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Muneo HORI 1 ) and Tsuyoshi ICHIMURA 2 )

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)

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Muneo HORI 1 ) and Tsuyoshi ICHIMURA 2 )

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  1. Application of Macro-Micro Analysis Method to Estimate Strong Motion Distribution and Resulting Structure Response Muneo HORI1)and Tsuyoshi ICHIMURA2) 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 motionusing 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. ■ Limitation of Computational Resources frequency 5[Hz] non-linear analysis for soil ■ Uncertainty of Crust and Ground Structures ground 50[m] resolution crust 2-3[km] resolution 1X1X1[m] mesh 100[m] 10X10X10[m] mesh 1000[m] 100X100X100[m] mesh 20-30[km] 40-50[km] DIFFICULTIES IN DEVELOPINGSTRONG MOTION SIMULATOR n:DOF no reliable model

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

  6. RESULTS OF MULTI-SCALE ANALYSIS 0.00018 exact and 2nd exact 0.00018 1st 0.00016 0.00016 0.00014 0.00014 strain strain 0.00012 0.00012 0.00010 0.00010 0.00008 0.00008 0.00006 0.00006 4950 4975 5000 5025 5050 4950 4975 5000 5025 5050 maximum error < 0.5%

  7. 0.012 0.010 PDF 0.008 0.006 0.004 0.002 0.6 0.8 1.2 1.4 1.6 1.8 2.0 1.0 displacement BOUNDING MEDIUM THEORY MC simulation Spring Problem average target of BMT ku=f f k: spring constant f: force u: displacement 1s k: normal distribution (m=1, s/m=0.1)

  8. 0.012 0.010 PDF 0.008 0.006 0.004 0.002 0.6 0.8 1.2 1.4 1.6 1.8 2.0 1.0 displacement RESULTS OFBOUNDING MEDIUM THEORY average kupper bound of BMT: displacement of kupper and klower < mean response < k: stochastic klower Kupper & klower:computed by using Hashin-Shtrikman variational principle(which leads to kinematic/geometric mean of k)

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

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

  11. MACRO-MICRO ANALYSIS METHOD FOR STRONG MOTION SIMULATOR(3) Application of Multi-Scale Analysis upper model Macro-Analysis Micro-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. 139.5E 140.0E 140.5E 35.5N 35.5N km 0 7.5 15 35.0N 35.0N 140.0E 139.5E 140.5E TARGET: YOKOHAMA CITY ■ Verify validity of numerical code of macro-micro analysis ■ Compare prediction with data measured at 13 sites as06 Yokohama City hd06 epicenter is06 August 11, 1999

  13. ■ Accuracyup to 1.2[Hz] ■ Faultpoint source ■ SimulationVFEMWilson q methodparaxial boundary ■ Elementsize: 40x40x40 ～240x240x240[m]node: 8NDF: 57,012,396 ■ ORIGIN2000 (8CPU)steps: 5000 (Dt=0.01[sec])time: 80[h]memory: 4,388[MB] DISCRETIZATION OF MACRO-ANALYSIS

  14. 140.5E 139.5E 140.0E 35.5N 35.5N 35.0N 35.0N 140.0E 140.5E 139.5E MACRO-ANALYSIS MODEL between 1st and 2nd layers between 2nd and 3rd layers between 3rd and 4th layers [m] [m] [m] 0 0 0 -2500 -1250 -500 -5000 -2500 -1000

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

  16. RESULTS OF MACRO-ANALYSIS:EW VELOCITY COMPONENT AT hd01d velocity [kine] velocity [kine] computed computed measured measured time [sec] time [sec] case1 case2 Two cases of earthquakes are simulated.

  17. DISCRETIZATION OF MICRO-ANALYSIS ■ Accuracyup to 2.5[Hz] ■ Inputwave of macro-analysis ■ SimulationVFEMfrequency domainparaxial boundary ■ Elementsize: 2x2x2[m]node: 8NDF: 413,343 ■ ORIGIN 2000 (1 CPU)steps: 27 (df=0.098[Hz])time: 6.0[h]memory: 180[MB]

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

  19. RESULTS OF MICRO-ANALYSIS:EW VELOCITY COMPONENT AT hd01d velocity [kine] velocity [kine] micro-upper micro-upper measured measured micro-lower micro-lower time[sec] time[sec] case1 case2 Two cases of earthquakes are simulated.

  20. 50 N 25 max. velocity [kine] 0 0.22 -25 0.11 -50 -50 -25 0 25 50 a) upper case 50 N 50 N N 25 max. velocity 25 [kine] relative 0 difference[%] 0.14 0 0 24.2 -13 -25 -25 -25 0.06 -37 -4.9 -50 -50 -25 0 25 50 -50 a) upper case -50 -25 0 25 50 -50 -25 0 25 50 RESULTS OF MICRO-ANALYAIS CONCENTRATION OF MAX. VELOCITY case 1 case 2 depth to bed rock difference of distribution 50 25 depth[m] -50

  21. 50 N 25 depth[m] 0 -13 e d -25 f -37 g -50 -50 -25 0 25 50 c b a RESULTS OF MICRO-ANALYAISVELOCITY REPONSE SPECTRAL depth of bed rock max. velocity response [kine] period[sec] local topographical effect: difference of 10 times in 40[m]

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

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

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

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

  27. STRUCTURE MODEL m ■ MDOF Analysis:model for multi-story building • mass: model of floor • spring: model for columns and walls ■ Modal Analysis k design code building MDOF

  28. STRONG MOTION DISTRIBUTION and SHAKING OF VIRTURAL TOWN

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

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

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