Extending models of granular avalanche flows GEOPHYSICAL GRANULAR & PARTICLE-LADEN FLOWS Newton Bristol 28 October 2003 Bruce Pitman The University at Buffalo and if you see my reflection in the snow covered hills well the landslide will bring it down the landslide will bring it down M. Fleetwood

Supported by NSF Interdisciplinary team: Camil Nichita (Math) Abani Patra, Kesh Kesavadas, Eliot Winer, Andy Bauer (MAE) Mike Sheridan, Marcus Bursik (Geology) Chris Renschler (Geography) and a cast of students – Long Le (Math)

Casita disaster, Nicaragua

2D - depth averaged equations, dry flow: two parameters – internal and basal friction Model System – Dry Flow

TITAN 2D qSimulation environment, currently for dry flow only qIntegrate GRASS GI data for topographical map qHigh order numerical solver, adaptive mesh, parallel computing qExtension to include erosion (Bursik)

Little Tahoma Peak, 1963 avalanche several avalanches, total of 10 7 m 3 of broken lava blocks and other debris 6.8 km horizontal and 1.8 km vertical run estimate pile run-up on terminal moraine gives reasonable comparison with mapped flow; we miss the run-up on Goat Island Mt.

Little Tahoma Peak, 1963 avalanche Tahoma peak (deposit area extent) Tahoma peak, Mount Rainier (debris avalanche, 1963)

Debris Flows qMass flows containing fluid ubiquitous and important qIverson (’97) 1D Mixture model; Iverson and Denlinger 2D mixture model and simulations qHow to model fluid/pore pressure motion?

2-Fluid Approach uModel equations used in engineering literature uContinuum balance laws of mass and momentum for interpenetrating solids and fluid uDrag terms transfer momentum

2-Fluid Approach

Decide constitutive relations for solid and fluid stresses (frictional solids, Newtonian fluid) Phenomenological volume-fraction dependent function in drag Depth average – introduces errors that we will examine (and live with)

Free boundary and basal surface ground flowing mass Upper free surface F s (x,t) = s(x,y,t) – z = 0, Basal material surface F b (x,t) = b(x,y) – z = 0 Kinematic BC:

Scales  Characteristic length scales (mm to km)  e.g for Mount St. Helens (mudflow –1985)  Runout distance  31,000 m  Descent height  2,150 m  Flow length(L)  100-2,000  Flow thickness(H)  1-10 m  Mean diameter of sediment material m  Scale: ε═H/L – several terms small and are dropped (data from Iverson 1995, Iverson & Denlinger 2001)

Model System-Depth Average Theory 2D to 1D Depth average solids conservation: where

Model System – 1D

Errors in modeling

Special Solutions

hφ constant (lower curve) h evolves in time (upper curve)

Special Solutions

constant velocities u,v hφ faster h slower

Time Evolution uMixed hyperbolic-parabolic system

Time Evolution

uOn inclined plane, volume fraction changes small qspecial solution uInteraction with ‘topography’ induces variation in φ

Modeling questions uEvolution equation for fluid velocity? uEfficient methods for computing 2D system including realistic topography

Comments on model Continuum model In situ, there is a distribution of particle sizes. Models are operating at the edge where the discreteness of solids particles cannot be ignored Depth averaged velocity Are recirculation and basal slip velocity important? There is no simple scaling arguments from tabletop experiments to real debris avalanches (No Re, Ba, Sa)