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. 2024 Sep 2;15:7379. doi: 10.1038/s41467-024-51491-7

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© The Author(s) 2024

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Illustration of the experimental setup. b Extracted slab–weak-layer assembly with added weights at 60° prior to cutting the weak layer. c Critical cut lengths values, the measured length at which the artificially introduced crack becomes unstable, for the present study (green, ∣S∣ = 88, where S is the set of experimental samples) and from the literature⁴⁴ (orange, ∣S∣ = 183). The literature dataset contains only upslope cuts (φ ≤ 0°) but several different weak layers and slab assemblies such that recorded cut lengths scatter widely. Tests on the same slab–weak-layer assembly with constant added weights (site A), 1.59 kN/m², show a trend of increasing critical cut lengths a_c with inclination for downslope cuts (φ > 0°). Increasing surface dead loads (site B) with extra load, 2.53 kN/m², vs. site B, 1.48 kN/m², breaks the observed trend. Critical cut lengths were measured with ±1 cm uncertainty and slope angles with ±2° uncertainty. d Mode II energy release rate at the onset of unstable crack propagation as a fraction of the total energy release rate. The mode II fraction increases rapidly with inclination for downslope cuts (φ > 0°) but only moderately for upslope cuts (φ < 0°). All data points (site A, site B, site B with extra load, literature data) follow the same trend with little scatter. The literature dataset comprises almost no mode II contribution, even at inclinations as high as 36°. Mode-ratio uncertainties were calculated from error propagation of uncertainties in cut length (±1 cm), inclination (±2°), and weak-layer thickness (±1 mm). e–g Stacked histograms truncated at 20 counts per bin. The distribution of tested inclinations (e) shows that, historically, propagation saw tests were predominantly performed in flat terrain and cut upslope (orange) while the present study (green) focuses on steep downslope cuts. Critical cut lengths (f) are distributed uniformly with mean and standard deviation of a_c = 31.0 ± 14.4 cm indicating equal likelihood for a wide range of cut lengths. The distribution of mode II fractions of the total energy release rate (g) shows that the literature data (orange) contains no information on mode II energy release rates while the present study (green) covers the full range between pure mode I and pure mode II fracture toughness of weak layers.