Where curling stones collide with rock physics: Cyclical damage accumulation and fatigue in granitoids

Leung, Derek D. V.; Fusseis, Florian; Butler, Ian B.

doi:10.5194/egusphere-2025-3499

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https://doi.org/10.5194/egusphere-2025-3499

Preprints

14 Aug 2025

| 14 Aug 2025

Where curling stones collide with rock physics: Cyclical damage accumulation and fatigue in granitoids

Derek D. V. Leung, Florian Fusseis, and Ian B. Butler

Abstract. Fatigue and damage accumulation in granitoids are classical, but poorly characterised, rock mechanics problems. We explore these phenomena by examining curling stone impacts. Curling stones are slid on ice and made to collide along a circumferential striking band. This well constrained scenario involves uniaxial compression of convex surfaces (i.e., Hertzian contacts). Each stone experiences about 2900 impacts per season, over a lifespan of 10–15 years before refurbishment, providing a unique opportunity to study fatigue and damage accumulation under cyclic loading.

Here, we first determine the stress magnitudes of head-on curling stone impacts using on-ice experiments involving a high-speed camera and pressure-sensitive films. We then characterise the damage observed in aged stones using photogrammetry, microtomography, and microscopy. For high-velocity impacts (2.93 ± 0.15 ms⁻¹), a curling stone is locally and momentarily stressed to at least 300–680 MPa, exceeding its unconfined compressive strength. Curling stone impacts are dynamic in nature, as evidenced by strain rates (24 ± 4 s⁻¹) that resemble seismic magnitudes, ejection of rock powder during collisions, and prevalence of Hertzian cone fractures in aged stones. In the striking band, damage is confined to macroscopic Hertzian cone fractures and their immediate collet zones, and does not appear to extend beyond about 3–5 cm into the stones (radially). The circumferential density of cone fractures is limited to about 2–2.5 fractures per cm.

We propose that (1) early, high-velocity impacts initiate cone fractures up to a specific spatial density, and (2) with subsequent collisions in the same regions of the striking band, cone fractures progressively propagate and coarsen. This concentrates and channels the accumulated damage, shielding the rest of the stones from reaching critical stress levels for damage. Our findings are significant for applications where rocks are exposed to repetitive, high-stress impacts and suggest that narrow damage zones can dampen high-impact stresses.

Received: 30 Jul 2025 – Discussion started: 14 Aug 2025

Competing interests: Some authors are members of the editorial board of Solid Earth

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

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Derek D. V. Leung, Florian Fusseis, and Ian B. Butler

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-3499', Anonymous Referee #1, 15 Sep 2025
Review of Leung et al., 2025 in Geosphere: "Where curling stones collide with rock physics: Cyclical damage accumulation and fatigue in granitoids"
The authors aim to understand damage in granites subjected to cyclic loading. To do so, they see an opportunity in studying curling stones, made from granite and subjected to repeated impact loading. Using high speed camera footage and pressure-sensitive film, the authors obtain first-order estimates of stress, strain, strain rates, and energy dissipated by permanent (fracture) damage. An extensive microstructural study reveals the geometry of the fracture damage and sheds some light on the mechanics responsible for creating it. The authors finally conclude that the repeated loading is dynamic in nature, it may be an analogue for some dynamic processes in nature. Finally, the authors present a conceptual model of how a damage zone forms and evolves with repeated impact loadings.
On the technical execution part of the paper (performing the experiments, the microstructural study) I have little to no comments. The main issues with the manuscript are 1) the oversimplified mechanical analysis of the problem, 2) the applicability of the experiments to natural deformation processes and the insufficient embedding of this study within existing (experimental) studies. More on these main issues follows next, but they are also often at the basis of the more detailed comments given further below. Since these issues are key to the conclusions of the paper, I recommend major revisions.
The mechanical analysis (section 2): Averages for stress, strain, and strain rate over the duration of loading are presented first, following impact mechanics. A second measure, the maximum stress, is based on contact mechanics of two elastic bodies. Both are insufficient for these experiments:
First, they do not take into account that stress at such high loading rates/impacts now propagate as waves. The stress, strain, and strain rate fields vary highly in space and time. The paper attempts to explain the observation of damage concentrated near the impact, and heterogeneous stresses that decay away from the impact may be a key component that is overlooked by the authors. Understanding this and achieving “stress equilibrium” over an entire sample (i.e., stress is the same everywhere, but still varies over time) is already a challenge in typical simple uniaxial experiments on Split-Hopkinson Pressure Bars (SHPSs) performed at comparable strain rates (e.g., Nemat‐Nasser et al., 1991; Zhang and Zhao, 2013; Aben et al., 2017), but a necessary one to say something about representative dynamic material parameters or constitutive dynamic behaviour. The impact mechanics approach uses a time average, which may provide a first-order rough sample-wide estimate, but does not provide the level of detail to match with the microstructures. The contact mechanics approach entirely lacks any consideration for the dynamic nature of the experiments.

Second, the average strain from the impact mechanics approach and the entire contact mechanics approach are based on the assumption of linear elastic behaviour of the material. The microstructural study reveals this is not the case, and inelastic deformation (most likely at higher stresses) is accumulated. This affects the stress-strain relation and the assumption of linear elasticity leads to an overestimation of the actual stresses at the contact. How this combines with the dynamics at the contacts previously mentioned is unclear, and so the calculated maximum stress estimates are unfounded.

Finally, it may be beyond the presented study to measure and/or model the full stress field during the impact loading, as it will be hard to measure on a large sample with a complex geometry. However, the issue of dynamic loading and wave propagation should be addressed nonetheless so that readers can place the averaged stress/strain/strain rate estimates in the correct context, and it may aid to explain the microstructural results. I recommend to remove the maximum stress estimates all together.
Scientific context of the study: The previous major comment is partially related to the issue of sub-par scientific context given in the manuscript. Starting with the introduction, the scientific aim remains elusive and vague. What is specifically the question that needs to be answered regarding repeated impact loading? What is the current state of knowledge? Very little literature is cited on the subject of dynamic loading (I have provided a few references throughout and at the end of this review), let alone on the effects of repeated dynamic loading (e.g., Doan & d’Hour (2012), Aben et al (2016); Braunagel & Griffith 2019). A decent set of literature to set up the specific problem to be solved in this manuscript is not only helpful for the reader, but would also have highlighted the difficulties in performing and analysing dynamic loading experiments to the authors (see first main issue). On the issue of applicability of the impact experiments to natural deformation processes, the comparisons with stresses and strain rates are too hasty and incorrect (see detailed comments on them below). One field (which happens to be my expertise) where indeed the experiments could be analogues are dynamic loading in fault damage zones (e.g., Doan & Gary 2009; Yuan 2011; Braunagel & Griffith 2019). Here, the idea of a damage zone “protecting” undamaged regions has also been opted (Ostermeijer et al., 2022). This has been overlooked by the authors, which makes me worry about other potentially overlooked but relevant literature. I hope that a substantial effort on embedding this study within existing literature can help to mature the paper considerably, as it now feels to much as a fun “gimmick” with curling stones where the application was an afterthought.
Detailed comments
Line 63: Double meaning for the notation a (acceleration and semi-major axis).
Line 156: “Higher probability thresholds… in some tiles.”: Why is this an issue? At least, with a 90% threshold, the remaining 90% of pixels has been robustly identified, which is not the case when using a low threshold of 50% probability. The aim of the identification exercise is to identify the components of the rock with a certain amount of confidence, not to identify everything by basically just guessing.
Line 171: Why were the other 21 experiments discarded/not reported here?
304-325: This whole section is full of statements without proper arguments or references to support them. In more detail:
Line 305: Why potentially?

Line 307-309: What is the evidence for this statement?

Line 317: Who does the 4% compare with other studies on energy dissipation by fracturing during geo-dynamic events such as earthquakes?

Line 318-319: I do not agree with/do not understand this sentence, what exactly is significant (possibly use another word here, as it is inherently related to statistical metrics)? The sentence implies that the calculations are a surprising outcome relative to a hypothesis that is never stated. Aside, the stresses are not instantaneously (they are “transferred” from stone to stone by stress waves at the P-wave speed of the material). What is meant by the stresses are recovered by the acceleration of the resting stone?

Line 320-321: This sentence contains a lot unclarity: What does “efficient in dissipating energy” mean? That the rock dissipates a lot of the impact energy, or that it does not dissipate a lot? “once it is saturated in fractures”: Where are the numbers to back this up, does the 4% mentioned earlier change with number of impacts?

Line 333-334: The sentence damage must exceed a threshold to produce fatigue damage is vague and needs more explanation. Is this conditional on repeated loadings at the same stress level? Clarify that Zhou et al (2018) performed high strain rate (i.e., dynamic) loading experiments. Are the strain rates comparable? Similar, but earlier, work on repeated dynamic loading in compression was done by Doan & d’Hour (2012), Aben et al (2016)).
Paragraph starting on Line 335 and table 1: This comparison exercise with stress magnitudes of natural deformation processes is too simplistic and leads to erroneous analogies between processes: Stress is a tensorial quantity, the curling experiments performed here are by approximation uniaxial so that what is described as “the” stress is one of the diagonal uniaxial stress component. This cannot be compared to earthquake stress drops, which are shear stresses, or to lithostatic stresses which are meaningless without knowing the other principal stress magnitudes. It is unclear how thermal and mining-induced stresses are defined (are they stress invariants or uniaxial stress components?). In short, from this table, the only directly comparable ones are rockfalls and ballistic impacts.
Line 378: I guess the authors mean that, rather than dampening damage (if such a thing is possible), the stresses are dampened by energy dissipation in the damage zone.
Table 2: Similar comment as to table 1, be cautious when comparing strain rates with other strain rates. Comparing uniaxial strain rates with coseismic slip rates is incorrect, as the latter is a shear strain rate. There is plenty of literature on high strain rate deformation experiments at uniaxial conditions in compression that should be used to put this work into context.
Line 361: It is confusing to encounter stress component notation whilst the rest of the manuscript only speaks of a peak and average stress. How does this stress component relate to the stresses derived from the experiments? Clarify that this specific stress component mentioned here is the maximum tensile stress component in the vicinity of the Hertzian contact.
Figure 14 is not referenced in the main text.

References
Nemat‐Nasser, S., J. B. Isaacs, and J. E. Starrett (1991), Hopkinson techniques for dynamic recovery experiments, Proc. R. Soc. London, Ser. A, 435(1894), 371–391.
Zhang, Q. B., and J. Zhao (2013), A review of dynamic experimental techniques and mechanical behaviour of rock materials, Rock Mech. Rock Eng., doi:10.1007/ s00603‐013‐0463‐y
Aben, F. M., Doan, M.-L., Gratier, J.-P., & Renard, F. (2017). Coseismic damage generation and pulverization in fault zones: Insights from dynamic Split-Hopkinson Pressure Bar experiments. In M. Y. Thomas, H. S. Bhat, & T. M. Mitchell (Eds.), Evolution of fault zone properties and dynamic processes during seismic rupture (pp. 47–80). Washington, DC: John Wiley & Sons
Doan, Mai-Linh, and Virginie d’Hour. "Effect of initial damage on rock pulverization along faults." Journal of Structural Geology 45 (2012): 113-124.
Aben, F. M., et al. "Dynamic fracturing by successive coseismic loadings leads to pulverization in active fault zones." Journal of Geophysical Research: Solid Earth 121.4 (2016): 2338-2360.
Xia, Kaiwen, and Wei Yao. "Dynamic rock tests using split Hopkinson (Kolsky) bar system–A review." Journal of Rock Mechanics and Geotechnical Engineering 7.1 (2015): 27-59.
Doan, Mai-Linh, and Gérard Gary. "Rock pulverization at high strain rate near the San Andreas fault." Nature Geoscience 2.10 (2009): 709-712.
Yuan, Fuping, Vikas Prakash, and Terry Tullis. "Origin of pulverized rocks during earthquake fault rupture." Journal of Geophysical Research: Solid Earth 116.B6 (2011).
Braunagel, Michael J., and W. Ashley Griffith. "The effect of dynamic stress cycling on the compressive strength of rocks." Geophysical Research Letters 46.12 (2019): 6479-6486.
Ostermeijer, Giles A., et al. "Evolution of co-seismic off-fault damage towards pulverisation." Earth and planetary science letters 579 (2022): 117353.
Citation: https://doi.org/10.5194/egusphere-2025-3499-RC1
- AC1: 'Reply on RC1', Derek D.V. Leung, 10 Dec 2025
  
  Dear Anonymous Reviewer 1:
  Please see the attached document for a summary of our responses to your comments, as well as a list of proposed modifications intended to address these comments and improve the manuscript.
  Sincerely,
  Derek Leung
  
  Citation: https://doi.org/10.5194/egusphere-2025-3499-AC1
RC2:
'Comment on egusphere-2025-3499', Elma Charalampidou, 26 Sep 2025
The paper by Leung and co-workers focuses on understanding the effect of cyclic damage and fatigue on curling stones. This is a very interesting paper, in my opinion, trying to link the game induced damage due to curling stone collision with the damage observed in nature (natural materials). For this analysis a combination of non-destructive experimental methods, such as high-speed cameras and pressure-sensitive films, photogrammetry, microtomography and microscopy is used. The authors discuss the data in terms of a) the boundary conditions of curling stone collision; b) understanding how damage accumulates in curling stones and in particular damage linked to crescent-shaped fractures; c) a proposed evolution model for curling stones that integrates the previous points.
A general observation relates to the clarity around the materials studied. It’s not always evident which results correspond to Ailsa Craig Common Green and which to Ailsa Craig Blue Hone. While this distinction is made in some sections of the manuscript, it’s missing in others, which makes interpretation more difficult. Additionally, it’s not consistently clear whether the two rock types exhibit similar or different mechanical behaviours across the various analyses - especially since different types of results are presented for each (with the exception of a couple of graphs).
It would also be helpful to clarify how pristine rock samples are identified, which ones have experienced greater loading, and what information is available regarding samples/rocks that were previously used extensively (or used in varying numbers of games) prior to testing. I believe, including this context would strengthen the narrative and better support the findings.
That said, I find this to be a very compelling and valuable piece of work!
Some more precise comments follow:
Is it rock physics or mostly rock mechanics for the title?

Is there any difference between Ailsa Craig Common Green and Blue Home in terms of the structure, minerals, grain size etc.?

Lines 118-119: Could you visualise by eyes the rock powder? What was the advantage using the high-speed camera instead, if the powder was retrieved post experiment? Which type of curling stone was used during these experiments (Common Green or Blue Hone)? Have you observed any differences in the quantity of powder generated and the microstructure (if you have tested both Common Green and Blue Hone)?

Section 3.3: What about the Ailsa Crag Common Green stone? Why not used for thin sections? Is it Crag or Craig (see line 75)?

What about the rest 21 experiments? Is there any reason why were not analysed/presented herein?

On-ice experiments: what about lower impact velocities (~0.5 ms/-1)? Do you have an example that can provide a narrative/argument like that of hight velocities?

How have you defined the impact velocity range (0.5-2.9 ms-1)? I mean why this range?

5: My understanding is that all these are different experiments. Which of the two materials were used herein (Common Green and Blue Hone)? Is there any info about the history of deformation, i.e., which cycle each of those images show?

6: Does the Common Green stone show similar type of fractures?

Is Fig. 6 and 7 from the same sample?

8: How the grey and colour lines corelate – i.e. which data set is the coloured one if the whole dataset is in grey colours? What does ‘n’ stand for? 8e: what do the small circles represent? Which is the damage state – graph showing theta?

Line 218: pls erase second have.

9: What does the length (i.e., 30 cm) stand for? How do you define maturity? What does ‘n’ stand for?

10: How do you know that some of these fractures were not pre-existing (existing before the experiment), or else pre-existing fractures have not further propagated? Which of the two Ailsa Craig rocks is the one in Fig. 10?

Lines 271: how do you identify pristine and juvenile stages?

Line 381: why rock physics and not rock mechanics?

Line 385: The damage evolution of curling stones consists of several damage states: pristine, weakly incipient, incipient, juvenile, and mature. How are those stages defined? If the same curling stone was used for previous games, how do you define the pristine sample? – I think I’m missing something here.

Lines 385-410: it would be great to support this narrative with images you have presented before in the results (or the accompanied material).

I can see a damage evolution – can you please elaborate more on the actual model? I would possibly name it conceptual model.

Conclusions- they need a bit of extra work and some narrative instead only bullet points.

All the best,
Elma Charalampidou
Citation: https://doi.org/10.5194/egusphere-2025-3499-RC2
- AC2: 'Reply on RC2', Derek D.V. Leung, 11 Dec 2025
  
  Dear Dr. Charalampidou,
  Thank you for your constructive comments on our manuscript. We present a response to your comments in the attached document, which includes a summary of the ways in which we have improved the manuscript.
  Cheers,
  Derek Leung
  
  Citation: https://doi.org/10.5194/egusphere-2025-3499-AC2

Derek D. V. Leung, Florian Fusseis, and Ian B. Butler

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derekdvleung/curling-stones: curling-stones-2025-07 Derek D. V. Leung, Florian Fusseis, and Ian B. Butler https://doi.org/10.5281/zenodo.16191540

Derek D. V. Leung, Florian Fusseis, and Ian B. Butler

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Short summary

Curling stones often collide with each other during a game. Over time, these collisions cause damage in the striking bands on the sides of the stones. We determined experimentally how hard these stones collide into one another. We then looked at old curling stones to understand how damage builds up in these rocks. We found that early, fast impacts produce fractures until the striking band is saturated in fractures. Repeated impacts after this stage make fractures grow.


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