the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 May 2026
Recovery of Strength in Thermally Cracked Freshwater and Salt-Water Ice
Abstract. The integrity of ocean and lake ice covers is increasingly threatened by climate change, which reduces ice extent and promotes breakup. In addition to thinner ice and larger waves, thermal cracking may also contribute to ice cover failure. This study investigates the impact of thermal cracking on the flexural strength of freshwater and sea ice. Laboratory experiments show that when a narrow region of ice is thermally shocked, the flexural strength of both freshwater and sea ice initially decreases but subsequently recovers completely. In contrast, when the entire surface is thermally shocked, strength recovery is only partial in freshwater ice, while sea ice again fully recovers its strength. Repeated cycles of cracking followed by healing do not affect the recovered flexural strength. Additional experiments involving creep demonstrate that compressive stress enhances healing, highlighting the role of ice sintering in strength recovery. The differing behavior between localized and full-surface cracking is attributed to residual compressive stresses that develop during healing when only a narrow region is shocked. Rapid healing observed in sea ice is likely facilitated by its porous structure and the presence of brine, suggesting that natural sea ice may retain significant mechanical integrity even after thermal cracking.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2464', Anonymous Referee #1, 15 Jul 2026
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RC2: 'Comment on egusphere-2026-2464', Anonymous Referee #2, 16 Jul 2026
The manuscript investigates the flexural strength of freshwater and saline ice and the effect of thermal cracks on its recovery through laboratory-scale experiments. By combining results from the authors' previous studies with new experimental data, the paper provides a more complete analysis of this topic. The new experiments extend the earlier work by considering specimens with full-surface cracking, in addition to specimens containing cracks confined to a narrow band. This distinction is important, as full-surface cracking is more representative of conditions expected in natural ice. The manuscript distinguishes between previously published results and the new contributions. The amount of new experimental data and analysis is sufficient to constitute a meaningful contribution.
While several aspects would benefit from clarification and some figures need improvements, the manuscript fits well within the scope of the journal and should be of interest to its readership. The reviewer recommends publication after revisions.
Comments and suggestions
- Although the experimental setup has been presented in detail in the authors' previous publications, it would be beneficial to include a schematic or photograph of the setup in the present manuscript. This would improve the paper's self-contained nature and make it more accessible to readers unfamiliar with the earlier work.
- It would also be valuable to include representative images of specimens exhibiting narrow-band cracking and specimens with full-surface cracking. In particular, the latter appears to represent new experimental conditions and would help readers appreciate the distinction between the two cases.
- It remains somewhat unclear where the reader should look in Figures 3 and 4 to identify the relevant results. How are the full-surface cracked specimens represented in this figure? Do they exhibit healing behavior comparable to the narrow-band cracked specimens? A brief clarification in either the figure caption or the main text would improve readability.
- The manuscript needs an experimental matrix summarizing the performed tests, including the different test categories and the number of experiments conducted in each case. At present, this information is difficult to compile from the text and, in some instances, may not even be there.
- For a more coherent presentation of the methodology and results, Figures 3 and 4 would benefit from explicitly including the test categories (i)–(v) in the legends. The current legends provide detailed descriptions of each category, but these are difficult to relate to the figures, particularly given the large amount of data displayed. This is especially true for Figure 4, which presents data divided into seven categories, which do not match the ones in the text.
- The captions of Figures 3 and 4 could also provide brief guidance on how the figures should be interpreted (for example, highlighting the main trends or indicating which datasets should be compared). While the text explains these aspects, a small amount of guidance in the captions would make the figures easier to interpret independently. In addition, the markers and axis labels are rather small, and using larger symbols and fonts would improve readability.
- Lines 237–239 (and 312–314): It is not immediately apparent that the temperature evolution was not measured directly but instead estimated using a model. This only becomes clear later in the manuscript (Lines 312–314). A brief explanation at the earlier point, or a reference to the model used for the temperature estimates, would help avoid confusion.
- Line 335: The sentence beginning on this line appears to be incomplete or may be missing a few words.
- Effect of creep and compression: One limitation of the current study is that all experiments were conducted using a single compressive stress level. While the presented analysis is consistent with the available data, investigating additional compressive stress levels in future work would strengthen confidence in the generality of the conclusions. The reviewer is not suggesting that further experiments are necessary for the present manuscript, but it would be appropriate for the authors to acknowledge this as a limitation of the study.
- Some references require attention. For example, the manuscript cites Murdza et al. (2022) in several places, whereas the reference list only contains Murdza et al. (2022a) and Murdza et al. (2022b). Please ensure that all in-text citations correspond correctly to the bibliography. There are also a few minor technical issues throughout the manuscript, such as instances where references are placed in parentheses unnecessarily. These are relatively minor and will likely be addressed during the revision process.
Citation: https://doi.org/10.5194/egusphere-2026-2464-RC2
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- 1
This paper draws conclusions about the micro scale physics that takes place during the recovery of strength of ice after thermal cracking. The physical behavior is deduced from a series of tests: full surface thermal cracking (no data shown); narrow band thermal cracking (previously presented in Murzda et al., 2022a); repeated cycles of cracking and healing (no data shown); compressive stress influence on healing (no data shown); creep-assisted crack tip blunting by cycling (data presented in Fig 3). The arguments are coherent and the experiments appear to support the authors' conclusions. However I believe the paper would be significantly improved if their data were presented in figures (histograms, box plots, etc).
Presentation of data: Data presentation is especially important as the paper draws on new, as well as previously published data, to come to microstructural conclusions. The authors are careful to delineate the previously published work. On line 117-120, they state “the full-surface thermal cracking, repeated cracking–healing, compressive-creep, and sea-ice cyclic-loading experiments are newly reported here. Some cyclic-loading results from Murdza et al. (2023) are also reinterpreted in the context of creep-assisted crack-tip blunting.” However the lack of new experimental data in the paper leave the reader wondering about their number and quality. I also felt there were details missing that I would have liked.
Surface temperature calculation: It seems that the surface temperature of the ice was simulated (see Supporting Information) rather than measured. Were there any “calibration” experiments to check that the correct order of magnitude was simulated. For example, what is the justification for choosing the value of the heat transfer coefficient? In addition, was the latent heat of the phase change of the liquid nitrogen taken into account? Surely the temperature change would be very dependent on the volume of liquid nitrogen discharged. Was this carefully controlled?
Experimental parameters: What was the frequency of cycling in the creep-assisted crack tip blunting? How are time and cycles distinguished from each other in these experiments? How many experiments were performed in all cases where flexural strength is quoted with an error.
Minor comments and typos
Line 50-51: “the present study aims to explore how thermal shock and subsequent healing impact the flexural strength of both freshwater ice and sea ice.” Was the work carried out in order to understand the physics of the healing of thermal cracks in ice; or was the aim to simulate ice in its natural environment?
Line 102: “underlying”
Lines 181-189: The data on healing after full-surface thermal cracking are not presented. These could be displayed as, for example, histograms of flexural strength values for each condition. Or as box plots? How many experiments were performed?
Line 191: Fig 2 (which is Fig 2 of Murzda et al., 2022a with the normalized temperature added) is referred to in line 191 before the description of the normalization (lines 230-236). The normalization description could be given in the Methods.
Line 200: Rather than “comparable” I would say “within error”
Line 210-214: How many experiments? Does it matter how long the ice crept under compression? No data are presented.
Line 216-226: Frequency of cycling? It would be interesting to have these data presented, and to know the number of tests, rather than just have the flexural strengths stated.
Line 236-239: Flexural strength experiments seem to have been conducted in clusters, within 1s, between 4-10 s and from 300s after cracking. Thus the strength recovery time can either be vague or needs to be defined. The reader also needs to know the uncertainties in the simulation of surface temperature in order to assess whether it is it reasonable to state that “surface temperature recovers significantly faster than strength”
Line 276-279: It would increase the impact of this paragraph if there were data presented.
Line 280: “a narrow band of the freshwater ice”
Line 335: I don’t understand what the “real” and “apparent” area of the contact face mean. This is made more confusing because subscript r is used to mean “recovered” and to mean “real”. Please could you also briefly explain why the recovered strength is proportional to the ratio of real to apparent contact area.
Lines 337-349: I think that the effective bending stress of 0.5 MPa is used on line 342 because of the applied outer-fiber stress of 1 MPa in test sequence (iv)? However this is explained, without reference to 1 MPa in test sequence (iv), after the calculation. Again it would be much more impactful if the reader was presented with the data.
Line 355: Fig 3 does not have time and we are not told the frequency of cycling.
Line 359-361: “by Renshaw and Schulson (2001), crack blunting dominates crack growth”
Eq (6): What is σe?
Line 363: Where does σt appear? What is c?
Eq (7): What is c?
Eq (8): Are n and B the same as in Eq (5)? What is E?