Entrainment of bed material by Earth‐surface mass flows: Review and reformulation of depth‐integrated theory

Reviews of Geophysics - Tập 53 Số 1 - Trang 27-58 - 2015
Richard M. Iverson1,2,3, Chaojun Ouyang4
1R. M. Iverson,
2U.S. Geological Survey Cascades Volcano Observatory, Vancouver, Washington, USA
3[email protected]
4Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, China

Tóm tắt

AbstractEarth‐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

10.1029/2003JF000052

10.1098/rsta.2005.1593

10.1017/S0022112005004283

10.1016/j.cageo.2007.11.008

10.1098/rspa.1954.0186

10.1098/rsta.1956.0020

Benkhaldoun F., 2011, Finite Volumes for Complex Applications VI—Problems & Perspectives, 75

10.1016/j.advwatres.2011.02.016

10.1063/1.4823857

10.5194/hess-14-705-2010

10.1017/S002211209300148X

10.1007/s00707-007-0534-9

10.1139/t92-040

Briukhanov A. V., 1967, Physics of Snow and Ice, 1223

10.1080/00221680009498297

10.1017/S0022143000011242

10.1086/629211

10.1061/(ASCE)0733-9429(2004)130:7(689)

10.1029/2011GL049408

10.1017/S0022112098002250

Chadwick P., 1999, Continuum Mechanics Concise Theory and Problems

10.1680/geot.2006.56.5.305

10.1061/(ASCE)HY.1943-7900.0000821

10.1016/j.enggeo.2008.10.004

10.1029/2006JB004471

Egashira S., 2001, Experimental study on the entrainment of bed material into debris flow, Phys. Chem. Earth Part C, 26, 645

10.1016/j.coldregions.2005.03.005

10.1086/629522

10.1016/S0098-3004(03)00133-X

10.1017/S0022112002008455

10.1061/9780784408148.ch02

10.1029/92JC02404

10.1002/fld.2298

10.1098/rspa.2013.0820

Gilbert G. K.(1914) The transportation of debris by running water U.S. Geol. Surv. Prof. Pap. 86 p. 263.

10.1007/978-1-4612-0713-9

10.1017/S0022112001004736

10.1016/S1001-6279(13)60001-3

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/.]

10.1029/91WR02380

Heim A., 1932, Bergsturz and Menschenleben, 218

10.1086/629442

10.1139/t90-083

10.1139/t95-063

10.1130/B25362.1

10.1007/3-540-27129-5_7

10.5194/nhess-12-3075-2012

10.1029/97RG00426

10.1029/2011JF002189

Iverson R. M., 2013, Handbook of Environmental Fluid Dynamics, 573

10.1680/geot.12.D.007

10.1029/2000JB900329

10.1098/rspa.2013.0819

10.1029/2009JF001514

10.1038/NGEO1040

Jakob M., 2005, Debris‐Flow Hazards and Related Phenomena, 739

10.1017/S0022112003005342

10.1029/2007JF000831

10.1137/060677501

10.1016/S0013-7952(01)00090-4

10.1017/S0962492911000043

10.1007/s10346-012-0316-x

Malvern L. E., 1969, Introduction to the Mechanics of a Continuous Medium

10.1029/2011JF002278

10.1139/t04-052

10.1007/s10346-007-0102-3

10.1016/j.jcp.2010.08.006

10.1023/B:GEOP.0000006083.47240.4c

10.1029/2001WR001253

10.1007/s10346-014-0484-y

10.1017/S0022112007008567

10.1016/0377-0273(90)90082-Q

10.1680/geot.10.P.074

10.3934/dcdsb.2003.3.589

10.1016/B978-0-444-41507-3.50016-7

Pudasaini S. P., 2007, Avalanche Dynamics

10.1061/(ASCE)0733-9429(1999)125:2(117)

10.1016/j.enggeo.2011.04.007

Reid M. E., 2011, Fifth International Conference on Debris‐flow Hazards Mitigation, Mechanics, Prediction and Assessment, 367

10.1029/2012JC008306

Rickmers W. R., 1913, The Duab of Turkestan

10.2113/gseegeosci.16.3.257

10.1016/j.jcp.2008.08.007

10.1098/rspa.1962.0193

10.1017/S0022112089000340

10.1002/esp.1127

10.1029/2001WR000681

10.1029/2004EO150001

Simpson J. E., 1987, Gravity Currents in the Environment and the Laboratory

10.5194/nhess-2-169-2002

10.1029/2005JF000391

10.1007/s004450050162

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

10.1002/fld.3809

10.1007/s00707-007-0560-7

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

10.1130/0016-7606(1997)109<0143:TOMFMR>2.3.CO;2

10.1139/t89-075

10.1061/(ASCE)HY.1943-7900.0000214

Voight B., 1978, Rockslides and Avalanches, 1 Natural Phenomena

10.1007/978-94-015-8354-1

10.1016/S0013-7952(02)00289-2

10.1061/(ASCE)0733-9429(2007)133:1(48)

Xu Q., 2010, The 13 August 2010 catastrophic debris flows in Sichuan Province: Characteristics, genetic mechanism and suggestions, J. Eng. Geol., 18, 596

10.1007/s11069-012-0395-y

10.1080/00221686.2008.9521854

Thông tin
Thông tin xuất bản

Reviews of Geophysics

Tập 53 Số 1

27-58

Thông tin tác giả