the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Jul 2024
Comparative Analysis of μ (I) and Voellmy-Type Grain Flow Rheologies in Geophysical Mass Flows: Insights from Theoretical and Real Case Studies
Abstract. The experimental-based μ(I) rheology is now prevalent to describe the movement of gravitational mass flows. Here, we reformulate μ(I) rheology as a Voellmy-type relationship to illustrate its physical implications. Through one-dimensional block modeling and a real case study, we explore the equivalence between μ(I) and widely-used Voellmy-type grain flow rheologies. Results indicate that μ(I) rheology utilizes a dimensionless inertial number to mimic contributions of granular temperature/fluctuation energy. In terms of Voellmy, the μ(I) rheolgy contains a velocity-dependent turbulent friction coefficient modelling shear thinning behavior. This turbulent friction assumes the production and decay of fluctuation energy are in balance, exhibiting no difference during accelerative and dipositional phases. The constant Coulomb friction coefficient prevents μ(I) rheology from accurately modeling the dispositional characteristics of actual mass flows. Our results highlight the strengths and limitations of both μ(I) and Voellmy rheologies, bolstering the theoretical foundation of mass flow modeling while revealing practical engineering challenges.
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RC1: 'Comment on nhess-2024-87', Anonymous Referee #1, 31 Aug 2024
This manuscript, based on theoretical derivation and practical cases, comparatively analyzes the μ(I) and Voellmy-type rheological relationships in geophysical mass flows. The study has positive value for modeling granular flows. Specific suggestions are as follows: (1) Please clearly specify the information about the case study in the abstract. (2) Provide more information about Figure 4, including the latitude and longitude grid and the location of the event on a larger map, so that readers can easily identify where the event occurred. (3) In the discussion, it is recommended to add a description and analysis of the limitations of the methods and results of this manuscript, as well as future work prospects. (4) Add a conclusion section. In summary, major revisions are recommended."
Citation: https://doi.org/10.5194/nhess-2024-87-RC1 -
AC1: 'Reply on RC1', Yu Zhuang, 18 Sep 2024
This manuscript, based on theoretical derivation and practical cases, comparatively analyzes the μ(I) and Voellmy-type rheological relationships in geophysical mass flows. The study has positive value for modeling granular flows. Specific suggestions are as follows:
(1) Please clearly specify the information about the case study in the abstract.
Response: Following your comment, we will provide more information about the case study in the abstract.
(2) Provide more information about Figure 4, including the latitude and longitude grid and the location of the event on a larger map, so that readers can easily identify where the event occurred.
Response: Many thanks for your comment. The grid in the image represents the longitude and latitude of the study area. We will further provide a larger map to show the location of the event.
(3) In the discussion, it is recommended to add a description and analysis of the limitations of the methods and results of this manuscript, as well as future work prospects.
Response: Many thanks for your comment. One of our goals is to talk about the advantages and limitations of the classic Voellmy rheology and 𝝁(I) rheology in calculating the mass flow movement. We have made a discussion and analysis in “Discussion” (e.g., Lines 259-264, 270-276 in the manuscript). Following your valuable comment, we will make a better analysis, as well as future work prospects.
(4) Add a conclusion section. In summary, major revisions are recommended."
Response: Following your comment, we will add a conclusion section in the revised manuscript.
Citation: https://doi.org/10.5194/nhess-2024-87-AC1
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AC1: 'Reply on RC1', Yu Zhuang, 18 Sep 2024
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RC2: 'Comment on nhess-2024-87', Anonymous Referee #2, 04 Sep 2024
This study compares the 𝝁(I) rheology and Voellmy-type grain flow rheologies, revealing their equivalences and differences through theoretical and case study analyses. The results not only deepen our understanding of the dynamics of geophysical mass flows but also highlight practical engineering challenges, providing theoretical support for future natural hazard risk assessment and mitigation. The paper is well written and structured. However, in this reviewer’s opinion it suffers some minor issues that need to be addressed before being considered for publication in NHESS.
Specific comments are following below.
（1）Could you please provide specific quantitative results or key data in the abstract to give readers immediate insight into the magnitude of differences or similarities found between the 𝝁(I) and Voellmy-type grain flow rheologies?
(2) More detailed explanation about the key terms should be given, such as "granular temperature/fluctuation energy" and "inertial number".
(3) Authors should expand the discussion on the calibration and validation of the models used in simulations. Specifically, address how the model parameters were chosen and their sensitivity to the predicted outcomes.
(4) Discuss specific instances or types of geophysical events where the comparative analysis of these rheologies could be particularly beneficial. if possible, please provide one more case study or hypothetical application.
Citation: https://doi.org/10.5194/nhess-2024-87-RC2 -
AC2: 'Reply on RC2', Yu Zhuang, 18 Sep 2024
This study compares the 𝝁(I) rheology and Voellmy-type grain flow rheologies, revealing their equivalences and differences through theoretical and case study analyses. The results not only deepen our understanding of the dynamics of geophysical mass flows but also highlight practical engineering challenges, providing theoretical support for future natural hazard risk assessment and mitigation. The paper is well written and structured. However, in this reviewer’s opinion it suffers some minor issues that need to be addressed before being considered for publication in NHESS.
Specific comments are following below.
(1) Could you please provide specific quantitative results or key data in the abstract to give readers immediate insight into the magnitude of differences or similarities found between the 𝝁(I) and Voellmy-type grain flow rheologies?
Response: Many thanks for your valuable comment. We can provide specific quantitative results in the abstract to make readers a better understand.
(2) More detailed explanation about the key terms should be given, such as "granular temperature/fluctuation energy" and "inertial number".
Response: Following your advice, we will provide detailed explanations about these terms in the revised manuscript.
(3) Authors should expand the discussion on the calibration and validation of the models used in simulations. Specifically, address how the model parameters were chosen and their sensitivity to the predicted outcomes.
Response: Many thanks for your comment. Actually, Voellmy, 𝝁(I) and 𝝁(R) rheologies have been widely applied in the gravitational mass flow calculations and the sensitivity analysis of rheological parameters has been conducted. All three rheological models are validated in many previous literatures. We will add some related references in the revised manuscript. Also, following your comment, we will provide explanations about the parameter selection in the revised manuscript.
(4) Discuss specific instances or types of geophysical events where the comparative analysis of these rheologies could be particularly beneficial. if possible, please provide one more case study or hypothetical application.
Response: Many thanks for your comment. We are very willing to add one more case study in the revised manuscript.
Citation: https://doi.org/10.5194/nhess-2024-87-AC2
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AC2: 'Reply on RC2', Yu Zhuang, 18 Sep 2024
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