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 |
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.