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A Cyclic Constitutive Model for Earthquake Response Analysis Kangwon National University KIM, Yong-Seong

Earthquake Response Analysis

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Page 1: Earthquake Response Analysis

A Cyclic Constitutive Model forEarthquake Response Analysis

Kangwon National UniversityKIM, Yong-Seong

Page 2: Earthquake Response Analysis

1. IntroductionThe 1995 Hyogo-ken Nambu Earthquake

Page 3: Earthquake Response Analysis

The 1995 Hyogo-ken Nambu Earthquake

Railway

Wharf Facilities

Page 4: Earthquake Response Analysis

sand

clay

claysand

liquefaction ?

amplification or damping of earthquake motion?earthquake

The 1995 Hyogo-ken Nambu Earthquake

Page 5: Earthquake Response Analysis

Up to now

sand layer :

elasto-plastic model

clay layer :

elastic model

Cyclic Viscoelasto-viscoplastic model for clay besed on non-linear kinematic hardening rule

time dependent characteristics of clay in wide range of strain

Cyclic Model for Earthquake Response Analysis

1964 Niigata Earthquake

Page 6: Earthquake Response Analysis

Three elements viscoelastic model

(Voigt model + linear elastic spring)

Kondner and Ho (1965) : dynamic behavior of clay Hori (1974) : Wave propagation test for sandy soil and clay Murayama (1983) : Distribution of relaxation time di Benedetto and Tatsuoka (1997) : Sand, soft rock

2. Review of Previous Studies

Page 7: Earthquake Response Analysis

Viscoelastic - Viscoplastic Model

Small

viscoelastic

viscoplastic

Strain level

Large

cyclic viscoplastic model

viscoelastic3 parameter model

G1

G2

Infinitesimal

3. Cyclic Viscoelastic-Viscoplstic Model

Page 8: Earthquake Response Analysis
Page 9: Earthquake Response Analysis

Elastic Component

3 Elements Viscoelastic Component

Voigt Viscoelastic Component

Page 10: Earthquake Response Analysis

Formulation of Viscoplastic Component

Overconsolidation Boundary Surface

Page 11: Earthquake Response Analysis

Static Yield Function

Evolutional Law of *ij

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Plastic Potential Function

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Flow Rule

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A Proposed Cyclic Viscoelastic and Viscoplastic Constitutive Model

Three elements viscoelastic model+

Cyclic viscoplastic model

Page 15: Earthquake Response Analysis

Cyclic Triaxial Deformation Tests

Page 16: Earthquake Response Analysis

0

4

8

12

16

20

Experiment(damping ratio)

Single amplitude axial strain, ( a)SA(%)

Hysteretic damping ratio, h(%)

1E- 3 0.01 0.10

40

80

120

160

200

Experiment(Young's modulus)

Equiv

alent

You

ng's

mod

ulus,

E eq(M

Pa)

T- 4, f=0.05(Hz)

Viscoelastic- viscoplastic Model

Elastic- viscoplastic Model

The results of the Cyclic Triaxial Deformation Test

Page 17: Earthquake Response Analysis

- 10 - 5 0 5

- 100

- 50

0

50

100

- 10 - 5 0 5

- 100

- 50

0

50

100

0 5 10 15- 150

- 100

- 50

0

50

100

150

- 15 - 10 - 5 0 5- 150

- 100

- 50

0

50

100

150

0 50 100 150 200 250- 150

- 100

- 50

0

50

100

150

- 5 0 5 10 15- 150

- 100

- 50

0

50

100

150

0 50 100 150 200 250- 150

- 100

- 50

0

50

100

150

- 15 - 10 - 5 0 5- 150

- 100

- 50

0

50

100

150

0 50 100 150 200 250- 150

- 100

- 50

0

50

100

150

0 50 100 150 200 250

- 100

- 50

0

50

100

0 50 100 150 200 250

- 100

- 50

0

50

100

0 50 100 150 200 250- 150

- 100

- 50

0

50

100

150

Nc : 22Simulation

Devia

tor s

tress

, q(k

Pa)

Axial strain, a(%)

No. of cycle : 22Experiment

Devia

tor s

tress

, q(k

Pa)

Axial strain, a(%)

Nc : 23Experiment

Devia

tor s

tress

,q(kP

a)

Axial strain, a(%)

Nc : 5Experiment

Devia

tor s

tress

, q(k

Pa)

Axial strain, a(%)

Nc : 5Experiment

Devia

tor s

tress

, q(k

Pa)

Mean effective stress, p'(kPa)

Nc : 23Simulation

Devia

tor s

tress

, q(k

Pa)

Axial strain, a(%)

Nc : 23Simulation

Devia

tor s

tress

, q(k

Pa)

Mean effective stress, p'(kPa)

Nc : 5Simulation

Devia

tor s

tress

, q(k

Pa)

Axial strain, a(%)

(b) Effective stess path

(b) Effective stess path

(b) Effective stess path

(a) Stress- strain relation

(a) Stress- strain relation

(a) Stress- strain relation

Nc : 5Simulation

Devia

tor s

tress

, q(k

Pa)

Mean effective stress, p'(kPa)

Nc : 22Experiment

Devia

tor s

tress

,q(kP

a)

Mean effective stress, p'(kPa)

Nc : 22Simulation

Devia

tor s

tress

, q(k

Pa)

Mean effective stress, p'(kPa)

Nc : 23Experiment

Devia

tor s

tress

, q(k

Pa)

Mean effective stress, p'(kPa)

T-1 (d/2c=0.268)

T-2 (d/2c=0.332)

T-3 (d/2c=0.324)

Page 18: Earthquake Response Analysis

4. Earthquake Response Analysis

LIQCA-2D(VE-VP) Effective stress analysis

based on infinitesimal strain theory u-p formulation FEM and FDM for the spatial discretization Newmark’s method for the time discretization A cyclic elasto-plastic model for sand A cyclic viscoelastic-viscoplastic model for clay

Page 19: Earthquake Response Analysis

Port Island 1995/01/18 Liquefied Area

Page 20: Earthquake Response Analysis

Kyoto

KobeOsaka

Port Island

Rokko Island

Page 21: Earthquake Response Analysis

Soil profile Finite element meshes

Page 22: Earthquake Response Analysis

Observed records during main shock at Port Island

(a) G.L. 0.0m (b) G.L. -83.0m

Input seismic wave

Page 23: Earthquake Response Analysis

Governing Equations Using u-p Formulation

Page 24: Earthquake Response Analysis
Page 25: Earthquake Response Analysis

0 5 10 15 20

-400

0

400

-400

0

400

Time (sec)

Acc

eler

atio

n (g

al)

VE-VP Model NS 32.0m Acc. Max. -437(gal)

Observed Record NS 32.0m Acc. Max. 543.594(gal)

E-VP Model NS 32.0m Acc. Max. -389(gal)

(c) Acceleration vs. time relations at 32.0m sand layer

Page 26: Earthquake Response Analysis

0 5 10 15 20

-400

0

400

-400

0

400

P

VE-VP Model NS 16.0m Acc. Max. -340(gal)

P

Time (sec)

Acc

eler

atio

n (g

al)

Observed Record NS 16.0m Acc. Max. 564.875(gal)

E-VP Model NS 16.0m Acc. Max. -351(gal)

(b) Acceleration vs. time relations at 16.0m sand layer

Page 27: Earthquake Response Analysis

0 5 10 15 20-400

-200

0

200

400-400

-200

0

200

400

Acc

eler

atio

n (g

al)

Time (sec)

VE-VP Model NS 0.0m Acc. Max. -242(gal)

Observed Record NS 0.0m Acc. Max. -341.219(gal)

E-VP Model NS 0.0m Acc. Max. -244(gal)

(a) Acceleration vs. time relations at 0.0m sand layer

Page 28: Earthquake Response Analysis

Maximum Value Distributions of Earthquake Response Analysis

Page 29: Earthquake Response Analysis

Excess Pore Water Pressure Ratio vs. Depth Relations

Page 30: Earthquake Response Analysis

Acceleration Response Calculated by E-VP and VE-VP Model

1995/01/17 05:53

After-Shock

G.L 0.0m sand layer

G.L -16.0m sand layer

G.L -32.0m sand layer

Page 31: Earthquake Response Analysis

0.0 2.5 5.0 7.5 10.0

-40

0

40

-40

0

40

NS component

VE-VP Model; Max. 59.9(gal)

Time (sec)

Acc

eler

atio

n (g

al)

NS component

Obtained record; Max. 63.625(gal)

Obtained record; Max. 63.625(gal)

E-VP Model; Max. 60.7(gal)

(c) Acceleration vs. time relations at 32.0m sand layer

Page 32: Earthquake Response Analysis

0.0 2.5 5.0 7.5 10.0

-30

0

30

-30

0

30

NS component

VE-VP Model; Max.-38.4(gal)

NS component

Obtained record; Max.-45.5(gal)

Acc

eler

atio

n (g

al)

Time (sec)

Obtained record; Max.-45.5(gal)

E-VP Model; Max.-51.5(gal)

(b) Acceleration vs. time relations at 16.0m sand layer

Page 33: Earthquake Response Analysis

0.0 2.5 5.0 7.5 10.0

-60

0

60

-60

0

60

NS component

VE-VP Model; Max. 63.7(gal)

Acc

eler

atio

n (g

al)

Time (sec)

NS component

Obtained record; Max. 79.188(gal)

Obtained record; Max. 79.188(gal)

E-VP Model; Max. 85.5(gal)

(a) Acceleration vs. time relations at 0.0m sand layer

Page 34: Earthquake Response Analysis

A Cyclic viscoelastic-viscoplastic model based on the non-linear kinematic hardening rule and three parameter theory was proposed.

The viscoelastic behavior of clay at the small strain range is an important characteristic during dynamic motion and the proposed model very well describes the viscoelastic behavior characteristics of cohesive soils in element simulations.

5. Conclusions

Page 35: Earthquake Response Analysis

The accelerations calculated from the proposed model were in close agreement with the recorded accelerations on the Port Island down-hole array.

This study reveals that the viscoelastic-viscoplastic model can describe the damping characteristics of clay accurately at small strain levels, whereas the elastic-viscoplastic model cannot do so.