Flow front mobility of rock avalanches as a function of flow volume, grain size, channel width, basal friction and flow scale

Abstract

The ability to predict the mobility of rock avalanches is necessary when designing strategies to mitigate the risks they pose. A popular mobility indicator of the flow front is the Heim’s apparent friction coefficient μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document}. In the field, μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document} shows a decrease in value as flow volume V increases. But this correlation has been a mystery as to whether it is due to a causal relationship between V and mobility since: (1) field data of μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document} do not collapse onto a single curve because typically widely scattered and (2) laboratory experiments have shown an opposite volume effect on the center of mass mobility of miniature flows. My numerical simulations confirm for the first time the existence of a functional relationship of scaling parameters where μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document} decreases as V increases in unsteady and nonuniform 3D flows. Data scatter is caused by μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document} that is affected by numerous other variables besides V. The interplay of these variables produces different granular regimes with opposite volume effects. In particular, μH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{H}$$\\end{document} decreases as V increases in the regime characterized by a relatively rough subsurface. The relationship holds for large-scale flows that, like rock avalanches, consist of a very large number of fine clasts traveling in wide channels. In these dense flows, flow front mobility increases as flow volume increases, as channel width increases, as grain size decreases, as basal friction decreases and as flow scale increases. Larger-scale flows are more mobile because they have larger Froude number values.