the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Scaling between volume and runout of rock avalanches explained by a modified Voellmy rheology
Stefan Hergarten
Abstract. Rock avalanches reach considerably greater runout lengths than predicted by Coulomb friction. While it has been known for a long time that runout length increases with volume, explaining the increase qualitatively is still a challenge. In this study, the widely used Voellmy rheology is reinterpreted and modified. Instead of adding a Coulomb friction term and a velocity-dependent term, the modified rheology assigns the two terms to different regimes of velocity. While assuming a transition between Coulomb friction and flow at a given velocity is the simplest approach, a reinterpretation of an existing model for the kinetic energy of random particle motion predicts a dependence of the crossover velocity on the thickness of the rock avalanche. Analytical solutions for a lumped mass on a simple 1-D topography reveal the existence of a slope-dominated and a height-dominated regime within the regime of flow. In the slope-dominated regime, the kinetic energy at the foot of the slope depends mainly on the slope angle, while the absolute height relative to the valley floor has little effect, and vice versa. Both regimes can be distinguished by the ratio of a length scale derived from the rheology and the length scale of the topography. Long runout occurs in the height-dominated regime. In combination with empirical relations between volume, thickness, and height, the approach based on the random kinetic energy model reproduces the scaling of runout length with volume observed in nature very well.
Stefan Hergarten
Status: open (until 06 Jul 2023)
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RC1: 'Comment on egusphere-2023-144', Anonymous Referee #1, 28 Mar 2023
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Paper is definitely interesting, but for me (i'm geologist) it was difficult to flollow. the explanation.
It would be really useful if you will add a list of all parameters used in the equations with all these quantities dimensions and their physical meaning (may be a schematic cross-section). It will help a lot to readers from the geological community to follow your explanations.
Some comments are in the attached file.
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CC1: 'Comment on egusphere-2023-144', Matthias Rauter, 20 May 2023
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The manuscript deals with the unsolved problem of extreme runouts of large landslides and rock avalanches. I not nesesarrily agree with the approach, but it is a pressing issue and intersting viewpoint and deserves more discussion. The figures are great and clean!
I suggest the publication after a major revision.
Major issues:
The scope of the manuscript is a bit unclear to me. Is it to understand and explain the mechanisms in large avalanches? To develop a better friction model? (Then the issue below should be discussed in more depth) Should it be a physically consistent or an empirical approach? The interpretation of lambda as a length should then also be discussed in more depth.
I do not understand the scaling (section 4). The runout scales with the friction term but reinterpreting it as a length scales does not seem to be useful to me. I also cannot follow Eq. (24). I also think that physical relations and parameters are mixed together with emprical relations which does not always make sense. I would check this section carefully.
The biggest problem I have is the sharp transition between the regimes and the jump in the friction. This seems rather unphysical to me and might lead to sever numerical issues.
I would also bring in some real case examples. Even using the simple model it can showcase the behaviour of the rheology.
Minor issues:
I am not sure how strict this journal is with structuring of the manuscript, but the structure is rather unconventional, mixing methods, results and discussion.
We went trough the same exercise a couple of years ago, deriving a modified Voellmy model from kinetic theory (Rauter et al., 2016). We came to a few different conclusions.
Line 19:" H/L < 0.1, while typical values of mu for Coulomb friction are between 0.5 and 1."
It should be described why and how these are connected/correlated.
Line 34: "Water is present in many rock avalanches and may play a part as well as air. Frictional heating may also have a strong effect on the mechanical properties. Alternatively, the increase in runout length with volume may be an inherent property of granular flow without any specific process beyond the interaction of particles."
This needs to be backed up with references. I also suggest to look at Kesseler et al. (2020) in this context.
Line 46: "The most widely used relation for the basal shear stress".
The role of the basal shear stress should be explained. How is it connected with mu and H/L?
Line 150: "More important, however, it defines the length scale of adjustment of the velocity to the slope."
I do not agree with this statement. A length scale would be the typical height H or length L. I also do not understand "adjustment of the velocity to the slope". Is it the slope length at which terminal velocity is obtained?
Line 156: "the slope length l"
I would prefer a large L, since this is usually a rough scale like as in line 19. If it is not, it deserves an explaination. Generally, i would distinguish clearer between scales and real distances.
Line 165: "phase space trajectories".
This term is new for me for this kind of diagram.
Line 188: "The relation to the RKE model"
This model has (as most models) some issues (Issler et al. 2018). I would make sure that they do not change your conclusions.
Line 235: "Figure 5(a) shows the dependence of S/l on lambda/l"
The runout scales with the friction coefficient. That seems obvious. Why the division with l?
Line 241: "The existence of two different scaling regimes"
I am not sure about this. Are there really two regimes? In the following section you look only at very extreme scenarios. This is hard to say without some real world examples.
Line 244: "For lambda << l, Eq. (18) yields"
So basically an infinite slope?
Line 247: "lambda >> l"
Basically frictionless?
Line "the runout length increases with increasing slope length"
Are they not the same or diffent by a factor cos(beta) at most? I wonder if we are turning in a circle by multiplying all kind of relations.
Line 289: "L/H mostly decreases with l/lambda"
If l=L then this would just mean lambda decreases with H?
Line 289: " So the ratio L/H decreases with increasing slope length"
Isn't L the slope length?
Dieter Issler, James T. Jenkins, and Jim N. McElaine (2018). "Comments on avalanche flow models based on the concept of random kinetic energy." https://doi.org/10.1017/jog.2017.62
Matthew Kesseler, Valentin Heller and Barbara Turnbull (2020), Grain Reynolds Number Scale Effects in Dry Granular Slides. https://doi.org/10.1029/2019JF005347
Matthias Rauter, Jan-Thomas Fischer, Wolfgang Fellin, and Andreas Kofler (2016), Snow avalanche friction relation based on extended kinetic theory. https://doi.org/10.5194/nhess-16-2325-2016
Citation: https://doi.org/10.5194/egusphere-2023-144-CC1
Stefan Hergarten
Stefan Hergarten
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