High performance hybrid FEM/DEM modelling approach for an improved simulation of railway track

Transcription

1 High performance hybrid FEM/DEM modelling approach for an improved simulation of railway track Frédéric Dubois 1, Mathieu Renouf 1, Paul Taforel 1, Charles Voivret 2 1 Laboratoire de Mécanique et Génie Civil, 2 SNCF Innovation & Recherche

2 Layout General introduction Numerical approach Study case 2/20

3 The ballast in few words... Ballast coarse granular material numerous functions played in the railway track - stress transmission to the layers of soil, - attenuation of vibrations, - lateral anchorage of pads and rails, - evacuation of drainage water critical component of the railway track Study of this material using 3D numerical simulations improve the understanding of the physical behaviour & optimize common restoration procedures (tamping) [ DEM (Discrete Element Method) approach ] 3/20

4 From DEM to FEM/DEM model of the railway track 3D modelling of the ballast DEM : Non-Smooth Contacts Dynamics (NSCD) implemented in the free software LMGC90 Model : - polyhedral shape of the grains - grains as rigid bodies - contacts Signorini Coulomb conditions - rigid foundation Numerous work on this topic (PhD thesis, post-doc): - G. Saussine (multibodies simulations with polyhedric particles) - E. Azema (study of tamping process) - T.M. Phuong-Haong (Domain Decomposition Method) -... realistic simulations of the ballast Influence of the resulting lack of deformability of the system on its global behaviour? FEM/DEM railway track model pictures, E. AZEMA (LMGC) 4/20

5 Newton-Euler: rigid blocks without contact NSCD method generic FEM/DEM approach soit with contact : prediction/correction scheme with deformable blocks: 5/20

6 NSCD method contact laws Unilateral condition : Signorini-Coulomb 6/20

7 1- Contact detection «Candidate/Antagonist approach» Adaptation of the generic FEM/DEM approach Surface element on the mesh of the deformable bodies = Candidate Polyhedrons rigid bodies = Antagonist Characteristic length of the mesh d Huge number of elements Memory & CPU times BUT description of local phenomena like stamping 7/20

8 1- Contact detection «Candidate/Antagonist approach» Adaptation of the generic FEM/DEM approach Surface element on the mesh of the deformable bodies = Candidate Polyhedrons rigid bodies = Antagonist Characteristic length of the mesh d Huge number of elements Memory & CPU times BUT description of local phenomena like stamping 7/20

9 1- Contact detection New «Candidate/Antagonist approach» Adaptation of the generic FEM/DEM approach Polyhedrons rigid bodies = Candidate Surface element on the mesh of the deformable bodies = Antagonist Reduction of the number of elements in the mesh BUT very macroscopic behaviour of the soil 8/20

10 1- Contact detection Adaptation of the generic FEM/DEM approach Reduction of the number of elements in the mesh BUT very macroscopic behaviour of the soil 8/20

11 1- Contact detection Adaptation of the generic FEM/DEM approach Reduction of the number of elements in the mesh BUT very macroscopic behaviour of the soil 8/20

12 2- Resolution Adaptation of the generic FEM/DEM approach Linear system solved using MUMPs instead of LaPack Difference on the way to store the system to solve : «dense» (LaPack) or «sparse» (MUMPS) storage 3- Non Linearities in the model of soil? - bulk behaviour of the deformable foundation : elastic linear - how to model permanent deformation? stamping? Introduction of «plastic» phenomena at the interaction scale using a Controlled incremental interpenetration law plastic interaction model g g g g 9/20

13 Ballast (rigid grains) Model and Sollicitation Model 3D sample Railway crossing (20x20x20 cm 3 ) confined in a Soil 1 (E=80 MPa, ν=0,3) 2-layers foundation (section of the column 1m 2, de The bottom of the column of soil is fixed (nu Contact between grains and between the so (m = 0,80) Soil 2 (E=40, 80, 120 or 160 MPa, ν=0.3) 10/20

14 Model and Sollicitation Sollicitation Cycle 1 loading phasis relaxation save data for comparison F v trav, FREQ - for each cycle: loading phasis (set of oscillations) + relaxation - constant amplitude of the signal : F v trav, max = 150 KPa x S trav - variation of the frequency : 5 30 Hz (rate 5 Hz) - constant «energy» introduced in the system : number of oscillations in each cycle depending on the frequency so that F v trav, FREQ1 (t) dt = F v trav, FREQ2 (t) dt - comparison of the results at the end of each cycle (relaxed state) - full simulation = 5 cycles 11/20

15 Macroscopic response of the sample Settlement of the sleeper Study case : allcycles, f = 20 Hz 12/20

16 Macroscopic response of the sample Settlement of the railway crossing due to local rearrangements of the ballast X trav z (t) X z soil (t) X z GRANULAR (t) = [X z trav (t) X z trav (0)] [X z soil (t) - X z soil (0)] 13/20

17 Macroscopic response of the sample Settlement of the railway crossing due to local rearrangements of the ballast Deformable foundation computed as a rigid body («DefoAsRig model») E = 40 MPa E = 40 MPa X trav z (t) X z soil (t) «DefoAsRig model» condition : Same behaviours for the other study cases X z soil (t) = 0, " t Which influence of the frequency of the sig X z GRANULAR (t) = [X z trav (t) X z trav (0)] [X z soil (t) - X z soil (0)] Dispersion increased with the number of c 14/20

18 Macroscopic response of the sample Standard deviation around the settlement mean (average on the responses for the different 15/20

19 Microscopic response of the sample Distribution around the center of the railway crossing of contacts soil/grains for the different cycles Study case : E = 40 MPa, f = 05 Hz Y S N i = S r n a / A i i X d 0 r grain 16/20

20 Microscopic response of the sample Distribution around the center of the railway crossing of contacts soil/grains for the different frequencies or different soil characteristics Study case : E = 40 MPa, cycle 3 Study case : f = 20 Hz, cycle 4 17/20

21 Microscopic response of the sample Repartition weak/strong contacts grain/grain Study case : E = 40 MPa, f = 10 Hz 18/20

22 Microscopic response of the sample Repartition weak/strong contacts grain/grain Study case : E = 40 MPa, cycle 2 18/20

23 Microscopic response of the sample Sliding or quasi-sliding contacts Contacts in the granular material (grain/grain) Study case : E = 120 MPa, f = 10 Hz Contacts soil/ballast Quasi-sliding status : R T R N > (1 e ) x m % of quasi-sliding contactcs = nb of quasi-sliding contacts / nb of contacts 19/20

24 Developments of numerical tools to the FEM/DEM approach - generation of the FEM/DEM sample - automatisation of the post-processing tools Adaptation of the numerical approach - contact detection new contact detection module - interaction law - solver robustness - numerical validation on a set of basic study cases First analysis on a «representative» sample of railway track - post processing of the macrosccopic response of the system - analysis at the interaction scale no real tendancies to underline the effects of the FEM/DEM coupling with the selected criteria Outlook - improve analysis - simplify the sample (single layer, adaptation of the sollicitations (need to increase the n - extension of the coupling to element of structure of the railway track (Sleepers) 20/20

25 Thank you for your attention