uncertainties in modelling and simulation of …sokocalo.engr.ucdavis.edu/~jeremic/ modeling and...

Motivation Modeling and Parametric Uncertainty Real ESSI Simulator System Summary

Uncertainties in Modelling and Simulation ofEarthquake Soils Structures Interaction

Boris Jeremic

University of California, DavisLawrence Berkeley National Laboratory, Berkeley

Earthquake Research InstituteUniversity of Tokyo

Tokyo, Japan, January 2016

Jeremic

ESSI under Uncertainty


Outline

MotivationIntroductionUncertainties

Modeling and Parametric UncertaintyModeling Uncertainty: Seismic Motions for NPPsParametric Uncertainty: Uncertain Material

Real ESSI Simulator SystemReal ESSI Simulator

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 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

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Uncertainties

Outline




Summary

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Uncertainties

Modeling Uncertainty: Simplified Models

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 and Loads

Example: Elastic 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)N

orm

aliz

ed F

requ

ency

Transformation of SPT N-value: 1-D Young’s modulus, E (cf. Phoon and Kulhawy (1999B))

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Modeling Uncertainty: Seismic Motions for NPPs

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, 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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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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Synthetic Test MotionsI Develop free field models with sources withinI Sources are simple, point (mostly), line and surfaceI Sources will send both P and S wavesI Variation in strike and dipI Simulation programs, Real ESSI Simulator and SW4

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Synthetic Test Motions, 6D vs 1DI Danger of picking one component of motions for 1D or

3×1D (it is done all the time!)I Excellent (forced) fit, but not a prediction and information is

lost (goal is to predict and inform and not (force) fit)

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Stress Test Source SignalsI Gauss

I Ricker (1st, 2nd)

-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]

I 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]

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Layered and Dyke/Sill Models

I Uniform soil/rock, to show surface wavesI Horizontally layered geology (a), to show

bending/refraction and more surface wavesI Dyke/Sill intrusion within layered geology (b), to show

effects of local geology on free field motions

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Variable Sources

I Epicenter is 2500m away from the location of interestI Source depth 850m (softer layers) and 2500m (hard rock)I Variation: source locations, strike and dip, magnitude,

frequenciesI Different wave propagation path to the object location

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Layered System , Displacement Traces

I Surface wavesI Surface waves not filtered outI Incoherent motions

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Layered System, Variable Source Depth

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Dyke/Sill Intrusion, Variable Source Depth

I Incoherent motionsI Surface wavesI Lower amplitudes than with

layered only model!

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Dyke/Sill Intrusion, Variable Source Depth

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Dyke/Sill as Seismic Energy SinkI Dyke/Sill (right Fig), made of stiff rock, is an energy sink,

as well as energy reflectorI Variable wave lengths behave differently, depending on

dyke/sill geometry and location

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Importance of Realistic Seismic Motion Fields

I Developed synthetic (!) free field motions need to excite anumber of (all!) possible responses from a nuclear facility

I Knowledge of detailed geology is needed, geometry andmaterial properties, including inelasticity of shallow layers

I Reduction of modeling uncertainty

I Direct use for Realistic ESSI simulations

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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


Parametric Uncertainty: Uncertain Material

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 Dynamic Finite Elements

Mu + Cu + Kepu = F

I Incremental elastic-plastic constitutive equation

∆σij = EEPijkl ∆εkl =

[Eel

ijkl −Eel

ijmnmmnnpqEelpqkl

nrsEelrstumtu − ξ∗h∗

]∆εkl

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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 SystemI Developed with funding from US-DOE, US-NRC, US-NSF

and CNSC-CCSN

I The Real ESSI simulator system is designed based onpremise of high fidelity, high performance, modeling andsimulation

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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Real ESSI Simulator

Real ESSI Modelling

input

loading stage

increment

iteration

output

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Real ESSI Simulator

Real ESSI: Components

I Variety of solid, structural and special finite elementsI Variety of material modelsI Variety of static and dynamic solution advancement

algorithmsI Seismic (realistic) input using DRMI High performance parallel computing for elastic-plastic

FEM and multiple performance CPUs and networks usingPlastic Domain Decomposition method

I Stochastic Elastic-Plastic Finite Element Method(SEPFEM)

I Extensive Verification, working on Validation

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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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