Application of MacroMicro Analysis Method to Estimate Strong

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. utokyo. ac. jp) 2) Department of Civil Engineering, Tohoku University& RISTEX (tichim@msd. civil. tohoku. ac. jp)

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

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 material

DIFFICULTIES IN DEVELOPING STRONG MOTION SIMULATOR ■ Limitation of Computational Resources – frequency 5[Hz] – non-linear analysis for soil Memory[GB] computation FEM 10, 000 n FDM 10, 000 n BEM 250 n 2 n: DOF ■ Uncertainty of Crust and Ground Structures – ground – crust 50[m] resolution 2 -3[km] resolution 100[m] 1 X 1 X 1[m] mesh 1000[m] 10 X 10[m] mesh 20 -30[km] 100 X 100[m] mesh 40 -50[km] no reliable model

MULTI-SCALE ANALYSIS BASED ON SINGULAR PERTUBATION Bar Problem 10000[m] need to know domain of 100[m] with spatial resolution 1[m] highly heterogeneous equivalent model with low resolution procedures: center domain 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

RESULTS OF MULTI-SCALE ANALYSIS 0. 00018 exact 1 st 0. 00018 0. 00016 0. 00014 strain 0. 00016 exact and 2 nd 0. 00012 0. 00010 0. 00008 0. 00006 4950 4975 5000 5025 5050 maximum error < 0. 5%

BOUNDING MEDIUM THEORY MC simulation Spring Problem average k: spring constant f: force u: displacement PDF ku=f f target of BMT 0. 012 0. 010 0. 008 0. 006 0. 004 1 s 0. 002 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 displacement k: normal distribution (m=1, s/m=0. 1) 2. 0

RESULTS OF BOUNDING MEDIUM THEORY average < mean response < k: stochastic PDF kupper 0. 012 bound of BMT: 0. 010 displacement of 0. 008 kupper and klower 0. 006 0. 004 0. 002 0. 6 klower 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 displacement Kupper & klower: computed by using Hashin-Shtrikman variational principle (which leads to kinematic/geometric mean of k)

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

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

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.

TARGET: YOKOHAMA CITY Verify validity of numerical code of macro-micro analysis ■ Compare prediction with data measured at 13 sites ■ 139. 5 E as 06 140. 0 E 140. 5 E Yokohama City 35. 5 N hd 06 epicenter is 06 km 0 7. 5 15 35. 0 N 139. 5 E 140. 0 E August 11, 1999 140. 5 E

DISCRETIZATION OF MACROANALYSIS ■ Accuracy up to 1. 2[Hz] ■ Fault point source ■ Simulation VFEM Wilson q method paraxial boundary ■ Element size: 40 x 40 ～ 240 x 240[m] node: 8 NDF: 57, 012, 396 ■ ORIGIN 2000 (8 CPU) steps: 5000 (Dt=0. 01[sec]) time: 80[h] memory: 4, 388[MB]

MACRO-ANALYSIS MODEL 139. 5 E 140. 0 E 35. 5 N 35. 0 N 35. 5 N 139. 5 E 140. 0 E between 1 st and 2 nd layers [m] 0 140. 5 E 35. 0 N 140. 5 E between 2 nd and 3 rd layers [m] 0 -500 -1250 -1000 -2500 between 3 rd and 4 th layers 0 [m] -2500 -5000

VISUALIZATION OF MACROANALYSIS 139. 5 E 35. 5 N Yokohama City 10. 8[sec] top view 12. 6[sec] 11. 4[sec] 13. 2[sec] 12. 0[sec] 13. 8[sec]

RESULTS OF MACRO-ANALYSIS: EW VELOCITY COMPONENT AT hd 01 d velocity [kine] computed measured time [sec] case 1 case 2 Two cases of earthquakes are simulated.

DISCRETIZATION OF MICROANALYSIS ■ Accuracy up to 2. 5[Hz] ■ Input wave of macro-analysis ■ Simulation VFEM frequency domain paraxial boundary ■ Element size: 2 x 2 x 2[m] node: 8 NDF: 413, 343 ■ ORIGIN 2000 (1 CPU) steps: 27 (df=0. 098[Hz]) time: 6. 0[h] memory: 180[MB]

MICRO-ANALYSIS MODEL Ex. ) model for micro-analysis at hd 01 d N 160[m] b[m/sec] 600 40[m] a) upper bounding medium b) lower bounding medium 50

RESULTS OF MICRO-ANALYSIS: EW VELOCITY COMPONENT AT hd 01 d velocity [kine] micro-upper measured micro-lower time[sec] case 1 case 2 Two cases of earthquakes are simulated.

RESULTS OF MICRO-ANALYAIS CONCENTRATION OF MAX. VELOCITY case 1 case 2 50 50 N 25 max. velocity [kine] 0 0. 22 -25 -50 0. 14 -25 0. 11 -25 0 25 50 -50 -25 a) upper case 0 25 50 0. 06 a) upper case depth to bed rock difference of distribution 50 50 N N 25 25 relative difference[%] 0 depth[m] 0 -13 24. 2 -25 -50 -4. 9 -25 0 25 50 -37 -50 -25 0 25 50

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

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

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

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

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

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

STRUCTURE MODEL k m ■ MDOF Analysis: model for multi-story building – mass: model of floor – spring: model for columns and walls design code building Materials Fundamental Period Wooden buildings varies from 0. 2 sec. to 0. 7 sec. R. C. T=0. 02 H S. R. C. T=0. 03 H MDOF ■ Modal Analysis

STRONG MOTION DISTRIBUTION and SHAKING OF VIRTURAL TOWN

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

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

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