Rock Glacier Dynamics by a Thermo-Elastic-Viscoplastic Constitutive Relationship

Round 1

Reviewer 1 Report

This paper develops a one-dimensional model to evaluate the role of different forcing factors on rock glacier dynamics. The authors benchmark their model agains observations from the Murtèl-Corvatsch rock glacier in Switzerland. The conclusions offer a way to parameterize rock glacier flow and predict how kinematics and temperature depend on geometry and thermal boundary conditions. I see this paper as a potentially valuable contribution, after significant revision. In its present form, I cannot recommend publication.

Major points

One of the characteristics of rock glaciers is that they are of limited spatial extent, with irregular boundaries and heterogeneous interiors. A quasi-planar shear zone may be present in many, but not necessarily extend across the feature. This is to say that to convince me that a one-dimensional approach explains a spatially complex feature, I would need to see significantly more justification. For example: What part and how much of the rock glacier does the model represent? How representative is the planar shear zone geometry? What degree of longitudinal and transverse heterogeneity would markedly influence the vertical thermal and velocity structure? The model set-up is not particularly customized to the unique characteristics of a rock glacier, and without incorporating those features (or explaining why they are irrelevant to the velocity structure), I find it hard to see how this approach will gain traction in the community.

To center the paper around a new model, I think the authors would be well served to spend more time describing the theory – both delayed plasticity itself and why alternatives don't meet the needs.

The validation is not sufficient for me to feel comfortable extrapolating predictions such as to those shown in Fig 10. Additional validation and benchmarking would include comparison with analytical solutions and/or more than one observational dataset.

The writing throughout the manuscript would benefit from a careful editorial review. In several places, only some of which I mention below, I found that the word choices or sentence structure made it difficult to discern the meaning.

 

Specific comments

Line 36: should “increments” be “increase”?

Line 42: “increase” feels to be in the wring tense

Line 47: “increment does not feel like the best word choice”

I suggest explaining how Eq 1 derives from the classic Tresca formulation

c* in eq 3 is better described as something other than a dummy variable

Fig 1: I don't understand the need to have 0 cohesion at 0 degrees. The presence of liquid water would affect cohesion, but that is a discontinuity, rather than a continuous change to 0 kPa. A linear fit to the Yamamoto and Springman data, with an intercept around 200kPa, seems appropriate. Perhaps I am missing something about the mechanics. Corollary, on Line 153: Why is the goal to obtain an linear fit in log space? I would appreciate a more physics-based rationale.

Line 128 and through Eq 4: Plastic potential and viscous nucleus would benefit from more explanation. They are not widely understood terms.

Line 184: wording is awkward

Line 186: I am not clear of the purpose of the reference to heat generation

How accurate is the assumption of homogeneity within the shear horizon? Although perhaps considering a larger area, Line 237 reports significant heterogeneity in the rock glacier.

Fig. 3: (1) Please outline the rock glacier. (2) The legend for aspect is too small to read. (3) I suggest plotting on the figure where the comparative hole is located.

 

Author Response

Dear Reviwer,

thank you for your suggestions. 

We tried to improve the paper through your work!

 

See the attachement.

 

Best,

 

Stefano Alberti

Author Response File: Author Response.pdf

Reviewer 2 Report

It is an interesting investigation and it comes to fill an important gap in the subject matter, the constitutive aspect and geotechnical modeling of the rocky glacier.

See comments on page 2 and 6 of attached document:

It would be good to put a diagram or figure of what is explained of the rocky galciar. Parts and definition. The geomorphological aspect of a rocky glacier is not obvious to every researcher.

The geomorfology of the rock glacier is not clearly identify and explained, cannot see legend of c) at Figure 6
see example on how to indicate where the glacier is:

https://uvadoc.uva.es/bitstream/handle/10324/40655/Geomatic-methods-LaPa%c3%bal-Rock.pdf?sequence=1&isAllowed=y

These comments are just to improve the paper, because i think the shape of the rock glacier is not fully explained and understandable in Figure 6

Author Response

Dear Reviewer,

thank you for your suggestions. 

We tried to improve the paper through your work!

 

See the attachment.

 

Best,

 

Stefano Alberti

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The changes the authors have made clarify aspects of the manuscript and make it easier for the reader to follow their reasoning. I appreciate their effort. I still expect that by addressing the remaining comments through changes in the text, the manuscript would be stronger. The updated manuscript does not appear to reflect the explanations of those remaining comments in the authors' letter. To take them point by point:

 

I agree with the author's perspective that in the absence of sufficient 2- and 3-D data, a 1-D model can provide useful insights. The authors provide some explanation of their position in the letter, but do not appear to address the concern in the text. I believe that additional discussion about the suitability of a 1-D model is warranted in the text, regardless of how many other studies utilize it. As an aside, there are plenty of instances in which data in the other dimensions are unavailable and a 1-D model is not a good approximation. One way to address the issue is to explore parameter space with geologically reasonable values in the other dimensions, then compare the results to the 1-D case. The idea of modeling is not to simulate the natural situation perfectly, but rather to gain insight into the overall system behavior. For the present paper, I do not suggest running 2- or 3-D models. But I do suggest that the authors include a clearer statement of the limitations of the modeling. Lines 52-60 describe the heterogeneity, so it will help the reader to know what information the 1-D model can provide and where it falls short of representing the natural system.

 

I could have been more clear in my comment about the model setup vis a vis a rock glacier. I have no doubt that the temperature profile derives from an exceptional dataset. My concern is that the model is one of a simple shear zone between two rigid blocks (line 228). Moreover, line 225 suggests that the deformation of the upper block is negligible. However, and maybe I am missing something obvious here, I read Figure 4d as indicating that approximately 40% of the total surface displacement is accommodated by the domain that is held rigid in the model (Domain 2). Thus the domain that accommodates 100% of the deformation in the model accommodates only 60% in the natural setting. On top of that, the model appears to over-predict the surface motion. It is this behavior where I have trouble matching the modeled approach to the geologic situation. I feel this is an important discrepancy the authors should address in the text.

 

The explanation the authors provide about the validation is understandable, though does not change the confidence level in the model. In addition, recognition of this limitation should appear in the text.

 

I understand the explanation about the cohesion, though I am not convinced it will drop to zero – I would think it would still be in the few tens of kPa. Nevertheless, the shape of the curve does not appear supported by data and it is unclear to me how much the shape of the curve affects the results. I would guess minimally given the temperature expected for the shear zone, but some discussion to this affect would benefit the paper.

 

My comments all center around the idea that the paper does a good job setting up the problem but that I leave the paper uncertain how useful the model is. One conclusion claims that the model reproduces surface displacement well to within an order of magnitude (Line 370). I don't believe the authors show a direct comparison of measured vs calculated displacements; it appears that the model overestimates displacement by approximately a factor of ~4 and does not account for deformation in the upper domain. That does not give me much confidence that the model captures the essential physics. However, being that close may well be sufficient for the authors' goals – additional discussion of the accuracy and therefore utility of the model would make me more confident this study will find greater value with the readers.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

 

I appreciate the additions the authors have made to the text. Those changes will inform the reader much better about the robustness and strength of the conclusions.

 

I have a two minor comments to help the final version read more smoothly:

1. (366) move “is crucial” to the end of the sentence

2. (371-372) I suggest rewording “Furthermore, nevertheless the heterogeneity shows by quaternary forms as rock glaciers, a simplification on homogeneity of shear band is necessary in all the cases in which the information regarding the geometry and the composition/mechanical behaviour of the material in the shear zone are very limited.” to something like “Furthermore, due to the limitations of constraining the geometry and composition/mechanical behaviour, the model simplifies the shear band to be homogeneous and planar.”