High Fidelity Modeling and Simulation of SFS …sokocalo.engr.ucdavis.edu/~jeremic/...High Fidelity Modeling and Simulation of SFS Interaction: Energy Dissipation by Design Boris Jeremi´c

Motivation Seismic Energy Flow Energy Dissipation Examples Summary

High Fidelity Modeling and Simulation ofSFS Interaction:

Energy Dissipation by Design

Boris Jeremicwith contributions by

Nima Tafazzoli (UCD), Guanzhou Jie (Wachovia Corp), MahdiTaiebat (UBC), Zhao Cheng (EarthMechanics Inc.)

CompGeoMech group, CEE Dept. UCD

SFSI Auckland, NZ

Boris Jeremic Computational Geomechanics Group

High Fidelity Modeling and Simulation of SFS Interaction: Energy Dissipation by Design


Outline

Motivation

Seismic Energy FlowInputDissipation

Energy Dissipation ExamplesSoft SoilLiquefaction

Summary




Motivation

Motivation

I Improving seismic design for infrastructure objects

I Use of high fidelity numerical models in analyzing seismicbehavior of soil–structure systems

I Accurately (high fidelity modeling and simulations)following the flow of seismic energy in the soil–structuresystem

I Directing, in space and time, seismic energy flow in thesoil–structure system




Motivation

Hypothesis

I Interplay of Earthquake with Soil and Structure (ESS) intime domain plays major role in failures (and successes).

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), we could optimizesoil–structure system for

I Safety andI Economy




Motivation

The Very First Published Work on SFSI

I Professor Kyoji SuyehiroI Ship engineer (Professor of Naval Arch. at U. of Tokyo),I Witnessed Great Kanto earthquake (Tokyo, 1st. Sept.

1923 11:58am(7.5), 12:01pm(7.3), 12.03pm(7.2), shakinguntil 12:08pm)

I Saw earthquake surface waves travel and buildings swayI Became founding Director of the Earthquake Engineering

Research Institute at the Univ. of Tokyo),I Published records show four times more damage to soft

wooden buildings on soft ground then same buildings onstiff soil




Motivation

Predictive Capabilities

I Verification provides evidence that the model is solvedcorrectly. 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: Develop predictive capabilities with low KolmogorovComplexity




Input

Seismic Energy Source

I Large energy releases,I Northridge, 1994, MRichter = 6.7, Er = 6.8× 1016JI Loma Prieta, 1989, MRichter = 6.9, Er = 1.1× 1017JI Sumatra-Andaman, 2004, MRichter = 9.3, Er = 4.8× 1020JI Valdivia, Chile, 1960, MRichter = 9.5, Er = 7.5× 1020J

I Part that energy is radiated as waves (≈ 1.6× 10−5) andmakes it to the surface

I For comparison, specific energy of TNT is 4.2× 106J/kg.




Input

Seismic Energy Input Into the SFS SystemI Kinetic energy flux through closed surface Γ includes both

incoming and outgoing waves (using Domain ReductionMethod by Bielak et al.)

Eflux =[0;−MΩ+

be u0e − K Ω+

be u0e ; MΩ+

eb u0b + K Ω+

eb u0b

]i× ui

I Alternatively, Eflux = ρAc∫ t

0 u2i dt

I Outgoing kinetic energyis obtained from outgoingwave field (wi , in DRM)

I Incoming kinetic energyis then the difference.

0ub

ui0

Pe(t)

Ω+

0ue

0ue Γe

Γ +

Local feature

Γ

Ω




Dissipation

Seismic Energy Dissipation for Soil–Structure Systems

I Mechanical dissipation outside of SFS domain:I wave reflectionI SFS system oscillation radiation

I Mechanical dissipation/conversion inside SFS domain:I plasticity of soil (different subdomains)I viscous coupling of porous solid with pore fluid (air, water)I plasticity/damage of the structure (different parts)I viscous coupling of structure with surrounding fluidsI potential←→ kinetic energy

I Numerical energy dissipation/production




Dissipation

Energy Dissipation by Plasticity

I Plastic work (W =∫

σijdεplij )

I Energy dissipation 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




Dissipation

Energy Disipation by Viscous CouplingI Viscous coupling of porous solid and fluidI Energy loss per unit volume is Evc = n2k−1(Ui − ui)

2

I Natural in u − p − U formulation:

24 (Ms)KijL 0 00 0 00 0 (Mf )KijL

35264 uLj

pN

ULj

375 +

24 (C1)KijL 0 −(C2)KijL

0 0 0−(C2)LjiK 0 (C3)KijL

35264 uLj

pN

ULj

375+

24 (K EP)KijL −(G1)KiM 0−(G1)LjM −PMN −(G2)LjM

0 −(G2)KiL 0

35 24 uLj

pMULj

35 =

264 fsolidKi

0f

fluidKi

375(C(1,2,3))KijL =

ZΩ

N(u,u,U)K n2k−1

ij N(u,U,U)L dΩ




Dissipation

Numerical Energy Dissipation

I Newmark and Hilber–Hughes–Taylor can be madenon–dissipative for elastic systemα = 0.0, β = 0.25; γ = 0.5,

I Or dissipative (for elastic) for higher frequency modes:I N: γ ≥ 0.5, β = 0.25(γ + 0.5)2,I HHT: −0.33 ≤ α ≤ 0, γ = 0.5(1− 2α), β = 0.25(1− α)2

I For nonlinear problems, energy cannot be maintainedI Energy dissipation for steps with reduction of stiffnessI Energy production for steps with increase of stiffness

ui

Re

ui

Re




Soft Soil

Earthquake–Soil–Bridge SystemI Inelastic soils (el–pl, Armstrong-Frederick, stiff and soft),

inelastic structure (columns), inelastic piles, DRM forseismic input,

I Construction processI Deconvolution of surface ground motionsI No artificial damping,

only plastic dissipationand radiation

I Plastic DomainDecomposition Methodfor parallel computing

I 1.6 M DOFs(15cm element size)




Soft Soil

Northridge and Kocaeli Input Motions

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)

0 5 10 15 20 25 30 35

−2

0

2

Time (s)

Acc

eler

atio

n (m

/s2 ) Acceleration Time Series − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

0 5 10 15 20 25 30 35−0.4

−0.2

0

0.2

Time (s)

Dis

plac

emen

t (m

) Displacement Time Series − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)




Soft Soil

Northridge Energy: Strain (dissipated) and Kinetic

0 5 10 15 20 25−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)

SSS CCC

0 5 10 15 20 250

0.05

0.1

0.15

0.2

Time [s]

Relat

ive V

elocit

y Ene

rgy [

J/kg]

CCCSSS




Soft Soil

Kocaeli Energy: Strain (dissipated) and Kinetic

0 5 10 15 20 25 30 35−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)

SSS CCC

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time [s]

Rel

ativ

e V

eloc

ity E

nerg

y [J

/kg]

CCCSSS




Liquefaction

Uniform and Layered Soils

medium dense

(e=0.80)

medium dense

(e=0.80)

loose

(e=0.96,0.875)




Liquefaction

Acceleration Time History




Liquefaction

Kinetic Energy at the Surface

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

Time [s]

Ene

rgy

(Lay

ered

) [J/

kg]

UniformLayered




Summary

I Interplay of Earthquake, Soil and Structure in timedomain plays a decisive role in catastrophic failures andgreat successes

I Opportunity to improve design through high fidelitysimulations: design, direct the flow of seismic energy inthe SFS systems

I Ability to direct seismic energy flow, in space and time,for a complete SFS system will lead to an increase insafety and economy

I Public domain tools, such as FEI andwww.OpenHazards.com



www.OpenHazards.com

Documents

High Fidelity Modeling and Simulation of SFS …sokocalo.engr.ucdavis.edu/~jeremic/...High Fidelity Modeling and Simulation of SFS Interaction: Energy Dissipation by Design Boris Jeremi´c