Effects of loading velocity, stiffness, and inertia on the dynamics of a single degree of freedom Spring‐Slider System

Abstract

Numerical simulation of the nonlinear dynamics of a single degree of freedom spring‐slider system can provide useful insight into the effects of loading velocity, friction environment, elastic stiffness, and inertia on the stress drop and dynamic behavior of earthquakes. In our numerical simulations using a rate‐ and state‐dependent friction law, we varied the loading velocity by 7 orders of magnitude, the stiffness by 2 orders of magnitude, the mass by 5 orders of magnitude, and the velocity‐weakening parameter (B‐A) by a factor of 160. Four stability regimes were identified in the load point velocity‐stiffness space when inertia was taken into account. For cyclic stick‐slip instabilities, the stress drop amplitude increases with decreasing load point velocity, with decreasing stiffness, with increasing velocity weakening parameter B‐A, and with decreasing mass. Simple scaling relations for the static stress drop, dynamic stress drop, “static” friction, and shear fracture energy with the natural logarithm of load point velocity were observed. Using the scaling relation for static stress drop, we infer the normalized velocity weakening parameter b‐a (with respect to normal stress) to range from 0.0011 to 0.0039 for triaxial experiments on saw cut Westerly granite specimens sandwiched with a simulated gouge layer of ultrafine quartz at pressures from 10 MPa to 100 MPa. Unless we take b‐a throughout the seismogenic layer to be much higher than experimental measurements, the effect of loading velocity by itself is not sufficient to account for the increase of stress drop with increasing earthquake recurrence time inferred from seismological data. To the extent that our simple system can be treated as an analog for earthquakes, our study shows that the velocity weakening parameter (B‐A) controls the magnitude of the static stress drop far more than the loading velocity. If velocity weakening increases systematically with increasing healing time, then the coupled effect of loading velocity variation and change in friction environment can account for the seismological observations.