Erosion and mobility in granular collapse over sloping beds

[1] We describe laboratory experiments of granular material flowing over an inclined plane covered by an erodible bed, designed to mimic erosion processes of natural flows travelling over deposits built up by earlier events. Two controlling parameters are the inclination of the plane and the thickness of the erodible layer. We show that erosion processes can increase the flow mobility (i.e., runout) over slopes with inclination close to the repose angle of the grains θr by up to 40%, even for very thin erodible beds. Erosion efficiency is shown to strongly depend on the slope of the topography. Entrainment begins to affect the flow at inclination angles exceeding a critical angle θc ≃ θr/2. Runout distance increases almost linearly as a function of the thickness of the erodible bed, suggesting that erosion is mainly supply-dependent. Two regimes are observed during granular collapse: a first spreading phase with high velocity followed by a slow thin flow, provided either the slope or the thickness of the erodible bed is high enough. Surprisingly, erosion affects the flow mostly during the deceleration phase and the slow regime. The avalanche excavates the erodible layer immediately at the flow front. Waves are observed behind the front that help to remove grains from the erodible bed. Steep frontal surges are seen at high inclination angles over both rigid or erodible bed. Finally, simple scaling laws are proposed making it possible to obtain a first estimate of the deposit and emplacement time of a granular collapse over a rigid or erodible inclined bed.

[1]  C. Ancey Powder-snow avalanches: approximation as non-Boussinesq clouds with a Richardson number-dependent entrainment function , 2004 .

[2]  R. Sparks,et al.  Erosion, transport and segregation of pumice and lithic clasts in pyroclastic flows inferred from ignimbrite at Lascar Volcano, Chile , 2000 .

[3]  J. J. Stoker Water Waves: The Mathematical Theory with Applications , 1957 .

[4]  Oldrich Hungr,et al.  Quantitative analysis of debris torrent hazards for design of remedial measures , 1984 .

[5]  Rich R. Kerswell,et al.  Planar collapse of a granular column: Experiments and discrete element simulations , 2008 .

[6]  PirulliMarina,et al.  The effect of the earth pressure coefficients on the runout of granular material , 2007 .

[7]  A. Hogg,et al.  Two-dimensional granular slumps down slopes , 2007 .

[8]  P. Burlando,et al.  Field experiments and numerical modeling of mass entrainment in snow avalanches , 2006 .

[9]  N. Balmforth,et al.  Granular collapse in two dimensions , 2005, Journal of Fluid Mechanics.

[10]  R. Sparks,et al.  Experimental study of gas-fluidized granular flows with implications for pyroclastic flow emplacement , 2004 .

[11]  J. N. Hutchinson,et al.  A review of the classification of landslides of the flow type , 2001 .

[12]  R. Kerswell,et al.  Dam break with Coulomb friction: a model for granular slumping , 2005 .

[13]  R. Roche,et al.  Numerical modeling of a landslide-generated tsunami following a potential explosion of the Montserrat volcano , 1999 .

[14]  Marina Pirulli,et al.  The effect of the earth pressure coefficients on the runout of granular material , 2007, Environ. Model. Softw..

[15]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[16]  Giovanni B. Crosta,et al.  Numerical modelling of entrainment/deposition in rock and debris-avalanches , 2009 .

[17]  D. Montgomery,et al.  Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by rivers and debris flows , 2005 .

[18]  Chih-Yu Kuo,et al.  A new model of granular flows over general topography with erosion and deposition , 2008 .

[19]  Oldrich Hungr,et al.  Estimating landslide motion mechanism, travel distance and velocity , 2005 .

[20]  Lev S. Tsimring,et al.  Avalanche mobility induced by the presence of an erodible bed and associated entrainment , 2007 .

[21]  Jean-Pierre Vilotte,et al.  Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme , 2003 .

[22]  Christophe Ancey,et al.  Dry granular flows down an inclined channel: experimental investigations on the frictional-collisional regime. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Olivier Pouliquen,et al.  SCALING LAWS IN GRANULAR FLOWS DOWN ROUGH INCLINED PLANES , 1999 .

[24]  Alessandro Simoni,et al.  Debris flow monitoring in the acquabona watershed on the Dolomites (Italian alps) , 2000 .

[25]  P. Heinrich,et al.  Analytical Solution for Testing Debris Avalanche Numerical Models , 2000 .

[26]  Herbert E. Huppert,et al.  Static and flowing regions in granular collapses down channels , 2007 .

[27]  William E. Dietrich,et al.  Erosion of steepland valleys by debris flows , 2006 .

[28]  R. Sparks,et al.  Erosion by pyroclastic flows on Lascar Volcano, Chile , 1997 .

[29]  Richard M. Iverson,et al.  Surge dynamics coupled to pore-pressure evolution in debris flows , 2003 .

[30]  J. Phillips,et al.  Experiments on deaerating granular flows and implications for pyroclastic flow mobility , 2002 .

[31]  T. Pierson,et al.  Erosion and deposition by debris flows at Mt Thomas, North Canterbury, New Zealand , 1980 .

[32]  Kolumban Hutter,et al.  Avalanche dynamics: Dynamics of rapid flows of dense granular avalanches , 2016 .

[33]  N. Mangold,et al.  Debris flows over sand dunes on Mars: Evidence for liquid water , 2003 .

[34]  Rou-Fei Chen,et al.  Simulation of Tsaoling landslide, Taiwan, based on Saint Venant equations over general topography , 2009 .

[35]  B. Zanuttigh,et al.  Instability and surge development in debris flows , 2007 .

[36]  Jean-Pierre Vilotte,et al.  Numerical modeling of self‐channeling granular flows and of their levee‐channel deposits , 2006 .

[37]  Jean-Pierre Vilotte,et al.  On the use of Saint Venant equations to simulate the spreading of a granular mass , 2005 .

[38]  M. Malin,et al.  Mars Global Surveyor Mars Orbiter Camera: Interplanetary cruise through primary mission , 2001 .

[39]  Tamotsu Takahashi,et al.  What is debris flow , 2007 .

[40]  Marina Pirulli,et al.  Results of Back-Analysis of the Propagation of Rock Avalanches as a Function of the Assumed Rheology , 2008 .

[41]  S. Savage,et al.  Gravity flow of cohesionless granular materials in chutes and channels , 1979, Journal of Fluid Mechanics.

[42]  S. Savage,et al.  The motion of a finite mass of granular material down a rough incline , 1989, Journal of Fluid Mechanics.

[43]  F. Bouchut,et al.  On new erosion models of Savage–Hutter type for avalanches , 2008 .

[44]  H. Suwa,et al.  Dissection of valleys by debris flows , 1980 .

[45]  Manuel Jesús Castro Díaz,et al.  A new Savage-Hutter type model for submarine avalanches and generated tsunami , 2008, J. Comput. Phys..

[46]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[47]  Arshad Kudrolli,et al.  Failure of a granular step. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Jean-Pierre Vilotte,et al.  Spreading of a granular mass on a horizontal plane , 2004 .

[49]  R. Fernández-Feria Dam-Break Flow for Arbitrary Slopes of the Bottom , 2006 .

[50]  O. Hungr,et al.  A model for the analysis of rapid landslide motion across three-dimensional terrain , 2004 .

[51]  T. Druitt,et al.  Propagation and hindered settling of laboratory ash flows - art. no. B02202 , 2008 .

[52]  P. Gauer,et al.  Possible erosion mechanisms in snow avalanches , 2004, Annals of Glaciology.

[53]  Two scenarios for avalanche dynamics in inclined granular layers. , 2005, Physical review letters.

[54]  L. Tsimring,et al.  Nonlocal rheological properties of granular flows near a jamming limit. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  M. Papa,et al.  Critical conditions of bed sediment entrainment due to debris flow , 2004 .

[56]  N. Thomas,et al.  Relation between dry granular flow regimes and morphology of deposits: formation of levées in pyroclastic deposits , 2003, cond-mat/0312541.

[57]  François Bouchut,et al.  Sinuous gullies on Mars: Frequency, distribution, and implications for flow properties , 2010 .

[58]  Betty Sovilla,et al.  Observations and modelling of snow avalanche entrainment , 2002 .

[59]  R. Ecke,et al.  Avalanche dynamics on a rough inclined plane. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  L. F. Smoll,et al.  Investigation of the origin and magnitude of debris flows from the Payhua Creek basin, Matucana area, Huarochirí Province, Perú , 2005 .

[61]  E. Cl'ement,et al.  Erosion waves: Transverse instabilities and fingering , 2005, cond-mat/0507163.

[62]  Richard M. Iverson,et al.  Flow of variably fluidized granular masses across three‐dimensional terrain: 1. Coulomb mixture theory , 2001 .

[63]  A. Tamburrino,et al.  Experimental observations of water‐like behavior of initially fluidized, dam break granular flows and their relevance for the propagation of ash‐rich pyroclastic flows , 2008 .

[64]  Lev S. Tsimring,et al.  Comparison between discrete and continuum modeling of granular spreading , 2006 .

[65]  Olivier Pouliquen,et al.  Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane , 2001, Journal of Fluid Mechanics.

[66]  Lev S Tsimring,et al.  Continuum theory of partially fluidized granular flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[67]  W. Dietrich,et al.  Experimental study of bedrock erosion by granular flows , 2008 .

[68]  C. Ancey,et al.  An exact solution for ideal dam‐break floods on steep slopes , 2008 .

[69]  Kyoji Sassa,et al.  Downslope volume enlargement of a debris slide–debris flow in the 1999 Hiroshima, Japan, rainstorm , 2003 .

[70]  L. Benda The influence of debris flows on channels and valley floors in the Oregon Coast Range, U.S.A. , 1990 .

[71]  Timothy R. H. Davies,et al.  A fragmentation-spreading model for long-runout rock avalanches , 1999 .

[72]  J. Vilotte,et al.  Memory of the unjamming transition during cyclic tiltings of a granular pile. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[73]  B. Dalloz-Dubrujeaud,et al.  Bidisperse granular avalanches on inclined planes: A rich variety of behaviors , 2007, The European physical journal. E, Soft matter.

[74]  F. Legros The mobility of long-runout landslides , 2002 .

[75]  H. Huppert,et al.  Axisymmetric collapses of granular columns , 2004, Journal of Fluid Mechanics.

[76]  Oldrich Hungr,et al.  Entrainment of debris in rock avalanches: An analysis of a long run-out mechanism , 2004 .

[77]  C. F. Lee,et al.  Erosional effects on runout of fast landslides, debris flows , 2006 .

[78]  Stéphane Douady,et al.  Two types of avalanche behaviour in granular media , 1999, Nature.

[79]  O. Hungr Simplified models of spreading flow of dry granular material , 2008 .

[80]  Anne Mangeney,et al.  Mobility and topographic effects for large Valles Marineris landslides on Mars , 2007 .

[81]  Giovanni B. Crosta,et al.  Numerical modeling of 2‐D granular step collapse on erodible and nonerodible surface , 2009 .

[82]  Herbert E. Huppert,et al.  Static and flowing regions in granular collapses down channels: Insights from a sedimenting shallow water model , 2007 .