Transcript 広域強震動シミュレーター に関する基礎研究

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 ([email protected])
2) Department of Civil Engineering, Tohoku University& RISTEX ([email protected])
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 materials
DIFFICULTIES IN DEVELOPING
STRONG MOTION SIMULATOR
■
Limitation of Computational
Resources
– frequency 5[Hz]
– non-linear analysis for soil
Memory[GB]
■
Uncertainty of Crust and Ground
Structures
– ground
– crust
computation
FEM
10,000
n
FDM
10,000
n
BEM
250
n2
n:DOF
50[m] resolution
2-3[km] resolution
100[m]
1X1X1[m] mesh
1000[m]
10X10X10[m] mesh
20-30[km]
100X100X100[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 1st solution at resolution
10[m]
2.
for center domain of 100[m], obtain 2nd
solution using 1st solution
RESULTS OF MULTI-SCALE ANALYSIS
0.00018
exact
1st
0.00018
0.00016
0.00014
0.00014
strain
strain
0.00016
exact and 2nd
0.00012
0.00012
0.00010
0.00010
0.00008
0.00008
0.00006
4950
0.00006
4950
4975
5000
5025
5050
4975
5000
5025
5050
maximum error < 0.5%
BOUNDING MEDIUM THEORY
MC simulation
Spring Problem
average
ku=f
k: spring constant
f: force
u: displacement
0.010
PDF
f
target of BMT
0.012
0.008
0.006
0.004
1s
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
displacement
Kupper & klower:
computed by using Hashin-Shtrikman variational principle
(which leads to kinematic/geometric mean of k)
2.0
MACRO-MICRO ANALYSIS METHOD
FOR STRONG MOTION SIMULATOR(1)
Make stochastic model
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
■
139.5E
as06
140.0E
140.5E
Yokohama City
35.5N
35.5N
hd06
epicenter
is06
km
0
7.5
15
35.0N
35.0N
139.5E
140.0E
140.5E
August 11, 1999
Lat.
Long. Depth Strike
35.4N 139.8E
53km
62
Dip
Rake
Mag.
85
73 4.0Mw
DISCRETIZATION OF MACRO-ANALYSIS
■ Accuracy
■
Element
size: 40x40x40
～240x240x240[m]
node: 8
NDF: 57,012,396
■
ORIGIN2000 (8CPU)
steps: 5000
(Dt=0.01[sec])
time:
80[h]
memory: 4,388[MB]
up to 1.2[Hz]
■
■
Fault
point source
Simulation
VFEM
Wilson q method
paraxial boundary
MACRO-ANALYSIS MODEL
N
139.5E
140.0E
35.5N
140.5E
E
40[km]
35.5N
70[km]
35.0N
139.5E
140.0E
35.0N
140.5E
30[km]
p wave veloc.[m/sec]
s wave veloc.[m/sec]
density[kg/m 3]
mate.1
1040
600
1800
mate.2
1730
1000
2000
mate.3
2950
1700
2300
between 1st and 2nd layers
0
[m]
mate.4
5200
3000
2500
mate.1
mate.2
mate.3
mate.4
between 2nd and 3rd layers
[m]
0
-500
-1250
-1000
-2500
between 3rd and 4th layers
0
-2500
-5000
[m]
VISUALIZATION OF MACRO-ANALYSIS
139.5E
35.5N
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 hd01d
velocity [kine]
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
velocity [kine]
0.01
computed
computed
0.005
0
-0.005
measured
measured
-0.01
0
2
4
time [sec]
case1
6
8
0
2
4
time [sec]
6
case2
Two cases of earthquakes are simulated.
8
DISCRETIZATION OF MICRO-ANALYSIS
■ Accuracy
■
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]
up to 2.5[Hz]
■
■
Input
wave of macro-analysis
Simulation
VFEM
frequency domain
paraxial boundary
MICRO-ANALYSIS MODEL
Ex.) model for micro-analysis at hd01d
N
160[m]
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 hd01d
velocity [kine]
0.1
micro-upper
0.05
0
-0.05
measured
micro-lower
-0.1
0
2
4
time[sec]
case1
6
velocity [kine]
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
8
micro-upper
measured
micro-lower
0
2
4
time[sec]
6
case2
Two cases of earthquakes are simulated.
8
RESULTS OF MICRO-ANALYAIS
CONCENTRATION OF MAX. VELOCITY
case 1
case 2
50
50
N
25
max. velocity
[kine]
0
N
25
max. velocity
[kine]
0
0.22
-25
-50
0.14
-25
0.11
-50
-25
0
25
50
-50
-50
-25
a) upper case
0
25
0.06
50
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
-25
-50
-4.9
-50
-25
0
25
50
-37
-50
-50
-25
0
25
50
max. velocity response [kine]
RESULTS OF MICRO-ANALYAIS
VELOCITY REPONSE SPECTRAL
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
e
d
f
g
depth of bed rock
50
c
b
N
a
0
0.5
1
1.5
period[sec]
local topographical effect:
difference of 10 times in 40[m]
25
2
2.5
depth[m]
0
-13
-25
-37
-50
-50
-25
0
25
50
OVERVIEW OF
EARTHQUAKE DISASTER SIMULATOR
Earthquake Disaster Simulator
: Unify simulators
: Full Simulation
Construct Virtual Metropolis
: Simulate Dynamic Behavior
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.)
structure response
- building-wise
no
enough?
yes
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
3rd
ground surface
60[m]
300[m]
1st interface
300[m]
4th
chacteristics of soil layers
num ber oflayer
1
2
3
4
5
bottom
soiltype
surface soil
loam
sand
clay
fine sand
rock
3
density(g/cm )
1.625
1.550
1.800
1.750
1.900
1.850
S _v(m /s) P _v(m /s)
120.0
204.0
135.0
229.5
400.0
680.0
200.0
340.0
425.0
722.5
600.0
1020.0
2nd
5th
STRUCTURE MODEL
k
m
■
MDOF Analysis:
model for multi-story building
– mass: model of floor
– spring: model for columns and walls
design code
building
MDOF
■
Materials
Fundamental Period
Wooden buildings
varies from 0.2 sec. to 0.7 sec.
R.C.
T=0.02H
S.R.C.
T=0.03H
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
Human Behavior
Simulation
Result
Steel Structure
Soil Structure