Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modelling and Simulation of Static andDynamic Soils Structures Interaction Under
Uncertainty
Boris Jeremic
University of California, DavisLawrence Berkeley National Laboratory, Berkeley
Géodynamique et Structure,BAGNEUX, France, November 2015
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Introduction
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Introduction
Motivation
I Improve seismic design of soil structure systems
I Earthquake Soil Structure Interaction (ESSI) in time andspace, plays a major role in successes and failures
I Accurate following and directing (!) the flow of seismicenergy in ESSI system to optimize for
I Safety andI Economy
I Development of high fidelity numerical modeling andsimulation tools to analyze realistic ESSI behavior:Real ESSI simulator
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Introduction
Predictive CapabilitiesI Verification provides evidence that the model is solved
correctly. Mathematics issue.
I Validation provides evidence that the correct model issolved. Physics issue.
I Prediction under Uncertainty (!): use of computationalmodel to predict the state of SSI system under conditionsfor which the computational model has not been validated.
I Modeling and Parametric Uncertainties
I Predictive capabilities with low Kolmogorov Complexity
I Modeling and simulation goal:predict and inform, rather than (force) fit
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Uncertainties
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Uncertainties
Modeling Uncertainty
I Simplified modeling: Features (important ?) are neglected(6D ground motions, inelasticity)
I Modeling Uncertainty: unrealistic and unnecessarymodeling simplifications
I Modeling simplifications are justifiable if one or two levelhigher sophistication model shows that features beingsimplified out are not important
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Uncertainties
Parametric Uncertainty: Material Stiffness
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
cy
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Uncertainties
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
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
3D Dam – Slope Stability
I 3D earth slope part of a concrete, earth damI Movements recorded during lowering of reservoirI 3D slope unstable (?), no one could tell, all commercial
software does 2D slope stabilityI 2D vs 3D slope stabilityI Shear strength (?) as the only material parameterI (")Expert(") increased value of measured shear strengthI Load cases: lowering and raising reservoir, slow and fastI Dam build using untreated alluvium
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam, Satellite Photo
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam, 3D Slope, Satellite Photo
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
3D Slope
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
3D Slope, Ground Photo
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam, Construction Photo
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam, Section
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam, Model
//
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: 3D Dam/Slope Model
Dam Slope, Failure Modes
I 3D failure patternI 3D has lower FS than 2DI Original Su FS barely enough,I With "increased" Su a bit higher
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
Modeling and Simulation of Nuclear Power Plants
I Nuclear Power Plants (NPPs) design based on a numberof simplified assumptions!
I Linear elastic material behavior
I Seismic Motions: 1D or 3 × 1D, or real 3D (6D)
I Savings in construction cost possible with more accuratemodeling of NPPs
I Improvements in safety of NPPs also possible, even withhigher seismic motions, as inelastic effects "eat up"(dissipate) seismic energy
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
Nuclear Power Plants: 6D or 1D Seismic MotionsI Assume that a full 6D (3D) motions at the surface are only
recorded in one horizontal directionI From such recorded motions one can develop a vertically
propagating shear wave in 1DI Apply such vertically propagating shear wave to the same
soil-structure system
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D Free Field Motions
(MP4)
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D Free Field Motions (closeup)
(MP4)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D Free Field at Location
(MP4)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D Earthquake Soil Structure Interaction
(MP4)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
1D Free Field at Location
(MP4)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
1D ESSI of NPP
(MP4)
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D vs 1D NPP ESSI Response Comparison
(MP4)
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Modeling Uncertainty: Nuclear Power Plant
6D vs 1D: Containment Acceleration Response
0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3
Acce
l-X [g
]
Containment building bottom
0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3
Acce
l-Y [g
]
3-D1-D
0.0 0.5 1.0 1.5 2.0Time [s]
0.30.20.10.00.10.20.3
Acce
l-Z [g
]
0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3
Acce
l-X [g
]
Containment building top
0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3
Acce
l-Y [g
]
3-D1-D
0.0 0.5 1.0 1.5 2.0Time [s]
0.30.20.10.00.10.20.3
Acce
l-Z [g
]
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Uncertain Material Parameters and Loads
I Decide on modeling complexity
I Determine model/material parameters
I Model/material parameters are uncertain!I MeasurementsI TransformationI Spatial variability
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Uncertainty Propagation through Inelastic System
I Incremental el–pl constitutive equation
∆σij = EEPijkl ∆εkl =
[Eel
ijkl −Eel
ijmnmmnnpqEelpqkl
nrsEelrstumtu − ξ∗h∗
]∆εkl
I Dynamic Finite Elements
Mu + Cu + Kepu = F
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Probabilistic Elasto-Plasticity: von Mises Surface
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Gradient Theory of Probabilistic Elasto-Plasticity:Verification, Elastic-Perfectly Plastic
0.03 0.02 0.01 0.00 0.01 0.02 0.03εx
1.0
0.5
0.0
0.5
1.0
σx [M
pa]
RBFMCS
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Wave Propagation Through Uncertain Soil
0 100 200 300 400 500Shear modulus G [MPa]
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
min COVmax COV
30 20 10 0 10 20 30 40 50 60Shear strength τ [kPa]
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
min COVmax COV
0.0 0.1 0.2 0.3 0.4 0.5Time [s]
0.03
0.02
0.01
0.00
0.01
0.02
0.03
Disp
lace
men
t [m
]
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Uncertain Elastic Response at the Surface (COV = 120%)
0.0 0.1 0.2 0.3 0.4 0.5Time [s]
0.08
0.06
0.04
0.02
0.00
0.02
0.04
0.06
0.08
0.10
Disp
lace
men
t [m
]
MM - SD
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Displacement PDFs at the Surface (COV = 120%)
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Displacement CDFs (Fragilities) at the Surface (COV = 120%)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Parametric Uncertainty: Wave Propagation
Probability of Exceedance, disp = 0.1m (COV = 120%)
0.0 0.1 0.2 0.3 0.4 0.5Time [s]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Prob
. of e
xcee
danc
e (d
= 0
.1m
)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
Jeremic
ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI Simulator SystemI The Real ESSI-Program is a 3D, nonlinear, time domain,
parallel finite element program specifically developed forHi-Fi modeling and simulation of Earthquake Soil/RockStructure Interaction problems for NPPs (infrastructureobjects) on ESSI-Computers.
I The Real ESSI-Computer is a distributed memory parallelcomputer, a cluster of clusters with multiple performanceprocessors and multiple performance networks.
I The Real ESSI-Notes represent a hypertextdocumentation system (Theory and Formulation, Softwareand Hardware, Verification and Validation, and CaseStudies and Practical Examples) detailing modeling andsimulation of ESSI problems.
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI Simulator System
I Developed with funding from US-NRC, US-NSF,CNSC-CCSN, and US-DOE
I The Real ESSI simulator system is designed based onpremise of high fidelity modeling and simulation
I Reduction of modeling uncertainty and propagation ofparametric uncertainty
I Real ESSI simulator, also known as Vrlo Prosto, ,, Muy Fácil, Molto Facile, , Πραγματικά
Εύκολο, , , Très Facile, VistinskiLesno, Wirklich Einfach.
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI Modelling
input
loading stage
increment
iteration
output
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI: Finite ElementsI Dry/single phase solids (8, 20, 27, 8-27 node bricks),
elastic and/or inelasticI Saturated/two phase solids (8 and 27 node bricks,
liquefaction modeling), elastic and/or inelasticI Truss, elasticI Beams (six and variable DOFs per node), elastic, inelasticI Shell (ANDES) with 6DOF per node, linear elastic, inelastic
shell soonI Contacts (dry and/or saturated soil/rock - concrete, gap
opening-closing, frictional slip), inelasticI Base isolators (elastomeric, frictional pendulum), inelastic
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI: Material Models
I Linear and nonlinear, isotropic and anisotropic elastic
I Elastic-Plastic (von Mises, Drucker Prager, RoundedMohr-Coulomb, Leon Parabolic, Cam-Clay, SaniSand,SaniClay, Pisanò...). All elastic-plastic models can be usedas perfectly plastic, isotropic hardening/softening andkinematic hardening models.
I Viscous damping solids, Rayleigh and Caughey damping
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI: Solution Advancement AlgorithmsI Constitutive
I Explicit, Implicit, Sub-incrementation, Line SearchI Nonlinear Static FEM
I No equilibrium iterationI Equilibrium Iterations (full Newton, modified N, Initial Stiff.)I Hyperspherical constraint (arch length, displacement
control, load control)I Line SearchI Convergence criteria: displacement, load, energy
I Nonlinear Dynamic FEMI No equilibrium iterationI Equilibrium Iterations (full Newton, modified N, Initial Stiff.)I Constant or variable time steppingI Convergence criteria: displacement, load, energy
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI: Seismic Input
I Analytic input of seismic motions (both body (P, S) andsurface (Rayleigh, Love, etc., waves), including analyticradiation damping using Domain Reduction Method (Bielaket al.)
Pe(t)
ui
ub
ue
Γ
Large scale domain
Local feature
+Ω
Ω
Seismic source
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI Simulator Program: Parallel, HPC
I High Performance Parallel Computing: both parallel andsequential version available, however, for high fidelitymodeling, parallel is really the only option. Parallel RealESSI Simulator runs on clusters of PCs and on largesupercomputers (Distributed Memory Parallel machines,all top national supercomputers). Plastic DomainDecomposition Method (PDD, dynamic computational loadbalancing) for elastic-plastic computations with multipletypes of finite elements and on variable speed CPUs (andnetworks)
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Real ESSI Simulator
Real ESSI Simulator Program: Probabilistic/StochasticI Constitutive: Euler-Lagrange form of Fokker-Planck
(forward Kolmogorov) equation for probabilisticelasto-plasticity (PEP)
I Spatial: stochastic elastic plastic finite element method(SEPFEM)
Uncertainties in material and load are analytically taken intoaccount. Resulting displacements, stress and strain areobtained as very accurate (second order accurate for stress)Probability Density Functions. PEP and SEPFEM are notbased on a Monte Carlo method, rather they expand uncertaininput variables and uncertain degrees of freedom (unknowns)into spectral probabilistic spaces and solve for PDFs ofresulting displacement, stress and strain in a single run.
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Verification and Validation
Outline
MotivationIntroductionUncertainties
Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope ModelModeling Uncertainty: Nuclear Power PlantParametric Uncertainty: Wave Propagation
Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation
Summary
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Verification and Validation
High Fidelity Predictive Capabilities
I Verification provides evidence that the model is solvedcorrectly. Mathematics issue.
I Validation provides evidence that the correct model issolved. Physics issue.
I Goal: predictive capabilities with low information(Kolmogorov) Complexity
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Verification and Validation
VerificationI Code Verification (code coverage, memory leaks and
pointer assignment testing, static argument list testing, &c.)
I Solution verification (finite elements, constitutiveintegration, material models, algorithms, seismic input, &c.)based on analytic, closed form solutions
I Method of manufactured solutions for elasto-plasticverification
I Parameter bounds (finite elements, material models,algorithms, &c.)
I Develop error plots for elements, models, algorithms over arange of parameter
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Verification and Validation
ValidationI Traditional Experiments
I Improve the fundamental understanding of physics involvedI Improve the mathematical models for physical phenomenaI Assess component performance
I Validation ExperimentsI Model validation experimentsI Designed and executed to quantitatively estimate
mathematical model’s ability to simulate well definedphysical behavior
I The simulation tool (Real ESSI Simulator) (conceptualmodel, computational model, computational solution) is thecustomer
I New US-DOE project to validate inelastic seismic wavepropagation and soil-structure interaction
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Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Summary
Concluding Remarks
I Modeling and simulation of infrastructure object requireshigh sophistication
I Uncertainties (modeling and parametric) influences results
I Those uncertainties need to be addressed and propagatedto results and used in decision making
I Goal is to predict and inform, and not force fit
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ESSI under Uncertainty
Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary
Summary
Acknowledgement
I Funding from and collaboration with the US-NRC,US-DOE, US-NSF, CNSC, AREVA NP GmbH, and ShimizuCorp. is greatly appreciated,
I Collaborators: Prof. Yang, Dr Cheng, Dr. Jie, Dr. Tafazzoli,Prof. Pisanò, Mr. Watanabe, Mr. Vlaski, Mr. Orbovic, andUCD students: Mr. Abell, Mr. Karapiperis, Mr. Feng, Mr.Sinha, Mr. Luo, Mr. Lacour, Mr. Yang, Ms. Behbehani
I Real ESSI Simulator: http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/
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ESSI under Uncertainty