Earthquake Soil Structure Interaction for Nuclear Power …sokocalo.engr.ucdavis.edu/~jeremic/€¦ · · 2013-06-13Motivation ESSI Simulator SystemSummary Earthquake Soil Structure

Motivation ESSI Simulator System Summary

Earthquake Soil Structure Interaction forNuclear Power Plants,

Modeling and Computational Issues

B. JeremicN. Tafazzoli, P. Tasiopoulou, J.A. Abell Mena, B. Kamrani,C.-G. Jeong, F. Pisanò, M. Martinelli, K. Sett, M. Taiebat

Professor, University of California, DavisFaculty Scientist, Lawrence Berkeley National Laboratory, Berkeley

CompDyn, Kos, Greece, June, 2013

Jeremic et al.

Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues


Outline

MotivationProblem – SolutionUncertainty in Modeling

ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic

Summary

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Problem – Solution

Outline



Summary

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The Problem

I Seismic response of Nuclear Power Plants (f ≤ 50Hz!(20Hz))

I 3D, inclined seismic motions: body and surface waves

I Inelasticity (elastic, damage, plastic behavior of materials:soil, rock, concrete, steel, rubber, contact, etc.)

I Full coupling of pore fluids with soil, rock and concreteskeleton, including buoyancy effects

I Uncertainty in seismic sources, path, soil/rock andstructural response

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SolutionI Physics based modeling and simulation of seismic

behavior of soil-structure systems (NPP structures,components and systems)

I Development and use of high fidelity time domain,nonlinear numerical models, in deterministic andprobabilistic spaces, for licensing and professionalpractice (every day use)

I Accurate following of the flow of seismic energy (inputand dissipation) within soil-structure NPP system

I Directing, in space and time, with high (known)confidence, seismic energy flow in thesoil-foundation-structure system

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NPP Model(s)

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Uncertainty in Modeling

Outline



Summary

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Modeling Uncertainty

I Simplified (or inadequate/wrong) modeling: importantfeatures are missed (seismic ground motions, etc.)

I Introduction of uncertainty and (unknown) lack of accuracyin results due to use of un-verified simulation tools(software quality, etc.)

I Introduction of uncertainty and (unknown) lack of accuracyin results due to use of un-validated models (due to lack ofquality validation experiments)

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Complexity of and Uncertainty in Ground Motions

I 6D (3 translations, 3 rotations)

I Vertical motions usually neglected

I Rotational components usually not measured andneglected

I Lack of models for such 6D motions (from measured data))

I Sources of uncertainties in ground motions (Source, Path(Rock), Soil/Rock))

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Material Behavior Inherently Uncertain

I (a) Spatialvariability

I Point-wiseuncertainty,(b) testingerror,(c) transformationerror

(Mayne et al. (2000)

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System Components

Outline



Summary

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System Components

Desirable Modeling and Simulation CapabilitiesI Body (SH, SV, P) and Surface (Rayleigh, Love, etc) seismic

motions modeling and their input into finite element modelsI Elastic-plastic modeling of dry and saturated soil/rock

behavior beneath foundationsI Elastic-plastic modeling of soil/rock (limited data)I Soil/rock - foundation contact zone modeling (for dry and

saturated conditions)I Verification and Validation suiteI High performance, parallel simulation using dynamic

domain decomposition (Plastic Domain Decomposition) forelastic-plastic simulations

I Probabilistic elasto-plasticity and stochastic elastic-plasticfinite element methods

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System Components

ESSI Simulator System

I The 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 onESSI-Computer.

I The ESSI-Computer is a distributed memory parallelcomputer, a cluster of clusters with multiple performanceprocessors and multiple performance networks.

I The ESSI-Notes represent a hypertext documentationsystem detailing modeling and simulation of NPP ESSIproblems.

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System Components

ESSI Simulator ProgramI Based on a Collection of Useful Libraries (modular,

portable)

I Library centric software design

I Solids (dry, saturated), beams, shells, contacts, elastic orelastic-plastic

I Various public domain licenses (GPL, LGPL, BSD, CC)

I Verification (extensive) and Validation (not much)

I Program documentation (part of ESSI Notes)

I Target users: US-NRC staff, CNSC staff, IAEA, LBNL, INL,DOE, professional practice collaborators, expert users

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System Components

ESSI Simulator ComputerA distributed memory parallel (DMP) computer designed forhigh performance, parallel finite element simulations

I Multiple performance CPUsand Networks

I Most cost-performanceeffective

I Source compatibility withany DMP supercomputer

I Current systems: 208CPUs,and 40CPUs (8+32) and160CPUs (8x5+2x16+24+64)...

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System Components

ESSI Simulator Notes

I A hypertext documentation system describing in detailmodeling and simulations of NPP ESSI problems

I Theoretical and Computational Formulations (FEM, EL-PL,Static and Dynamic solution, Parallel Computing)

I Software and Hardware Platform Design (OO Design,Library centric design, API, DSL, Software Build Process,Hardware Platform)

I Verification and Validation (code V, Components V, Staticand Dynamic V, Wave Propagation V)

I Application to Practical Nuclear Power Plant EarthquakeSoil/Rock Structure Interaction Problems (ESSI with 3D,inclined, uncorrelated seismic waves, ESSI with foundationslip, Isolators)

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System Components

ESSI: High Fidelity ModelingI Seismic energy influx, body and surface waves, 3D,

inclinedI Mechanical dissipation outside of SSI domain:

I Radiation of reflected wavesI Radiation of oscillating SSI system

I Mechanical dissipation inside SSI domain:I Plasticity of soil/rock subdomainI Viscous coupling of porous solid with pore fluid (air, water)I Plasticity and viscosity of foundation – soil/rock contactI Plasticity/damage of the structureI Viscous coupling of structure/foundation with fluids

I Numerical energy dissipation/production

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System Components

ESSI: High Performance, Parallel Computing

I The ESSI Program can be used in both sequential andparallel modes

I For high fidelity models, parallel is really the only option

I High performance, parallel computing using PlasticDomain Decomposition Method, for elastic-plasticcomputations (dynamic computational load balancing)

I Developed for multiple/variable capability CPUs andnetworks (DMP and SMPs)

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Verification and Validation Suite

Outline



Summary

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Verification, Validation (V&V) and PredictionI Verification: the process of determining that a model

implementation accurately represents the developer’sconceptual description and specification. Mathematicsissue. Verification provides evidence that the model issolved correctly.

I Validation: The process of determining the degree to whicha model is accurate representation of the real world fromthe perspective of the intended uses of the model. Physicsissue. Validation provides evidence that the correct modelis solved.

I Prediction: use of computational model to foretell the stateof a physical system under consideration under conditionsfor which the computational model has not been validated

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Role of Verification and Validation

MathematicalModel

ComputerImplementationDiscrete Mathematics

Continuum Mathematics

Programming

Analysis

Code Verification

SimulationComputer

ValidationModel

Model Discovery

and Building

Knowledge aboutReality

Oberkampf et al. Oden et al.

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V&V for ESSI Modeling and Simulations

I Code Verification

I Material modeling and simulation (elastic, elastic-plastic...)

I Finite elements (solids, structural, special...)

I Solution advancement algorithms (static, dynamic...)

I Seismic input and radiation

I Finite element model verification

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Constitutive Integration Error MapsNormalized error: δr =

√(σij − σ∗ij )(σij − σ∗ij )/

√σ0

pqσ0pq

SaniSand2004, rot. kinematic hardening, bounding surface:

0 50 100 150 2000

20

40

60

80

100

p (kPa)

q (k

Pa)

0.05

0.05

0.1

0.1

0.1

0.1

0.15

0.15

0.15

0.15

0.15

0.2

0.2

0.2

0.2

0.2

0.2

0.25

0.25

0.25

0.3

0.3

0.35

0.4

(a) At θ = 0

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

θ (rad)

q (k

Pa)

0.05 0.05

0.10.1

0.150.15

0.20.2

0.25

(b) At p = 100 kPa

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Material Model Validation (SanSand2004)

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Verification ANDES Shell: Static

1

2

3

4

5

...

Mesh

Test 1 Test 2 Test 3 Test 4

1

2

3

4

5

6

7

8

Mesh

Test 5 Test 6 Test 7 Test 8

Material parameters chosen such that the exact solution isuz = 100.000 T = 1.0 s.Nz = 2, uz = 96.212 ; Nz = 7, uz = 100.096

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Verification ANDES Shell: Dynamic

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Verification for 27 Node Brick

d =PL3

3EI=

9N× 1000m3

3× 100000Pa× 112 m4

= 0.36m

errors : 0.47% 3.96% 22%

for nodal offset: 40% error: 2%

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Shock Wave Propagation, Step Displacement

x

x = 0

Boundary Condition:δ (0, t) = 1 x 10-3 cm

ux = Ux = 1 x 10-3 cm

0.01 cm

4 cm ux , Ux

(10-3 cm)

t (sec)

1

Semi-finiteSoil column

No lateral flow.No lateral

displacements.0

(a) (b) (c)

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Shock Wave Propagation: Porous Solid, Pore Fluid

4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1

x 10‐3 FEM Vs Analytical Solution

t [10‐6 sec]

solid

displacem

ent (cm

)

FEM (k = 10‐5 cm3s/g)

FEM (k = 10‐6 cm3s/g)

FEM (k = 10‐8 cm3s/g)

Analytical Solution (k = 10‐5 cm3s/g)



4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

‐3 FEM Vs Analytical Solution

t [10‐6 sec]fluid displacemen

t (cm

)

FEM (k = 10‐5 cm3s/g)

FEM (k = 10‐6 cm3s/g)

FEM (k = 10‐8 cm3s/g)




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Verification for Dry Contact Element:Truss Model, Normal Displacement

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Solution Advancement(Newmark, Hilber-Hughes-Taylor)

I Variable integrationsteps sizes,parameters (α, β, γ)

I Compare withtheoreticalalgorithmic damping(spectral radius)and period shift

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8dt/T

0

2

4

6

8

10

12

14

ξ

Numerical damping ratio [%]

First mode

Second mode

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8dt/T

0

2

4

6

8

10

12

14

Tn−T

T

Relative Period Error

First mode

Second mode

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Seismic Body and Surface Waves

I Both body (P, SV and SH) and surface (Rayleigh, Love,etc.) waves are present

I Surface waves carry most seismic energy

I Analytic (Aki and Richards, Trifunac and Lee, Hisada et al.,fk, etc.) and numerically generated, 3D, inclined (plane)body and surface waves are used in tests

I Seismic moment from a point source at 2km depth used

I Stress drop at the source: Ricker and/or Ormsby wavelets

I Seismic input into FE model using the DRM (Bielak at al.)

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Plane Wave Model0m

0m

70m

240m

DRM Layer

2km10km

5km

x

y

xy

1

1

22

2km

0.2km

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Seismic Source Mechanics

Stress drop, Ormsby wavelet

-0.003

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0 1 2 3 4 5 6 7

Dis

plac

emen

t (m

)

Time (s)

0

5e-06

1e-05

1.5e-05

2e-05

2.5e-05

3e-05

3.5e-05

4e-05

4.5e-05

0 5 10 15 20

FF

T F

unct

ion

Am

plitu

de

Frequency (Hz)

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Middle (Structure Location) Plane, Top 2km

2km10km

5km

x

y

xy

1

1

22

2km

0.2km

0 0 2 4 6 8 10 12

Time (s)

0.2 m/s2

z=3000m

z=3200m

z=3400m

z=3600m

z=3800m

z=4000m

z=4200m

z=4400m

z=4600m

z=4800m

z=5000m

0 0 2 4 6 8 10 12

Time (s)

0.2 m/s2

z=3000m

z=3200m

z=3400m

z=3600m

z=3800m

z=4000m

z=4200m

z=4400m

z=4600m

z=4800m

z=5000m

horizontal accelerations vertical accelerations

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Verification: Displacements, Top Middle Point

(X) (Z)

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0 2 4 6 8 10 12

Dis

plac

emen

t (m

)

Time (s)

DRMFault Slip Model

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0 2 4 6 8 10 12D

ispl

acem

ent (

m)

Time (s)

DRMFault Slip Model

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Verification: Disp. and Acc., Out of DRM

Displacement Acceleration

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0 2 4 6 8 10 12

Dis

plac

emen

t (m

)

Time (s)

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 2 4 6 8 10 12A

ccel

erat

ion

(m/s

2 )Time (s)

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Select Examples: Foundation Slip and Stochastic

Outline



Summary

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Influence of Inelastic Foundation-Soil/Rock Contact onthe NPP Response

I Soil/rock – foundation interface slip behavior

I Changes in Earthquake Soil/Rock Structure Interaction(reduction or increase in demand)

I Dissipation of seismic energy in the slip plane

I Passive (and active) base isolation

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Example Model, ESSI with Slip

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Full 3D (wave at 45o) Ricker Wavelet

-4

-3

-2

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4

Acc

eler

atio

n (m

/s2 )

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)

0m 5000m 10000m

5000m

0m

2000m

2000

m

Fault

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Acc. Response for a Full 3D (at 45◦) Ricker Wavelet

top X

-40

-20

0

20

40

0 1 2 3 4 5 6 7 8

Acc

eler

atio

n (m

/s2)

Time (s)

Slip BehaviorNo-slip Behavior

top Z

-40

-20

0

20

40

0 1 2 3 4 5 6 7 8

Acc

eler

atio

n (m

/s2)

Time (s)


bottom X

-40

-20

0

20

40

0 1 2 3 4 5 6 7 8

Acc

eler

atio

n (m

/s2)

Time (s)


bottom Z

-40

-20

0

20

40

0 1 2 3 4 5 6 7 8

Acc

eler

atio

n (m

/s2)

Time (s)


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FFT Response for a Full 3D (at 45◦) Ricker Wavelet

top X

0

1

2

3

4

5

6

0 5 10 15 20

FF

T A

mpl

itude

(m

s)

Frequency (Hz)


top Z

0

1

2

3

4

5

6

0 5 10 15 20

FF

T A

mpl

itude

(m

s)

Frequency (Hz)


bottom X

0

1

2

3

4

5

6

0 5 10 15 20

FF

T A

mpl

itude

(m

s)

Frequency (Hz)


bottom Z

0

1

2

3

4

5

6

0 5 10 15 20

FF

T A

mpl

itude

(m

s)

Frequency (Hz)


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SPT Based Determination of Young’s Modulus

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))Histogram of the residual (w.r.t the deterministic transformationequation) Young’s modulus, along with fitted probability densityfunction

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Uncertainty Propagation through Constitutive Eq.

I Incremental el–pl constitutive equation ∆σij = Dijkl∆εkl

Dijkl =

Del

ijkl for elastic

Delijkl −

DelijmnmmnnpqDel

pqkl

nrsDelrstumtu − ξ∗r∗

for elastic–plastic

I What if all (any) material parameters are uncertainI PEP and SEPFEM methods for spatially variable and point

uncertain material

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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 response

I Second-order exact to covariance of time (exact meanand variance)

I Any uncertain FEM problem (Mu + Cu + Ku = F) withI 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...

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Spectral Stochastic Elastic–Plastic FEM

I Minimizing norm of error of finite representation usingGalerkin technique (Ghanem and Spanos 2003):

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

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Full PDFs of all DOFs (and σij , εij , etc.)

I Stochastic Elastic-PlasticFinite Element Method(SEPFEM)

I Dynamic case

I Full PDF ateach time step ∆t

−400

0

200400

0

0.02

0.04

0.06

5

10

15

20

Tim

e (s

ec)

PDF

Displacement (mm)

−200

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PDF at each ∆t (say at 6 s)

−1000 −500 500 1000

0.0005

0.001

0.0015

0.002

0.0025

Displacement (mm)

PDF

Real Soil Data

Conservative Guess

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PDF→ CDF (Fragility) at 6 s

−1000 −500 500 1000

0.2

0.4

0.6

0.8

1

CD

F

Displacement (mm)

Real Soil DataConservative Guess

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Summary

I High fidelity, extensive V & V, time domain, nonlinear,earthquake soil structure interaction (ESSI) modeling andsimulations (deterministic and probabilistic) for nuclearpower plant licensing and design

I The ESSI Simulator System (Program, Computer, Notes)

I Educational effort is essential (US-NRC, CNSC, IAEA,LBNL, INL, companies), seminars, short courses

I Funding from the US-NRC, US-DOE, US-NSF, and theCNSC is much appreciated

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Documents

Earthquake Soil Structure Interaction for Nuclear Power …sokocalo.engr.ucdavis.edu/~jeremic/€¦ · · 2013-06-13Motivation ESSI Simulator SystemSummary Earthquake Soil Structure