Entrainment of bed material by Earth‐surface mass flows: Review and reformulation of depth‐integrated theory
Tóm tắt
Earth‐surface mass flows such as debris flows, rock avalanches, and dam‐break floods can grow greatly in size and destructive potential by entraining bed material they encounter. Increasing use of depth‐integrated mass and momentum conservation equations to model these erosive flows motivates a review of the underlying theory. Our review indicates that many existing models apply depth‐integrated conservation principles incorrectly, leading to spurious inferences about the role of mass and momentum exchanges at flow‐bed boundaries. Model discrepancies can be rectified by analyzing conservation of mass and momentum in a two‐layer system consisting of a moving upper layer and static lower layer. Our analysis shows that erosion or deposition rates at the interface between layers must, in general, satisfy three jump conditions. These conditions impose constraints on valid erosion formulas, and they help determine the correct forms of depth‐integrated conservation equations. Two of the three jump conditions are closely analogous to Rankine‐Hugoniot conditions that describe the behavior of shocks in compressible gasses, and the third jump condition describes shear traction discontinuities that necessarily exist across eroding boundaries. Grain‐fluid mixtures commonly behave as compressible materials as they undergo entrainment, because changes in bulk density occur as the mixtures mobilize and merge with an overriding flow. If no bulk density change occurs, then only the shear traction jump condition applies. Even for this special case, however, accurate formulation of depth‐integrated momentum equations requires a clear distinction between boundary shear tractions that exist in the presence or absence of bed erosion.
Từ khóa
Tài liệu tham khảo
Benkhaldoun F., 2011, Finite Volumes for Complex Applications VI—Problems & Perspectives, 75
Briukhanov A. V., 1967, Physics of Snow and Ice, 1223
Chadwick P., 1999, Continuum Mechanics Concise Theory and Problems
Egashira S., 2001, Experimental study on the entrainment of bed material into debris flow, Phys. Chem. Earth Part C, 26, 645
Gilbert G. K.(1914) The transportation of debris by running water U.S. Geol. Surv. Prof. Pap. 86 p. 263.
Griswold J. P. andR. M.Iverson(2008) Mobility statistics and automated hazard mapping for debris flows and rock avalanches U.S. Geological Survey Scientific Investigations Report 2007‐5276. [Available athttp://pubs.usgs.gov/sir/2007/5276/.]
Heim A., 1932, Bergsturz and Menschenleben, 218
Iverson R. M., 2013, Handbook of Environmental Fluid Dynamics, 573
Jakob M., 2005, Debris‐Flow Hazards and Related Phenomena, 739
Malvern L. E., 1969, Introduction to the Mechanics of a Continuous Medium
Pudasaini S. P., 2007, Avalanche Dynamics
Reid M. E., 2011, Fifth International Conference on Debris‐flow Hazards Mitigation, Mechanics, Prediction and Assessment, 367
Rickmers W. R., 1913, The Duab of Turkestan
Simpson J. E., 1987, Gravity Currents in the Environment and the Laboratory
Spinewine B.(2005) Two‐layer flow behaviour and the effects of granular dilatancy in dam‐break induced sheet‐flow PhD thesis no. 76 Univ. Catholique de Louvain Belgium.
Stiny J., 1910, Die Muren. Versuch Einer Monographie mit Besonderer Berücksichtigung der Verhältnisse in den Tiroler Alpen, 139
Stoker J. J., 1958, Water Waves: The Mathematical Theory With Applications
Takahashi T., 1978, Mechanical characteristics of debris flow, J. Hydrol. Div. Am. Soc. Civ. Eng., 104, 1153
Takahashi T., 1991, Debris Flow
Takahashi T., 1987, Erosion and Sedimentation in the Pacific Rim, 167
Voight B., 1978, Rockslides and Avalanches, 1 Natural Phenomena
Xu Q., 2010, The 13 August 2010 catastrophic debris flows in Sichuan Province: Characteristics, genetic mechanism and suggestions, J. Eng. Geol., 18, 596