Math @ Duke

Publications [#244111] of David G. Schaeffer
Papers Published
 Schaeffer, DG; Iverson, RM, Steady and intermittent slipping in a model of landslide motion regulated by porepressure feedback,
Siam Journal on Applied Mathematics, vol. 69 no. 3
(December, 2008),
pp. 769786, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361399 [Gateway.cgi], [doi]
(last updated on 2019/08/19)
Abstract: This paper studies a parsimonious model of landslide motion, which consists of the onedimensional diffusion equation (for pore pressure) coupled through a boundary condition to a firstorder ODE (Newton's second law). Velocity weakening of sliding friction gives rise to nonlinearity in the model. Analysis shows that solutions of the model equations exhibit a subcritical Hopf bifurcation in which stable, steady sliding can transition to cyclical, stickslip motion. Numerical computations confirm the analytical predictions of the parameter values at which bifurcation occurs. The existence of stickslip behavior in part of the parameter space is particularly noteworthy because, unlike stickslip behavior in classical models, here it arises in the absence of a reversible (elastic) driving force. Instead, the driving force is static (gravitational), mediated by the effects of porepressure diffusion on frictional resistance. © 2008 Society for Industrial and Applied Mathematics.


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