Modelling and Simulation of Earthquake Soils Structures...

Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary

Modelling and Simulation of Earthquake SoilsStructures Interaction Under Uncertainty

Boris Jeremic

University of California, DavisLawrence Berkeley National Laboratory, Berkeley

Southwest Jiaotong University,Chengdu, China, October 2015

Jeremic

ESSI under Uncertainty


Outline

MotivationIntroductionUncertainties

Modeling and Parametric UncertaintyModeling Uncertainty: Bridge ModelModeling Uncertainty: Nuclear Power PlantsParametric Uncertainty

Real ESSI Simulator SystemReal ESSI SimulatorVerification and Validation

Summary

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Introduction

Outline




Summary

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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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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 foretell the state of a physical system underconsideration under conditions for which the computationalmodel has not been validated.

I Modeling and Parametric Uncertainties

I Predictive capabilities with low Kolmogorov Complexity

I Modeling and simulation goal is to inform, not fit

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Uncertainties

Outline




Summary

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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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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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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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Modeling Uncertainty: Bridge Model

Outline




Summary

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Detailed 3D Bridge Model

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Modeling Issues

I Construction process

I Deconvolution of given surface ground motions

I No artificial damping (only mat. dissipation, radiation)

I Element size issues (filtering of frequencies)

elem. # elem. size fcutoff min. Gep/Gmax γ

12K 1.00 m 10 Hz 1.0 <0.5 %15K 0.90 m >3 Hz 0.08 <1.0 %

150K 0.30 m 10 Hz 0.08 <1.0 %500K 0.15 m 10 Hz 0.02 <5.0 %

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Short Period (Northridge) Input Motions

0 10 20 30 40 50 60

−2

0

2

Time (s)

Acc

eler

atio

n (m

/s2 ) Acceleration Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

0 10 20 30 40 50 60−0.2

0

0.2

Time (s)

Dis

plac

emen

t (m

) Displacement Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

1

2

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

0.2

0.4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

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Short Period Eq.: Left Bent, Displacements

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion

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Short Period Eq.: Left Bent, Moments.

0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


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Short Period E.: Left Bent, Bending Moments

0 5 10 15 20 25−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)

SSS CCC

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Short Period E.: Left Bent, Free Field vs Real Disp.

0 5 10 15 20 25

−0.1

−0.05

0

0.05

0.1

0.15

Time (s)

Dis

plac

emen

t (m

)

SSS CCC Freefield Input Motion

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Long Period (Kocaeli) Input Motions

0 5 10 15 20 25 30 35

−2

0

2

Time (s)

Acc

eler

atio

n (m

/s2 ) Acceleration Time Series − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

0 5 10 15 20 25 30 35−0.4

−0.2

0

0.2

Time (s)

Dis

plac

emen

t (m

) Displacement Time Series − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

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Long Period E.: Left Bent, Bending Moments.

0 5 10 15 20 25 30 35−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)

SSS CCC

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Modeling Uncertainty: Nuclear Power Plants

Outline




Summary

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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

I Significant savings in construction cost possible with moreaccurate modeling of NPPs

I Improvements in safety of NPPs also possible

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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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6D Free Field Motions

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input.mp4



6D Free Field Motions (closeup)

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4



6D Free Field at Location

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4



6D Earthquake Soil Structure Interaction

(MP4)

Jeremic


http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_3d.mp4



1D Free Field at Location

(MP4)

Jeremic


http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4



1D ESSI of NPP

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_1d.mp4



6D vs 1D NPP ESSI Response Comparison

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4



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

]

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Parametric Uncertainty

Outline




Summary

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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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Uncertainty Propagation through Inelastic System

I Incremental el–pl constitutive equation

∆σij = EEPijkl =

[Eel

ijkl −Eel

ijmnmmnnpqEelpqkl

nrsEelrstumtu − ξ∗h∗

]∆εkl

I Dynamic Finite Elements

Mu + Cu + Kepu = F

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Probabilistic Elasto-Plasticity: von Mises Surface

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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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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

PDF

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

PDF

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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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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Displacement PDFs at the Surface (COV = 120%)

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Displacement CDFs (Fragilities) at the Surface (COV = 120%)

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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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Real ESSI Simulator

Outline




Summary

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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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Real ESSI Simulator

Real ESSI Simulator System

I Philosophy of the Real ESSI simulator modeling andsimulation system is to predict and inform, not fit

I Real ESSI simulator, also known as Vrlo Prosto,, Muy Fácil, Molto Facile, , Πραγματικά

Εύκολο, , , Très Facile, Vistinski

Lesno, Wirklich Einfach, .

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Real ESSI Simulator

Real ESSI Modelling

input

loading stage

increment

iteration

output

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Real ESSI Simulator

Real ESSI: Finite ElementsI Dry/single phase solids (8, 20, 27, 8-27 node bricks),

elastic and/or inelastic

I Saturated/two phase solids (8 and 27 node bricks,liquefaction modeling), elastic and/or inelastic

I Truss, elastic

I Beams (six and variable DOFs per node), elastic

I Shell (ANDES) with 6DOF per node, linear elastic

I Contacts (dry and/or saturated soil/rock - concrete, gapopening-closing, frictional slip), inelastic

I Base isolators (elastomeric, frictional pendulum), inelastic

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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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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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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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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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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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Verification and Validation

Outline




Summary

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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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Fundamentals of Verifications and Validation

Real World

Benchmark PDE solutionBenchmark ODE solutionAnalytical solution

Complete System

Subsystem Cases

Benchmark Cases

Unit ProblemsHighly accurate solution

Experimental Data

Conceptual Model

Computational Model

Computational Solution

ValidationVerification

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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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Validation

I Traditional ExperimentsI 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

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Summary

Concluding Remarks

I Modeling and parametric uncertainty influences results ofnumerical predictions and must be taken into account

I Goal is to predict and inform, not fit

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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

Jeremic


Modelling and Simulation of Earthquake Soils Structures...

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