PhD Thesis Defense
Title: Laboratory Investigation of Shear Ruptures: Supersonic Propagation and Nucleation by Fluid Injection
Shear rupture nucleation and dynamic propagation is a challenging, nonlinear, highly interactive process with important practical implications. Here we focus on two aspects of this problem: propagation speeds and shock front radiation from the dynamic crack tip as well as nucleation of dynamic rupture due to fluid injection.
Spontaneously propagating cracks in solids emit pressure and shear waves and are, in part, driven by energy transfer due to them. When a shear crack propagates faster than the shear wave speed of the material, the coalescence of the shear wavelets emitted by the near-crack-tip region forms a shock front that significantly concentrates particle motion. The equivalent scenario involving a pressure shock front should not be possible, since cracks should not be able to exceed the pressure wave speed, at least in an isotropic linear-elastic solid. Here we present full-field experimental evidence of dynamic shear cracks in viscoelastic polymers that result in the formation of a pressure shock front, in addition to the shear one. In that sense, the crack appears to be supersonic. The apparent violation of classic theories is explained by the strain-rate-dependent material behavior of polymers: the increased wave speeds within the highly-strained region around the crack tip allow for supersonic crack propagation with respect to the (lower) wave speeds at short distances away from the interface, resulting in the formation of the pressure shock front. The crack speed remains below the pressure wave speed prevailing locally, about its tip, in agreement with basic physics and energy considerations of linear-elastic theories.
We find that the shock fronts emitted by the shear cracks in the viscoelastic materials are curved and propose a novel method to quantify the viscoelastic wave speeds of the solids in the dynamic range of strain rates based on the curvature. Only kinematic relationships are used in the method, without the need for the constitutive relationship of the material. Measuring or inferring the material properties at elevated strain rates in viscoelastic solids is a difficult task, because of practical limitations of obtaining accurate measurements in that regime.
The second part of the study concentrates on the nucleation of shear dynamic rupture due to fluid injection or, more broadly, on the interaction of frictional faulting with fluids. Fluid overpressure is recognized to play a fundamental role in promoting fault motion. A large number of observations has shed light on the interplay between fluids and faulting, both in natural events and in earthquakes induced by human activities, such as wastewater disposal associated with oil and gas extraction. Fluids can induce a variety of earthquake source behaviors ranging from unstable, dynamic motions to stable, quasi-static ones, which a number of field studies suggest that can coexist on the same fault areas at different times, depending on the local conditions.
Here, we explore the effect of the rate of the pore pressure increase on the rupture nucleation. We find that elevated injection rates induce triggering of the rupture at lower pressure values and minimal volumes of the injected fluid, if compared to slow injection rates. For the slow injection rates, we observe a large portion of in the experimental interface wetted by fluid and a phase of accelerated slip prior to the dynamic event (quasi-dynamic nucleation process). These findings suggest the presence of a prominent quasi-static nucleation process in the interface. In cases of rapid pore pressure increase, the nucleation process is much shorter in time and much more compact in space, being highly concentrated around the injection location. The dynamic events, once initiated, are qualitatively similar for the different injection rates, but quantitatively different, with the slow-injection ones experiencing higher stress drops and higher slips, perhaps due to the effect of fluids on the friction properties. These results suggest the need to develop nucleation size estimates that include the rate of the pore pressure increase and motivate further investigation of how friction properties depend on the presence of fluids. The details of the obtained experimental findings, once analyzed through numerical modeling, will place important constrains on the forms of the acceptable friction laws, including the effects of pore fluid pressure and its rate of change.
Advisors: Professor Ares Rosakis and Professor Nadia Lapusta