Mobility of dry granular debris flows over erodible beds: Experimental insights into the influence of flow&ndash;bed inertia

Wetterauer, Katharina; Müller, Sebastian; Krautblatter, Michael; Pudasaini, Shiva P.; Baselt, Ivo

doi:10.5194/egusphere-2026-1235

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https://doi.org/10.5194/egusphere-2026-1235

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19 Mar 2026

| 19 Mar 2026

Mobility of dry granular debris flows over erodible beds: Experimental insights into the influence of flow–bed inertia

Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

Abstract. Debris-flow mobility responds sensitively to erosion and entrainment that exchange mass and momentum across the flow-bed interface. Yet, the mechanical controls that cause some debris flows to accelerate during erosion while others decelerate are insufficiently understood. Recent theory attributes this divergent behavior to inertial contrasts between the moving mass and the erodible bed, suggesting that incorporating inertially weaker, neutral, or stronger substrate into the flow enhances, maintains, or reduces flow mobility, respectively. Here, we conducted flume experiments and surface-based measurements to assess how the inertia of the erodible bed affects the flow kinematics, erosion, entrainment, and runout of dry granular single-phase debris flows. We systematically imposed inertial contrasts by releasing a quartz slide of constant solid density over erodible beds with lower, equal, and higher solid densities representing inertially weak, neutral, and strong scenarios, and compare these alongside a reference case without erosion. Each scenario was repeated for fine sand and a sand-gravel mixture. Our results reveal consistent behavior across both particle-size distributions. Debris flows over low-density beds exhibit higher apparent mean erosion rates, faster flow fronts before deposition, and longer runout lengths, whereas flows over equal- and high-density beds evolve similarly, with shallower erosion, slower flow fronts, and shorter, more compact deposits. Relative to the neutral scenario, the entrainment of low-density material thus appears to enhance debris-flow mobility, while incorporating high-density material does not lead to the anticipated mobility loss. This asymmetric response suggests that solid-density contrasts alone are insufficient to explain the observed trends under the experimental conditions considered here. Differences in particle shape and internal friction likely also contribute. Whereas the low-density bed comprises more spherical particles with a lower friction angle facilitating entrainment, the equal- and high-density beds consist of angular particles with similar and higher internal friction angles, leading apparently to similar resistance to erosion despite their divergent densities. However, resolving whether more subtle differences persist between the inertial scenarios will require direct observations at the flow-bed interface to capture grain-scale dynamics and temporal variability in erosion intensity.

Received: 04 Mar 2026 – Discussion started: 19 Mar 2026

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28 Oct 2026

Mobility of dry granular flows over contrasting erodible bed materials in laboratory experiments

Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

Nat. Hazards Earth Syst. Sci., 26, 5315–5338, https://doi.org/10.5194/nhess-26-5315-2026,https://doi.org/10.5194/nhess-26-5315-2026, 2026

Short summary

Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2026-1235', Lonneke Roelofs, 26 Mar 2026

This is very interesting work. I really appreciate the careful comparison between the experimental trends presented in the paper and the trends predicted by models. After reading point (ii) in your conclusion I am trying to figure out if solid density would be able to explain all observed mobility and runout patterns if the grain shape in your inertially weak scenarios would be similar to those in the inertially neutral and strong scenarios.

Citation: https://doi.org/10.5194/egusphere-2026-1235-CC1
- AC5: 'Reply on CC1', Katharina Wetterauer, 08 Jul 2026
  
  We are thankful for the positive assessment of our work and appreciate this thoughtful reflection on our conclusions. We agree that this is an important question. While the primary objective of our experimental design was to isolate the influence of solid particle density, the current experiments do not allow us to fully disentangle the effects of solid particle density, particle shape and friction in the low-density scenarios, since the properties varied simultaneously. However, the comparable mobility and runout observed for the equal- and high-density scenarios, where grain shape and friction is similar, but density differs substantially, suggest that solid particle density alone is insufficient to explain the mobility behavior under the tested conditions. Further investigations in which these parameters can be varied independently would certainly help to continue assessing this question.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC5
CC2:
'Comment on egusphere-2026-1235', Hervé Vicari, 30 Apr 2026

Please find my comments attached.
Recommendation to the Editor: The manuscript by Wetterauer et al. presents an interesting experimental dataset on erosion of dry granular flows over beds of differing densities. The experiments themselves appear valuable. However, the manuscript interprets the results within the framework of Pudasaini and Krautblatter (2021), which Issler et al. (2024, Nature Communications, https://www.nature.com/articles/s41467-024-48605-6) showed to be incorrectly derived and to violate momentum and energy conservation. In my attached review, I explain why this mechanical interpretation is not valid.
My concern is not merely academic. If Pudasaini and Krautblatter (2021) were retained in a journal such as NHESS as a valid mechanistic basis for interpreting erosion experiments, this could further legitimize and encourage its implementation and use in numerical tools for landslide simulation and hazard mapping. Because the model is mechanically incorrect, such use could lead to erroneous predictions, with potentially serious consequences for hazard assessment and public safety.
For this reason, I do not believe that the manuscript can be accepted in its current form. That said, I do believe the experimental results could still form the basis of a useful contribution if the authors were to remove reliance on the Pudasaini and Krautblatter model from their interpretative framework. The manuscript could then be reconsidered on the basis of the dataset and a revised physical interpretation.
Given the history of this issue, and because I am not an official referee for this manuscript and may not be given the opportunity to comment on any eventual reply, I urge the Editor to assess with particular caution any response to my comments that argues in favor of the validity of the Pudasaini and Krautblatter model. The invalidity of that model was already examined during the review of our Matters Arising paper (Issler et al., 2024). If the Editor wishes to seek an additional opinion, I would strongly recommend consulting a reviewer with recognized expertise in continuum mechanics and depth-averaged modeling of geophysical mass flows, for example Richard M. Iverson (USGS), Nico Gray (University of Manchester), Dieter Issler (NGI), Peter Gauer (NGI), Johan Gaume (ETHZ), Anne Mangeney (IPGP), Thierry Faug (INRAE), or Christophe Ancey (EPFL).

Citation: https://doi.org/10.5194/egusphere-2026-1235-CC2
- AC4: 'Reply on CC2', Katharina Wetterauer, 08 Jul 2026
  
  We thank for the detailed feedback. The issues raised here are addressed in detail in our response to Review RC2 and will be considered in the revision of the manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC4
RC1:
'Comment on egusphere-2026-1235', Anonymous Referee #1, 10 May 2026

This study addresses an important and timely question in debris flow research, namely, how the inertial contrast between a flowing mass and an erodible bed influences erosion, entrainment, and runout mobility. The experimental approach is systematic and well-conceived in its basic structure, testing three inertial scenarios alongside a reference case and repeating each experiment three times to assess reproducibility. The finding that solid density contrast alone is insufficient to explain observed mobility patterns, and that particle shape and internal friction play important and previously underappreciated roles, is a scientifically valuable contribution that deserves attention from the debris flow and granular flow communities.
Despite my comments, the reviewer recognizes the originality and potential value of this experimental contribution. With careful revision addressing the scientific, structural, and linguistic issues outlined in the specific comments in the attached PDF, this manuscript could make a meaningful contribution to the understanding of erosion-driven debris flow mobility.

Citation: https://doi.org/10.5194/egusphere-2026-1235-RC1
- AC1: 'Reply on RC1', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC1
RC2:
'Comment on egusphere-2026-1235', Hervé Vicari, 21 May 2026

Following my community comment (CC2), I was invited to serve as an official reviewer of this manuscript. Please find my review attached. I recommend major revisions, followed by an additional round of review.

Citation: https://doi.org/10.5194/egusphere-2026-1235-RC2
- AC2: 'Reply on RC2', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC2
CC3:
'Comment on egusphere-2026-1235', Dieter Issler, 28 May 2026
This manuscript describes, analyzes and discusses chute experiments on granular flows over erodible beds of different bulk densities with the goal of testing the erosion theory of Pudasaini and Krautblatter (Nat. Comm. 12, 6793, 2021, henceforth called PK). In CC2 and RC2, Hervé Vicari pointed out that Issler et al. (Nat. Comm. 15, 4613, 2024) demonstrated that the results of PK hinge critically on counting the particle-borne momentum flux from the bed to the flow twice. If this error is corrected, the conclusions in PK revert to the standard formulation that has been known for decades.
This situation implies that the the present manuscript uses an interpretative framework that is not mathematically consistent. Accordingly, Vicari posits that all references to PK need to be removed and the discussion of the results reformulated before publication. I fully support Vicari's statement and also agree with him and the Reviewer #1 that the experiments described in the manuscript are interesting, valuable and do not depend on the interpretative framework of PK in any essential way. It should therefore be fairly straightforward to reformulate the analysis and discussion parts of the manuscript with an emphasis on the mass, momentum and energy balances and the associated stresses. There is hardly anything to add to Vicari's thorough and detailed review, but perhaps a few remarks from a different perspective could be useful in the revision of the paper.
It would be helpful if the authors could summarize early on in which respect their experiments differ from other, similar experiments.

In my opinion, the emphasis on inertia in this context is problematic. The notion has a history spanning more than two millennia (see the Wikipedia article for an interesting summary) and played an important conceptual role in the Theory of Relativity, yet it has not been linked to a measurable physical quantity. Perhaps a vague description like "the property of a body causing it to maintain its velocity in the absence of external forces acting on it" comes close to the essence of the concept. In contrast, PK and the present manuscript seem to oscillate between identifying inertia with bulk density or momentum density. If the authors want to use the term inertia, they need to define it unambiguously (and preferably in line with conventional usage). In my opinion, it would be best to eschew it in favor of a well-defined, measurable quantity.

There are many passages throughout the manuscript where the authors mention important aspects of the experiments, like the effect of particle shape, the stability and shear strength of the erodible bed, and the energetics of entrainment. These are key elements that need to be analyzed carefully and quantitatively where possible if one wishes to understand the experimental results. In the present version, these questions are discussed mostly where some discrepancy between PK theory and the experimental results was encountered. Instead, it would be preferable to start from these aspects of the experiments and discuss what their consequences are. This should help in distinguishing between firm conclusions, plausible inferences and conjectures.

It should be quite illuminating to clearly state (and if possible quantify) the connections between the entrainment rate , the mass balance and the momentum balance. An almost trivial but important point is that, in these experiments, the entrainable material is initially at rest and therefore does not increase the flow momentum when it is entrained. As the eroded material must be accelerated to the mean flow velocity or a fraction thereof, the entraining flow will accelerate less (or decelerate more) compared to the situation without entrainment (as has been known for a long time). Conversely, the entrainment rate is limited by the excess of the flow shear stress over the bed shear strength. For the granular materials used here, the shear strength can be estimated in terms of the difference between internal friction angle and slope angle and the bed-normal load. From the experiments without erodible bed, it should be possible to estimate the bed friction and to check whether the mass and momentum balances of the flow work out with the estimated entrainment rates. If the flow decelerated less than estimated, it could mean that the entrainment rate was lower than expected or that the eroded material is not thoroughly mixed into the flow but remains near the bed with lower velocity. Stronger deceleration could indicate deep failure of the substrate, i.e., a sudden, very high erosion rate; this could occur in the case of the Glass substrate since it is only meta-stable and is likely to fail throughout its depth once disturbed by the flow.

It is intriguing that entrainment has a decelerating effect on the flow, yet entraining flows can be significantly more mobile than non-entraining ones. Perhaps one could shed some light on this with one or two series of tests without entrainment, using mixtures of quartz and glass, and of quartz and magnetite. The fraction of glass or magnetite mass could be chosen to roughly correspond to the entrained mass in the reported experiments. In this way, the effect of the erosion and entrainment process on the momentum can be separated from the effect of the density and shape differences as well as the poly-dispersity.

I wish the authors success in the revision process and look forward to seeing the revised paper published.
Citation: https://doi.org/10.5194/egusphere-2026-1235-CC3
- AC3: 'Reply on CC3', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC3

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Submit a revised manuscript (10 Jul 2026) by Andreas Günther

AR by Katharina Wetterauer on behalf of the Authors (01 Aug 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (11 Aug 2026) by Andreas Günther

RR by Anonymous Referee #1 (23 Aug 2026)

RR by Hervé Vicari (23 Aug 2026)

RR by Anonymous Referee #3 (15 Sep 2026)

Suggestions for revision or reasons for rejection

This is an experimental paper describing the dynamics of granular materials as they flow down an incline over an erodible bed and out onto a flat runout pad. The aim is to investigate what effect the erodible bed has on the overall flow dynamics. The context is the paper of Pudasaini & Krautblatter (2021) who (if I understand the motivation correctly) predict that the erosive nature of the flow should be strongly dependent on the density difference between the parent flow and the erodible deposit. The problem of how to incorporate erosion and deposition into depth-averaged models for dry granular flows is a thorny one that many people have struggled with over the years, and there is still no consensus on how to do this. Indeed, Issler et al (2024) have claimed that the model of Pudasaini & Krautblatter (2021) violates energy conservation and is flawed. I won't get into this debate as part of my review -- as the experimental results in this paper don't depend upon it in any way. Indeed, perhaps the results will help to further constrain mathematical models in the future. I would recommend that the authors broaden the debate, as there are other approaches that seem to be moderately successful at modelling erosion and deposition in specific contexts that are not mentioned.

Specific points:-

1/. Incorporating basal erosion and deposition into depth-averaged avalanche/debris flow models is tricky. There should be more discussion about this. Early models ended up producing rocket like equations, where a deposit of mass, but no corresponding loss of momentum led to avalanches accelerating (Cannon and Savage, 1988; Hungr, 1990; Erlichson, 1991; Iverson 1997). It is also possible to set up equations in which there is no net acceleration or decelleration as material is entrained and deposited, see for instance the solutions for surface avalanches in rotating drums in Gray (2001). Some mention of this in the introduction would help to provide context.

(a) Cannon, S. H., and W. Z. Savage, A mass-change model for the estimation of debris-flow runout, J. Geol., 96, 221–227, 1988.
(b) Hungr, O., A mass-change model for the estimation of debris flow runout: A discussion, J. Geol., 98, 791, 1990.
(c) Erlichson, H., A mass-change model for the estimation of debris-flow runout, A second discussion: Conditions for the application of the rocket equation, J. Geol., 99, 633–634, 1991.
(d) Iverson, R.M. 1997 The physics of debris flows. Rev. Geophys. 35, 245–296.
(e) Gray, J.M.N.T. 2001 Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441, 1–29.

2/. Although the original motivation for the paper is erosion and deposition in debris flows, the title of the paper has now been changed to "Mobility of dry granular flows over erodible beds: Experimental insights into the influence of flow–bed density contrasts" and the experiments are performed solely with dry granular materials. There therefore needs to be a more thorough referencing of previous work on erosion and deposition in dry granular flows. In particular, it has been shown that at low fluxes discrete mobile wave pulses can form (so called erosion-deposition waves) that are able to flow through a static erodible bed, but come to rest on a fixed substrate at the same inclination (Edwards & Gray 2015, Rocha et al 2019). Moreover a discrete release onto an erodible substrate can (i) grow, (ii) propagate indefinitely or (iii) decay dependent on the thickness of the erosion layer and the bed inclination (Edwards et al 2017, Kokelaar et al. 2017, Viroulet et al. 2019). Colour change experiments show that erosion-deposition waves can propagate indefinitely by eroding and depositing granular material in exact balance, i.e. a release of yellow sand onto red sand, produces a flow in which all the yellow sand deposits, but the wave propagates through the red sand indefinitely (Edwards et al 2021). You can also get retrogressive failures that propagate upslope (Russell et al. 2019). Continuous releases of material at higher mass flux can also spontaneously self-channelize to form static lateral levees that prevent spreading and enhance runout (Mangeney 2007, Kokelaar et al 2014, Rocha et al. 2019). Although these experiments are in dry granular materials the same phenomena can also be seen in debris flows, see e.g. Aaron et al. 2025 and Wetter et al. 2026. All of these experiments and field observations are helping to constrain depth-averaged models and should be mentioned. Indeed, all of these experiments are performed with erodible material that is identical to the release material, so I wonder whether this is saying anything useful about the forms used by Pudasaini & Krautblatter (2021)? What happens in that model when the densities are the same?

(a) Pouliquen, O. & Forterre, Y. 2002 Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453, 133–151.
(b) Mangeney, A., Bouchut, F., Thomas, N., Vilotte, J. P. & Bristeau, M. O. 2007 Numerical modeling of self-channeling granular flows and of their levee-channel deposits. J. Geophys. Res. 112, F02017.
(c) B. P. Kokelaar, R. L. Graham, J. M. N. T. Gray And J. W. Vallance (2014) Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett. 385, 172-180
(d) A. N. Edwards & J. M. N. T. Gray (2015) Erosion-deposition waves in shallow granular free-surface flows. J. Fluid Mech. 762, 35-67
(e) A. N. Edwards, S. Viroulet, B. P. Kokelaar & J. M. N. T. Gray (2017) Formation of levees, troughs and elevated channels by avalanches on erodible slopes. J. Fluid Mech. 823, 278--315
(f) B. P. Kokelaar, R. S. Bahia, K. H. Joy, S. Viroulet & J. M. N. T. Gray (2017) Granular avalanches on the Moon: Mass-wasting conditions, processes, and features. J. Geophys. Res. Planets 122, 1893--1925.
(g) F. M. Rocha, C. G. Johnson & J. M. N. T. Gray (2019) Self-channelisation and levee formation in monodisperse granular flows. J. Fluid Mech. 876, 591--641
(h) S. Viroulet, A. N. Edwards, C. G. Johnson, B. P. Kokelaar & J. M. N. T. Gray (2019) Shedding dynamics and mass exchange by dry granular waves flowing over erodible beds. Earth and Planetary Sci. Lett. 523, 115700.
(i) A. S. Russell, C. G. Johnson, A. N. Edwards, S. Viroulet, F. M. Rocha & J. M. N. T. Gray (2019) Retrogressive failure of a static granular layer on an inclined plane. J. Fluid Mech. 869, 313--340.
(j) A.N. Edwards, S. Viroulet, C. G. Johnson & J. M. N. T. Gray (2021) Erosion-deposition dynamics and long distance propagation of granular avalanches. J. Fluid Mech. 915, A9
(k) J. Aaron, J. Langham, R. Spielmann, J. Hirschberg, B. McArdell, S. Boss, C.G. Johnson & J.M.N.T. Gray (2025) Detailed observations reveal the genesis and dynamics of destructive debris-flow surges. Commun. Earth Environ. 6, 556.
(l) Christoph Wetter, Fabian Walter, Brian W. McArdell, Felix Blumenschein, Raffaele Spielmann, Jordan Aaron, J.M.N.T. Gray, Anne Obermann & Andreas Fichtner (2026)Formation, propagation, and annihilation of surge waves in debris flows. Engineering Geology 367, 108648.

3/. Introduction: It is probably worth pointing out that all of the above experiments have been modelled with a depth-averaged dry avalanche model that uses the hysteretic friction law of Pouliquen & Forterre (2002). Here explicit basal erosion/deposition terms are neglected in the mass and momentum balance equations and the material is assumed to be moving or static through its entire depth. The hysteresis allows static and dynamic regions to coexist, so you can model levees, erosion deposition waves and retrogressive failures etc. While this is not a panacea for all problems with erosion and deposition, it seems to work well for shallow flows where the erodible horizon of the substrate is well defined. A more general erosion-deposition closure needs to at least be able to model all the above scenarios mentioned in 2/. (above).

4/. Introduction: The introduction should also mention another possibility -- that of non-depth-averaged models. My suspicion is that this is the only way to solve the erosion-deposition problem properly. However, one would have to say what the rheology of the flowing and erodible material was -- which is also problematic. Progress is being made in this regard, but I don't think that our understanding of the rheology of dry granular materials is sufficient to model all the phenomena in 2/. (above) in a non-depth-averaged way - let alone debris flows. However, simple flows in rotating drums and heaps (for example) have been modelled in this way (see Barker et al 2021, Maguire et al 2024, Blatny et al 2024, Lloyd et al 2025). In addition, Li et al. have used cohesion to model erosion-deposition wave formation in snow avalanches, which are also a form of granular flow. In these approaches, even defining where the interface between solid-like and fluid-like material is, is difficult, because there can be slow exponentially decreasing creep with depth (Komatsu et al. 2001) so it is not surprising that depth-averaged models are struggling, i.e. what do we really mean by the flow thickness and the depth-averaged velocity? Perhaps you can point some of this out?

(a) T. Barker, M. Rauter, E. S. F. Maguire, C. G. Johnson & J. M. N. T. Gray (2021) Coupling rheology and segregation in granular flows. J. Fluid Mech. 909, A22.
(b) E.S.F. Maguire, T. Barker, M. Rauter, C.G. Johnson & J.M.N.T. Gray (2024) Particle-size segregation patterns in a partially filled triangular rotating drum. J. Fluid Mech 979, A40.
(c) L. Blatny, J.M.N.T. Gray & J. Gaume (2024) A critical state μ(I)-rheology model for cohesive granular flows. J. Fluid Mech. 997, A67.
(d) H.A. Lloyd, E.S.F.Maguire, D. Mistry, G.K. Reynolds, C.G. Johnson & J.M.N.T. Gray (2025) On the formation of super-stable granular heaps. J. Fluid Mech 1002, A27.
(e) Xingyue Li, Betty Sovilla, John Mark Nicholas Timm Gray & Johan Gaume (2024) Transient wave activity in snow avalanches is controlled by entrainment and topography. Commun. Earth Environ. 5, 77.
(f) Komatsu, T.S., Inagaki, S., Nakagawa, N. & Nasuno, S. 2001 Creep Motion In A Granular Pile Exhibiting Steady Surface Flow. Phys. Rev. Lett. 86 (9), 1757–1760.

5/. section 2.1: You say "Inertia describes the resistance of moving material to a change of its velocity in magnitude and direction. In continuum mechanics, inertia is, beside velocity, proportional to mass density for a given material volume. Consequently, debris-flow inertia can be modified by incorporating mass from an erodible bed with a different density, solid volume fraction, friction, or different velocity. To test the inertia-based mobility concept proposed by Pudasaini and Krautblatter (2021), we designed a setup for dry granular debris-flow experiments, where the dry debris flow overrides a dry erodible bed initially at rest. In the present study any change in inertia can therefore only arise from a change in density." I don't agree with that statement. You have an experiment in a gravitational field, so when you release the grains they accelerate, i.e. the velocity increases and there is a change in inertia. It therefore can not be true to say "any change in inertia can therefore only arise from a change in density." Doesn't that at least partially undermine the motivation behind your experiments?

6/. section 120: You say "Accordingly, when the term “debris flow” refers to our tests, it specifically denotes these dry granular single-phase flows". This seems to be stretching the definition of debris flows too far. Why can't you just bill these as dry granular flow experiments? They are still interesting in their own right.

7/. section 125: What is your plywood coated with?

8/. section 265: You say "The reference experiments form elongated, well-confined lobes". It sounds as though the flow is starting to try and lay down levees (see Johnson et al 2012; Rocha et al. 2019)

9/. section 270: You say "The Glass experiments produce elongated lobes with undulating surfaces, but their shape differs markedly between the fine and coarse debris flow." As well as levees the undulations are probably due to waves forming in your chute and then being brough to rest, see Edwards & Gray (2015).

10/. Figure 6 and section 290 & 295: You say "Lateral cross sections through the Qtz–Glass and Qtz–Mag deposits reveal distinct internal sorting and spatial patterns in both fine (Supplement Fig. S8) and coarse experiments (Fig. 6). The mixed slide–bed deposits show a finer-grained core that coarsens toward the deposit surface (cross-checks of the Qtz–Qtz and reference deposits confirmed comparable sorting). The sorting is particularly evident in the coarse experiments, where the particle-size spectrum is wider. The material distribution, however, differs between the bed materials. In the Glass experiments (Fig. 6a and Supplement Fig. S8a), a sharp boundary occurs between the two materials. Qtz–slide particles are concentrated in the interior of the main body, while Glass-bed particles form the lateral edges. With increasing runout distance, the lateral Glass edges widen and the central Qtz core narrows. In the intermediate sections, Glass particles appear laterally shouldered onto a thin Qtz layer and the central Qtz core becomes disrupted by distinct Glass ridges. Toward the distal end of the main body, the deposits consist almost entirely of Glass. In the fine deposit (Glass/f; Supplement Fig. S8a), Glass also appears centrally along the deposit base. In the coarse deposit (Glass/c; Fig. 6a), the frontal meter consists of a fringe mainly composed of loosely dispersed coarse Glass with only a few Qtz particles." You have some nicely segregated deposits. I was a little unclear whether this was being attributed to particle-size segregation or particle-density segregation? Some of the mixtures shown in figure 1 appear to have quite wide size distributions? Which mixtures are these?

11/. section 330: You say "Finally, consistent with the expectation by Pudasaini and Krautblatter (2021), our experiments show enhanced mobility and extended runout when the debris flows entrain material from the low-density beds in the inertially weak scenarios, relative to the inertially neutral scenarios. However, the entrainment of significantly denser bed material does not result in the anticipated mobility reduction in the inertially strong scenarios under the experimental conditions considered here. Instead, both equal- and high-density beds lead to comparable deceleration of the debris flow, suggesting similar and higher energy consumption and momentum loss during bed erosion and entrainment compared to the low-density material." The experiments of Edwards et al (2017), Kokelaar et al. (2017), Viroulet et al. (2019) show that the mobility of the flow can be enhanced or diminished dependent on the erodible bed depth, the angle of slope inclination and the size of the avalanche even with parent and erodible material of the same bulk density. Doesn't this also contradict the results expected by Pudasaini and Krautblatter (2021)?

12/. section 335: You say "Consequently, when considering only externally observable flow and deposit characteristics, and not intrinsic process dynamics, our results based on density contrasts alone do not provide sufficient support for the inertia-based mobility hypothesis proposed by Pudasaini and Krautblatter (2021)." I think this is an interesting conclusion.

13/. section 365: In the reference list (Johnson et al., 2012; Edwards et al., 2023) you should also probably add references to

(q) Segregation-induced fingering instabilities in granular free surface flows.
M. J. Woodhouse, A. R. Thornton, C. G. Johnson, B. P. Kokelaar & J. M. N. T. Gray (2012) J. Fluid Mech. 709, 543-580

(r) Segregation-induced finger formation in granular free-surface flows.
J. L. Baker, C. G. Johnson & J. M. N. T. Gray (2016) J. Fluid Mech. 809, 168--212

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ED: Reconsider after major revisions (further review by editor and referees) (18 Sep 2026) by Andreas Günther

Dear Authors,

The recommendations on publication of your revised paper in our journal finally made by the two original referees are so extremely contrasting that it was necessary here to involve a third reviewer. I apologize this results in a longer peer-review process.
While referee #1 recommends publication of your revised paper as it stands, and I agree you´ve did a good job reworking your article, referee #2 claims for a rejection because the article still gives reference to, and is (from the point of the referee) framed too closely within, a mechanistic hypothesis formulated by two of the authors that is apparently flawed. However, I share the opinion of referee #3 that the experimental results described and discussed in your paper doesn’t depend on this in any way. Therefore, I think you´ve broadly succeeded in giving an acceptable reference to the problematic paper of Pudasaini & Krautblatter (2021), consequently citing it in conjunction with the associated review paper from Issler et al. (2024). Indeed, I think your study is very well presented and may potentially help to constrain mathematical models for erosion and deposition in geophysical mass flows. I share the observation of referee #2 that your lab setup cannot sufficiently isolate the influence of density properties against frictional (including grain shape) parameters in the flume experiments. In this case, I may encourage you not to focus your paper on flow-bed density contrasts, and I completely agree with referee #3 that an iteration of your paper is necessary here to put your study in a much wider context with previous, very similar lab experiments on dry granular flows. I think many of the concerns of reviewer #2 can also be addressed when reorganizing your paper in this manner. Finally, if you maintain citing the mobility model of Pudasaini & Krautblatter (2021) as a motivation for your study, I think it is required to clearly conclude that your experiments do not support it in any instance, as also suggested by reviewer #3.
To proceed, please consider the final comments of referee #2 and the comments of referee #3 when revising your paper. After resubmission of your manuscript together with a reply letter and a manuscript version in track change mode, your paper will be reviewed again by referee #3 and the editor.

Best regards, Andreas Günther

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AR by Ivo Baselt on behalf of the Authors (09 Oct 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (15 Oct 2026) by Andreas Günther

RR by Anonymous Referee #3 (15 Oct 2026)

ED: Publish as is (16 Oct 2026) by Andreas Günther

AR by Ivo Baselt on behalf of the Authors (18 Oct 2026) Manuscript

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2026-1235', Lonneke Roelofs, 26 Mar 2026

This is very interesting work. I really appreciate the careful comparison between the experimental trends presented in the paper and the trends predicted by models. After reading point (ii) in your conclusion I am trying to figure out if solid density would be able to explain all observed mobility and runout patterns if the grain shape in your inertially weak scenarios would be similar to those in the inertially neutral and strong scenarios.

Citation: https://doi.org/10.5194/egusphere-2026-1235-CC1
- AC5: 'Reply on CC1', Katharina Wetterauer, 08 Jul 2026
  
  We are thankful for the positive assessment of our work and appreciate this thoughtful reflection on our conclusions. We agree that this is an important question. While the primary objective of our experimental design was to isolate the influence of solid particle density, the current experiments do not allow us to fully disentangle the effects of solid particle density, particle shape and friction in the low-density scenarios, since the properties varied simultaneously. However, the comparable mobility and runout observed for the equal- and high-density scenarios, where grain shape and friction is similar, but density differs substantially, suggest that solid particle density alone is insufficient to explain the mobility behavior under the tested conditions. Further investigations in which these parameters can be varied independently would certainly help to continue assessing this question.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC5
CC2:
'Comment on egusphere-2026-1235', Hervé Vicari, 30 Apr 2026

Please find my comments attached.
Recommendation to the Editor: The manuscript by Wetterauer et al. presents an interesting experimental dataset on erosion of dry granular flows over beds of differing densities. The experiments themselves appear valuable. However, the manuscript interprets the results within the framework of Pudasaini and Krautblatter (2021), which Issler et al. (2024, Nature Communications, https://www.nature.com/articles/s41467-024-48605-6) showed to be incorrectly derived and to violate momentum and energy conservation. In my attached review, I explain why this mechanical interpretation is not valid.
My concern is not merely academic. If Pudasaini and Krautblatter (2021) were retained in a journal such as NHESS as a valid mechanistic basis for interpreting erosion experiments, this could further legitimize and encourage its implementation and use in numerical tools for landslide simulation and hazard mapping. Because the model is mechanically incorrect, such use could lead to erroneous predictions, with potentially serious consequences for hazard assessment and public safety.
For this reason, I do not believe that the manuscript can be accepted in its current form. That said, I do believe the experimental results could still form the basis of a useful contribution if the authors were to remove reliance on the Pudasaini and Krautblatter model from their interpretative framework. The manuscript could then be reconsidered on the basis of the dataset and a revised physical interpretation.
Given the history of this issue, and because I am not an official referee for this manuscript and may not be given the opportunity to comment on any eventual reply, I urge the Editor to assess with particular caution any response to my comments that argues in favor of the validity of the Pudasaini and Krautblatter model. The invalidity of that model was already examined during the review of our Matters Arising paper (Issler et al., 2024). If the Editor wishes to seek an additional opinion, I would strongly recommend consulting a reviewer with recognized expertise in continuum mechanics and depth-averaged modeling of geophysical mass flows, for example Richard M. Iverson (USGS), Nico Gray (University of Manchester), Dieter Issler (NGI), Peter Gauer (NGI), Johan Gaume (ETHZ), Anne Mangeney (IPGP), Thierry Faug (INRAE), or Christophe Ancey (EPFL).

Citation: https://doi.org/10.5194/egusphere-2026-1235-CC2
- AC4: 'Reply on CC2', Katharina Wetterauer, 08 Jul 2026
  
  We thank for the detailed feedback. The issues raised here are addressed in detail in our response to Review RC2 and will be considered in the revision of the manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC4
RC1:
'Comment on egusphere-2026-1235', Anonymous Referee #1, 10 May 2026

This study addresses an important and timely question in debris flow research, namely, how the inertial contrast between a flowing mass and an erodible bed influences erosion, entrainment, and runout mobility. The experimental approach is systematic and well-conceived in its basic structure, testing three inertial scenarios alongside a reference case and repeating each experiment three times to assess reproducibility. The finding that solid density contrast alone is insufficient to explain observed mobility patterns, and that particle shape and internal friction play important and previously underappreciated roles, is a scientifically valuable contribution that deserves attention from the debris flow and granular flow communities.
Despite my comments, the reviewer recognizes the originality and potential value of this experimental contribution. With careful revision addressing the scientific, structural, and linguistic issues outlined in the specific comments in the attached PDF, this manuscript could make a meaningful contribution to the understanding of erosion-driven debris flow mobility.

Citation: https://doi.org/10.5194/egusphere-2026-1235-RC1
- AC1: 'Reply on RC1', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC1
RC2:
'Comment on egusphere-2026-1235', Hervé Vicari, 21 May 2026

Following my community comment (CC2), I was invited to serve as an official reviewer of this manuscript. Please find my review attached. I recommend major revisions, followed by an additional round of review.

Citation: https://doi.org/10.5194/egusphere-2026-1235-RC2
- AC2: 'Reply on RC2', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC2
CC3:
'Comment on egusphere-2026-1235', Dieter Issler, 28 May 2026
This manuscript describes, analyzes and discusses chute experiments on granular flows over erodible beds of different bulk densities with the goal of testing the erosion theory of Pudasaini and Krautblatter (Nat. Comm. 12, 6793, 2021, henceforth called PK). In CC2 and RC2, Hervé Vicari pointed out that Issler et al. (Nat. Comm. 15, 4613, 2024) demonstrated that the results of PK hinge critically on counting the particle-borne momentum flux from the bed to the flow twice. If this error is corrected, the conclusions in PK revert to the standard formulation that has been known for decades.
This situation implies that the the present manuscript uses an interpretative framework that is not mathematically consistent. Accordingly, Vicari posits that all references to PK need to be removed and the discussion of the results reformulated before publication. I fully support Vicari's statement and also agree with him and the Reviewer #1 that the experiments described in the manuscript are interesting, valuable and do not depend on the interpretative framework of PK in any essential way. It should therefore be fairly straightforward to reformulate the analysis and discussion parts of the manuscript with an emphasis on the mass, momentum and energy balances and the associated stresses. There is hardly anything to add to Vicari's thorough and detailed review, but perhaps a few remarks from a different perspective could be useful in the revision of the paper.
It would be helpful if the authors could summarize early on in which respect their experiments differ from other, similar experiments.

In my opinion, the emphasis on inertia in this context is problematic. The notion has a history spanning more than two millennia (see the Wikipedia article for an interesting summary) and played an important conceptual role in the Theory of Relativity, yet it has not been linked to a measurable physical quantity. Perhaps a vague description like "the property of a body causing it to maintain its velocity in the absence of external forces acting on it" comes close to the essence of the concept. In contrast, PK and the present manuscript seem to oscillate between identifying inertia with bulk density or momentum density. If the authors want to use the term inertia, they need to define it unambiguously (and preferably in line with conventional usage). In my opinion, it would be best to eschew it in favor of a well-defined, measurable quantity.

There are many passages throughout the manuscript where the authors mention important aspects of the experiments, like the effect of particle shape, the stability and shear strength of the erodible bed, and the energetics of entrainment. These are key elements that need to be analyzed carefully and quantitatively where possible if one wishes to understand the experimental results. In the present version, these questions are discussed mostly where some discrepancy between PK theory and the experimental results was encountered. Instead, it would be preferable to start from these aspects of the experiments and discuss what their consequences are. This should help in distinguishing between firm conclusions, plausible inferences and conjectures.

It should be quite illuminating to clearly state (and if possible quantify) the connections between the entrainment rate , the mass balance and the momentum balance. An almost trivial but important point is that, in these experiments, the entrainable material is initially at rest and therefore does not increase the flow momentum when it is entrained. As the eroded material must be accelerated to the mean flow velocity or a fraction thereof, the entraining flow will accelerate less (or decelerate more) compared to the situation without entrainment (as has been known for a long time). Conversely, the entrainment rate is limited by the excess of the flow shear stress over the bed shear strength. For the granular materials used here, the shear strength can be estimated in terms of the difference between internal friction angle and slope angle and the bed-normal load. From the experiments without erodible bed, it should be possible to estimate the bed friction and to check whether the mass and momentum balances of the flow work out with the estimated entrainment rates. If the flow decelerated less than estimated, it could mean that the entrainment rate was lower than expected or that the eroded material is not thoroughly mixed into the flow but remains near the bed with lower velocity. Stronger deceleration could indicate deep failure of the substrate, i.e., a sudden, very high erosion rate; this could occur in the case of the Glass substrate since it is only meta-stable and is likely to fail throughout its depth once disturbed by the flow.

It is intriguing that entrainment has a decelerating effect on the flow, yet entraining flows can be significantly more mobile than non-entraining ones. Perhaps one could shed some light on this with one or two series of tests without entrainment, using mixtures of quartz and glass, and of quartz and magnetite. The fraction of glass or magnetite mass could be chosen to roughly correspond to the entrained mass in the reported experiments. In this way, the effect of the erosion and entrainment process on the momentum can be separated from the effect of the density and shape differences as well as the poly-dispersity.

I wish the authors success in the revision process and look forward to seeing the revised paper published.
Citation: https://doi.org/10.5194/egusphere-2026-1235-CC3
- AC3: 'Reply on CC3', Katharina Wetterauer, 08 Jul 2026
  
  Please see the attached document for our full author response.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1235-AC3

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Submit a revised manuscript (10 Jul 2026) by Andreas Günther

AR by Katharina Wetterauer on behalf of the Authors (01 Aug 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (11 Aug 2026) by Andreas Günther

RR by Anonymous Referee #1 (23 Aug 2026)

RR by Hervé Vicari (23 Aug 2026)

RR by Anonymous Referee #3 (15 Sep 2026)

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ED: Reconsider after major revisions (further review by editor and referees) (18 Sep 2026) by Andreas Günther

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AR by Ivo Baselt on behalf of the Authors (09 Oct 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (15 Oct 2026) by Andreas Günther

RR by Anonymous Referee #3 (15 Oct 2026)

ED: Publish as is (16 Oct 2026) by Andreas Günther

AR by Ivo Baselt on behalf of the Authors (18 Oct 2026) Manuscript

Journal article(s) based on this preprint

28 Oct 2026

Mobility of dry granular flows over contrasting erodible bed materials in laboratory experiments

Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

Nat. Hazards Earth Syst. Sci., 26, 5315–5338, https://doi.org/10.5194/nhess-26-5315-2026,https://doi.org/10.5194/nhess-26-5315-2026, 2026

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Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

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Katharina Wetterauer, Sebastian Müller, Michael Krautblatter, Shiva P. Pudasaini, and Ivo Baselt

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Contrasting mobility responses of erosive debris flows are poorly understood. Here, the role of bed inertia in debris-flow evolution and runout is experimentally assessed using distinct bed-density contrasts. Erosion is higher and runout longer over low-density beds, whereas equal- and high-density beds congruently show shallower erosion and shorter runout. The results indicate that solid density alone cannot explain mobility changes and that particle shape and internal friction also contribute.


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Mobility of dry granular debris flows over erodible beds: Experimental insights into the influence of flow–bed inertia

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