternative constitutive model, in which friction evolves only with interfacial slip, fits most of the data well with nearly identical parameters. This leads to the surprising conclusion that frictional strengthening is dominantly slip-dependent, even at subnanometric slip rates. 

The empirical constitutive modeling framework of rate‐ and state‐dependent friction (RSF) is commonly used to describe the time‐dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular‐physics‐based model of a fault shear zone, with time‐independent properties at the contact scale, reproduces the phenomenology of laboratory rock and gouge friction experiments in velocity‐step and slide‐hold (SH) protocols. A few slide‐hold‐slide (SHS) simulations further suggested that the granular model might outperform current empirical RSF laws in describing laboratory data. Here, we explore the behavior of the same Discrete Element Method (DEM) model in SH and SHS protocols over a wide range of sliding velocities, hold durations, and system stiffnesses, and provide additional support for this view. We find that, similar to laboratory data, the rate of stress decay during SH simulations is in general agreement with the “Slip law” version of the RSF equations, using parameter values determined independently from velocity step tests. During reslides following long hold times, the model, similar to lab data, produces a nearly constant rate of frictional healing with log hold time, with that rate being in the range of ∼0.5 to 1 times the RSF “state evolution” parameterb. We also find that, as in laboratory experiments, the granular layer undergoes log‐time compaction during holds. This is consistent with the traditional understanding of state evolution under the Aging law, even though the associated stress decay is similar to that predicted by the Slip and not the Aging law.

 

Rate‐ and state‐dependent friction (RSF) equations are commonly used to describe the time‐dependent frictional response of fault gouge to perturbations in sliding velocity. Among the better‐known versions are the Aging and Slip laws for the evolution of state. Although the Slip law is more successful, neither can predict all the robust features of lab data. RSF laws are also empirical, and their micromechanical origin is a matter of much debate. Here we use a granular physics‐based model to explore the extent to which RSF behavior, as observed in rock and gouge friction experiments, can be explained by the response of a granular gouge layer with time‐independent properties at the contact scale. We examine slip histories for which abundant lab data are available and find that the granular model (1) mimics the Slip law for those loading protocols where the Slip law accurately models laboratory data (velocity‐step and slide‐hold tests) and (2) deviates from the Slip law under conditions where the Slip law fails to match laboratory data (the reslide portions of slide‐hold‐slide tests), in the proper sense to better match those data. The simulations also indicate that state is sometimes decoupled from porosity in a way that is inconsistent with traditional interpretations of “state” in RSF. Finally, if the “granular temperature” of the gouge is suitably normalized by the confining pressure, it produces an estimate of the direct velocity effect (the RSF parametera) that is consistent with our simulations and in the ballpark of lab  data.