Earthquake-Soil-Structure Systems - Boris Jeremicsokocalo.engr.ucdavis.edu/~jeremic/ Systems Boris...

Goals ESS Systems Uncertain Seismic Motions Summary

Earthquake-Soil-Structure Systems

Boris Jeremic and Sashi Kunnathwith

Kallol Sett and Nima Tafazzoli

Department of Civil and Environmental EngineeringUniversity of California, Davis

Boris Jeremic Structural/Geotechnical Engineering



Outline

Goals

ESS SystemsHigh Fidelity, 3D ModelsBehavior for Short and Long Period Motions

Uncertain Seismic MotionsConstitutive and Spatial UncertaintiesSeismic Wave Propagation Through Uncertain Soils

Summary




FocusI Steady progress in software and hardware allows high

fidelity, detailed performance assessment (simulations) ofcritical (and other) infrastructure systems (bridges, dams,buildings, ports...)

I Interplay of Earthquake Soil Structure systems seems toplay a major role in catastrophic failures (and successes)

I Quantify uncertainty and variablity in soil and structuralbehavior

I Provide methodology (formulation, implementation) forprobabilistic performance based engineering (PEER type)

I Overcome traditional performance assessmentapproaches used in engineering practice (design usingprescriptive code!)




Historical Note (Full Circle?)

I Soil–Structure Interaction phenomena first realized anddescribed by Professor Kyoji Suyehiro

I Ship engineer (Professor of Naval Arch. at U. of Tokyo),I Earthquake engineer (First Director of the Earthquake

Research Institute at U. of Tokyo),I Was in Tokyo during Great Kanto earthquake (11:58am

(–12:08pm! slow?), 1st. Sept. 1923)I Saw earthquake surface waves travel and buildings sway

(ships in the ocean)I Presented his new SSI work in the USA (Caltech, UCB,

Stanford, MIT) in 1931...I Slow and Fast earthquakesI Uncertainty and variability (source, material...)




High Fidelity, 3D Models

Outline

Goals



Summary





Detailed 3D, FEM modelI Construction processI Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)I Deconvolution of given surface ground motionsI Use of the DRM (Prof. Bielak et al.) for seismic inputI Piles → beam-column elements in soil holesI No artificial damping (only mat. dissipation, radiation)I Structural model: collaboration UCD, UCB and UWI Element size issues (filtering of frequencies)

model size (el) el. size fcutoff min. G/Gmax γ

12K 1.0 m 10 Hz 1.0 <0.5 %15K 0.9 m >3 Hz 0.08 1.0 %

150K 0.3 m 10 Hz 0.08 1.0 %500K 0.15 m 10 Hz 0.02 5.0 %





FEM Mesh (one of)

B. Jeremic and G. Jie. "Parallel Soil–Foundation–Structure Computations", Chapter in Book: Progress inComputational Dynamics and Earthquake Engineering; Taylor and Francis Publishers, 2008.





Parallel Computer GeoWulfI Distributed memory

parallel computerI Multiple generation

compute nodesand networks

I Very cost effective!I Same architecture as

large parallel supercomputers(SDSC, TACC, EarthSimulator...)

I Local design, construction,available at all times!




Behavior for Short and Long Period Motions

Outline

Goals



Summary





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)

1 2 3 4 5 6 7 8 9 100

1

2

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

0.2

0.4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)





Parametric Simulation Results

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)


0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)


0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)


0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

Period (s)

Fou

rier

Am

plitu

de (

m)


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Period (s)

Fou

rier

Am

plitu

de (

m)


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Period (s)

Fou

rier

Am

plitu

de (

m)


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

8

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

3.5

4

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)


0 10 20 30 40 50 60−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)






Northridge 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)

1 2 3 4 5 6 7 8 9 100

1

2

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

0.2

0.4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)





Short Period E.: Left Bent, Structure and Soil, Disp.

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)


0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)






Short Period E.: Left Bent, Structure and Soil, Acc.Sp.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )






Short Period E.: Left Bent, Structure and Soil, M.

0 5 10 15 20 25−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time (s)

Mom

ent (

kN*m

)

SSS CCC

B. Jeremic, G. Jie, M. Preisig and N. Tafazzoli. "Soil–Foundation–Structure Interaction in non–Uniform Soils", inreview in Earthquake Engineering and Structural Dynamics, 2008.





Kocaeli Input Motions

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)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)

2 4 6 8 10 12 14 16 18 200

2

4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999)





Long Period E.: Left Bent, Structure and Soil, M.

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




Constitutive and Spatial Uncertainties

Outline

Goals



Summary





Problem Setup

I Incr. 3D el–pl: dσij =

{Del

ijkl −Del

ijmnmmnnpqDelpqkl

nrsDelrstumtu − ξ∗r∗

}dεkl

I phase density ρ of σ(x , t) varies in time according to acontinuity Liouville equation (Kubo 1963)

I Continuity equation written in ensemble average form (eg.cumulant expansion method (Kavvas and Karakas 1996))

I van Kampen’s Lemma (van Kampen 1976) →< ρ(σ, t) >= P(σ, t), ensemble average of phase density isthe probability density





Eulerian–Lagrangian FPK Equation

∂P(σ(xt , t), t)∂t

= − ∂

∂σ

»fiη(σ(xt , t), Del(xt), q(xt), r(xt), ε(xt , t))

fl+

Z t

0dτCov0

»∂η(σ(xt , t), Del(xt), q(xt), r(xt), ε(xt , t))

∂σ;

η(σ(xt−τ , t − τ), Del(xt−τ ), q(xt−τ ), r(xt−τ ), ε(xt−τ , t − τ)

–ffP(σ(xt , t), t)

–+

∂2

∂σ2

»Z t

0dτCov0

»η(σ(xt , t), Del(xt), q(xt), r(xt), ε(xt , t));

η(σ(xt−τ , t − τ), Del(xt−τ ), q(xt−τ ), r(xt−τ ), ε(xt−τ , t − τ))

– ffP(σ(xt , t), t)

–

B. Jeremic, K. Sett, and M. L. Kavvas, "Probabilistic Elasto–Plasticity: Formulation in 1–D", Acta Geotechnica,Vol. 2, No. 3, pp 197-210, 2007.





Euler–Lagrange FPK EquationI Advection-diffusion equation

∂P(σ, t)∂t

= − ∂

∂σ

[N(1)P(σ, t)− ∂

∂σ

{N(2)P(σ, t)

}]I Complete probabilistic description of responseI Solution PDF is second-order exact to covariance of time

(exact mean and variance)I It is deterministic equation in probability density spaceI It is linear PDE in probability density space → Simplifies

the numerical solution processI Template FPK diffusion–advection equation is applicable to

any material model → only the coefficients N(1) and N(2)

are different for different material modelsK. Sett, B. Jeremic and M.L. Kavvas, "The Role of Nonlinear Hardening/Softening in Probabilistic Elasto–Plasticity",International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 31, No. 7, pp 953-975, 2007





Spectral Stochastic Elastic–Plastic FEMN∑

n=1

Kmndni +N∑

n=1

P∑j=0

dnj

M∑k=1

CijkK ′mnk = 〈Fmψi [{ξr}]〉

Kmn =

∫D

BnDBmdV K ′mnk =

∫D

Bn√λkhkBmdV

Cijk =⟨ξk (θ)ψi [{ξr}]ψj [{ξr}]

⟩Fm =

∫DφNmdV

I SFEM: Ghanem and Spanos 2003I Material variables random field represented through a finite

number of random variables using KL-expansionI Unknown solution random variables represented using

polynomial chaos of (known) input random variablesI Fokker–Planck–Kolmogorov approach based probabilistic

constitutive integration at Gauss integration pointsBoris Jeremic Structural/Geotechnical Engineering



Seismic Wave Propagation Through Uncertain Soils

Outline

Goals



Summary





“Uniform” CPT Site Data





Random Field Parameters from Site DataI Maximum likelihood estimates of correlation length

Typical CPT qT

Finite Scale

Fractal





Seismic Wave Propagation through Stochastic Soil

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





Surface Displacement Time History

0.5 1 1.5 2

−20

20

−10

10

Dis

plac

emen

t (m

m)

Time (s)

0.5 1 1.5 2

2

4

6

8

Dis

plac

emen

t (m

m)

Time (s)

Deterministic/Mean Standard Deviation





Mean ± Standard Deviation

0.5 1 1.52

−30

30

−20

−10

10

20

Time (s)

Displacement (mm)





PDF of Surface Displacement Time History

I PDF at the finiteelement nodes can beobtained using, e.g.,Edgeworth expansion(Ghanem and Spanos2003)

I Numerous applications,especially where extremestatistics are critical

−0.03−0.015

0.0150.03

0

150

300

450

Displacement (m)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00

Prob

abili

ty D

ensi

ty o

f D

ispl

acem

ent

Time (s)





Most Probable Solution

−0.01 0.01 0.02 0.03 0.04 0.05

20

40

60

80

100

Displacement (m)

PDF

Mode = 0.02 m

At t = 1.1 sec





Tails of PDF

−0.01 0.01 0.02 0.03 0.04 0.05

20

40

60

80

100

Displacement (m)

PDF

P[0.010 < Displacement < 0.012] = 0.01654

At t = 1.1 sec





Probability of Exceedance

0.01 0.02 0.03 0.04 0.05

0.2

0.4

0.6

0.8

1

Displacement (m)

CD

F

Probability that displacement exceeds 0.025 m = 1 − 0.825 = 0.175

At t = 1.1 sec





Derivative Applications

I Performance based engineeringI Reliability index (β)I Probability of damage and/or failure (pf )

Value of Load or Resistance

PD

F

Resistance

MeanModeLoad

PD

F

Margin

µMarginfp

Marginβσ

Margin = Reistance − Load

I Sensitivity analysisI Financial risk analysisI In general, useful for applications where mean, mode and

extreme statistics are important




Summary

I Steady progress in software and hardware allows for highfidelity Model Based Simulations for performanceassessment of infrastructure systems

I Interplay of Earthquake(s) with Soil and StructureSystems plays a major role in catastrophic failures (andsuccesses)

I Probabilistic performance based engineering (uncertaintyin soil and structural behavior, earthquake motions...)

I Overcome traditional performance assessmentapproaches used in engineering practice (design usingprescriptive code!)



Earthquake-Soil-Structure Systems - Boris Jeremicsokocalo.engr.ucdavis.edu/~jeremic/ Systems Boris...

Documents

Transcript of Earthquake-Soil-Structure Systems - Boris Jeremicsokocalo.engr.ucdavis.edu/~jeremic/ Systems Boris...