The dynamics of fast and slow earthquake ruptures in viscoelastic materials

Classical theories using linear elasticity predict that crack propagation asymptotically approaches a limiting speed, beyond which the energy balance becomes unphysical. How- ever, geophysical and laboratory observations show that ruptures can propagate at either a very low, stable speed or a significantly high speed. Here, we use numerical simulations to show that frictional ruptures in viscoelastic materials can steadily propagate at a terminal speed, rather than asymptotically approaching the classical speed limit. The simulated terminal speed spans a continuum of values, ranging from slow ruptures to supershear ruptures. We develop a new theory incorporating viscoelasticity to predict all simulated rupture speeds. In addition to the ratio of fracture energy to static energy release rate, we find that three length scales also play a crucial role in governing the energy balance during rupture in viscoelastic materials. The theory predicts that stable rupture speeds are energetically allowed to be very small, which helps explain the widespread occurrence of slow earthquakes. Beyond the classical speed limit, the energy balance becomes independent of macroscopic length scales, being controlled solely by the local properties around the rupture tip. Furthermore, we find that the viscoelasticity of fault zones is significant in earthquake rupture propagation, even when the fault-zone geometrical scales are short relative to other fault dimensions. These numerical and theoretical findings fundamentally advance our understanding of dynamic rupture propagation.