I NTERREG I VC alcotra Marseille, January 27 th École Polytechnique Fédérale de Lausanne Laboratory for Rock Mechanics (LMR)

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1 POLITECNICO DI TORINO I NTERREG I VC alcotra Numerical modelling w ith a continuum mechanics approach: updatings (2) Claudio Scavia, () Vincent Labiouse, (2) Marina Pirulli, () Claire Sauthier, (2,) Gabriele Pisani () École Polytechnique Fédérale de Lausanne Laboratory for Rock Mechanics (LMR) (2) Politecnico di Torino Department of Structural and Geotechnical Engineering

2 Outline Continuum mechanics approach: DAN 3D and RASH 3D RASH 3D improvement: the centripetal acceleration New results w ith RASH 3D and comparison w ith DAN 3D Conclusions and future developments (continuum mechanics) Distinct element method approach: 3DEC 3DEC VERY preliminary results and future developments (discontinuous approach) 2

3 Continuum mechanics approach Hypothesis From a real heterogenous mass to a continuum equivalent fluid... Images courtesy of Hungr,995 Governing mass and momentum balance equations: mass balance v = momentum balance v ρ + v v = σ + ρ g t 3

4 Continuum mechanics approach Hypothesis 2 H L Images courtesy of Hungr,995 H << L DEP TH AVERAGED EQUATIONS I ntroduced in the context of granular material propagation by Savage and Hutter (989) Flow ing mass assumed as incompressible (i.e., constant density, ρ) Equations of mass and momentum in the x and y direction (local reference system): + div t t t ( h u ) ( ) ( ) 2 h u + h u + ( h u v ) = γ g h + ( h σ ) + ( h σ ) x x ( ) ( ) ( ) 2 h v + h u v + h v = γ y g h + ( h σ xy ) + ( h σ yy ) + T ty x = y y ρ x ρ x xx ρ y ρ y xy + T ρ ρ tx GOVERNING DIFFERENT NUMERICAL IMP LEMENTATIONS USING DIFFERENT MESH TYPES AND SOLVERS 4

5 Continuum mechanics approach RASH 3D (Bristeau,2; Mangeney et al., 23; P irulli, 25) DAN 3D (McDougall & Hungr,24) Analyses performed by Gabriele P isani & M arina P irulli Claire Sauthier 5

6 DAN 3D & RASH 3D DIFFERENT NUMERI CAL I MP LEMENTATI ONS USING DIFFERENT MESH TYP ES AND SOLVERS Aspect DAN 3D RASH 3D Framew ork Lagrangian Eulerian Mesh Meshless Finite Element mesh Computational method SP H Smoothed P article Hydrodynamics Kinetic scheme based on a finite volume approach Entrainment Y es Yes Implemented rheological Law s (parameters) Frictional () Voellmy (2) Frictional () Voellmy (2) Bingham (2) Quadratic (3) Numerical parameters 4 K condition Y es Yes K a / K p condition Yes (Gray et al., 999) Not completely Centripetal acceleration Y es No Yes 6

7 RASH 3D improvement m EFFECT OF THE CENTRI PETAL ACCELERATI ON introduced to take into account the normal stress increase due to the topography deflection C g on the plane (..and before..) N W,n = N = m g cosα W,t S = F,t F,t = W,t N tgϕ m a,t = m g(sinα cosαtgϕ ) W,n R S N S = N tgϕ (Coulomb) F,t W,n = W cosα W,t = W sinα W 2,n = W 2 cosβ W 2,t = W 2 sinβ W ϕ' β W,t α S 2 W 2,n W 2,t N 2 F 2,n W 2 F 2,t m 2 R S 2 = N 2 tgϕ (Coulomb) on the transition (..and now..) N 2 W 2,n = F 2,n N 2 = m 2 (gcosβ + a 2,c ) W 2,t S 2 = F 2,t F 2,t = W 2,t N 2 tgϕ m 2 a 2,t = m 2 [g(sinβ cosβtgϕ ) a 2,c tgϕ ) ] N 2 > N a 2,t < a,t 7

8 8 RASH 3D improvement Centripetal acceleration r v r v a x c 2 * 2 = = = = = = = =, *, 2 2, c x c c a r R v a R r a r affects only velocities in the X direction different curvatures in different zones EFFECT OF THE CENTRI PETAL ACCELERATI ON

9 P hysical modelling LABORATORY AP P ARATUS BENCHMARK & VALIDATION CASES Images from Manzella and Labiouse, 28 Lateral view P lane view Test number * # #2 #3 #4 Volume [l] Falling height [m].5.5 *Gravel (d=.5 4 mm), Slope=45, Radius=.5 m, ϕ=23.5 ±.5, δ=34± (i) 9

10 RASH 3D new results: benchmark case CALI BRATION Rheology: Coulomb P arameter: friction angle (ϕ) EXP. ϕ=24.5 ϕ=25 ϕ=25.5 [m] [m] [m] [m] Y [m].2.2 X CM % %.64 2.% Z CM.2.22.%.23 5.%.23 5.% R % %.28.8% L %.8 4.8%.6 2.9%.4 W.7.9.8% % %.6 LEGEND EXP ERIMENT #.8 RASH 3D ϕ=24.5 P lane view RASH 3D ϕ=25 Z [m] X [m] Longitudinal section RASH 3D ϕ=25.5 CURVED TRANSITION SECTION

11 RASH 3D versions: OLD vs NEW EXP ERI MENT # Volume: 4 l Falling height: m EXP. RASH 3D (OLD) ϕ=29.5 RASH 3D (NEW ) ϕ=25 [m] [m] [m] X CM % % Y [m] Z CM %.22 5.%.2 R % %.4 L %.8 4.8%.6 W.7.9.8% %.8 LEGEND EXP ERIMENT P lane view RASH 3D (O) ϕ=29.5 Z [m] X [m] Longitudinal section RASH 3D (N) ϕ=25 CURVED TRANSITION SECTION

12 RASH 3D versions: OLD vs NEW.8.6 OBSERVATI ONS Decrease in the friction angle by 4.5 ( ); Y [m] Overestimation of depth distribution in the rear part of the deposit and consequent moving backw ard of the centre of mass (longitudinal section); Better simulation of the length of the deposit (plane view and longitudinal section);.6 Almost no difference in terms of w idth of the deposit (plane view )..8 LEGEND EXP ERIMENT P lane view RASH 3D (O) ϕ=29.5 Z [m] X [m] Longitudinal section RASH 3D (N) ϕ=25 CURVED TRANSITION SECTION 2

13 RASH 3D new results: comparison w ith DAN 3D EXP ERI MENT # Volume: 4 l Falling height: m EXP. DAN 3D ϕ=23.7 RASH 3D ϕ=25 [m] [m] [m] X CM % % Y [m] Z CM %.22 5.%.2 R % %.4 L %.8 4.8%.6 W % %.8 LEGEND EXP ERIMENT P lane view DAN 3D ϕ=23.7 Z [m] X [m] Longitudinal section RASH 3D ϕ=25 CURVED TRANSITION SECTION 3

14 RASH 3D new results: comparison w ith DAN 3D EXP ERI MENT #2 Volume: 2 l Falling height: m EXP. DAN 3D ϕ=23.7 RASH 3D ϕ=25 [m] [m] [m] X CM %.67 3.% Y [m] Z CM % %.2 R.4.4.%.2 5.3%.4 L % %.6 W %.6 3.2%.8 LEGEND EXP ERIMENT P lane view DAN 3D ϕ=23.7 Z [m] X [m] Longitudinal section RASH 3D ϕ=25 CURVED TRANSITION SECTION 4

15 RASH 3D new results: comparison w ith DAN 3D EXP. EXP ERI MENT #3 DAN 3D ϕ=23.7 Volume: 4 l Falling height:.5 m RASH 3D ϕ=25 [m] [m] [m] X CM % % Y [m]..2 Z CM % % R % %.4 L.9..9%.6 2.8%.6 W % % Z [m] X [m] P lane view LEGEND Longitudinal section EXP ERIMENT DAN 3D ϕ=23.7 RASH 3D ϕ=25 CURVED TRANSITION SECTION 5

16 RASH 3D new results: comparison w ith DAN 3D EXP ERI MENT #4 Volume: 2 l Falling height:.5 m EXP. DAN 3D ϕ=23.7 RASH 3D ϕ=25 [m] [m] [m] X CM % % Y [m] Z CM..3 3.%.4 4.%.2 R %.4 2.%.4 L %.9 5.9%.6 W % %.8 LEGEND EXP ERIMENT P lane view DAN 3D ϕ=23.7 Z [m] X [m] Longitudinal section RASH 3D ϕ=25 CURVED TRANSITION SECTION 6

17 RASH 3D vs DAN 3D CONCLUSIONS Small difference ( ) betw een the friction angles required by DAN 3D and RASH 3D to reproduce the deposits characteristics in a satisfactory w ay (previous difference before RASH 3D s improvement: 6 ); DAN 3D better simulates the deposits s characheristics in terms of runout and position of the centre of mass, but in plane view the computed deposit presents a transversal symmetry w hich is in contraddiction w ith laboratory observations; RASH 3D better reproduces the length and the overall shape of the deposit in plane view, but the w idth is slightly overestimated; DAN 3D gives a better simulation of the deposit longitudinal profile, w hereas the results w ith RASH 3D show a slight different morphology in terms of position and peak value of the maximum thickness of the deposit, w hich are under and overestimated respectively. 7

18 Continuum mechanics approach FUTURE DEVELOP MENTS (/ 2) Simulations w ith sharp transition: effect of the centripetal acceleration different curvatures in different zones r = 2 r = 3 r = a a a, c 2, c 3, c = = = SLOW 3x SLOW 2x I nvestigation of motion dynamics in terms of mass spreading, front velocities and duration 8

19 Continuum mechanics approach 2 FUTURE DEVELOP MENTS (2/ 2).5 Transient evolution of the centre of mass and draw ing of the energy line LEGEND LEGEND Transition Topography Z [m] h d h t Transition Topography Potential Line Mass Total energy line P otential line Energy line.5 h k h p h k Energy Line (Total) P otential energy Kinetic energy h d Dissipation h p h t = h p + h k + h d = constant X [m] h t Total energy 9

20 Distinct Element Method Approach 3DEC (I tasca Engineering Consulting and Softw are) Discontinuous medium modeled as an assemblage of polyhedra (i.e., parallelepipeds); Rigid blocks (i.e., internal deformation is neglected); Discontinuities treated as boundary conditions betw een blocks; Motion along discontinuities governed by linear force displacement relations for movements in both the normal and shear directions (i.e. elastic/ plastic Mohr Coulomb slip failure); 7 parameters to be initialized: normal and shear stiffnesses (brick brick contact) normal and shear stiffnesses (brick ground contact) friction angle on brick brick contact surface friction angle on brick ground contact surface damping coefficient 2

21 3DEC VERY preliminary results P I LED BRI CKS Test Volume [l] Falling height [m] Slope angle [ ] Radius [m] Unit w eight [kn/ m 3 ] I nternal friction [ ] Dynamic friction [ ] Benchmark case ±.5 P HYSI CAL MODELLI NG 75 BRI CKS!!! DI STI NCT ELEMENT MODEL 24 BRI CKS!!! SLOW SLOW 3x SLOW 2x 2

22 Discontinuous approach w ith 3DEC FUTURE DEVELOP MENTS Optimization of the model (number of elements vs computation time!!); Calibration of the set of parameters for a benchmark case w ith a 4 litre volume of orderly piled bricks and comparison of deposits characteristics; Validation w ith other experiments w ith different falling heights, volumes and slope angle; Simulation of experiments w ith randomly arranged bricks (i.e., randomly poured in the release container) and comparison of deposits characteristics w ith the previous cases. 22

23 POLITECNICO DI TORINO I NTERREG I VC alcotra THANK YOU FOR YOUR ATTENTION! (2) Claudio Scavia, () Vincent Labiouse, (2) Marina Pirulli, () Claire Sauthier, (2,) Gabriele Pisani () École Polytechnique Fédérale de Lausanne Laboratory for Rock Mechanics (LMR) (2) Politecnico di Torino Department of Structural and Geotechnical Engineering