the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Sep 2023
Failure strength of glacier ice inferred from Greenland crevasses
Abstract. Ice fractures when subject to stress that exceeds the material failure strength. Previous studies have found that a von Mises failure criterion, which places a bound on the second invariant of the deviatoric stress tensor, is consistent with empirical data. Other studies have suggested that a scaling effect exists, such that larger sample specimens have a substantially lower failure strength, implying that estimating material strength from laboratory-scale experiments may be insufficient for glacier-scale modelling. In this paper, we analyze the stress conditions in crevasse onset regions to better understand the failure criterion and strength relevant for large-scale modelling. The local deviatoric stress is inferred using surface velocities and reanalysis temperatures, and crevasse onset regions are extracted from a remotely sensed crevasse density map. We project the stress state onto the failure plane spanned by Haigh–Westergaard coordinates, showing how failure depends on mode of stress. We find that existing crevasse data is consistent with a Schmidt–Ishlinsky failure criterion that places a bound on the absolute value of the maximal principal deviatoric stress, estimated to be (158 ± 44) kPa. Although the traditional von Mises failure criterion also provides an adequate fit to the data with a von Mises strength of (265 ± 73) kPa, it depends only on stress magnitude and is indifferent to the specific stress state, unlike Schmidt–Ishlinsky failure which has a larger shear failure strength compared to tensile strength. Implications for large-scale ice-flow and fracture modelling are discussed.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-1957', Anonymous Referee #1, 17 Oct 2023
Grinsted et al. use ice-sheet-wide geophysical datasets to assess the applicability of a previously untested failure criterion, the Schmidt-Ishlinsky (hereafter S-I) criterion, to predict ice failure across the Greenland Ice Sheet. This is done with the intention of being able to develop accurate predictors of crevasse formation and presence in large-scale ice-flow and fracture models. The paper is timely and is a clear evolution of the ongoing large-scale work being done on ice failure in recent years. It is a bit of an “open secret” that von Mises (hereafter vM) is a poor predictor of crevasse failure and it is good to see work being done to find better approaches, especially involving large-scale datasets. I have some thoughts regarding the failure criterion chosen, and in particular the lack of wider assessment given the prime opportunity provided by the datasets collated.
As written, it is unclear what motivation or hypothesis led the authors to propose and test the S-I failure criterion. After the abstract, the criterion is not mentioned again until the discussion (L136), where it is defined but without any clear motivation as to why. At this point, it is argued that although both vM and S-I perform quantitatively identically (L144), if measurement noise was better S-I would likely be the better performer (L144-146). It is not possible for the reader to assess whether S-I performs better or worse than any other alternative criteria common in the literature, as this data is ‘not shown’ (L147-148).
The S-I is not a criterion I have encountered before in the glaciological literature, and appears to be pretty niche outside the discipline as well - indeed, googling the phrase ‘Schmidt-Ishlinsky failure criterion’ includes this preprint among the top results. As a result, I think it is important that the authors do more to contextualise and explain the criterion, and their motivation for choosing it. This is especially true as the authors disregard even comparing the criterion to other options, as previously noted (L147-148). Given the clear effort that has been put into producing and collating the various ice-sheet-wide datasets, it would be very interesting to see a comparison/EDA of all previously suggested criteria, and make it more convincing that the S-I criterion is (qualitatively) a better option.
In the absence of this comparison, a deeper theoretical concern I have is that the S-I criterion doesn’t appear to improve upon a key weakness of the vM criterion, which is that it is relatively insensitive to the direction of stress - indeed, it is noted by the authors that the difference between compressive and tensile ice strength is an order of magnitude, and that this isn’t consistent with the vM criterion (L38-40). As the authors note, the S-I criterion does not significantly deviate strongly from this assumption (L154). Although they highlight that the S-I criterion implies ice is 15% stronger in shear relative to the tensile stress (L142), as far as I can tell from Fig. 4 the S-I criterion implies that ice is *exactly as strong* in tension and compression. However, examining Fig 4 appears to show far fewer crevasses in the compressive sections of the figure - especially if the color scale is log, which these plots often are. Therefore, although I am excited by the datasets and study design presented by the authors, the paper (at least, in its current form) leaves me questioning that crevasse failure can be adequately described by any prescribed radius in the π-plane.
MINOR COMMENTS
L95/Fig 1 - It is not mentioned in the methods exactly how the high-elevation exclusion zone is exactly derived. Manually determined? If so, the mask could be included as supplementary data.
L46 - Chudley et al. (2021) also use this data to assess crevasse formation, which is probably worth including/contrasting/comparing in the discussion.
L80/Fig 4 - Although I understand that plotting on the π-plane is a key point of this paper, I imagine most will be more familiar with plotting on a simple τ_1/τ_2 plot following Vaughan (1993). I highly suggest including this alternative visualisation in the supplementary material to aid the interested reader in comparing and contrasting, as well as in understanding how this visualisation differs from Vaughan’s approach.
Fig 3 - Some indicator of y axis scale might be nice (unless normalized?)
Fig 4 - color scale needed for quantities.
L114-115 - Observational evidence of this can be found in recent papers (Harrington et al. 2017, doi:10.3189/2015AoG70A945; Hubbard et al. 2021, doi:10.1029/2020AV000291). I agree that it is likely that modelled MAT represents a lower bound of likely temperatures. Though for practical purposes, I don’t have a better suggestion of how this can be approached.
L123-128 - This is absolutely fascinating. How could the seasonally varying regions be better represented? Is it a case of crevasse initiation being initiated at the maximum velocity/stress? Or limited by the minimum velocity/stress?
L129-132 - Or limited by resolution/ability of crevasse dataset? The crevasse dataset is taken from another source and no limitations are discussed in the paper.
L136 - does the data have a hexagonal pattern, or is the data clustered around the shear components and the hexagonal plotting style gives the impression that this is the case?Citation: https://doi.org/10.5194/egusphere-2023-1957-RC1 - AC1: 'Reply on RC1', Aslak Grinsted, 22 Dec 2023
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RC2: 'Comment on egusphere-2023-1957', Douglas Benn, 04 Dec 2023
- AC2: 'Reply on RC2', Aslak Grinsted, 22 Dec 2023
- AC3: 'Reply on RC2', Aslak Grinsted, 22 Dec 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-1957', Anonymous Referee #1, 17 Oct 2023
Grinsted et al. use ice-sheet-wide geophysical datasets to assess the applicability of a previously untested failure criterion, the Schmidt-Ishlinsky (hereafter S-I) criterion, to predict ice failure across the Greenland Ice Sheet. This is done with the intention of being able to develop accurate predictors of crevasse formation and presence in large-scale ice-flow and fracture models. The paper is timely and is a clear evolution of the ongoing large-scale work being done on ice failure in recent years. It is a bit of an “open secret” that von Mises (hereafter vM) is a poor predictor of crevasse failure and it is good to see work being done to find better approaches, especially involving large-scale datasets. I have some thoughts regarding the failure criterion chosen, and in particular the lack of wider assessment given the prime opportunity provided by the datasets collated.
As written, it is unclear what motivation or hypothesis led the authors to propose and test the S-I failure criterion. After the abstract, the criterion is not mentioned again until the discussion (L136), where it is defined but without any clear motivation as to why. At this point, it is argued that although both vM and S-I perform quantitatively identically (L144), if measurement noise was better S-I would likely be the better performer (L144-146). It is not possible for the reader to assess whether S-I performs better or worse than any other alternative criteria common in the literature, as this data is ‘not shown’ (L147-148).
The S-I is not a criterion I have encountered before in the glaciological literature, and appears to be pretty niche outside the discipline as well - indeed, googling the phrase ‘Schmidt-Ishlinsky failure criterion’ includes this preprint among the top results. As a result, I think it is important that the authors do more to contextualise and explain the criterion, and their motivation for choosing it. This is especially true as the authors disregard even comparing the criterion to other options, as previously noted (L147-148). Given the clear effort that has been put into producing and collating the various ice-sheet-wide datasets, it would be very interesting to see a comparison/EDA of all previously suggested criteria, and make it more convincing that the S-I criterion is (qualitatively) a better option.
In the absence of this comparison, a deeper theoretical concern I have is that the S-I criterion doesn’t appear to improve upon a key weakness of the vM criterion, which is that it is relatively insensitive to the direction of stress - indeed, it is noted by the authors that the difference between compressive and tensile ice strength is an order of magnitude, and that this isn’t consistent with the vM criterion (L38-40). As the authors note, the S-I criterion does not significantly deviate strongly from this assumption (L154). Although they highlight that the S-I criterion implies ice is 15% stronger in shear relative to the tensile stress (L142), as far as I can tell from Fig. 4 the S-I criterion implies that ice is *exactly as strong* in tension and compression. However, examining Fig 4 appears to show far fewer crevasses in the compressive sections of the figure - especially if the color scale is log, which these plots often are. Therefore, although I am excited by the datasets and study design presented by the authors, the paper (at least, in its current form) leaves me questioning that crevasse failure can be adequately described by any prescribed radius in the π-plane.
MINOR COMMENTS
L95/Fig 1 - It is not mentioned in the methods exactly how the high-elevation exclusion zone is exactly derived. Manually determined? If so, the mask could be included as supplementary data.
L46 - Chudley et al. (2021) also use this data to assess crevasse formation, which is probably worth including/contrasting/comparing in the discussion.
L80/Fig 4 - Although I understand that plotting on the π-plane is a key point of this paper, I imagine most will be more familiar with plotting on a simple τ_1/τ_2 plot following Vaughan (1993). I highly suggest including this alternative visualisation in the supplementary material to aid the interested reader in comparing and contrasting, as well as in understanding how this visualisation differs from Vaughan’s approach.
Fig 3 - Some indicator of y axis scale might be nice (unless normalized?)
Fig 4 - color scale needed for quantities.
L114-115 - Observational evidence of this can be found in recent papers (Harrington et al. 2017, doi:10.3189/2015AoG70A945; Hubbard et al. 2021, doi:10.1029/2020AV000291). I agree that it is likely that modelled MAT represents a lower bound of likely temperatures. Though for practical purposes, I don’t have a better suggestion of how this can be approached.
L123-128 - This is absolutely fascinating. How could the seasonally varying regions be better represented? Is it a case of crevasse initiation being initiated at the maximum velocity/stress? Or limited by the minimum velocity/stress?
L129-132 - Or limited by resolution/ability of crevasse dataset? The crevasse dataset is taken from another source and no limitations are discussed in the paper.
L136 - does the data have a hexagonal pattern, or is the data clustered around the shear components and the hexagonal plotting style gives the impression that this is the case?Citation: https://doi.org/10.5194/egusphere-2023-1957-RC1 - AC1: 'Reply on RC1', Aslak Grinsted, 22 Dec 2023
-
RC2: 'Comment on egusphere-2023-1957', Douglas Benn, 04 Dec 2023
- AC2: 'Reply on RC2', Aslak Grinsted, 22 Dec 2023
- AC3: 'Reply on RC2', Aslak Grinsted, 22 Dec 2023
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Discussed
Aslak Grinsted
Nicholas Mossor Rathmann
Ruth Mottram
Anne Munck Solgaard
Joachim Mathiesen
Christine Schøtt Hvidberg
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5426 KB) - Metadata XML