Eric G. Daub

Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids

We use shear transformation zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.

Vibration-induced slip in sheared granular layers and the micromechanics of dynamic earthquake triggering

We perform 2D Molecular Dynamics simulations of sheared granular layers in the presence of applied vibration. A primary goal is to understand the physics of dynamic earthquake triggering. We adopt a mesoscopic measure of non-affine deformation for characterizing the granular dynamics during slip without or with applied vibration. Our results show that the onset of non-affine strains correlates with the onset of slip and appears earlier in the presence of vibration than in its absence, in agreement with the evidence for triggered slip.

Constraining depth range of S wave velocity decrease after large earthquakes near Parkfield, California

We use noise correlation and surface wave inversion to measure the S wave velocity changes at different depths near Parkfield, California, after the 2003 San Simeon and 2004 Parkfield earthquakes. We process continuous seismic recordings from 13 stations to obtain the noise cross-correlation functions and measure the Rayleigh wave phase velocity changes over six frequency bands. We then invert the Rayleigh wave phase velocity changes using a series of sensitivity kernels to obtain the S wave velocity changes at different depths. Our results indicate that the S wave velocity decreases caused by the San Simeon earthquake are relatively small (similar to 0.02%) and access depths of at least 2.3 km. The S wave velocity decreases caused by the Parkfield earthquake are larger (similar to 0.2%), and access depths of at least 1.2 km. Our observations can be best explained by material damage and healing resulting mainly from the dynamic stress perturbations of the two large earthquakes.

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

We model laboratory earthquakes in a biaxial shear apparatus using the Shear-Transformation-Zone (STZ) theory of dense granular flow. The theory is based on the observation that slip events in a granular layer are attributed to grain rearrangement at soft spots called STZs, which can be characterized according to principles of statistical physics. We model lab data on granular shear using STZ theory and document direct connections between the STZ approach and rate-and-state friction. We discuss the stability transition from stable shear to stick-slip failure and show that stick-slip is predicted by STZ when the applied shear load exceeds a threshold value that is modulated by elastic stiffness and frictional rheology. We also show that STZ theory mimics fault zone dilation during the stick phase, consistent with lab observations.

Meso-mechanical analysis of deformation characteristics for dynamically triggered slip in a granular medium

The deformation characteristics of a sheared granular layer during stick–slip are studied from a meso-mechanical viewpoint, both in the absence and in the presence of externally applied vibration. The ultimate goal is to characterize the physics of dynamic earthquake triggering, where one earthquake, i.e., slip on one fault, is triggered via the seismic waves radiated by another spatially and temporally distant seismic event. Toward this goal, we performed Discrete Element Method simulations of a two-dimensional packing of disks, mimicking a mature geologic fault. These simulations were used to investigate the affine and non-affine deformations inside the granular layer and their spatial–temporal evolution across the stick–slip cycle. The simulation results show that slip in general is accompanied by the appearance of localized regions with high values of both affine and non-affine deformations. These regions are temporally correlated and are mainly concentrated in a shear zone at the interface between the granular layer and the driving block. Dynamic triggering is found to initiate slip when vibration is applied late in the stick–slip cycle, when the system is close to a critical state. It is also found that vibration itself introduces a large amount of affine and non-affine strains, which leads to the initiation of slip at lower shear stress than an equivalent slip event without vibration.

Energetics of strain localization in a model of seismic slip

[1] We quantify the energy dissipated to heat and to local disorder in a sheared layer of granular fault gouge. Local disorder is modeled using shear transformation zone theory, a continuum model of nonaffine deformation in amorphous solids that resolves spontaneous localization of strain. Strain localization decreases the total energy dissipated during slip. In addition, a fraction of this energy is dissipated to increasing local disorder as the material is sheared, thereby decreasing the amount of energy dissipated as thermal heat. We quantify the heat dissipated per unit area as a function of total slip in the presence and absence of strain localization and test the parameter dependence of these calculations. We find that less heat is dissipated per unit area compared to results obtained using a traditional heuristic energy partition.

Dynamically triggered slip leading to sustained fault gouge weakening under laboratory shear conditions

We investigate dynamic wave-triggered slip under laboratory shear conditions. The experiment is composed of a three-block system containing two gouge layers composed of glass beads and held in place by a fixed load in a biaxial configuration. When the system is sheared under steady state conditions at a normal load of 4 MPa, we find that shear failure may be instantaneously triggered by a dynamic wave, corresponding to material weakening and softening if the system is in a critical shear stress state (near failure). Following triggering, the gouge material remains in a perturbed state over multiple slip cycles as evidenced by the recovery of the material strength, shear modulus, and slip recurrence time. This work suggests that faults must be critically stressed to trigger under dynamic conditions and that the recovery process following a dynamically triggered event differs from the recovery following a spontaneous event.

A Suite of Exercises for Verifying Dynamic Earthquake Rupture Codes

We describe a set of benchmark exercises that are designed to test if computer codes that simulate dynamic earthquake rupture are working as intended. These types of computer codes are often used to understand how earthquakes operate, and they produce simulation results that include earthquake size, amounts of fault slip, and the patterns of ground shaking and crustal deformation. The benchmark exercises examine a range of features that scientists incorporate in their dynamic earthquake rupture simulations. These include implementations of simple or complex fault geometry, off‐fault rock response to an earthquake, stress conditions, and a variety of formulations for fault friction. Many of the benchmarks were designed to investigate scientific problems at the forefronts of earthquake physics and strong ground motions research. The exercises are freely available on our website for use by the scientific community.

Slow Dynamics and Strength Recovery in Unconsolidated Granular Earth Materials: A Mechanistic Theory

Rock materials often display long-time relaxation, commonly termed aging or “slow dynamics”, after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the Shear-Transformation-Zone (STZ) theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains, and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log-linear recovery of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady-state behavior at long times. We demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones.

Quantifying optimal accuracy of local primary sequence bioinformatics methods

MOTIVATION Traditional bioinformatics methods scan primary sequences for local patterns. It is important to assess how accurate local primary sequence methods can be. RESULTS We study the problem of donor pre-mRNA splice site recognition, where the sequence overlaps between real and decoy datasets can be quantified, exposing the intrinsic limitations of the performance of local primary sequence methods. We assess the accuracy of primary sequence methods generally by studying how they scale with dataset size and demonstrate that our new primary sequence ranking methods have superior performance.