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Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback

Publication ,  Journal Article
Schaeffer, DG; Iverson, RM
Published in: SIAM Journal on Applied Mathematics
December 1, 2008

This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation (for pore pressure) coupled through a boundary condition to a first-order 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, stick-slip motion. Numerical computations confirm the analytical predictions of the parameter values at which bifurcation occurs. The existence of stick-slip behavior in part of the parameter space is particularly noteworthy because, unlike stick-slip 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 pore-pressure diffusion on frictional resistance. © 2008 Society for Industrial and Applied Mathematics.

Duke Scholars

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

December 1, 2008

Volume

69

Issue

3

Start / End Page

769 / 786

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Schaeffer, D. G., & Iverson, R. M. (2008). Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback. SIAM Journal on Applied Mathematics, 69(3), 769–786. https://doi.org/10.1137/07070704X
Schaeffer, D. G., and R. M. Iverson. “Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback.” SIAM Journal on Applied Mathematics 69, no. 3 (December 1, 2008): 769–86. https://doi.org/10.1137/07070704X.
Schaeffer DG, Iverson RM. Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback. SIAM Journal on Applied Mathematics. 2008 Dec 1;69(3):769–86.
Schaeffer, D. G., and R. M. Iverson. “Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback.” SIAM Journal on Applied Mathematics, vol. 69, no. 3, Dec. 2008, pp. 769–86. Scopus, doi:10.1137/07070704X.
Schaeffer DG, Iverson RM. Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback. SIAM Journal on Applied Mathematics. 2008 Dec 1;69(3):769–786.

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

December 1, 2008

Volume

69

Issue

3

Start / End Page

769 / 786

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics