Site Specific Dynamics of Structures: From Seismic …sokocalo.engr.ucdavis.edu/~jeremic/ · Introduction Seismic Motions Inelasticity and Energy Dissipation Conclusion Site Speciﬁc

Introduction Seismic Motions Inelasticity and Energy Dissipation Conclusion

Site Specific Dynamics of Structures:From Seismic Source to the Safety of

Occupants and Content

Boris Jeremic

University of California, Davis, CALawrence Berkeley National Laboratory, Berkeley, CA

CompDyn2017Rodos, Greece

Jeremic et al.

Site Specific Dynamics of Structures


Outline

Introduction

Seismic MotionsObservations and Regional ModelsStress Test Motions

Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic Modeling

ConclusionSummary

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Motivation

Motivation

Improve seismic modeling and simulation for infrastructureobjects

Use of high fidelity numerical models to analyze seismicbehavior of soil structure systems

Reduction of modeling uncertainty, ability to performhigh(er) level of sophistication modeling and simulation

Accurately follow the flow of seismic energy in a soilstructure system

Personalization of the seismic problem

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Motivation

Seismic Hazard, World

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Motivation

Seismic Hazard, Rhodes

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Motivation

Seismic Hazard, USA

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Motivation

Seismic Hazard, DOE Facilities

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Observations and Regional Models

Outline

Introduction



ConclusionSummary

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3D (6D) Seismic Motions

I All (most) measured motions are full 3D (6D)I One example of an almost 2D motion (LSST07, LSST12)

I 1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017

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Regional Geophysical Models

I High fidelity free field seismic motions on regional scale

I Knowledge of geology (deep and shallow) needed

I High Performance Computing using SW4 on CORI (LBNL)

I Collaboration with LLNL: Dr. Rodgers, Dr. Pitarka andDr. Petersson

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Rodgers and PitarkaJeremic et al.





USGS

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Example Regional Model

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Example Regional Model (Rodgers)

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Seismic Motions: SW4 to Real ESSI

ESSI nodes

SW42ESSI

1 2 31 2 3 , ,( ), , ,u u u

72m×72m×56m36m embedded

300m ×300m ×100mGrid spacing ～ 5m

ESSI Box

30km × 14km ×5 km

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Dynamic Response of an Important Object (NPP)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linerar_Effects.mp4


Stress Test Motions

Outline

Introduction



ConclusionSummary

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Stress Test Motions

Stress Testing SSI SystemsI Excite SSI system with a suite of seismic motionsI Simple sources, variation in strike and dip, P and S waves,

surface waves (Rayleigh, Love, etc.)I Stress test soil-structure systemI Try to "break" the system, shake-out strong and weak links

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Stress Test Motions

Stress Test Source SignalsI Ricker

-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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Stress Test Motions

Layered and Dyke/Sill Models

I (a) Horizontal layersI (b) Dyke/Sill intrusion

I Source locations matrix (point sources)I Source strike and dip variationI Magnitude variationsI Range of frequencies

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Stress Test Motions

Layered System, Displacement TracesI Epicenter is 2500m away from the location of interestI Source depth 850m (left) and 2500m (right)I Different wave propagation path to the point of interestI Surface waves quite pronouncedI Layered geology did not filter out surface waves

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Stress Test Motions

Layered System, Variable Source Depth

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Layered_and_Dyke/Layered_850_ff.mp4

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Layered_and_Dyke/Layered_2500_ff.mp4


Stress Test Motions

Dyke/Sill Intrusion, Variable Source Depth

I Lower amplitudes than with layered only model!I Difference in body and surface wave arrivalsI Surface waves present, more complicated wave field

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Stress Test Motions

Dyke/Sill Intrusion, Variable Source Depth

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Layered_and_Dyke/Dyke_850_ff.mp4

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Layered_and_Dyke/Dyke_2500_ff.mp4


Stress Test Motions

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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Energy Dissipation

Outline

Introduction



ConclusionSummary

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Energy Dissipation

Seismic Energy Input and Dissipation

Seismic energy input, through a closed boundary (DRM)

Mechanical dissipation outside SSI domain:Reflected wave radiationSSI system oscillation radiation

Mechanical dissipation/conversion inside SSI domain:Inelasticity of soil and contact zoneInelasticity/damage of structure and foundationViscous coupling of fluids and soils and structure

Numerical energy dissipation/production

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Energy Dissipation

Incremental Plastic Work: dWp = σij dεplij

I Negative incremental energy dissipationI Plastic work is NOT plastic dissipation

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Energy Dissipation

Negative Incremental Energy Dissipation!

Direct violation of the second law of thermodynamics

600 papers since 1990 (!?!) repeat this error

Important form of energy missing: Plastic Free Energy

First described by Taylor and Quinney in 1934!

Plastic Work vs. Plastic Energy Dissipation

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Energy Dissipation

Energy Dissipation on Material LevelSingle elastic-plastic element under cyclic shear loading

Difference between plastic work and dissipationPlastic work can decrease, dissipation always increases

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Energy Dissipation

Energy Dissipation in a Large-Scale Model (NPP)

0

500

1000

1500

2000

2500

3000

0 10 20 30 40

Ener

gy D

ensi

ty [

J/m

3]

Time [s]

Energy Dissipation due toMaterial (Soil) Plasticity

Energy Dissipation in Contact Zone

Plastic Free Energy

Kinetic and Strain Energy

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Energy Dissipation

Energy Dissipation in Large-Scale Model (NPP)Elastoplastic soil with contact elements

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_with_Contact_vonMises.mp4


Energy Dissipation

Energy Dissipation in Large-Scale Model (SMR)

0

500

1000

1500

2000

2500

3000

0 5 10 15 20

Ener

gy D

ensi

ty [

J/m

3]

Time [s]

KE+SE+PF+PD

SE+PF+PD

PF+PD

PD

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Energy Dissipation

Energy Dissipation in Large-Scale Model (SMR)

Elastoplastic soil without contact elements

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_without_Contact_vonMises.mp4


Probabilistic Inelastic Modeling

Outline

Introduction



ConclusionSummary

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Parametric Uncertainty: Material and LoadsI Significant uncertainty in material and loadsI Propagate uncertainties in space and time

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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Stochastic Elastic-Plastic Finite Element Method(SEPFEM)

Material uncertainty expanded along stochastic shapefunctions: D(x , t , θ) =

∑Pdi=0 ri(x , t) ∗ Φi [{ξ1, ..., ξm}]

Loading uncertainty expanded along stochastic shapefunctions: f (x , t , θ) =

∑Pfi=0 fi(x , t) ∗ ζi [{ξm+1, ..., ξf ]

Displacement expanded along stochastic shape functions:u(x , t , θ) =

∑Pui=0 ui(x , t) ∗Ψi [{ξ1, ..., ξm, ξm+1, ..., ξf}]

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SEPFEM : FormulationStochastic system of equation resulting from Galerkin approach

∑Pdk=0 < Φk Ψ0Ψ0 > K (k) . . .

∑Pdk=0 < Φk ΨP Ψ0 > K (k)∑Pd

k=0 < Φk Ψ0Ψ1 > K (k) . . .∑Pd

k=0 < Φk ΨP Ψ1 > K (k)

.

.

....

.

.

....∑Pd

k=0 < Φk Ψ0ΨP > K (k) . . .∑M

k=0 < Φk ΨP ΨP > K (k)

u10...

uN0...

u1Pu...

uNPu

=

∑Pfi=0 fi < Ψ0ζi >∑Pfi=0 fi < Ψ1ζi >∑Pfi=0 fi < Ψ2ζi >

.

.

.∑Pfi=0 fi < ΨPu ζi >

# KL terms material # KL terms load PC order displacement Total # terms per DoF4 4 10 437584 4 20 3 108 1054 4 30 48 903 4926 6 10 646 6466 6 20 225 792 8406 6 30 1.1058 1010

... ... ... ...

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SEPFEM : Probabilistic Elastic-Plastic Modeling

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4



SEPFEM : Example in 1D

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4



SEPFEM : Example in 3D

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SFEM_Animation_3D.mp4


Summary

Outline

Introduction



ConclusionSummary

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Summary

US-DOE Project for ESSI of Nuclear FacilitiesThe Real ESSI Simulator (inelastic, deterministic andprobabilistic, time domain, 3D FEM)Modeling from seismic source to NPP (SW4, Real ESSI)Extensive Verification (NQA-1, ISO), and Validation

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Summary

SummaryImportance of using proper models correctly (verification,validation, level of sophistication)

Personalization of the Earthquake Soil StructureInteraction (ESSI) problem

Development of the Real ESSI Simulator systemhttp://real-essi.us

Collaborators: Feng, Lacour, Han, Behbehani, Sinha,Wang, Pisanó, Abell, McCallen, McKenna, Petrone,Rodgers, Petersson, Pitarka

Funding from and collaboration with the US-DOE,US-NRC, US-NSF, CNSC-CCSN, UN-IAEA, and ShimizuCorp. is greatly appreciated,

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http://real-essi.us

Documents

Site Specific Dynamics of Structures: From Seismic …sokocalo.engr.ucdavis.edu/~jeremic/ · Introduction Seismic Motions Inelasticity and Energy Dissipation Conclusion Site Speciﬁc