Broad-band 3-D Physics-Based Simulation of Earthquake-induced Wave-Field at the Kashiwazaki-Kariwa Nuclear Power Plant (Japan): an All-Embracing Source-to-Site Approach.

Abstract

The influence of the regional 3-D geology on the synthetic earthquake ground motion prediction is herein assessed, studying the seismic response of Kashiwazaki-Kariwa nuclear power plant (KKNPP), during the 2007 Niigata seismic sequence (west Japan), so to explore the potentiality and practicability of the innovative computational tools available. This applicative case study was chosen within the framework of the SINAPS@ project, the first French research project which aims to propose a continuous approach from the fault to the structure and equipment’s, accounting explicitly for the uncertainties related to the databases and the models. A source-to-site numerical model of the region (≈ 60 km wide) is built-up and calibrated for small aftershocks including surface topography, Japan sea and complex 3-D underground foldings. The impact of complex 3-D geology in terms of seismic response at KKNPP is quantified, by comparison with the simplified transverse
isotropic geology. This validation stresses the importance of the 3-D geology and explicates the observed high ground motion spatial variability, as well as the strong dependence of the site response on the incident wave obliquity. The synthetic wave-field (0-5 Hz) is obtained by employing SEM3D, a high-scalable software tailored based on the Spectral Element Method. This high-fidelity code performs efficiently (thanks to its high scalability on parallel supercomputers) when refining the model spatial discretization and increasing the bedrock-to-sediment shear wave velocity gradient. The synthetic wave-motion simulated was exploited as input motion for a Soil-Structure Interaction numerical model (Finite Element Method - Boundary Element Method, Code_Aster-MISS3D) of the standard reactor building at KKNPP. The impact of the 3-D geology is assessed therefore on the structural components, highlighting a considerable amplification compared to the case of layered one.

Full text

Broad-band 3-D physics-based
simulation of earthquake-induced
wave-field at the Kashiwazaki-Kariwa
Nuclear Power Plant (Japan): an
all-embracing source-to-site approach
F. Gatti1
F. Lopez-Caballero1-D.Clouteau1-R.Paolucci2
1Lab. MSSMat UMR CNRS 8579 - CentraleSup´
elec
2DICA - Politecnico di Milano
1 / 24

An excursus on SINAPS@
An excursus on SINAPS@
2 / 24
S´
eisme et Installations Nucl´
eaires, Am´
eliorer et P´
erenniser la Sˆ
uret´
e
Improvement in Seismic Risk & Vulnerability assessment of
French Nuclear Facilities
Which were the open issues back in 2012 ?
IUncertainty quantification : Numerical vs Experimental modelling
ISafety Margins Estimation : Deterministic vs Probabilistic assessment
ICritical Perspective on current Design Standards : Risk & Vulnerability

An excursus on SINAPS@
An excursus on SINAPS@
2 / 24
S´
eisme et Installations Nucl´
eaires, Am´
eliorer et P´
erenniser la Sˆ
uret´
e
Improvement in Seismic Risk & Vulnerability assessment of
French Nuclear Facilities
Which were the open issues back in 2012 ?
IUncertainty quantification : Numerical vs Experimental modelling
ISafety Margins Estimation : Deterministic vs Probabilistic assessment
ICritical Perspective on current Design Standards : Risk & Vulnerability
Which were the open issues now in 2018 ?
IUncertainty quantification : How to integrate data and synthetics ?
ISafety Margins Estimation :
Span the scenario’s space with numerical simulations ?
ICritical Perspective on current Design Standards : Risk & Vulnerability

Improved broad-band physics-based numerical modelling
Improved broad-band physics-based numerical modelling
3 / 24
A new horizon
IRegional scale deterministic numerical simulation : SKY IS THE LIMIT !
+Fu et al. (2017) 18.9-Pflops Nonlinear Earthquake Simulation on Sunway
TaihuLight : Enabling Depiction of 18-Hz and 8-Meter Scenarios. Proceedings
of the International Conference for High Performance Computing,
Networking, Storage and Analysis, ACM, 2 :1-2 :12
IStudy the accuracy of numerical analysis !
IWithin the basin :
VSmin =650 m/s
IHeterogeneous ρ:
I`C,h=90 m
I`C,v=40 m
ItCPU =1487 h (30
sec)
I216 MPI cores
Mygdonian basin(7 Hz) Gatti, Touhami, Lopez-Caballero, Pitilakis NUMGE2018

Improved broad-band physics-based numerical modelling
Improved broad-band physics-based numerical modelling
3 / 24
A new horizon
IIntegrate data and numerical simulations
+Paolucci, Gatti, Infantino, Ozcebe, Smerzini & Stupazzini (2018)
Broad-band ground motions from 3D physics-based
numerical simulations using Artificial Neural Networks. BSSA
IHolistic approach : wave-propagation & structural vibration
http://news.mit.edu/sites/mit.edu.newsoce/ les/images/2013/20130906170823-0_0_0.jpg
IWithin the basin :
VSmin =650 m/s
IHeterogeneous ρ:
I`C,h=90 m
I`C,v=40 m
ItCPU =1487 h (30
sec)
I216 MPI cores

Improved broad-band physics-based numerical modelling
Improved broad-band physics-based numerical modelling
4 / 24
HPC platform for broad-band modelling
LEGO approach
Andrianov et al. (2011) (c)

A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
5 / 24

A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
Niigata-Ken Ch¯
uetsu-Oki Earthquake 16/07/2007
Niigata-Ken Ch¯
uetsu-Oki Earthquake 16/07/2007
5 / 24
Figure 1–Map of the surroundings of KKNPP and epicenters’
locations.
IMagnitude
IMw 6.6 - MJMA 6.8
IDepth
IHypocenter : ≈9 km
Max. ≈17 km
IFault mechanism
IBuried reverse-slip

A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
Niigata-Ken Ch¯
uetsu-Oki Earthquake 16/07/2007
Niigata-Ken Ch¯
uetsu-Oki Earthquake 16/07/2007
5 / 24
Figure 1–Map of the KKNPP site
IKashiwazaki-Kariwa Nuclear
Power Plant (KKNPP)
I7 reactors
I1st threshold : Operating Basis
Earthquake (OBE)
I2nd threshold : Safe Shutdown
Earthquake (SSE)
IDISTANCE
I15-20 km
IPGA SSE
Iground settlements ≈15cm
Ifire & damage to pipelines
Ipartial shut down till 2011
Gatti et al. Bull. Earthquake Eng. 2018 10.1007/s10518-017-0255-y
IHigh spatial variability
INear-field conditions
ILarge non-linear site effects (a few cases of liquefaction)

3-D numerical simulation of the NCO earthquake
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
6 / 24

3-D numerical simulation of the NCO earthquake
Construction of earthquake scenario
Construction of earthquake scenario
6 / 24
Targets
ICharacterize geology of Niigata area
ICharacterize geology in KK-NPP surroundings
Modelling features
IModel 1 : 90 km ×83 km ×83 km
1. Aftershock AS1 (MW4.4)
2. fmax = 3.75Hz
3. VS,min = 1000m/s
4. LAYERED geology
5. Topography

3-D numerical simulation of the NCO earthquake
Construction of earthquake scenario
Construction of earthquake scenario
6 / 24
Targets
ICharacterize geology of Niigata area
ICharacterize geology in KK-NPP surroundings
Modelling features
IModel 2 : 68 km ×50 km ×50 km
1. Aftershocks :
?AS1 (MW4.4)
?AS2 (MW4.2)
2. fmax = 5.0−7.0Hz
3. VS,min = 700m/s
4. FOLDED geology
5. Topography
6. Japan sea

3-D numerical simulation of the NCO earthquake Computational 3-D wave-propagation
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
Computational 3-D wave-propagation
NCO wave-field in the Niigata region : Model 1
Include local geology at KK-NPP : Model 2
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
7 / 24

3-D numerical simulation of the NCO earthquake Computational 3-D wave-propagation
SEM3D
SEM3D
7 / 24
Solve 3D Wave Propagation at Regional Scale
Spectral Element Method
High order FEM for 3D Solid and Fluid media
(Faccioli et al., 1997; Komatitsch, 1997)
ILagrange polynomials
IGauss-Lobatto-Legendre (GLL)
INaturally diagonal Mass matrix
ILeap-Frog solver
ISpectral Convergence (in p)
IABC : Perfectly Matched Layers (PML)
Efficiency and low numerical dispersion
IMassively parallel implementation
Moulon M´esocentre (Paris Saclay University)

3-D numerical simulation of the NCO earthquake NCO wave-field in the Niigata region : Model 1
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
Computational 3-D wave-propagation
NCO wave-field in the Niigata region : Model 1
Include local geology at KK-NPP : Model 2
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
8 / 24

3-D numerical simulation of the NCO earthquake NCO wave-field in the Niigata region : Model 1
Using aftershock to calibrate geological profile
Using aftershock to calibrate geological profile
8 / 24
Aftershocks AS1 : 07/16/2007 - MW4.4 ($$)
IPoint-wise double couple source
IMethodology
IWNI method ($$$) -fmax =0.5 Hz
ISEM3D analysis - fmax =3.75 Hz

3-D numerical simulation of the NCO earthquake NCO wave-field in the Niigata region : Model 1
Predict regional wave-field
Predict regional wave-field
9 / 24
Figure 2–Mesh of the Niigata region :
220988 nodes - 211410 elements - 3.7·108GLL.
≈12h on FUSION (Universit´
e Paris-Saclay) - 192 MPI cores.
7

3-D numerical simulation of the NCO earthquake NCO wave-field in the Niigata region : Model 1
Predict regional wave-field (0.1-3.75 Hz)
Predict regional wave-field (0.1-3.75 Hz)
10 / 24
10 20 30 40 50 60
10-1
100
101
102
103
PGAH[cm/s/s]
AS: Mj 4.4 2007-07-16 21:08
[km]
10 20 30 40 50 60
10-1
100
101
102
103
PGAH[cm/s/s]
[km]
AS: Mj 4.4 2007-07-16 21:08
Rise time estimation
Dreger et al. (2007)
Duputel et al. (2013)
0 0.4 0.8 1.2 1.6
t[s]
0
4
8
12
16
20 SVF

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
Computational 3-D wave-propagation
NCO wave-field in the Niigata region : Model 1
Include local geology at KK-NPP : Model 2
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
11 / 24

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Coupling regional model with local geological structures
Coupling regional model with local geological structures
11 / 24
Tsuda et al. (2011) geological model
Figure 3–Folded geology beneath KK-NPP Tsuda et al. (2011)

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Improved geological model : from 1D to 3D structure
Improved geological model : from 1D to 3D structure
12 / 24
SW
Mj4.4 - 16/07/2007-21:08
KKNPP
(a)
SC
Mj4.4 - 16/07/2007-21:08
KKNPP
(b)
SC
SW
Folding
Smoothing bands
SE
N

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Assess the effect of local foldings
Assess the effect of local foldings
13 / 24
EW
NS
AS - 07/16/07 - 17:42 - Mw 4.2
AS - 07/16/07 - 21:08 - Mw 4.4
SG1-G.L. -2.4 m
SG4-G.L. -250 m
1G1-G.L. 0 m
5G1-G.L. 0 m
1G1
[cm/s/s]
5G1
SH
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
LAYERED vs FOLDED
fmax ≈5 Hz
Gatti et al. (2018) GJI 213, 1073-1092. doi : 10.1093/gji/ggy027

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Assess the effect of local foldings
Assess the effect of local foldings
13 / 24
EW
NS
AS - 07/16/07 - 17:42 - Mw 4.2
AS - 07/16/07 - 21:08 - Mw 4.4
SG1-G.L. -2.4 m
SG4-G.L. -250 m
1G1-G.L. 0 m
5G1-G.L. 0 m
1G1
[cm/s/s]
5G1
SH
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
0.01 0.1 1 23
0
20
40
60
80
100 EW
0.01 0.1 1 23
0
20
40
60
80
100 NS
AS1
LAYERED vs FOLDED
fmax ≈5 Hz
Gatti et al. (2018) GJI 213, 1073-1092. doi : 10.1093/gji/ggy027

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Assess the effect of local foldings
14 / 24
EW
NS
AS - 07/16/07 - 17:42 - Mw 4.2
AS - 07/16/07 - 21:08 - Mw 4.4
SG1-G.L. -2.4 m
SG4-G.L. -250 m
1G1-G.L. 0 m
5G1-G.L. 0 m
1G1
[cm/s/s]
5G1
SH
0.01 0.1 1 23
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 2
3
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 EW
LAYERED vs FOLDED
fmax ≈5 Hz
Gatti et al. (2018) GJI 213, 1073-1092. doi : 10.1093/gji/ggy027

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Assess the effect of local foldings
14 / 24
EW
NS
AS - 07/16/07 - 17:42 - Mw 4.2
AS - 07/16/07 - 21:08 - Mw 4.4
SG1-G.L. -2.4 m
SG4-G.L. -250 m
1G1-G.L. 0 m
5G1-G.L. 0 m
1G1
[cm/s/s]
5G1
SH
0.01 0.1 1 23
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 EW
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 NS
0.01 0.1 1 23
0
10
20
30
40
50 EW
AS2
LAYERED vs FOLDED
fmax ≈5 Hz
Gatti et al. (2018) GJI 213, 1073-1092. doi : 10.1093/gji/ggy027

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
Assess the effect of local foldings (fmax = 5 Hz)
Assess the effect of local foldings (fmax = 5 Hz)
15 / 24
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
t[s]
-2.4
-1.6
-0.8
0
0.8
1.6
2.4
vFN (t) [cm/s]
Mj 4.4 2007/07/16-21:08
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
t[s]
-2.4
-1.6
-0.8
0
0.8
1.6
2.4
vFN (t) [cm/s]
Mj 4.4 2007/07/16-21:08
Figure 4–Velocigrams along FN direction @ 1G1 (Unit 1 - Free-Field)

3-D numerical simulation of the NCO earthquake Include local geology at KK-NPP : Model 2
On the accuracy of 3D physics-based model
On the accuracy of 3D physics-based model
16 / 24
0.01 0.1 0.5 1
T [s]
1
1.2
1.4
1.6
1.8
2
2.2
2.4
log 10 Sa [cm/s/s]
Mj 4.4 2007/07/16-21:08@1G1
0.01 0.1 0.5 1
T [s]
1
1.2
1.4
1.6
1.8
2
2.2
2.4
log 10 Sa [cm/s/s]
Mj 4.4 2007/07/16-21:08@5G1
All time-histories filtered at 7 Hz
0.01 0.1 1 2 3
T [s]
0
50
100
150
200
SaGMH [cm/s/s]
Mj 4.4 2007/07/16-21:08@1G1
5! GL L
7! GL L
10 ! GLL
3 4 5 6 7 8 9 10 11 12
GLL [1]
5
10
50
100
200
300
400
500
CPU-Time [1e6 s]
Figure 5 – f5GLL
max ≈3.5Hz ;f7GLL
max ≈5.0Hz ;f10GLL
max ≈7.0Hz

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
17 / 24

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Broadband modelling : hybrid approach
17 / 24
Broadband modelling
IModelling challenge
IDeal with computational burden
IHF/SP is Deterministic ?
→Stochastic

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Broadband modelling : hybrid approach
17 / 24
NUMERICAL
SIMULATION
HYBRID
Numerical Simulations:
Range of applicability
f [Hz]
[1]
STOCHASTIC/EMPIRICAL
ACCURACY?
Broadband modelling
IModelling challenge
IDeal with computational burden
IHF/SP is Deterministic ?
→Stochastic
LF/HF Hybridization
Graves and Pitarka (2004)
ILow-Frequency :
→3D Physics-Based Simulation
IHigh-Frequency :
→Empirical
→(Semi-)Stochastic

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Broadband modelling : hybrid approach
17 / 24
Paolucci et al. (2018) BSSA.
doi : 10.1785/0120170293
Broadband modelling
IModelling challenge
IDeal with computational burden
IHF/SP is Deterministic ?
→Stochastic
LF/HF Hybridization
Graves and Pitarka (2004)
ILow-Frequency :
→3D Physics-Based Simulation
IHigh-Frequency :
→Empirical
→(Semi-)Stochastic
→Alternative Approach...

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Alternative Hybrid Broadband modelling : ANN2BB
Alternative Hybrid Broadband modelling : ANN2BB
18 / 24
NUMERICAL
SIMULATION
HYBRID
ANN
Numerical Simulations:
Range of applicability
SPEED
SEM3D

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB Weak coupling with structural model
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
Weak coupling with structural model
4Conclusions and Perspectives
19 / 24

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB Weak coupling with structural model
From source to the structure
From source to the structure
19 / 24
SEM3D+MISS3D+CODE ASTER
7-R2
7-R1
E
W
SEM3D
MISS3D

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB Weak coupling with structural model
ANN2BB to SEM3D simulations
ANN2BB to SEM3D simulations
20 / 24
0.01 0.1 1 2 3
T [s]
0
80
160
240
320
Sa GMH [cm/s/s]
AS1 @SG1
0.01 0.1 1 2 3
T [s]
0
80
160
240
320
Sa GMH [cm/s/s]
AS1 @1G1
Figure 6–ANN2BB pseudo-acceleration spectra (T?=0.75 s)
IImproved outcrop motion prediction
ISEM3D records filtered at fmax =5 Hz
IRecords and ANN2BB synthetics are
filtered at fmax =30 Hz

Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB Weak coupling with structural model
Response at reactor building basement
Response at reactor building basement
21 / 24
SEM3D+MISS3D+CODE ASTER
0.01 0.1 1 2 3
T[s]
0
20
40
60
80
100
Sa(T)[cm/s/s]
7R2
7-R2
7-R1
E
W
SEM3D
MISS3D

Conclusions and Perspectives
Outline
1A complex test case : the 2007 NCO earthquake and the KK-NPP seismic site
response
23-D numerical simulation of the NCO earthquake
3Broad-band earthquake simulations via Artificial Neural Networks : ANN2BB
4Conclusions and Perspectives
22 / 24

Conclusions and Perspectives
So far, so good
So far, so good
22 / 24
Large scale S2S analysis
→towards fmax =10 Hz
Progressive refinement of regional/near wave-field
→Small heterogeneities in the Earth’s crust
Site effects
→Include complex soil rheology (non-linearity) and buried topography
(basin)

Conclusions and Perspectives
So far, so good
So far, so good
22 / 24
Large scale S2S analysis
→towards fmax =10 Hz
Progressive refinement of regional/near wave-field
→Small heterogeneities in the Earth’s crust
Site effects
→Include complex soil rheology (non-linearity) and buried topography
(basin)
Hybrid modelling
→ANN2BB to reach 30 Hz
→Coherent distribution of peak values at HF
→Structural analysis

Conclusions and Perspectives
Future Perspectives
Future Perspectives
23 / 24
Main shock simulation
→include kinematic fault modelling (fractal model fmax =10 Hz)
→dynamic rupture
(Ruiz et al., 2011)

Conclusions and Perspectives
Future Perspectives
Future Perspectives
23 / 24
Main shock simulation
→include kinematic fault modelling (fractal model fmax =10 Hz)
→dynamic rupture
Modelling site effects
→Refine non-linear rheology
→Include complex heterogeneous structure (von Karman, anisotropic)
→SSI : SEM3D-SEM3D Domain Reduction Method
Pe
Ωext
Ω0
ue
ub
ui
Γb
Γe
-Pb
Pb
0
0
0
0
0

Conclusions and Perspectives
Future Perspectives
Future Perspectives
23 / 24
Main shock simulation
→include kinematic fault modelling (fractal model fmax =10 Hz)
→dynamic rupture
Modelling site effects
→Refine non-linear rheology
→Include complex heterogeneous structure (von Karman, anisotropic)
→SSI : SEM3D-SEM3D Domain Reduction Method
Pe
Ωext
Ωint
ue
ub
ui
Γb
Γe
-Pb
Pb
(Bielak et al., 2003)

Conclusions and Perspectives
24 / 24
Make CivEng Great Again !
Filippo Gatti
filippo.gatti@centralesupelec.fr
filippo.gatti@polimi.it
https://github.com/FilLTP89
Science has limits : A few things that science does not do
No moral judgment
No aesthetic judgment
No rules in how to use it
No conclusions on supernatural phenomena
http://undsci.berkeley.edu/article/0 0 0/whatisscience 12

Andrianov, S., Ivanov, A., and Podzyvalov, E. (2011). A LEGO Paradigm For Virtual Accelerator Cocept. In ICALEPCS2011, volume 3, pages
728–730.
Bielak, J., Loukakis, K., Hisada, Y., Yoshimura, C., Chiaki, Y., Ferna, A., Bielak, J., Hisada, Y., and Ferna, A. (2003). Domain Reduction Method for
Three-Dimensional Earthquake Modeling in Localized Regions. Part 1 : Theory. Bulletin of the Seismological Society of America, 93(2) :817–840.
Dreger, D., Hurtado, G., Chopra, A. K., and Larsen, S. (2007). Near-Fault Seismic Ground Motions. Technical Report 59A0435, California
Department of Transportation.
Duputel, Z., Tsai, V. C., Rivera, L., and Kanamori, H. (2013). Using centroid time-delays to characterize source durations and identify earthquakes
with unique characteristics. Earth and Planetary Science Letters, 374 :92–100.
Faccioli, E., Maggio, F., Paolucci, R., and Quarteroni, A. (1997). 2D and 3D elastic wave propagation by a pseudo-spectral domain decomposition
method. Journal of Seismology, 1(3) :237–251.
Graves, R. W. and Pitarka, A. (2004). Broadband time history simulation using a hybrid approach. In 13th World Conference on Earthquake
Engineering, Vancouver, B.C., Canada.
Hisada, Y. (1994). An efficient method for computing Green’s Functions for layered half-space with sources and receivers at close depths. Bulletin of
the Seismological Society of America, 84(5) :1456–1472.
Komatitsch, D. (1997). M´ethodes spectrales et ´el´ements spectraux pour l’´equation de l’´elastodynamique 2D et 3D en milieu h´et´erog`ene (Spectral
and spectral-element methods for the 2D and 3D elastodynamics equations in heterogeneous media). PhD thesis, Institut de Physique du Globe,
Paris, France. 187 pages.
Ruiz, J. A., Baumont, D., Bernard, P., and Berge-Thierry, C. (2011). Modelling directivity of strong ground motion with a fractal, k-2, kinematic
source model. Geophysical Journal International, 186(1) :226.
Tsuda, K., Hayakawa, T., Uetake, T., Hikima, K., Tokimitsu, R., Nagumo, H., and Shiba, Y. (2011). Modeling 3D Velocity Structure in the Fault
Region of the 2007 Niigataken Chuetu-Oki Earthquake with Folding Structure. In 4th IASPEI/IAEE International Symposium-Effects of Surface
Geology on Seismic Motion, pages 1–11.
1/1