1 / 29

Extending models of granular avalanche flows

Extending models of granular avalanche flows. 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. Bruce Pitman The University at Buffalo.

luz
Download Presentation

Extending models of granular avalanche flows

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Extending models of granular avalanche flows 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 Bruce Pitman The University at Buffalo GEOPHYSICAL GRANULAR & PARTICLE-LADEN FLOWS Newton Institute @ Bristol28 October 2003

  2. 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) Supported by NSF

  3. Casita disaster, Nicaragua

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

  5. TITAN 2D • Simulation environment, currently for dry flow only • Integrate GRASS GI data for topographical map • High order numerical solver, adaptive mesh, parallel computing • Extension to include erosion (Bursik)

  6. Little Tahoma Peak, 1963 avalanche • several avalanches, total of 107 m3 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.

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

  8. Debris Flows • Mass flows containing fluid ubiquitous and important • Iverson (’97) 1D Mixture model; Iverson and Denlinger 2D mixture model and simulations • How to model fluid/pore pressure motion?

  9. 2-Fluid Approach • Model equations used in engineering literature • Continuum balance laws of mass and momentum for interpenetrating solids and fluid • Drag terms transfer momentum

  10. 2-Fluid Approach

  11. 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)

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

  13. 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 10-3-10 m • Scale: ε═H/L – several terms small and are dropped (data from Iverson 1995, Iverson & Denlinger 2001)

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

  15. Model System – 1D

  16. Model System – 1D

  17. Model System – 1D

  18. Errors in modeling

  19. Special Solutions

  20. Special Solutions

  21. Special Solutions hφ constant (lower curve) h evolves in time (upper curve)

  22. Special Solutions

  23. Special Solutions constant velocities u,v hφ faster h slower

  24. Time Evolution • Mixed hyperbolic-parabolic system

  25. Time Evolution

  26. Time Evolution • On inclined plane, volume fraction changes small • special solution • Interaction with ‘topography’ induces variation in φ

  27. Modeling questions • Evolution equation for fluid velocity? • Efficient methods for computing 2D system including realistic topography

  28. 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)

More Related