<p>Debris flows are rapid, destructive mass movements prevalent in mountainous regions, posing significant risks to infrastructure and communities. While their general dynamics are well studied, in situ surface velocity data from full-scale natural events remain rare, limiting the ability to test and calibrate empirical flow models. This study applies ground-based pulse-Doppler (PD) radar to obtain continuous, high-resolution surface velocity measurements during four events in 2022 at Illgraben, Switzerland, three debris flows and one debris flood. We evaluate four classical mean-velocity equations: Newtonian Laminar Flow, Dilatant Grain Shearing, Manning–Strickler, and Chézy. Resistance coefficients are back-calculated to assess performance and variability. Best-fit coefficients for the Manning–Strickler (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10346_2025_2611_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$n$</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation> = 0.14 for debris flows; 0.08 for the debris flood) and Dilatant Grain Shearing (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10346_2025_2611_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\xi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation> = 31; <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10346_2025_2611_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\xi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation> = 62, respectively) equations are used to estimate discharge and volume. Substantial intra- and inter-event variability in these coefficients challenges the assumption of constant resistance in debris-flow models. Intercept analysis of flow height–velocity relationships reveals finite threshold heights, consistent with critical or yield stress behaviour, and varies between surges, indicating changes in bulk rheology and transitions toward more fluidised flow regimes. Finally, we apply a flow resistance scaling framework based on normalised velocity (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10346_2025_2611_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">$V/ {v}^{*}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>V</mi> <mo stretchy="false">/</mo> <mmultiscripts> <mrow> <mi>v</mi> </mrow> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>) and relative flow depth (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10346_2025_2611_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$h / {D}_{90}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">/</mo> <msub> <mi>D</mi> <mn>90</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>), enabling dimensionless comparison across flow regimes. This represents the first high-resolution, intra-event application of such a framework using direct radar measurements. Our findings offer new empirical constraints on flow resistance in steep, surge-dominated channels and support the development of dynamically calibrated resistance models for debris-flow simulation.</p>

Flow resistance variability in debris flows: evaluating equations, critical stress, and scaling from high-resolution field data

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2025年9月6日

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Tobias Schöffl,
Brian McArdell,
Richard Koschuch,
Helmut Schreiber,
Christoph Graf,
Johannes Hübl,
Roland Kaitna

摘要

Debris flows are rapid, destructive mass movements prevalent in mountainous regions, posing significant risks to infrastructure and communities. While their general dynamics are well studied, in situ surface velocity data from full-scale natural events remain rare, limiting the ability to test and calibrate empirical flow models. This study applies ground-based pulse-Doppler (PD) radar to obtain continuous, high-resolution surface velocity measurements during four events in 2022 at Illgraben, Switzerland, three debris flows and one debris flood. We evaluate four classical mean-velocity equations: Newtonian Laminar Flow, Dilatant Grain Shearing, Manning–Strickler, and Chézy. Resistance coefficients are back-calculated to assess performance and variability. Best-fit coefficients for the Manning–Strickler ( $n$ $n$ = 0.14 for debris flows; 0.08 for the debris flood) and Dilatant Grain Shearing ( $\xi$ $ξ$ = 31; $\xi$ $ξ$ = 62, respectively) equations are used to estimate discharge and volume. Substantial intra- and inter-event variability in these coefficients challenges the assumption of constant resistance in debris-flow models. Intercept analysis of flow height–velocity relationships reveals finite threshold heights, consistent with critical or yield stress behaviour, and varies between surges, indicating changes in bulk rheology and transitions toward more fluidised flow regimes. Finally, we apply a flow resistance scaling framework based on normalised velocity ( $V/ {v}^{*}$ $V / v^{*}$ ) and relative flow depth ( $h / {D}_{90}$ $h / D_{90}$ ), enabling dimensionless comparison across flow regimes. This represents the first high-resolution, intra-event application of such a framework using direct radar measurements. Our findings offer new empirical constraints on flow resistance in steep, surge-dominated channels and support the development of dynamically calibrated resistance models for debris-flow simulation.