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Open AccessArticle

Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation

School of Mathematics and Statistics, University of Melbourne, Parkville 3010, Australia
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 67;
Received: 31 October 2019 / Revised: 25 December 2019 / Accepted: 1 January 2020 / Published: 4 January 2020
(This article belongs to the Special Issue Applications of Nonlinear Diffusion Equations)
Patterns in motion characterize failure precursors in granular materials. Currently, a broadly accepted method to forecast granular failure from data on motion is still lacking; yet such data are being generated by remote sensing and imaging technologies at unprecedented rates and unsurpassed resolution. Methods that deliver timely and accurate forecasts on failure from such data are urgently needed. Inspired by recent developments in percolation theory, we map motion data to time-evolving graphs and study their evolution through the lens of explosive percolation. We uncover a critical transition to explosive percolation at the time of imminent failure, with the emerging connected components providing an early prediction of the location of failure. We demonstrate these findings for two types of data: (a) individual grain motions in simulations of laboratory scale tests and (b) ground motions in a real landslide. Results unveil spatiotemporal dynamics that bridge bench-to-field signature precursors of granular failure, which could help in developing tools for early warning, forecasting, and mitigation of catastrophic events like landslides. View Full-Text
Keywords: explosive percolation; shear band; landslide; kinematics explosive percolation; shear band; landslide; kinematics
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Singh, K.; Tordesillas, A. Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation. Entropy 2020, 22, 67.

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