A rate- and state-dependent ductile flow law of polycrystalline halite under large shear strain and implications for transition to brittle deformation

We have conducted double-shear biaxial deformation experiments in layers of NaCl within its fully-plastic (FP) regime up to large shear strains (γ < 50) with velocity steps. From this, we have empirically formulated a rate- and state-dependent flow law which explains the transient mechanical behavior. The steady state flow stress in the FP regime can be explained by a power-law with a stress exponent ~8.5 and an activation enthalpy of ~1.3 eV, with the instantaneous response having a higher stress exponent (13 ± 8), although there is data scatter. The transition to brittle regime is associated with weakening from the ductile flow law. In FP regime, the mechanical response is characterized by a monotonic decay to a new steady state while in the transitional regime, by a peak-decay behavior. The transient flow law obtained here is of considerable importance in the study of the brittle-ductile transition in rocks

Frictional experiments of dolerite at intermediate slip rates with controlled temperature: Rate weakening or temperature weakening?

A rotary shear apparatus has been newly set up in Chiba University which can control the temperature near a sliding surface, T_meas, up to 1000°C independently from slip rate, V. Frictional experiments at 0.010 m/s, 1 MPa normal stress, and variable T_meas for dolerite have revealed a remarkable effect of temperature on the friction coefficient, f. With increasing T_meas, f starts from 0.7 to 0.8 at room temperature (RT), decreases down to 0.5–0.6 at 400°C, increases until 800°C, and then decreases again. We have also conducted XRD analyses of the wear materials (mainly submicron particles) and investigated microstructures of the sliding surfaces developed at different temperatures T_meas, and we found that there is a negative correlation between f and the amount of amorphous material except at RT and 1000°C. The generation of the amorphous phase probably causes the weakening. There is no amorphous phase recognized for a sample at 1000°C which is an aggregate of rounded crystals. EBSD analyses show that the material on the sliding surface at 1000°C contains randomly oriented hematite grains, which together with the observed microstructural features suggests that granular flow was taking place. We have also demonstrated that f depends not only on the instantaneous value of temperature, but also on its history. By comparing with conventional rotary shear friction experiment for the same dolerite without temperature control, we conclude that strong “rate weakening” as recently observed in high-velocity frictional experiments without an active control of the temperature has a significant amount of contribution from the temperature effect

Constitutive properties of clayey fault gouge from the Hanaore fault zone, southwest Japan

Velocity step tests at a range of slip rates (0.0154–155.54 μm s^(−1)) are performed using natural fault gouge containing smectite, mica, and quartz collected from an outcrop of the Hanaore Fault, southwest Japan. Field and microscopic observations reveal that the shear deformation is localized to a few centimeters or thinner layer of black clayey fault gouge. This layer is formed by multiple stages, and determining the width of the shear zone due to a single event is difficult to determine. The experimental data on the abrupt jumps in the load point velocity are fitted by a rate‐ and state‐dependent frictional law, coupled with the spring‐slider model, the stiffness of which is treated as a fitting parameter. This treatment is shown to be essential to determine the constitutive parameters and their errors. The velocity steps are successfully fit with typically two state variables: larger b_1 with shorter d_(c1) and smaller b_2 with longer d_(c2). At slip rates higher than 1 μm s^(−1), negative b_2 is required to fit the data in most of the cases. Thin gouge layers (∼200 μm) in the experiment enables us to simulate large averaged shear strain which is important to recognize the evolution of the state variable associated with negative b_2 and long d_(c2). Observation of microscopic structure after experiments shows poor development of Y planes. This may be consistent with the mechanical behavior observed: weak occurrence of initial peak strength at yielding and displacement hardening throughout the experiments

Three-dimensional earthquake sequence simulations with evolving temperature and pore pressure due to shear heating: Effect of heterogeneous hydraulic diffusivity

A new methodology for three-dimensional (3-D) simulations of earthquake sequences is presented that accounts not only for inertial effects during seismic events but also for shear-induced temperature variations on the fault and the associated evolution of pore fluid pressure. In particular, the methodology allows to capture thermal pressurization (TP) due to frictional heating in a shear zone. One-dimensional (1-D) diffusion of heat and pore fluids in the fault-normal direction is incorporated using a spectral method, which is unconditionally stable, accurate with affordable computational resources, and highly suitable to earthquake sequence calculations that use variable time steps. The approach is used to investigate the effect of heterogeneous hydraulic properties by considering a fault model with two regions of different hydraulic diffusivities and hence different potential for TP. We find that the region of more efficient TP produces larger slip in model-spanning events. The slip deficit in the other region is filled with more frequent smaller events, creating spatiotemporal complexity of large events on the fault. Interestingly, the area of maximum slip in model-spanning events is not associated with the maximum temperature increase because of stronger dynamic weakening in that area. The region of more efficient TP has lower interseismic shear stress, which discourages rupture nucleation there, contrary to what was concluded in prior studies. Seismic events nucleate in the region of less efficient TP where interseismic shear stress is higher. In our model, hypocenters of large events do not occur in areas of large slip or large stress drop

Steady‐State Effective Normal Stress in Subduction Zones Based on Hydraulic Models and Implications for Shallow Slow Earthquakes

The spatial distribution of effective normal stress, σₑ, is essential for understanding the fault motion. Although Rice (1992, https://doi.org/10.1016/s0074-6142(08)62835-1) proposed a steady-state solution for a vertical strike-slip fault zone with constant fluid properties, models that are based on the concept by Rice (1992, https://doi.org/10.1016/s0074-6142(08)62835-1) and are applicable for other tectonic settings have not yet been developed. Such a model is particularly important in subduction zones because the relationship between low σₑ and slow earthquakes is often discussed. To quantitatively examine the causes of a local decrease in σₑ on a shallow region of the subduction zone, we performed model calculations that incorporated mechanisms characteristic to subduction zones. Our basic model, which considers the effect of smectite dehydration and the mechanical effect of subduction, yields results that are consistent with those reported by Rice (1992, https://doi.org/10.1016/s0074-6142(08)62835-1): the gradient of σₑ remarkably decreases with the increase in depth, whereas the realistic fluid properties rule out nearly constant σₑ at depth. We obtained a monotonic increase in σₑ with the increase in depth for the physically sound solutions and failed to generate a local decrease in σₑ . The presence of a splay fault and fluid leakage though it cannot decrease σₑ locally. We found that a local decrease in permeability decreased σₑ locally around an impermeable zone and, thus, possibly led to the occurrence of shallow slow earthquakes. The water release caused by the dehydration reaction may not be the dominant factor, although smectite dehydration releases silica and promotes its precipitation

Comparison of average stress drop measures for ruptures with heterogeneous stress change and implications for earthquake physics

Stress drop, a measure of static stress change in earthquakes, is the subject of numerous investigations. Stress drop in an earthquake is likely to be spatially varying over the fault, creating a stress drop distribution. Representing this spatial distribution by a single number, as commonly done, implies averaging in space. In this study, we investigate similarities and differences between three different averages of the stress drop distribution used in earthquake studies. The first one, Δσ¯¯¯¯¯M, is the commonly estimated stress drop based on the seismic moment and fault geometry/dimensions. It is known that Δσ¯¯¯¯¯M corresponds to averaging the stress drop distribution with the slip distribution due to uniform stress drop as the weighting function. The second one, Δσ¯¯¯¯¯A, is the simplest (unweighted) average of the stress drop distribution over the fault, equal to the difference between the average stress levels on the fault before and after an earthquake. The third one, Δσ¯¯¯¯¯E, enters discussions of energy partitioning and radiation efficiency; we show that it corresponds to averaging the stress drop distribution with the actual final slip at each point as the weighting function. The three averages, Δσ¯¯¯¯¯M, Δσ¯¯¯¯¯A, and Δσ¯¯¯¯¯E, are often used interchangeably in earthquake studies and simply called ‘stress drop’. Yet they are equal to each other only for ruptures with spatially uniform stress drop, which results in an elliptical slip distribution for a circular rupture. Indeed, we find that other relatively simple slip shapes—such as triangular, trapezoidal or sinusoidal—already result in stress drop distributions with notable differences between Δσ¯¯¯¯¯M, Δσ¯¯¯¯¯A, and Δσ¯¯¯¯¯E. Introduction of spatial slip heterogeneity results in further systematic differences between them, with Δσ¯¯¯¯¯E always being larger than Δσ¯¯¯¯¯M, a fact that we have proven theoretically, and Δσ¯¯¯¯¯A almost always being the smallest. In particular, the value of the energy-related Δσ¯¯¯¯¯E significantly increases in comparison to the moment-based Δσ¯¯¯¯¯M with increasing roughness of the slip distribution over the fault. Previous studies used Δσ¯¯¯¯¯M in place of Δσ¯¯¯¯¯E in computing the radiation ratio ηR that compares the radiated energy in earthquakes to a characteristic part of their strain energy change. Typical values of ηR for large earthquakes were found to be from 0.25 to 1. Our finding that Δσ¯¯¯¯¯E≥Δσ¯¯¯¯¯M allows us to interpret the values of ηR as the upper bound. We determine the restrictions placed by such estimates on the evolution of stress with slip at the earthquake source. We also find that Δσ¯¯¯¯¯E can be approximated by Δσ¯¯¯¯¯M if the latter is computed based on a reduced rupture area