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M. Stupazzini

Politecnico di Milano Dep. of Structural Engineering. Center for Advanced Research and Studies in Sardinia. Ludwig Maximilians University Dep . of Earth and Environmental Sciences - Geophysics. Grenoble 3D benchmark. M. Stupazzini. 23 rd of July 200 6

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M. Stupazzini

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  1. Politecnico di Milano Dep. of Structural Engineering Center for Advanced Research and Studies in Sardinia Ludwig Maximilians University Dep. of Earth and Environmental Sciences - Geophysics Grenoble 3D benchmark M. Stupazzini 23rd ofJuly 2006 Kinsale – Ireland (3rd SPICE workshop)

  2. Seismic wavePropagation and Imaging inComplex media: aEuropean network • MARCO STUPAZZINI • Experienced Researcher • Host Institution: LMU Munich • Date of Birth: 26 / 10 / 1974 • Place of Origin: Milano, Italy • Key Words: Computational Seismology, Spectral Element Method, Visco Plasticity, Soil-Structure Interaction • Appointment Time: May 2004 • Task Groups: TG 2: Numerical Methods

  3. 3D numerical simulation of seismic wave propagation in the Grenoble valley (M6 earthquake)

  4. 36 km 30 km 3D numerical simulation of seismic wave propagation in the Grenoble valley (M6 earthquake)

  5. Synthetic seismograms

  6. Peak ground velocities

  7. Spectral ratios for the fault parallel component

  8. Max. Displacement E. Faccioli and A. Rovelli: Project S5 of “DPC-INGV” "Definizione dell’input sismico sulla base degli spostamenti attesi" (1 giugno 2005 - 30 giugno 2006)

  9. Max. Displacement E. Faccioli and A. Rovelli: Project S5 of “DPC-INGV” "Definizione dell’input sismico sulla base degli spostamenti attesi" (1 giugno 2005 - 30 giugno 2006)

  10. Conclusions • www.spice-rtn.org • www.stru.polimi.it/Ccosmm/ccosmm.htm

  11. 3rd 1st Landslides Liquefaction Subsidence 2nd General problem

  12. Soil-Structure interaction EFFECTIVE NODAL FORCESP Pe(t) • A sub-structuring method : the Domain Reduction Method • (Bielak et al. 2003) Method for the simulation of seismic wave propagation from a half space containing the seismic source to a localized region of interest, characterized by strong geological and/or topographic heterogeneities or soil-structure interaction. Local geological feature Boundary region Inner region External region

  13. Pe(t) • DRM : 2 steps method Step I( AUXILIARY PROBLEM ) • The auxiliary problem simulates the seismic source and propagation path effects encompassing the source and a background structure from which the localized feature has been removed. • The free field displacement u0 may be calculated by different methods Analytical solutions (e.g.: Inclined incident waves) Numerical method (e.g.: FD, SEM, BEM, ADER-DG)

  14. Boundary region ub ui Inner region EFFECTIVE NODAL FORCES we External region • DRM : 2 steps method Step II( REDUCED PROBLEM ) • The reduced problem simulates the local site effects of the region of interest • The input is a set of equivalent localized forces derived from step I Inner region Boundary region External region • The effective forces act only within a single layer of elements adjacent to the interface between the external and internal regions where the coupled term of stiff matrix does not vanish

  15. Study case railway bridge

  16. Wave propagation in 2D “Source“ & “ Deep propagation“ zoom Fault “ Site effects “ & “ Soil Structures Interactions “ zoom

  17. 1.177 10-5 570 620 190.0 Computational comparison:

  18. Computational comparison:

  19. The computation with DRM is 2.8 times faster + Computational comparison:

  20. Dynamic rupture modelling (Festa G., IPGP) Interface behavior via friction Slip weakening law + Stress distribution Initial Principal stresses : 4.0 107 Pa s1 1.8 108 Pa s3 100° Orientation 0.67 Static friction 0.525 Dynamic friction 0.4 m DC 150-300m Cohesive zone thickness Kinematic source:Seismic moment tensor density (Aki and Richards, 1980):MW = 4.2, slip = 50 cm

  21. Comparison

  22. Comparison

  23. DRM Study case Outlook GeoELSE

  24. GeoELSE(GEO-ELasticity by Spectral Elements) • GeoELSE is a Spectral Elements code for the study of wave propagation phenomena in 2D or 3D complex domain • Developers: • CRS4 (Center for Advanced, Research and Studies in Sardinia) • Politecnico di Milano, DIS (Department of Structural Engineering) • Native parallel implementation • Naturally oriented to large scale applications ( > at least 106 grid points)

  25. Formulation of the elastodynamic problem Dynamic equilibrium in the weak form: where ui= unknown displacement function vi= generic admissible displacement function (test function) ti= prescribed tractions at the boundary  fi= prescribed body force distribution in 

  26. Spatial discretization Spectral element method SEM (Faccioli et al., 1997) Time advancing scheme Finite difference 2nd order (LF2 – LF2) Courant-Friedrichs-Levy (CFL) stability condition

  27. Why using spectral elements ? • Suitable for modelling a variety of physical problems (acoustic and elastic wave propagation, thermo elasticity, fluid dynamics) • Accuracy of high-order methods • Suitable for implementation in parallel architectures • Great advantages from last generation of hexahedral mesh creation program (e.g.: CUBIT, Sandia Lab.)

  28. n=1 n=2 Acoustic wave propagation through an irregular domain. Simulation with spectral degree 1 (left) exhibits numerical dispersion due to poor accuracy. Simulation with spectral degree 2 (right) provides better results.Change of spectral degree is done at run time. Why using spectral elements ?acoustic problem

  29. Internal domain: External domain: • DRM : 2 steps method Internal domain Navier’s equation: Fault External domain

  30. Mass and stiffness matrices do not change because properties in + do not change External domain (0): Change of variables : • DRM : 2 steps method Internal domain (0) AUSILIARY PROBLEM (Step I) ujo= vector of nodal displacements j = i, b, e Pbo= forces from domain + to 0 Faglia External domain (0)

  31. Dominio interno: • DRM : 2 steps method External domain - External domain (0):

  32. REDUCED PROBLEM (Step II) (Step II) • DRM : 2 steps method • M and K matrices of the original problem • P localization within a single layer of elements in +adjacentto 

  33. The effectiveness of the method depend on the accuracy of the absorbing boundary conditions • DRM : 2 steps method Non linear properties in the internal domain

  34. DRM : 2D Validationsusing Spectral Elements (GeoELSE) Homogeneous valley in a layered half space

  35. Total displacements (u=w+uo) DRM : 2D Validationsusing Spectral Elements (GeoELSE) Homogeneous valley in a layered half space Relative displacements (w) Internal points External points

  36. DRM : 2D Validationsusing Spectral Elements (GeoELSE) Canyon in a homogeneous half space

  37. Total displacements (u=w+uo) DRM : 2D Validationsusing Spectral Elements (GeoELSE) Canyon in a homogeneous half space Relative displacements (w) Internal points External points

  38. I STEP Calculation of u0 for a homogeneous model • Analytical solution • Numerical methods (Ex. Hisada, 1994) • Same method used for step II (ex. SE) Interface elements Nodes b P Nodes e • DRM : 2 steps method ORIGINAL PROBLEM Oblique propagation of plane waves inside a valley II STEP Analysis of wave propagation inside the reduced model. Calculation of effective forces Pb and Pe

  39. Comparison

  40. Conclusions • Capabilities of DRM to handle „source to structure“ wave propagation problem with reduced CPU time • Dialog between numerical codes oriented for different purposes • Kinematic model are satisfactory to describe the low frequency bahaviour (e.g.: PGD and PGV) while PGA seems to be overestimated (nucleation, constant rupture velocity and instantaneous drop of the slip on the fault boundaries?).

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