The dynamic earthquake problem spans a broad range of length scales, from microscopic grain contacts through faults that are hundreds of kilometers long. A major goal of dynamic earthquake modeling is to develop friction laws that capture the small scale physics and that can also be used to model fault scale rupture. However, friction laws used in studying earthquake rupture are often simply fits to data, and give little physical insight into the rupture process. The goal of this work is to develop a model for the deformation of amorphous materials such as granular fault gouge, and to investigate the dynamics of instabilities at larger scales. The model is based on Shear Transformation Zone (STZ) Theory, a microscopic physical model for plastic deformation in dense amorphous materials such as fault gouge, granular materials, glasses, foams, and colloids. STZ Theory captures fracture and deformation features that are observed in numerical simulations, and remains tractable for modeling friction at larger scales. STZ Theory ties fault weakening to the evolution of an effective temperature, which quantifies the configurational disorder in the gouge and serves as the dynamic state variable in STZ Theory.
STZ Theory predicts logarithmic rate dependence and that the length scale for frictional evolution increases with increasing average strain rate, which are observed in laboratory experiments. Additionally, STZ Theory captures the spontaneous formation and growth of narrow shear bands in the fault gouge. Shear bands within a layer of gouge are observed in many studies of faulting, which indicates that resolving the dynamics of shear banding is important for capturing the small scale physics during earthquake slip.
At the scale of frictional interfaces, we investigate the role of strain localization for stick-slip instabilities in an elastic block slider system. We perform a linear stability analysis to predict the critical value of the spring stiffness when steady sliding becomes unstable, and verify our results through numerical integration. We find that when a shear band forms, steady sliding becomes unstable at a larger spring stiffness.
We also investigate the implications of STZ Theory and strain localization in dynamic earthquake simulations. We compare STZ Theory without strain localization, Dieterich-Ruina (DR) friction, and linear slip-weakening (SW). The dynamic rupture governed by STZ Theory accelerates more rapidly to the limiting wave speed, exhibits a decreased peak slip rate, and transitions to supershear rupture at a lower initial shear stress than equivalent ruptures with DR or SW friction.
For dynamic ruptures where a shear band does form, strain localization alters fault behavior because localization is a mechanism for dynamic weakening. The dynamic weakening of strain localization increases the slip rate during rupture, and also increases the stress drop. We also show that strain localization occurs below seismogenic depths where constitutive properties are rate strengthening due to slip propagating down dip from the seismogenic zone. Our results indicate that the small scale physics occurring within the gouge can have a large scale impact on the dynamics of friction and the propagation of slip on earthquake faults.
|Advisor:||Carlson, Jean M.|
|Commitee:||Archuleta, Ralph J., Israelachvili, Jacob, Langer, James S.|
|School:||University of California, Santa Barbara|
|School Location:||United States -- California|
|Source:||DAI-B 70/11, Dissertation Abstracts International|
|Subjects:||Geophysics, Low Temperature Physics|
|Keywords:||Amorphous materials, Constitutive laws, Earthquake dynamics, Earthquake ruptures, Stick-slip, Strain localization|
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