Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Modeling and Simulation of Earthquakes,
Soils, Structures, and their Interaction
Boris Jeremic
University of California, Davis, CALawrence Berkeley National Laboratory, Berkeley, CA
ETH Seminar,
Zurich, Switzerland
May 2018
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Motivation
Improve modeling and simulation for infrastructure objects
Use of high fidelity numerical modeling and simulation to
analyze earthquakes, and/or soils and/or structures and
their interaction (ESSI)
Reduce modeling uncertainty, perform desired level of
sophistication modeling and simulation
Follow evolution of parametric uncertainty
Le doute n’est pas un état bien agréable, mais l’assurance
est un état ridicule. (François-Marie Arouet, Voltaire)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Earthquake Motions, 6C vs 3×1C vs 1C
◮ Danger of picking one component of motions (1C) from 3C
◮ Excellent (forced) fit, but not a prediction, information is lost
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
6C vs 1C NPP ESSI Response Comparison
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Elastic and Inelastic Response: Differences
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Material Behavior Inherently Uncertain
◮ Spatial
variability
◮ Point-wise
uncertainty,
testing
error,
transformation
error
(Mayne et al. (2000)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Parametric Uncertainty: Material and Loads
5 10 15 20 25 30 35
5000
10000
15000
20000
25000
30000
SPT N Value
You
ng’s
Mod
ulus
, E (
kPa)
E = (101.125*19.3) N 0.63
−10000 0 10000
0.00002
0.00004
0.00006
0.00008
Residual (w.r.t Mean) Young’s Modulus (kPa)
Nor
mal
ized
Fre
quen
cyTransformation of SPT N-value: 1-D Young’s modulus, E (cf. Phoon and Kulhawy (1999B))
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Motivation
Parametric Uncertainty: Material Properties
20 25 30 35 40 45 50 55 60Friction Angle [ ◦ ]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
10 20 30 40 50 60 70 80Friction Angle [ ◦ ]
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
0 200 400 600 800 1000 1200 1400Undrained Shear Strength [kPa]
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
0 200 400 600 800 1000 1200 1400Undrained Shear Strength [kPa]
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
Field φ Field cu
20 25 30 35 40 45 50 55 60Friction Angle [ ◦ ]
0.00
0.05
0.10
0.15
0.20
0.25
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
10 20 30 40 50 60 70 80Friction Angle [ ◦ ]
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
0 50 100 150 200 250 300Undrained Shear Strength [kPa]
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
0 50 100 150 200 250 300 350 400Undrained Shear Strength [kPa]
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
Prob
abili
ty D
ensi
ty fu
nctio
n
Min COVMax COV
Lab φ Lab cu
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Observations
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Observations
3C (6C) Seismic Motions
◮ All (most) measured motions are full 3C (6C)
◮ Example of an almost 2D motion (LSST07, LSST12)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Observations
San Pablo Earthquake, 14Jun2017
Courtesy of http://www.strongmotioncenter.org/
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Regional Geophysical Models
◮ High fidelity free field seismic motions on regional scale
◮ Knowledge of geology (deep and shallow) needed
◮ High Performance Computing using SW4 on CORI (LBNL)
◮ Collaboration with LLNL: Dr. Rodgers, Dr. Pitarka and
Dr. Petersson
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Regional Geophysical Models
Rodgers and Pitarka
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Regional Geophysical Models
USGS
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Example Regional Model
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Example Regional Model (Rodgers)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Regional Geophysical Models
Seismic Motions: SW4 to MS-ESSI
ESSI nodes
SW42ESSI
1 2 31 2 3 , ,( ), , ,u u u θ θ θ
72m×72m×56m
36m embedded
300m ×300m ×100m
Grid spacing ~ 5m
ESSI Box
30km × 14km ×5 km
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Stress Testing SSI Systems◮ Excite SSI system with a suite of seismic motions◮ Simple sources, variation in strike and dip, P and S waves,
surface waves (Rayleigh, Love, etc.)◮ Stress test soil-structure system◮ Try to "break" the system, shake-out strong and weak links
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Stress Test Source Signals◮ Ricker
-0.005
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0 2 4 6 8 10 12 14 16 18 20Ric
ker2
nd F
unct
ion
Am
plitu
de
Time [s]
0
2e-05
4e-05
6e-05
8e-05
0.0001
0.00012
0.00014
0.00016
0 2 4 6 8 10
Ric
ker2
nd F
FT
Am
plitu
de
Frequency [Hz]
◮ Ormsby
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0 1 2 3 4 5 6
Orm
sby
Fun
ctio
n A
mpl
itude
Time [s]
0
5e-05
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0.0005
0 5 10 15 20 25 30
Orm
sby
FF
T A
mpl
itude
Frequency [Hz]
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Layered and Dyke/Sill Models
◮ (a) Horizontal layers◮ (b) Dyke/Sill intrusion
◮ Source locations matrix (point sources)◮ Source strike and dip variation◮ Magnitude variations◮ Range of frequencies
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Layered System, Displacement Traces◮ Epicenter is 2500m away from the location of interest◮ Source depth 850m (left) and 2500m (right)◮ Different wave propagation path to the point of interest◮ Surface waves quite pronounced◮ Layered geology did not filter out surface waves
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Layered System, Variable Source Depth
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Dyke/Sill Intrusion, Variable Source Depth
◮ Lower amplitudes than with layered only model!◮ Difference in body and surface wave arrivals◮ Surface waves present, more complicated wave field
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Dyke/Sill Intrusion, Variable Source Depth
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Dyke/Sill as Seismic Energy Sink
◮ Dyke/Sill (right Fig), made of stiff rock, is an energy sink,
as well as energy reflector◮ Variable wave lengths behave differently, depending on
dyke/sill geometry and location
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Plane Wave Stress Test Motions
◮ Plane wave stress test motions: 3D-6C (Haskel’s solution
for plane harmonic waves) and/or 3D-3×1C and/or 3D-1C
and or 1D-1C motions
◮ Knowledge of geology and the site is important
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Stress Test Motions
◮ Variation in inclination, frequency, energy and duration
◮ Try to "break" the system, shake-out strong and weak links
L oL w
L oL w
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Free Field, Variation in Input Wave Angle, f = 5Hz
(MP4)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
SMR ESSI, Variation in Input Wave Angle, f = 5Hz
(MP4)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
Free Field, Variation in Input Frequency, θ = 60o
(MP4)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
SMR ESSI, Variation in Input Frequency, θ = 60o
(MP4)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
SMR ESSI, Variation in Input Frequency, REAL TIME
(MP4)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Stress Test Motions
3D wave effects - different frequencies
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
0.50
0.25
0.00
0.25
0.50
Ax [
g]
SMR Free field
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
60
30
0
30
60
Ax [
g]
SMR Free field
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
60
30
0
30
60
Ax [
g]
SMR Free field
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
0.50
0.25
0.00
0.25
0.50
Az [
g]
SMR Free field
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
60
30
0
30
60
Az [
g]
SMR Free field
0.0 0.2 0.4 0.6 0.8 1.0Time [s]
60
30
0
30
60
Az [
g]
SMR Free field
AB
C
Jeremic et al.
MS ESSI
Acceleration response - Surface center point A
X direction
Z direction
(a) f = 1Hz θ = 60o (b) f = 5Hz θ = 60o (c) f = 10Hz θ = 60o
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Seismic Energy Input and Dissipation
Seismic energy input, through a closed boundary
Mechanical dissipation outside SSI domain:
Reflected wave radiation
SSI system oscillation radiation
Mechanical dissipation/conversion inside SSI domain:
Inelasticity of soil and contact zone
Inelasticity/damage of structure and foundation
Viscous coupling of fluids and soils and structure
Numerical energy dissipation/production
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Incremental Plastic Work: dWp = σij dǫplij
◮ Negative incremental energy dissipation◮ Plastic work is NOT plastic dissipation
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Negative Incremental Energy Dissipation!
Direct violation of the second law of thermodynamics
600 papers use Uang and Bertero (1990) and repeat their
error
Important form of energy missing: Plastic Free Energy
Observed by Farren and Taylor (1925) and explained by
Taylor and Quinney (1934)
Plastic Work vs. Plastic Energy Dissipation
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Energy Dissipation on Material Level
Single elastic-plastic element under cyclic shear loading
Difference between plastic work and dissipation
Plastic work can decrease, dissipation always increases
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Plastic Free Energy◮ Multi-scale effect of particle interlocking/rearrangement
◮ Strain energy on particle level
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Energy Transformation in Elastic-Plastic Material
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Energy Dissipation in Large-Scale Model (NPP)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Energy Dissipation
Energy Dissipation in Large-Scale Model (SMR)
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Probabilistic Inelastic Modeling
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Probabilistic Inelastic Modeling
Uncertainty Propagation through Inelastic System
◮ Incremental el–pl constitutive equation
∆σij = EEPijkl ∆ǫkl =
[
Eelijkl −
EelijmnmmnnpqEel
pqkl
nrsEelrstumtu − ξ∗h∗
]
∆ǫkl
◮ Dynamic Finite Elements
Mui + Cui + K epui = F (t)
◮ What if all (any) material and load parameters are
uncertain
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Probabilistic Inelastic Modeling
Probabilistic Elastic-Plastic Response
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Probabilistic Inelastic Modeling
3D FPK Equation
∂P(σij(xt , t), t)
∂t=
∂
∂σmn
[{⟨
ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t))
⟩
+
∫ t
0
dτCov0
[
∂ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t))
∂σab
;
ηab(σab(xt−τ , t − τ),Dabcd (xt−τ ), ǫcd (xt−τ , t − τ)
]}
P(σij(xt , t), t)
]
+∂2
∂σmn∂σab
[{∫ t
0
dτCov0
[
ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t));
ηab(σab(xt−τ , t − τ),Dabcd (xt−τ ), ǫcd (xt−τ , t − τ))
]}
P(σij(xt , t), t)
]
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Probabilistic Inelastic Modeling
FPK Equation
◮ Advection-diffusion equation
∂P(σ, t)
∂t= −
∂
∂σ
[
N(1)P(σ, t)−∂
∂σ
{
N(2)P(σ, t)}
]
◮ Complete probabilistic description of response
◮ Solution PDF is second-order exact to covariance of time
(exact mean and variance)
◮ It is deterministic equation in probability density space
◮ It is linear PDE in probability density space → simplifies
the numerical solution process
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
Direct Probabilistic Constitutive Modeling in 1D
◮ Zero elastic region elasto-plasticity with stochastic
Armstrong-Frederick kinematic hardening
∆σ = Ha∆ǫ− crσ|∆ǫ|; Et = dσ/dǫ = Ha ± crσ
◮ Uncertain: init. stiff. Ha, shear strength Ha/cr , strain ∆ǫ:Ha = ΣhiΦi ; Cr = ΣciΦi ; ∆ǫ = Σ∆ǫiΦi
◮ Resulting stress and stiffness are also uncertain
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
Probabilistic Elastic-Plastic Modeling
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
Stochastic Elastic-Plastic Finite Element Method◮ Material uncertainty expanded into stochastic shape f-ion
◮ Loading uncertainty expanded into stochastic shape f-ion
◮ Displacement expanded into stochastic shape f-ion
◮ Time domain integration using Newmark and/or HHT, in
probabilistic spaces
∑Pdk=0
< ΦkΨ0Ψ0 > K (k) . . .∑Pd
k=0< ΦkΨPΨ0 > K (k)
∑Pdk=0
< ΦkΨ0Ψ1 > K (k) . . .∑Pd
k=0< ΦkΨPΨ1 > K (k)
.
.
.
.
.
.
.
.
.
.
.
.∑Pd
k=0< ΦkΨ0ΨP > K (k) . . .
∑Mk=0 < ΦkΨPΨP > K (k)
∆u10
.
.
.∆uN0
.
.
.∆u1Pu
.
.
.∆uNPu
=
∑Pfi=0
fi < Ψ0ζi >∑Pf
i=0fi < Ψ1ζi >
∑Pfi=0
fi < Ψ2ζi >
.
.
.∑Pf
i=0fi < ΨPu
ζi >
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
SEPFEM: System Size
◮ SEPFEM offers a complete solution (single step)
◮ It is NOT based on Monte Carlo approach
◮ System of equations does grow (!)
# KL terms material # KL terms load PC order displacement Total # terms per DoF
4 4 10 43758
4 4 20 3 108 105
4 4 30 48 903 492
6 6 10 646 646
6 6 20 225 792 840
6 6 30 1.1058 1010
8 8 10 5 311 735
8 8 20 7.3079 109
8 8 30 9.9149 1011
... ... ... ...
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Direct Solution for Probabilistic Stiffness and Stress in 1D
SEPFEM: Example in 1D
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Outline
IntroductionMotivation
Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions
Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D
Summary
Jeremic et al.
MS ESSI
Introduction Seismic Motions Inelasticity and Energy Dissipation Summary
Summary
Importance of using proper models correctly (verification,
validation)
Availability of different levels of sophistication of modeling
is important for reduction of modeling uncertainty
Development of the MS-ESSI Simulator system
http://ms-essi.info
Collaborators: Feng, Abell, Han, Sinha, Wang, Lacour,
Pisanó, Kovacevic, McCallen, McKenna, Petrone, Rodgers
Funding from and collaboration with the US-DOE,
US-NRC, US-NSF, CNSC-CCSN, UN-IAEA, and Shimizu
Corp. is greatly appreciated,
Jeremic et al.
MS ESSI