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. 2022 Jul 25;18(9):1094–1098. doi: 10.1038/s41567-022-01662-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Extended Data Fig. 6 — a, Application of the EVM method on a 2D PST simulation on flat terrain. The top left panel shows the simulation result and the bottom left panel shows the EVM result for one selected frame. The plot on the right shows the crack tip position as a function of time based on the simulation analysis and the EVM method, showing a good agreement. b, same as a for a 30 degrees slope. c, Application of the EVM method on a 3D MPM simulation of a slab - weak layer system on a 30 degrees slope. In this simulation the radius of a circular crack in the weak layer is increased until the crack propagates. The left panel shows the weak layer failure state (top view) and the middle panel shows the EVM analysis based on slab deformation (top view). The EVM method gives a good estimate of the crack propagation speed both in the up-slope and cross slope directions.