Modeling and Simulation of Earthquakes, Soils, …sokocalo.engr.ucdavis.edu/~jeremic/...analyze earthquakes, and/or soils and/or structures and their interaction (ESSI) Reduce modeling

Introduction Seismic Motions Inelasticity and Energy Dissipation Summary

Modeling and Simulation of Earthquakes,

Soils, Structures, and their Interaction

Boris Jeremic

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

ETH Seminar,

Zurich, Switzerland

May 2018

Jeremic et al.

MS ESSI


Outline

IntroductionMotivation

Seismic MotionsObservationsRegional Geophysical ModelsStress Test Motions

Inelasticity and Energy DissipationEnergy DissipationProbabilistic Inelastic ModelingDirect Solution for Probabilistic Stiffness and Stress in 1D

Summary

Jeremic et al.

MS ESSI


Motivation

Outline




Summary

Jeremic et al.

MS ESSI


Motivation

Motivation

Improve modeling and simulation for infrastructure objects

Use of high fidelity numerical modeling and simulation to

analyze earthquakes, and/or soils and/or structures and

their interaction (ESSI)

Reduce modeling uncertainty, perform desired level of

sophistication modeling and simulation

Follow evolution of parametric uncertainty

Le doute n’est pas un état bien agréable, mais l’assurance

est un état ridicule. (François-Marie Arouet, Voltaire)

Jeremic et al.

MS ESSI


Motivation

Earthquake Motions, 6C vs 3×1C vs 1C

◮ Danger of picking one component of motions (1C) from 3C

◮ Excellent (forced) fit, but not a prediction, information is lost

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MS ESSI


Motivation

6C vs 1C NPP ESSI Response Comparison

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Motivation

Elastic and Inelastic Response: Differences

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Motivation

Material Behavior Inherently Uncertain

◮ Spatial

variability

◮ Point-wise

uncertainty,

testing

error,

transformation

error

(Mayne et al. (2000)

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MS ESSI


Motivation

Parametric Uncertainty: Material and Loads

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

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

Jeremic et al.

MS ESSI


Motivation

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

Jeremic et al.

MS ESSI


Observations

Outline




Summary

Jeremic et al.

MS ESSI


Observations

3C (6C) Seismic Motions

◮ All (most) measured motions are full 3C (6C)

◮ Example of an almost 2D motion (LSST07, LSST12)

Jeremic et al.

MS ESSI


Observations

San Pablo Earthquake, 14Jun2017

Courtesy of http://www.strongmotioncenter.org/

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MS ESSI

http://www.strongmotioncenter.org/


Regional Geophysical Models

Outline




Summary

Jeremic et al.

MS ESSI




◮ High fidelity free field seismic motions on regional scale

◮ Knowledge of geology (deep and shallow) needed

◮ High Performance Computing using SW4 on CORI (LBNL)

◮ Collaboration with LLNL: Dr. Rodgers, Dr. Pitarka and

Dr. Petersson

Jeremic et al.

MS ESSI




Rodgers and Pitarka

Jeremic et al.

MS ESSI




USGS

Jeremic et al.

MS ESSI



Example Regional Model

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MS ESSI



Example Regional Model (Rodgers)

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MS ESSI



Seismic Motions: SW4 to MS-ESSI

ESSI nodes

SW42ESSI

1 2 31 2 3 , ,( ), , ,u u u θ θ θ

72m×72m×56m

36m embedded

300m ×300m ×100m

Grid spacing ～ 5m

ESSI Box

30km × 14km ×5 km

Jeremic et al.

MS ESSI


Stress Test Motions

Outline




Summary

Jeremic et al.

MS ESSI


Stress Test Motions

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

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

Jeremic et al.

MS ESSI


Stress Test Motions

Stress Test Source Signals◮ 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]

◮ 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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MS ESSI


Stress Test Motions

Layered and Dyke/Sill Models

◮ (a) Horizontal layers◮ (b) Dyke/Sill intrusion

◮ Source locations matrix (point sources)◮ Source strike and dip variation◮ Magnitude variations◮ Range of frequencies

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MS ESSI


Stress Test Motions

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

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MS ESSI


Stress Test Motions

Layered System, Variable Source Depth

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MS ESSI


Stress Test Motions

Dyke/Sill Intrusion, Variable Source Depth

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

Jeremic et al.

MS ESSI


Stress Test Motions

Dyke/Sill Intrusion, Variable Source Depth

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MS ESSI


Stress Test Motions

Dyke/Sill as Seismic Energy Sink

◮ Dyke/Sill (right Fig), made of stiff rock, is an energy sink,

as well as energy reflector◮ Variable wave lengths behave differently, depending on

dyke/sill geometry and location

Jeremic et al.

MS ESSI


Stress Test Motions

Plane Wave Stress Test Motions

◮ Plane wave stress test motions: 3D-6C (Haskel’s solution

for plane harmonic waves) and/or 3D-3×1C and/or 3D-1C

and or 1D-1C motions

◮ Knowledge of geology and the site is important

Jeremic et al.

MS ESSI


Stress Test Motions

Stress Test Motions

◮ Variation in inclination, frequency, energy and duration

◮ Try to "break" the system, shake-out strong and weak links

L oL w

L oL w

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MS ESSI


Stress Test Motions

Free Field, Variation in Input Wave Angle, f = 5Hz

(MP4)

Jeremic et al.

MS ESSI

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_inclination.mp4


Stress Test Motions

SMR ESSI, Variation in Input Wave Angle, f = 5Hz

(MP4)

Jeremic et al.

MS ESSI

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_4_inclindations.mp4


Stress Test Motions

Free Field, Variation in Input Frequency, θ = 60o

(MP4)

Jeremic et al.

MS ESSI

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4


Stress Test Motions

SMR ESSI, Variation in Input Frequency, θ = 60o

(MP4)

Jeremic et al.

MS ESSI

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4


Stress Test Motions

SMR ESSI, Variation in Input Frequency, REAL TIME

(MP4)

Jeremic et al.

MS ESSI

http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4


Stress Test Motions

3D wave effects - different frequencies

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

0.50

0.25

0.00

0.25

0.50

Ax [

g]

SMR Free field

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

60

30

0

30

60

Ax [

g]

SMR Free field

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

60

30

0

30

60

Ax [

g]

SMR Free field

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

0.50

0.25

0.00

0.25

0.50

Az [

g]

SMR Free field

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

60

30

0

30

60

Az [

g]

SMR Free field

0.0 0.2 0.4 0.6 0.8 1.0Time [s]

60

30

0

30

60

Az [

g]

SMR Free field

AB

C

Jeremic et al.

MS ESSI

Acceleration response - Surface center point A

X direction

Z direction

(a) f = 1Hz θ = 60o (b) f = 5Hz θ = 60o (c) f = 10Hz θ = 60o


Energy Dissipation

Outline




Summary

Jeremic et al.

MS ESSI


Energy Dissipation

Seismic Energy Input and Dissipation

Seismic energy input, through a closed boundary

Mechanical dissipation outside SSI domain:

Reflected wave radiation

SSI system oscillation radiation

Mechanical dissipation/conversion inside SSI domain:

Inelasticity of soil and contact zone

Inelasticity/damage of structure and foundation

Viscous coupling of fluids and soils and structure

Numerical energy dissipation/production

Jeremic et al.

MS ESSI


Energy Dissipation

Incremental Plastic Work: dWp = σij dǫplij

◮ Negative incremental energy dissipation◮ Plastic work is NOT plastic dissipation

Jeremic et al.

MS ESSI


Energy Dissipation

Negative Incremental Energy Dissipation!

Direct violation of the second law of thermodynamics

600 papers use Uang and Bertero (1990) and repeat their

error

Important form of energy missing: Plastic Free Energy

Observed by Farren and Taylor (1925) and explained by

Taylor and Quinney (1934)

Plastic Work vs. Plastic Energy Dissipation

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MS ESSI


Energy Dissipation

Energy Dissipation on Material Level

Single elastic-plastic element under cyclic shear loading

Difference between plastic work and dissipation

Plastic work can decrease, dissipation always increases

Jeremic et al.

MS ESSI


Energy Dissipation

Plastic Free Energy◮ Multi-scale effect of particle interlocking/rearrangement

◮ Strain energy on particle level

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Energy Dissipation

Energy Transformation in Elastic-Plastic Material

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Energy Dissipation

Energy Dissipation in Large-Scale Model (NPP)

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MS ESSI


Energy Dissipation

Energy Dissipation in Large-Scale Model (SMR)

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MS ESSI


Probabilistic Inelastic Modeling

Outline




Summary

Jeremic et al.

MS ESSI



Uncertainty Propagation through Inelastic System

◮ Incremental el–pl constitutive equation

∆σij = EEPijkl ∆ǫkl =

[

Eelijkl −

EelijmnmmnnpqEel

pqkl

nrsEelrstumtu − ξ∗h∗

]

∆ǫkl

◮ Dynamic Finite Elements

Mui + Cui + K epui = F (t)

◮ What if all (any) material and load parameters are

uncertain

Jeremic et al.

MS ESSI



Probabilistic Elastic-Plastic Response

Jeremic et al.

MS ESSI



3D FPK Equation

∂P(σij(xt , t), t)

∂t=

∂

∂σmn

[{⟨

ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t))

⟩

+

∫ t

0

dτCov0

[

∂ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t))

∂σab

;

ηab(σab(xt−τ , t − τ),Dabcd (xt−τ ), ǫcd (xt−τ , t − τ)

]}

P(σij(xt , t), t)

]

+∂2

∂σmn∂σab

[{∫ t

0

dτCov0

[

ηmn(σmn(xt , t),Dmnrs(xt), ǫrs(xt , t));

ηab(σab(xt−τ , t − τ),Dabcd (xt−τ ), ǫcd (xt−τ , t − τ))

]}

P(σij(xt , t), t)

]

Jeremic et al.

MS ESSI



FPK Equation

◮ Advection-diffusion equation

∂P(σ, t)

∂t= −

∂

∂σ

[

N(1)P(σ, t)−∂

∂σ

{

N(2)P(σ, t)}

]

◮ Complete probabilistic description of response

◮ Solution PDF is second-order exact to covariance of time

(exact mean and variance)

◮ It is deterministic equation in probability density space

◮ It is linear PDE in probability density space → simplifies

the numerical solution process

Jeremic et al.

MS ESSI


Direct Solution for Probabilistic Stiffness and Stress in 1D

Outline




Summary

Jeremic et al.

MS ESSI



Direct Probabilistic Constitutive Modeling in 1D

◮ Zero elastic region elasto-plasticity with stochastic

Armstrong-Frederick kinematic hardening

∆σ = Ha∆ǫ− crσ|∆ǫ|; Et = dσ/dǫ = Ha ± crσ

◮ Uncertain: init. stiff. Ha, shear strength Ha/cr , strain ∆ǫ:Ha = ΣhiΦi ; Cr = ΣciΦi ; ∆ǫ = Σ∆ǫiΦi

◮ Resulting stress and stiffness are also uncertain

Jeremic et al.

MS ESSI



Probabilistic Elastic-Plastic Modeling

Jeremic et al.

MS ESSI



Stochastic Elastic-Plastic Finite Element Method◮ Material uncertainty expanded into stochastic shape f-ion

◮ Loading uncertainty expanded into stochastic shape f-ion

◮ Displacement expanded into stochastic shape f-ion

◮ Time domain integration using Newmark and/or HHT, in

probabilistic spaces

∑Pdk=0

< ΦkΨ0Ψ0 > K (k) . . .∑Pd

k=0< ΦkΨPΨ0 > K (k)

∑Pdk=0

< ΦkΨ0Ψ1 > K (k) . . .∑Pd

k=0< ΦkΨPΨ1 > K (k)

.

.

.

.

.

.

.

.

.

.

.

.∑Pd

k=0< ΦkΨ0ΨP > K (k) . . .

∑Mk=0 < ΦkΨPΨP > K (k)

∆u10

.

.

.∆uN0

.

.

.∆u1Pu

.

.

.∆uNPu

=

∑Pfi=0

fi < Ψ0ζi >∑Pf

i=0fi < Ψ1ζi >

∑Pfi=0

fi < Ψ2ζi >

.

.

.∑Pf

i=0fi < ΨPu

ζi >

Jeremic et al.

MS ESSI



SEPFEM: System Size

◮ SEPFEM offers a complete solution (single step)

◮ It is NOT based on Monte Carlo approach

◮ System of equations does grow (!)

# KL terms material # KL terms load PC order displacement Total # terms per DoF

4 4 10 43758

4 4 20 3 108 105

4 4 30 48 903 492

6 6 10 646 646

6 6 20 225 792 840

6 6 30 1.1058 1010

8 8 10 5 311 735

8 8 20 7.3079 109

8 8 30 9.9149 1011

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

Jeremic et al.

MS ESSI



SEPFEM: Example in 1D

Jeremic et al.

MS ESSI


Outline




Summary

Jeremic et al.

MS ESSI


Summary

Importance of using proper models correctly (verification,

validation)

Availability of different levels of sophistication of modeling

is important for reduction of modeling uncertainty

Development of the MS-ESSI Simulator system

http://ms-essi.info

Collaborators: Feng, Abell, Han, Sinha, Wang, Lacour,

Pisanó, Kovacevic, McCallen, McKenna, Petrone, Rodgers

Funding from and collaboration with the US-DOE,

US-NRC, US-NSF, CNSC-CCSN, UN-IAEA, and Shimizu

Corp. is greatly appreciated,

Jeremic et al.

MS ESSI

http://ms-essi.info

Documents

Modeling and Simulation of Earthquakes, Soils, …sokocalo.engr.ucdavis.edu/~jeremic/...analyze earthquakes, and/or soils and/or structures and their interaction (ESSI) Reduce modeling