Paris 16 / 04 / 2013

1. Discrete modelling of rock avalanches Mollon, Richefeu, Villard, Daudon 3SRLab, Grenoble, France Paris 16 / 04 / 2013

2. Pirulli and Mangeney, 2007 103 m3- 105 m3 Frank slide, 30 103 m3 Discretemodelling of rock avalanches The propagation of a rock avalanche on a natural slope is controlled by the collective behavior of the blocks. In order to predict the deposition areas of such events, this behavior needs to be well understood and reproduced. The present analysis is performed using the numerical tools of discrete modelling. Pirulli and Mangeney (2007) Introduction 2

3. Discretemodelling of rock avalanches Before tackling a real event, a first step is to reproduce experimental results from the literature. The considered laboratory experiments reproduce the flow and the deposition of granular materials on a slope, tracking the kinematics of the flow and the geometry of the granular deposit. The granular material is composed of 6000 to 10000 small clay bricks (30mm long), for an apparent volume of 40L. Manzella and Labiouse (2009) Introduction 3

4. Discretemodelling of rock avalanches The discrete modelling consists in solving, using an explicit time-step scheme, the equations of motion applied to each solid composing the granular mass, based on the forces they are submitted to. The relations between the relative motions of the contacting blocks and the contact forces are defined by the contact law. The contact law used here is as simple as possible and is based on 4 parameters (2 parameters of stiffness, and 2 parameters of energy dissipation). Introduction 4

5. A. Experimental assessment of the contact parameters Paris 16 / 04 / 2013

6. Discretemodelling of rock avalanches In order to assess the contact parameters, several additional experiments are conducted with the same materials as the target experiment. A large number of isolated impacts of single bricks are performed and filmed by two cameras (1000 frames/sec). Impacts may be brick-support or brick-brick, we are thus looking for 8 parameters. A. Experimental assessment of the contact parameters 6

7. Discretemodelling of rock avalanches After stages of synchronization and scaling, a first back-analysis is performed to determine the brick kinematics just before and after the impact. Three points are tracked on each camera, two points being redundant on the two cameras. After fitting, we get three coordinates of the velocity and three coordinates of the angular velocity, before and after impact. A. Experimental assessment of the contact parameters 7

8. Discretemodelling of rock avalanches The discrete numerical model is then used as a classical back-analysis tool to assess the contact parameters. Experimentalmeasurements VxVyVz ωxωyωz Measuredbefore impact VxVyVz ωxωyωz Measuredafter impact Comparison Introduction in the discrete model VxVyVz ωxωyωz Simulatedafter impact Errorfunction : err(en2, μ, kn, kt) Numerical simulation for a given set of parameters (en2, μ, kn, kt) Minimization A. Experimentalassessment of the contact parameters 8

9. Discretemodelling of rock avalanches The projection of the error function in 2D spaces shows that : -a very clear minimum exists for a couple of dissipation parameters -the stiffness parameters only have a very limited influence Parameters of energy dissipation Parameters of contact stiffnesses (z-scaledilated 10 times) A. Experimentalassessment of the contact parameters 9

10. Discretemodelling of rock avalanches The optimum parameters are fitted in average on the totality of the experimental impacts. They remain rather consistent when applied to a single experiment. A. Experimentalassessment of the contact parameters 10

11. B. Model validation Paris 16 / 04 / 2013

12. Discretemodelling of rock avalanches The fitted contact parameters are introduced in the simulation of the full experiment. B. Model validation 12

13. Discretemodelling of rock avalanches The comparison between numerical and experimental deposits is satisfactory, and the comparison between the deposition kinematics is acceptable. These results allow a first interpretation of the kinematics of the deposition process. Experimental error B. Model validation 13

14. Discretemodelling of rock avalanches The deposit topography is described using an algorithm of non-convex close envelope. A final apparent volume of 57L is obtained, for an initial apparent volume of 40L. B. Model validation 14

15. Discretemodelling of rock avalanches Interpolation methods make it possible to plot the fields of velocity, angular velocity, and local granular density, in the plane of symetry of the flow. B. Model validation 15

16. Discretemodelling of rock avalanches The study of energy conservation shows a maximum of the kinetic energy just after the impact of the avalanche on the horizontal plane. Most of the energy dissipation occurs by friction between the bricks and the slope. A peak of dissipation occurs around the transition zone between the slope and the horizontal plane, and a large amount of inter-particle dissipations occur in this area. B. Model validation 16

17. C. Parametric study Paris 16 / 04 / 2013

18. Discretemodelling of rock avalanches The simulation of reference is consistent with the target experiment, but does not represent well a real rock avalanche because the slope is too smooth. A macro-roughness is introduced in the model to evaluate its influence on the flow. C. Parametricstudy 18

19. Discretemodelling of rock avalanches The fields of velocity and of angular velocity exhibit a qualitatively different behavior when compared to a smooth slope. A vertical velocity gradient develops, and block rotations are important everywhere on the slope : the flow is sheared. C. Parametricstudy 19

20. Discretemodelling of rock avalanches The patterns of dissipation of the kinetic energy are also different. The roughness triggers more inter-particle dissipation, which means that the flow regime is much mode collisionnal. C. Parametricstudy 20

21. Discretemodelling of rock avalanches Threedifferentsizes of bricks are introduced, both on the smooth and on the rough slopes. Smoothslope Rough slope C. Parametricstudy 23

22. Discretemodelling of rock avalanches On a smooth slope, the size of blocks has a limited influence on the deposition area, but strongly influences the morphology of the deposit. Small blocks lead to a slightly more extended deposit, but with softer slopes and with a reduced « plateau ». C. Parametricstudy 24

23. Discretemodelling of rock avalanches The roughness of the slope has very different effects on the avalanche depending on the particles size. Small bricks tend to remain much more on the slope, but large bricks escape much more from the main flow. Standard bricks Large bricks Small bricks C. Parametricstudy 25

24. D. Perspectives Paris 16 / 04 / 2013

25. Introduction de particules complexes dans une modélisation discrète Introduction of realistic block shapes, based on shape descriptors statistically consistent with in-situ measurements. Daytona Sand Ottawa Sand D. Perspectives 27

26. Discretemodelling of rock avalanches Block-slope interaction in case of a soft substrate : improvement of the contact law. Franck Bourrier (IRSTEA) D. Perspectives 28

27. Discretemodelling of rock avalanches Introduction in the digital model of a real site : implementation issues, initial network of fractures, etc. D. Perspectives 29

28. Thank you for your attention Mollon, Richefeu, Villard, Daudon 3SRLab, Grenoble, France