earthquake soil structure interaction (essi) modeling and ...sokocalo.engr.ucdavis.edu/~jeremic/ ·...

Intro ESSI System ESSI Examples Summary

Earthquake Soil Structure Interaction(ESSI)

Modeling and Simulation

Boris Jeremic

Consulting Engineer, Jeremic Engineering ConsultantsProfessor, University of California, Davis

Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley

INL Steering Committee MeetingDecember 2013

Jeremic JEC

ESSI Modeling and Simulation


Outline

IntroMotivationFlow of Seismic EnergyModeling Uncertainty

ESSI SystemESSI Program

ESSI Examples3D, Inclined, Body and SurfaceModel Verification, Mesh Size EffectsSeismic Wave Propagation Through Uncertain Soils

Summary

Jeremic JEC



Motivation

Outline




Summary

Jeremic JEC



Motivation

Motivation

I Improving seismic design for Nuclear Power Plants (NPPs)

I Use of high fidelity numerical models for analyzing seismicbehavior of NPP soil structure interaction (SSI) system

I Accurately follow, and direct (!), in space and time, flow ofseismic energy through the NPP SSI system

Jeremic JEC



Motivation

Hypothesis

I Interplay of an Earthquake with Soil/Rock and Structure, intime domain, plays a major role in seismic responsesuccesses and failures.

I Timing and spatial location of energy dissipationdetermines location and amount of damage.

I If timing and spatial location of energy dissipation can becontrolled (directed, designed), NPP soil structure systemscan be optimized for

I Safety andI Economy

Jeremic JEC



Motivation

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

I Goal: physics based predictive capabilities with lowKolmogorov Complexity

I High Fidelity, hierarchical, predictive capabilities, aim forhigher modeling sophistication then needed

Jeremic JEC



Flow of Seismic Energy

Outline




Summary

Jeremic JEC




Seismic Energy Input and DissipationI Seismic energy influx through closed boundary

I Mechanical dissipation outside of NPP SSI domain:I reflected wave radiationI NPP SSI system oscillation radiation

I Mechanical dissipation inside NPP SSI domain:I plasticity of soil subdomainsI viscous coupling of porous solid with pore fluid (air, water)I plasticity/damage of the parts of structure/foundationI viscous coupling of structure/foundation with fluidsI potential←→ kinetic energy

I Numerical energy dissipation/production

Jeremic JEC




Energy Dissipation by Soil Plasticity

Energy dissipation (plastic work) capacity for different soils

0

10

20

30

40

50

60

0 2 4 6 8 10Shear Strain Cycle (%)

Ener

gy D

issi

pate

d (J

/m3 )

Loose SandSoft Clay

Dense Sand

Stiff Clay

Jeremic JEC



Modeling Uncertainty

Outline




Summary

Jeremic JEC





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)

Jeremic JEC




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))

Jeremic JEC




Complexity of and Uncertainty in Material ModelingI All engineering materials experience inelastic deformations

for working loads

I This is even more so for hazard loads (earthquakes)

I Pressure sensitive materials (soil, rock , concrete, etc) canhave very complex constitutive response, tying togethernonlinear stress-strain with volume response

I Simplistic material modeling (elastic, G/Gmax , etc.)introduce (significant) uncertainties in response results

I In addition, man-made and natural materials are spatiallyvariable and their material modeling parameters areuncertain

Jeremic JEC




Material Behavior Inherently Uncertain

I Spatialvariability

I Point-wiseuncertainty,testingerror,transformationerror

(Mayne et al. (2000)

Jeremic JEC




SPT Based Determination of Shear Strength

10 20 30 40

100

200

300

400

500

SPT N value

Su = (101.125*0.29) N 0.72

Und

rain

ed S

hear

Str

engt

h (k

Pa)

−300 −200 −100 0 100 200

0.002

0.004

0.006

0.008

0.01

Nor

mal

ized

Fre

quen

cy

Residual (w.r.t Mean) Undrained Shear Strength (kPa)

Transformation of SPT N-value→ un-drained shear strength,su (cf. Phoon and Kulhawy (1999B)Histogram of the residual (w.r.t the deterministic transformationequation) un-drained strength, along with fitted probabilitydensity function (Pearson IV)

Jeremic JEC




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

Jeremic JEC



ESSI Program

Outline




Summary

Jeremic JEC



ESSI Program

ESSI Simulator SystemI ESSI-Program is a 3D, nonlinear, time domain, parallel

finite element program specifically developed for Hi-Fimodeling and simulation of Earthquake Soil/Rock StructureInteraction of NPPs on ESSI-Computer.

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

I ESSI-Notes are a hypertext documentation system(Theory and Formulation, Software and Hardware,Verification and Validation, and Case Studies and PracticalExamples) detailing modeling and simulation of ESSIproblems.

Jeremic JEC



ESSI Program

ESSI 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, buoyant forces)

I Quad (ANDES) Shell (6DOFs per node)

I Beams (6DOFs and variable DOFs per node)

I Truss

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

I Base isolators (elastomeric, frictional pendulum)

Jeremic JEC



ESSI Program

ESSI Program: Material Models

I Linear and nonlinear, isotropic and anisotropic elastic

I Elastic-Plastic (von Mises, Drucker Prager, RoundedMohr-Coulomb, Parabolic Leon, Cam-Clay, SaniSand(Dafalias-Manzari), SaniClay, Pisanò...)

I All elastic-plastic models can be used as perfectly plastic,isotropic hardening/softening and kinematic hardeningmodels

Jeremic JEC



ESSI Program

ESSI Program: Seismic Input

I Analytic input of seismic motionsI Body waves (P, SH, SV)I Surface waves (Rayleigh, Love, etc.)I Analytic radiation damping

I Domain Reduction Method (Bielak et al.)

I Synthetic and realistic seismic motions (Hisada, fk, FEM,etc.)

Jeremic JEC



ESSI Program

ESSI Program: Verification and Validation

I Detailed Verification (math issue)I Finite elementsI Material modelI Solution algorithmsI Analysis procedureI Code documented in detail in ESSI Notes.

I (Not so) Detailed Validation (physics issue) (lack of highquality experimental data)

I Detailed V&V documentation in ESSI Notes

Jeremic JEC



ESSI Program

ESSI Program: High Performance Computing, Parallel

I Sequential computing: available for all models, however

I High Performance Parallel Computing: for high fidelitymodeling, parallel is really the only option. Parallel ESSIProgram available on

I Single, multi-core/multi-CPU PCs,I Clusters of (multi-core/multi-CPU) PCs,I Distributed memory parallel (DMP) supercomputers (all top

national supercomputers).

I Template metaprograms for local, element and materialmodel level high performance computing

Jeremic JEC



ESSI Program

ESSI Program: Probabilistic/StochasticI Constitutive: Fokker-Planck-Kolmogorov equation for

probabilistic elasto-plasticity (PEP)I Spatial: stochastic elastic plastic finite element method

(SEPFEM)I Uncertain: material (LHS) and loads (RHS):

MAacB ¨uBc + CAacB ˙uBc + K EPAacB uBc = FAa

I Results (ui , σij , εij) are very accurate (second orderaccurate for stress) Probability Density Functions (PDFs)

I PEP and SEPFEM are not based on a Monte Carlomethod,

I Uncertain input variables and uncertain DOFs areexpanded into spectral probabilistic spaces, single runsolution

Jeremic JEC



ESSI Program

Probabilistic Elastic-Plastic Response

Jeremic JEC



3D, Inclined, Body and Surface

Outline




Summary

Jeremic JEC




Earthquake Ground Motions

Realistic earthquake ground motions

I Body waves: P and S waves

I Inclined waves

I 3D (6D!) waves

I Surface waves: Rayleigh, Love waves, etc.

I Surface waves carry most seismic energy of interest

I Lack of correlation (incoherence)

Jeremic JEC




3D Synthetic Seismic Motions

I Development of analytic and numerical 3D, inclined,uncorrelated seismic motions for verification, stress testingof NPPs, etc.

I Large scale model

I Point shear source

I Stress drop:I Wavelet (Ricker,

Ormsby, etc)I Analytic

I Seismic input using DRM (Bielak et al (2003))

0m 5000m 10000m

5000m

0m

2000m

2000

m

Fault

Jeremic JEC




Plane Wave Model0m

0m

70m

240m

DRM Layer

2km10km

5km

x

y

xy

1

1

22

2km

0.2km

Jeremic JEC




Seismic Source Mechanics

Stress drop, Ormsby waveletcontrolled frequency range

-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)

Jeremic JEC




Middle (NPP 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

Jeremic JEC




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

Jeremic JEC




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)

Jeremic JEC



Model Verification, Mesh Size Effects

Outline




Summary

Jeremic JEC




Motion Filtering: Mesh Size EffectsI Finite element mesh "filters out"

high frequenciesI Usual rule of thumb: 10-12 elements

needed per wave lengthI 1D wave propagation modelI 3D finite elements (same in 3D)I Motions applied as displacements at the bottomI Linear elastic and elastic – linear hardening plastic material

case model height [m] Vs [m/s] El.size [m] fmax (10el) [Hz]3 1000 1000 10 104 1000 1000 20 56 1000 1000 50 2

Jeremic JEC




Ormsby Wavelet Input Motions

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0 0.5 1 1.5 2 2.5 3 3.5 4

Dis

plac

emen

t (m

)

Time [s]

Jeremic JEC




Linear Elastic Material: Surface Motions

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0 0.5 1 1.5 2 2.5 3 3.5 4

Dis

plac

emen

t (m

)

Time [s]

Element Size: 10m

Element Size: 20m

Element Size: 50m

Jeremic JEC




Linear Elastic Material, FFT of Input and SurfaceMotions

0

2e-05

4e-05

6e-05

8e-05

0.0001

0.00012

0.00014

0.00016

0 2 4 6 8 10

FF

T A

mpl

itud

e

Frequency [Hz]

Input MotionElement Size: 10mElement Size: 20mElement Size: 50m

Jeremic JEC




Elastic Plastic Material, Stress-Strain Response

Jeremic JEC




Elastic Plastic Material, Surface Response

Jeremic JEC



Seismic Wave Propagation Through Uncertain Soils

Outline




Summary

Jeremic JEC




"Uniform" CPT Site Data

Jeremic JEC




Random Field Parameters from Site Data

I Soil as 12.5 m deep 1–D soil column (von Mises Material)I Properties (including testing uncertainty) obtained through

random field modeling of CPT qT〈qT 〉 = 4.99 MPa; Var [qT ] = 25.67 MPa2;Cor. Length [qT ] = 0.61 m; Testing Error = 2.78 MPa2

I qT was transformed to obtain G: G/(1− ν) = 2.9qT

I Assumed transformation uncertainty = 5%〈G〉 = 11.57MPa; Var [G] = 142.32MPa2

Cor. Length [G] = 0.61m

I Input motions: modified 1938 Imperial Valley

Jeremic JEC




Decision About Site (Material) Characterization

I Do nothing about site characterization (rely onexperience): conservative guess of soil data,COV = 225%, correlation length = 12m.

I Do better than standard site characterization:COV = 103%, correlation length = 0.61m)

I Improve site (material) characterization if probabilities ofexceedance are unacceptable!

Jeremic JEC




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

Jeremic JEC




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

Jeremic JEC




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

Jeremic JEC



Summary

Current NPP Model(s)

I General 3D seismic wavesI Foundation slip – gapI Isolators, dissipatorsI Uncorrelated (incoherent) motionsI Saturated dense vs loose soil with buoyant forcesI Piles and pile groupsI Uncertain material (LHS) and seismic motions (RHS)

Jeremic JEC



Summary

Summary

I Interplay of uncertain earthquake, uncertain soil, anduncertain structure, in time domain, probably plays adecisive role in seismic performance of NPPs

I Improve risk informed decision making (design⇒safety and economy) through high fidelity, modeling andsimulation (ESSI Simulator System)

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

Jeremic JEC



Summary

Acknowledgement

I Funding from and collaboration with the US-NRC, US-NSF,US-DOE, CNSC, LLNL, INL, AREVA NP GmbH, ShimizuCorp., and EDF is greatly appreciated,

I Collaborators, students: Mr. Abell, Mr. Jeong, Mr. Aldridge.Mr. Kamranimoghadam, Mr. Karapiperis, Mr. Watanabe,Mr. Chao, Dr. Tafazzoli, Dr. Pisanò, Dr. Martinelli, Dr.Preisig, Dr. Chang, Prof. Sett (U. Bufallo), Prof. Taiebat (U.British Columbia), Prof. Yang (U. Alaska)

Jeremic JEC


earthquake soil structure interaction (essi) modeling and ...sokocalo.engr.ucdavis.edu/~jeremic/ ·...

Documents