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Uvod Program Analize Zakǉuqak

Dinamika tla i konstrukcije prizemǉotresima, nepouzdani modeli,nepouzdani parametri i teorija

verovatno�a

Boris Jeremi�

University of California, Davis, CA, USALawrence Berkeley National Laboratory, Berkeley, CA, USA

Beograd, Decembar 2016

Jeremi�

Modelovaǌe tla i konstrukcije


Sadr�aj

UvodMotivacijaModeling and Parametric Uncertainty

ProgramReal ESSI Simulator SystemReal ESSI Simulator Components

AnalizeBranaBetonski MostNuklearna ElektranaMehanika i Teorija Verovatno�a

ZakǉuqakZakǉuqak

Jeremi�



Motivacija




ZakǉuqakZakǉuqak

Jeremi�



Motivacija

Motivacija

I Poboǉxaǌe modelovaǌa i simulacija za sistemetla i konstrukcije

I Razvoj ekspertnog sistema za numeriqke analize

I Upotreba preciznih modela za analize statike idinamike sistema tla i konstrukcije

I Ciǉ je razvoj metodologije za numeriqkapredvi�aǌa i informisaǌe korisnika, struqǌaka, ane rezultati koji prate neku zadatu liniju, na silu

Jeremi�



Motivacija

Pretpostavka

I Interakcija dinamiqkih karakteristikazemǉotresa, tla i konstrukcije kontrolixe nivooxte�eǌa konstrukcije

I Mesto i vreme disipacije zemǉotresne energijeodre�uje lokaciju i nivo oxte�eǌa konstrukcije

I Kontrolisaǌem protok zemǉotresne energije kroztlo i konstrukciju, mo�emo da poboǉxamo

I SigurnostI Ekonomiqnost

Jeremi�



Motivacija

Taqnost Modelovaǌa i Simulacija

I Verifikacija: dokaz da je model taqno rexen,matematiqki problem

I Validacije: dokaz da je rexen pravi model,mehaniqki problem

I Numeriqko analiza: korix�eǌe numeriqkog modelaza predvicjaǌe staǌa sistema za optere�eǌa kojanisu korix�ena pri testiraǌu (validaciji)

I Predvi�aǌe/analiza uz teoriju verovatno�a:I Nesigurnost modelaI Nesigurnost parametara

Jeremi�



Modeling and Parametric Uncertainty




ZakǉuqakZakǉuqak

Jeremi�




Modeling Uncertainty: Simplified ModelsI Simplified modeling: Features (important ?) are neglected

(6D ground motions, inelasticity)I Modeling Uncertainty: unrealistic and unnecessary

modeling simplificationsI Modeling simplifications: justifiable iff higher level

sophistication model shows are features not important

Jeremi�




Parametric Uncertainty: Material and LoadsI Significant uncertainty in material and loadsI Need to propagate uncertainty through simulation, to give

regulators and engineers information for design, licensing...

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

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

Jeremi�



Real ESSI Simulator System




ZakǉuqakZakǉuqak

Jeremi�




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.

Jeremi�




Real ESSI Simulator Modeling and Simulation Process

input

loading stage

increment

iteration

output

Jeremi�



Real ESSI Simulator Components




ZakǉuqakZakǉuqak

Jeremi�




Real ESSI Simulator: DSL

[fragile]

I Domain Specific Language (DSL), Yacc & Lex

I English like modeling and simulation language

I Parser and compiler, can define functions, models, etc.

I Can extend models and methods

I Requires units!

Jeremi�




Real ESSI DSL Example1 model name "UNR Test Setup";2 new loading stage "First, static";3 add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;4 add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;5 add element # 1 type beam_elastic with6 nodes (1, 2) cross_section=1.0*m^27 elastic_modulus=1.0e5*KN/m^28 shear_modulus=2.0e4*KN/m^29 torsion_Jx=2*0.083*m^4

10 bending_Iy=0.083*m^4 bending_Iz=0.083*m^411 mass_density=2500.0*kg/m^312 xz_plane_vector = (0, -1, 0)13 joint_1_offset = (0.0*m, 0.0*m, 0.0*m)14 joint_2_offset = (0.0*m, 0.0*m, 0.0*m);

Jeremi�




Real ESSI DSL Example1 fix node No 1 dofs all;2 add load # 1 to node # 2 type3 linear Fx=-9*kN;4 define load factor increment 0.01;5 define solver UMFPack;6 define convergence test7 Norm_Displacement_Increment8 tolerance = 1e-59 maximum_iterations = 20

10 verbose_level = 4;11 define algorithm Newton;12 simulate 100 steps using static algorithm;1314 dovidjenja;

Jeremi�




Real ESSI Simulator Program: Finite Elements

I Dry/single phase solids (8, 20, 27, 8-27 node bricks),I Saturated/two phase solids (8 and 27 node bricks,

liquefaction modeling),I Truss, Beams, linear and nonlinearI Nonlinear concrete shell and linear shell (ANDES)I Contacts (dry and/or saturated soil/rock - concrete, gap

opening-closing, frictional slip),I Base isolators (elastomeric, frictional pendulum)I Stochastic Elastic-Plastic FEM (1D and 3D solid)

Jeremi�




Real ESSI Simulator Program: Material Models

I Elastic (solids): Linear, nonlinear, isotropic and anisotropic

I Elastic-Plastic (solids): von Mises, Drucker Prager,Rounded Mohr-Coulomb, Leon Parabolic, Cam-Clay,SaniSand, SaniClay, Pisanò. All elastic-plastic models canbe used as perfectly plastic, isotropic hardening/softeningand kinematic hardening models.

I Elastic-Plastic (structures, 1D fibers): concrete and steel

I Probabilistic Elasto-Plasticity

Jeremi�




Real ESSI Simulator Program: Seismic Input

Analytic input of seismic motions using Domain ReductionMethod (Bielak et al.)

I Body (P, S) seismic waves

I Surface (Rayleigh, Love, etc.) seismic waves,

I Analytic radiation damping.

Jeremi�




Real ESSI Simulator Program: V&V

I Verification: mathematics issue,I Each element, model, algorithm and procedure has been

extensively verified (math issue),

I Validation: physics issue,I Limited, current DOE project will provide a wealth of data

for soil, SSI, &c.

Jeremi�



Examples

I Earth and Concrete Dam: level of sophistication and theinfluence of human factor (expert opinion)

I Concrete Bridge: matching of earthquake, soil andstructure dynamic characteristics

I Nuclear Power Plant: 3D (6D) vs 1D seismic motions

I Stochastic Elastic Plastic Finite Element Method: risk ofundesirable performance

Jeremi�



Brana




ZakǉuqakZakǉuqak

Jeremi�



Brana

Dam, Satellite Photo

Jeremi�



Brana

Dam, 3D Slope, Satellite Photo

Jeremi�



Brana

3D Slope

Jeremi�



Brana

3D Slope, Ground Photo

Jeremi�



Brana

Dam, Construction Photo

Jeremi�



Brana

3D Dam – Slope StabilityI 3D earth slope part of a concrete, earth damI Movements recorded during lowering of reservoir (and

significant rain!)I 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 (a single) measured shear

strengthI Load cases: lowering and raising reservoir, slow and fastI Dam build using untreated alluvium

Jeremi�



Brana

Dam, Section

Jeremi�



Brana

Dam, Model

//

Jeremi�



Brana

Dam Slope, Failure ModesI 3D failure patternI 3D has lower FS than 2D (!)I Original Su: FS barely enoughI With "increased" Su, FS a bit higherI Seismic: immediate slope failure

Jeremi�



Betonski Most




ZakǉuqakZakǉuqak

Jeremi�



Betonski Most

Post-Tensioned Concrete Bridge in Variable SoilI Linear elastic deck/box girder, concrete, post-tensionedI Nonlinear frame, r. concreteI Nonlinear piles, r. concreteI Nonlinear soil (Sand, Clay)

Jeremi�



Betonski Most

Variable SoilI Stiff frames (bends) in variable stiffness soils

I Short periodearthquake

I Matching EQ, soiland structurestiffness

I Variable soilcreates extrademand on maingirder

Jeremi�



Betonski Most

Short Period Earthquake, NorthridgeI Usual assumption: soft soil is a problemI Design: static pushover, single bent, soft soilI Actual critical behavior: system in stiff and variable soil

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)

Jeremi�



Betonski Most

Detailed 3D Bridge Model, 3 Bends

Jeremi�



Betonski Most

Short Period E.: Moments, Bent #1, SSS, CCS, CCC

Jeremi�



Betonski Most


Jeremi�



Nuklearna Elektrana




ZakǉuqakZakǉuqak

Jeremi�



Nuklearna Elektrana

Nuclear Power Plants, Modelling Issues

I Nuclear Power Plants (NPPs), early use of SSI analysis(SASSI, CLASSI, &c.)

I State of practice for ESSI analysis of NPPs:I Linear elastic materialI 1D seismic motionsI Incoherent seismic motions

I Current state of art for ESSI analysis of NPPs:I Nonlinear soil, rock, contact, structureI 3D (6D) seismic motions

I Seismic motions issue/problem

Jeremi�



Nuklearna Elektrana

Example Earthquake: M 6.6, Norcia, Italy, 30Oct2016

StrongMotions.com

Jeremi�



Nuklearna Elektrana

1D, 2D, 3D Earthquakes?

I SMART-1 array, Lotung, Taiwan,I LSST07: almost 2D (the only one!)I LSST12: full 3D

Jeremi�



Nuklearna Elektrana

3D (6D) or 1D Seismic Motions for NPPsI 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

Jeremi�



Nuklearna Elektrana

Synthetic (Realistic) Test Motions

Jeremi�


http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4


Nuklearna Elektrana

Synthetic Test Motions, 6D vs 1D

I Danger of picking one component (1D) of motionsI Excellent (forced) fit, but it is not a prediction

Jeremi�


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

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


Nuklearna Elektrana

6D vs 1D NPP ESSI Response Comparison

Jeremi�


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


Nuklearna Elektrana

6D vs 1D NPP ESSI, Top of Containment, Differences

Jeremi�



Mehanika i Teorija Verovatno�a




ZakǉuqakZakǉuqak

Jeremi�




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

Jeremi�




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

Jeremi�




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

I What if all (any) material and load parameters areuncertain

Jeremi�




Probabilistic Elasto-Plasticity: von Mises Surface

Jeremi�




Probabilistic Stress Solution:Eulerian–Lagrangian form of FPK Equation

∂P(σij(xt , t), t)∂t

=∂

∂σmn

[{⟨ηmn(σmn(xt , t),Emnrs(xt), εrs(xt , t))

⟩+

∫ t

0dτCov0

[∂ηmn(σmn(xt , t),Emnrs(xt), εrs(xt , t))

∂σab;

ηab(σab(xt−τ , t − τ),Eabcd(xt−τ ), εcd(xt−τ , t − τ)

]}P(σij(xt , t), t)

]+

∂2

∂σmn∂σab

[{∫ t

0dτCov0

[ηmn(σmn(xt , t),Emnrs(xt), εrs(xt , t));

ηab(σab(xt−τ , t − τ),Eabcd(xt−τ ), εcd(xt−τ , t − τ))

]}P(σij(xt , t), t)

](Jeremic et al. 2007, Sett and Jeremic 2010, Sett et al. 2007, 2011)

Jeremi�




Eulerian–Lagrangian FPK Equation and (SEP)FEMI Advection-diffusion equation

∂P(σij , t)∂t

= − ∂

∂σab

[N(1)

ab P(σij , t)−∂

∂σcd

{N(2)

abcdP(σij , t)}]

I Complete probabilistic description of responseI Second-order exact to covariance of time (exact mean

and variance)I Any uncertain FEM problem (Mu + Cu + Ku = F) with

I uncertain material parameters (stiffness matrix K),I uncertain loading (load vector F)

can be analyzed using PEP and SEPFEM to obtain PDFsof DOFs, stress, strain...

Jeremi�




Probabilistic Elastic-Plastic Response

Jeremi�




Spectral Stochastic Elastic–Plastic FEM

I Minimizing norm of error of finite representation usingGalerkin technique (Ghanem and Spanos 2003, Sett et al.2011):

N∑n=1

K epmndni +

N∑n=1

P∑j=0

dnj

M∑k=1

CijkK′epmnk = 〈Fmψi [{ξr}]〉

K epmn =

∫D

BnEepBmdV K′epmnk =

∫D

Bn√λkhkBmdV

Cijk =⟨ξk (θ)ψi [{ξr}]ψj [{ξr}]

⟩Fm =

∫DφNmdV

Jeremi�




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

]

Jeremi�




Uncertain 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

Jeremi�




Displacement PDFs at the Surface (COV = 120%)

Jeremi�




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

Jeremi�




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

)

Jeremi�



Zakǉuqak




ZakǉuqakZakǉuqak

Jeremi�



Zakǉuqak

SummaryI High fidelity modeling and simulation allows reduction of

modeling uncertainty and direct propagation of parametricuncertainties through the dynamic ESSI system

I Development and expert use of high fidelity modeling andsimulation numerical tools: Real ESSI Simulator System

I Education and training of users (researchers, designers,regulators, owners) will prove essential

I Collaborators: Yang, Cheng, Jie, Sett, Taiebat, Tafazzoli,Karapiperis, Abell, Pisanò, Feng, Sinha, Lacour, Yang,Behbehani, Wang, Petrone, Wong, McKenna, McCallen

I Funding from and collaboration with the US-NRC, US-NSF,US-DOE, CNSC, LBNL, LLNL, INL, ILEE, AREVA NPGmbH, and Shimizu Corp. is greatly appreciated,

Jeremi�


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