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Speaker: Sohom Ray; Ph.D. student at Tufts University
We assess quasistatic development of slip on faults under slip rate and state dependence of fault’s shear strength [e.g., Dieterich, 1978; Ruina, 1983]. The steady-state shear strength could either weaken or strengthen with increasing sliding or slip rate; and depending on that, an initial perturbation could manifest, respectively, into an instability or an aseismic fault creep. Here, we find self-similar solutions of diverging and of diffusing rate of slip, and show their relevance, respectively, for rupture nucleation of earthquakes and accelerated creep of landslides. In particular, generic spatial distributions of frictional properties, spanning a range of wavelength, and its effect on slip instabilities and aseismic slip are considered.
Multiple blowup solutions (of diverging slip rate) exist when fault frictional properties are nonuniformly distributed, owed to a broken spatial invariance [Ray & Viesca, 2017]. Only a subset of them are attractive (stable), and, can be determined using a nonlinear stability analysis. While the blowup solutions always occur at the critical points, respectively, at the maxima and minima of parameter variations and sometimes between them, the stability of the blowup solutions are not identical for all wavelength of parameter variations (L). The blowup solutions are found to be most stable or unstable when the wavelength L attunes with an intrinsic elastofrictional lengthscale; and, could be considered analogous to resonance exhibited by simple mechanical or electrical systems when an external or a driving frequency attunes with natural frequency. Further, the analysis could be used as a probe to determine when homogenizing–using an average estimate–of an otherwise nonuniform frictional property may be appropriate. We show that homogenization is valid only when the wavelength of variation is much larger or smaller than the nucleation lengthscale.
Accelerating creep of landslides could be considered an evolution of slip of a deformable thin elastic layer over a rigid base such that basal friction strengthens with slip rate. We find self-similar solutions of nonlinear slip diffusion under relevant initial conditions of external stress or slip rate. A close analogy could be drawn with the Stokes’ first problem wherein a plate beneath a semi-infinite region of initially stagnant incompressible fluid is suddenly moved to result in (self-similar) diffusion of momentum within the fluid layer. Likewise, we find relevant lengthscale and nonlinear manner of diffusion of slip rate when a creeping slope is suddenly imposed with a high stress or slip rate.