Comparative analysis of <i>μ</i>(<i>I</i>) and Voellmy-type grain flow rheologies in geophysical mass flows: insights from theoretical and real case studies
<p>The experimentally based <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology is now prevalent in describing the movement of gravitational mass flows. We reinterpret the <span class="inline-formula"><i>μ</i>...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2025-06-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | https://nhess.copernicus.org/articles/25/1901/2025/nhess-25-1901-2025.pdf |
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| Summary: | <p>The experimentally based <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology is now prevalent in describing the movement of gravitational mass flows. We reinterpret the <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology as a Voellmy-type relationship to highlight its connection to grain flow theory and demonstrate its practical applications. Using one-dimensional block modeling and two real-world case studies – the 2017 Piz Cengalo rock–ice avalanche and an experimental snow avalanche at the Swiss Vallée de la Sionne test site – we demonstrate the relationship between the dimensionless number <span class="inline-formula"><i>I</i></span> and the granular temperature <span class="inline-formula"><i>R</i></span>, establishing the equivalence between <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> and widely used Voellmy-type grain flow rheologies <span class="inline-formula"><i>μ</i>(<i>R</i>)</span>. Results indicate that <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology utilizes the dimensionless inertial number <span class="inline-formula"><i>I</i></span> to mimic contributions of granular temperature/fluctuation energy to flow behavior. In terms of Voellmy, the <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology contains a velocity-dependent turbulent friction coefficient that models shear-thinning behavior. This turbulent friction assumes the production and decay of fluctuation energy are in balance, exhibiting no difference during accelerative and depositional phases of avalanche flow. The constant Coulomb friction coefficient prevents <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology from accurately modeling the dispositional characteristics of actual mass flows. The modeled evolution of the snow avalanche using the <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> rheology is too slow, lagging 5 <span class="inline-formula">s</span> behind the measured values. More importantly, the calculated runout extends approximately 200 <span class="inline-formula">m</span> beyond the observed limits, with significant deposit anomalies in the valley. By incorporating non-steady production and decay of fluctuation energy in the <span class="inline-formula"><i>μ</i>(<i>R</i>)</span> framework, it becomes possible to achieve a good match with both the measured velocities and the observed runout. Our results highlight the strengths and limitations of both <span class="inline-formula"><i>μ</i>(<i>I</i>)</span> and Voellmy <span class="inline-formula"><i>μ</i>(<i>R</i>)</span> rheologies, bolstering the theoretical foundation of mass flow modeling while revealing practical engineering challenges.</p> |
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| ISSN: | 1561-8633 1684-9981 |