SCEC Award Number 17179 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Self-similar behavior of rate-strengthening faults
Investigator(s)
Name Organization
Robert Viesca Tufts University
Other Participants Lichen Wang (Ph.D. student), Pierre Dublanchet (visiting assistant professor)
SCEC Priorities 1e, 3b, 2c SCEC Groups FARM, CS, SDOT
Report Due Date 06/15/2018 Date Report Submitted 12/01/2021
Project Abstract
 Goal of the project is to understand the spatiotemporal evolution of slip of rate-strengthening faults in response to external loadings. We examine a linear viscous fault strength and extend the results to a non-linear rate- and state-dependence. In the case of a linear viscous fault, we derive analytical solutions and an asymptotic expansion of long-time behavior. In the case of non-linear, rate-strengthening friction, we perform a non-linear perturbation expansion to find the long-time decay of slip rate and state back to steady-state sliding, including the deviation of behavior from the linear case. The principal implication is for models for post-seismic slip. We show that logarithmic accumulation of surface displacements following an earthquake are not necessarily indications of a logarithmic dependence of strength on sliding rate, as found previously, assuming spring-block-type restriction of fault slip. Instead, we show that continuum models accounting for the spatial spread and temporal decay of elevated slip rates following an earthquake lead to logarithmic (or near-logarithmic) time dependence of surface displacements, when considering a linear viscous fault strength or a non-linear, but linearizable, strength.
Intellectual Merit Frequent evidence for stable, aseismic fault slip—in which there is no runaway, earthquake-nucleating instability—includes observations of transient slow slip events, interseismic creep, and postseismic slip. A common presumption is that runaway acceleration of fault slip in these instances is suppressed by the self-limiting effect of a slip-rate-strengthening friction. This may be due to a non-linear viscous rheology, in which fault strength has a power-law dependence on sliding rate, or a non-linear rate and state dependence of friction, in which strength depends logarithmically on the sliding rate, as well as its history. How do such slip-rate-dependent friction laws couple with elastic deformation to determine the spatiotemporal evolution of slip on a fault in response to a driving force? How does an elevated slip rate spread along the fault, at what rate does it decay, and how are these integrated to affect displacement at the surface?
Broader Impacts This project provided support for one graduate student (Lichen Wang), international collaboration (with Pierre Dublanchet, MINES ParisTech), and the extension of results developed for fault mechanics to landslide modelling.
Exemplary Figure Figure 2. (top) A strike-slip fault in the x-z plane intersects the free surface at x = 0. The solution to a sudden step in stress \tau_b at t = 0 along the fault (x > 0) is found by method of images. The hatched area is the net force exerted on the fault (per unit distance along z), which determines the leading-order coefficient a1 of the asymptotic expansion. (left) Boxcar step in stress imposed at t = 0. (right) Evolution of the anti-plane displacement component uz at the free surface, to one side of the fault. The displacement quickly approaches a logarithmic asymptote (dashed).