1. Application of Macro-Micro Analysis Method to Estimate Strong Motion Distribution and Resulting Structure Response Muneo HORI 1) and Tsuyoshi ICHIMURA 2) 1) Earthquake Research Institute, University of Tokyo& RISTEX (hori@eri.u-tokyo.ac.jp) 2) Department of Civil Engineering, Tohoku University& RISTEX (t-ichim@msd.civil.tohoku.ac.jp)

2. CONTENTS ■ Strong Motion Simulator –Macro-micro analysis method based on multi-scale analysis ■ What is Earthquake Disaster Simulator ■ Construction of virtual metropolis and estimation of strong motion using macro-micro analysis method –Virtual Roppongi is shaken! ■ Plan for Earthquake Disaster Simulator –unify simulators –platform & plug-in

3. STRONG MOTION SIMULATOR ■ From Fault to Structures –fault mechanism –wave propagation –local site effects ■ Usage of Strong Motion Simulator –design code for buildings –planning for earthquake-resistant city required: high spatial and time resolution high accuracy accounting for non-linearity of soil materials

4. DIFFICULTIES IN DEVELOPING STRONG MOTION SIMULATOR ■ Limitation of Computational Resources –frequency5[Hz] –non-linear analysis for soil ■ Uncertainty of Crust and Ground Structures –ground50[m] resolution –crust2-3[km] resolution Memory[GB]computation FEM10,000n FDM10,000n BEM250n2n2 n:DOF 20-30[km] 100[m] 1000[m] 40-50[km] 1X1X1[m] mesh 10X10X10[m] mesh 100X100X100[m] mesh no reliable model

5. MULTI-SCALE ANALYSIS BASED ON SINGULAR PERTUBATION 10000[m] highly heterogeneous Bar Problem need to know domain of 100[m] with spatial resolution 1[m] procedures: 1.construct equivalent model at resolution 10[m], and obtain 1 st solution at resolution 10[m] 2.for center domain of 100[m], obtain 2 nd solution using 1 st solution equivalent model with low resolution center domain

6. RESULTS OF MULTI-SCALE ANALYSIS strain 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016 0.00018 49504975500050255050 exact 1 st 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016 0.00018 49504975500050255050 strain exact and 2 nd maximum error < 0.5%

7. BOUNDING MEDIUM THEORY ku=f Spring Problem k: spring constant f: force u: displacement f MC simulation k: normal distribution (  ) average 11 target of BMT

8. RESULTS OF BOUNDING MEDIUM THEORY k: stochastic k upper k lower mean response < < bound of BMT: displacement of k upper and k lower average K upper & k lower : computed by using Hashin-Shtrikman variational principle (which leads to kinematic/geometric mean of k)

9. MACRO-MICRO ANALYSIS METHOD FOR STRONG MOTION SIMULATOR(1) stochastic model fault surface Make stochastic model Boring data Curst data, Soil data Uncertainty(probability distribution)

10. stochastic model fault surface upper structure lower structure < < expected behavior Application of Bounding Media Theory MACRO-MICRO ANALYSIS METHOD FOR STRONG MOTION SIMULATOR(2)

11. MACRO-MICRO ANALYSIS METHOD FOR STRONG MOTION SIMULATOR(3) upper model Macro-Analysis Micro-Analysis Application of Multi-Scale Analysis Simulate wave propagation from fault to surface with 100[m] order. Simulate wave amplification near surface with 1[m] order by solution of macro-analysis and soil structure.

12. TARGET: YOKOHAMA CITY ■ Verify validity of numerical code of macro-micro analysis ■ Compare prediction with data measured at 13 sites August 11, 1999 epicenter as06 is06 hd06 Yokohama City

13. DISCRETIZATION OF MACRO-ANALYSIS ■ Accuracy up to 1.2[Hz] ■ Fault point source ■ Simulation VFEM Wilson  method paraxial boundary ■ Element size: 40x40x40 ～ 240x240x240[m] node: 8 NDF: 57,012,396 ■ ORIGIN2000 (8CPU) steps: 5000 (  t=0.01[sec]) time: 80[h] memory: 4,388[MB]

14. MACRO-ANALYSIS MODEL 0 -500 -1000 [m] 0 -2500 -5000 [m] 0 -1250 -2500 [m] between 1 st and 2 nd layers between 2 nd and 3 rd layers between 3 rd and 4 th layers

15. VISUALIZATION OF MACRO-ANALYSIS 10.8[sec] 11.4[sec]12.0[sec] 12.6[sec]13.2[sec]13.8[sec] top view 139.5E 35.5N Yokohama City

16. RESULTS OF MACRO-ANALYSIS: EW VELOCITY COMPONENT AT hd01d case1case2 time [sec] velocity [kine] measured computed measured computed Two cases of earthquakes are simulated.

17. ■ Element size: 2x2x2[m] node: 8 NDF: 413,343 ■ ORIGIN 2000 (1 CPU) steps: 27 (df=0.098[Hz]) time: 6.0[h] memory: 180[MB] ■ Accuracy up to 2.5[Hz] ■ Input wave of macro-analysis ■ Simulation VFEM frequency domain paraxial boundary DISCRETIZATION OF MICRO-ANALYSIS

18. MICRO-ANALYSIS MODEL Ex.) model for micro-analysis at hd01d 50 600  [m/sec] N 160[m] 40[m] a) upper bounding mediumb) lower bounding medium

19. RESULTS OF MICRO-ANALYSIS: EW VELOCITY COMPONENT AT hd01d case1case2 time[sec] velocity [kine] measured micro-upper micro-lower measured micro-upper micro-lower Two cases of earthquakes are simulated.

20. RESULTS OF MICRO-ANALYAIS CONCENTRATION OF MAX. VELOCITY 0.14 0.06 max. velocity [kine] N case 2 0.22 0.11 max. velocity [kine] N case 1 25 50 -50 24.2 -4.9 N relative difference[%] difference of distribution -13 -37 N depth[m] depth to bed rock

21. RESULTS OF MICRO-ANALYAIS VELOCITY REPONSE SPECTRAL a b c d e f g max. velocity response [kine] period[sec] local topographical effect: difference of 10 times in 40[m] depth of bed rock

22. OVERVIEW OF EARTHQUAKE DISASTER SIMULATOR Earthquake Disaster Simulator : Unify simulators : Full Simulation fault Fault Mechanism Wave Propagation Local Site Effect Strong Motion Simulator Construct Virtual Metropolis : Simulate Dynamic Behavior

23. VIRTURAL METEROPOLIS ■ GIS (Geological Information System) is used to construct virtual metropolis –ground structure information –structure information: buildings, infrastructures, life lines, etc. ■ Metropolis is shaken by Macro-Micro Analysis for suitable scenario of big earthquake –building-wise simulation –room-wise simulation

24. GIS AND MACRO-MICRO ANALYSIS ground structure bore hole, etc. MMA structure image, CAD, etc. FEM yes structure response - room-wise enough? FEM yes no strong motion basic information (floor, type, etc.) enough? no structure response - building-wise detailed information (materials, etc.) GIS

25. VIRTUAL TOWN FOR ROPPONGI Roppongi Area GIS for bore holes (surface layers) GIS for buildings

26. SURFACE GROUND MODEL 300[m] 60[m] ground surface 1 st interface 2 nd 3 rd 4 th 5 th chacteristics of soil layers

27. STRUCTURE MODEL ■ MDOF Analysis: model for multi-story building –mass: model of floor –spring: model for columns and walls ■ Modal Analysis m k MaterialsFundamental Period Wooden buildingsvaries from 0.2 sec. to 0.7 sec. R.C.T=0.02H S.R.C.T=0.03H design code buildingMDOF

28. STRONG MOTION DISTRIBUTION and SHAKING OF VIRTURAL TOWN

29. MULTI-SCALE ANALYSIS OF STRUCTURE macro-scale model for structure micro-scale model for floor target structure equivalent mass & spring simulation of how each floor or each room will be shaken simulation of how overall structure will be shaken

30. NEXT STEP ■ Strong Motion Simulator –fast and efficient computation –larger DOF –Visualization ■ Combination of GIS –more realistic modeling of virtual city –multi-scale dynamic analysis of life-line and infra-structure ■ Earthquake Disaster Simulator –unify simulators –platform & plug-in

31. EARTHQUAKE DISASTER SIMULATOR AS PLATFORM & PLUG-IN Architecture Structure Fault Mechanism Local Site Effects Wave Propagation Model Information Simulation Result GIS Earthquake Disaster Simulator Strong Motion Simulator Simulate Behavior of Virtual Metropolis Human Behavior Soil Structure Steel Structure RC Structure Platform Simulators(Plug-in)