Effective-stress Based Dynamic Analysis and

Centrifuge Simulation of Earth Dam

Yii-Wen Pan1 Hui-Jung Wang1 C.W.W. Ng2

1National Chiao-Tung University

2Hong Kong University of Science and Technology

Contents Introduction Constitutive Model of Compacted Soil Numerical Analysis and Centrifuge Tests Comparison of Calculated and

Experimental Results Application Conclusions

• Objectives • Effective-stress modeling for earth dam• Verification by centrifuge models

• Purposes of dynamic analysis for earth dam• to evaluate dam response under earthquake

• Stress / Acceleration • Liquefaction Potential• Permanent deformation/settlement 

• Types of analysis• Total stress analysis• Effective stress analysis

Introduction Dynamic Stress Analysis for Earth Dam

Effective Stress Constitutive Models for Soil under Cyclic Loading

• v= f(, , No of cycles,…)• e.g., ： Martin-Finn (1975)

• dilatancy = f( stress state, state parameters,…)•e.g., Li et al. (2000)

Ueng and Lee (1990)

u = f(damage parameters)

u = f(k) or v = f (k) •e.g., Finn et al.(1981) endochronic model

Park(2000) disturbed state concept• Elasto-plastic model

•e.g., Manzari ＆ Dafalias (1997) , Prevost（ 1985 ）

Pastor et al, (1990), Iai et al. (2000)

Effective-stress BasedDynamic Analysis

FEM & FDM incorporating effective stress model appropriate for cyclic loadinge.g.,

Zienkiewicz, et al. (1981, 1984) Beaty and Byrne (1999) Dakoulas and Eltaher (1998) Ming and Li (2003) among others

Application on dynamic response of earth dam Simulation of failure case

e.g., Lower San Fernando Dam – built by hydraulic fill

Typical Behavior of heavily compacted fill

=10-3% =10-2% =10-1% ~1%

A Constitutive Model of Compacted Soil

Stress-strain relation1. Incrementally linear 2. Stress-level dependent3. Modulus degradation - disturbed state concept4. Irrecoverable dilatancy

AssumptionSaturated Soil

DSC ( Disturbed State Concept) Desai and co-workers (1991)

1. Disturbance due to external loading2. RI (Related Intact)FA (fully adjusted )

Follows a specific rule3. Separate Constitutive laws for RI ＆ FA

cia DD )1(

cd

id

ad D d D d ) 1(

Constitutive Relations

G

dqd i

3

Seed-Idriss formula (1970) 5.00(max)2max )(1000 KG

)(

0max

pGG

As Dd RI State :

FA State : As Dd

Along the failure line =M

KM

dq

G

dqd c

3Li and Dafalias (2000)

M

Intermediate state

For an arbitrary disturbed state (i.e., for 1>Dd

dq D

KM

dq

G

dqd

3

d

t GDKMd

GKMdG

3

Accounting for stress history

)1/()3

( Sd

t WGDKM

GKMG

qdWs

cd

id

ad D d D d ) 1(

Modeling Pore Water Pressure Build-

up

)()tan)((

'

a

ovd p

p

p

qC

: slope of phase transformation line tanC & : material parameters

: shear strain incrementvd

: plastic volumetric strain

tvd Ku

Irrecoverable Dilatancy

Pore Water Pressure Build-up

1. Progressive yielding

2.

3. Stress history

4. Pore pressure build-up

Summary of Model

da D

KMd

dq

G

dqd

3

)(

R

Rd M

D

M)(

0max p

pGG

GK)21(3

)1(2

)1/()3

( Sd

t WGDKMd

GKMdG

qdWs

d

p

p

p

qC

avd

)()tan)(( 0

tvd Ku

'm

)( '0 mfG

Model BehaviorStress Path Stress-Strain

Pore Water Pressure Build-up

Calibration of Parameters

m

i

n

jijij WPWS

1 1

1)(

Type of parameters

Elastic Constants

Modulus Related

DilatancyCritical States

Parameters Kmax, Gmax β, λ , C,ω M, ψμ

m

i

n

jij

ij

ijijij

ij

ijij WPEP

PPEPWS

ES

PSESBest

1 1

22 )()(

m

i

n

jijij WPWS

1 1

1)(

• Calibration by optimization (through GA, Nonlinear)

• Objective function

• Parameters

Centrifuge Testing

Purposes Observation of the dynamic response of

model earth dam subjected to dynamic loadings

Verification of Numerical Model Centrifuge tests

Carried out in Hong Kong University of Science and Technology

Capacity : 400 g-tons Arm radius : about 4.2m Maximum centrifuge acceleration : 70g Shaker: max. shaking acceleration 40g

Model Embankment Dam

Detail of the model embankment dam in rectangular rigid container 712mm x 432mm x 440mm symmetrical slopes (slope ratio 1:2) height and base width : 190 mm and 660 mm Leighton-Buzzard sand with Dr=90% Carboxy methylcellulose (CMC) as the substituted pore fluid

(Dewoolkar et al 1999) to take time conflict of dynamic and diffusion problems i

nto account CMC is a water-soluble cellulose ether

odorless, harmless, use in food & pharmacy

Installed miniature sensors:accelometers, pore pressure transducers , LVDTs, Laser sensors

60

660

712

150

440

46 46

LS-h1

LS-h2

LVDT

Laser sensor

ACC3ACC7 ACC6

ACC2

PPT3PPT7

PPT1

PPT2

PPT6

ACC1

1:2 1:2

Laser sensor

Unit: mm

CMC solution

Camera

ACCb-X,Y,ZACCb1-X

ACC5PPT5 PPT4ACC4

1040

5050

120 120

75 75

X

Z

Model Embankment Dam

Triaxial Tests Purpose:

Calibration of parameters for the material as same as the model embankment dam (Dr=90%)

Types of Test Cyclic triaxial tests

Stress controlled cyclic triaxial tests c=0.3 、 0.5 、 1kg/cm2

Monotonic CU tests c= 0.3 、 0.5 、 1 kg/cm2

                      

 

Dam Construction Modeling

Static Stress Analysis Modeling

 

Seepage Analysis(obtain steady state phreatic surface)

Stress Analysis after Steady State Seepage

(static equilibrium after steady state seepage)

Dynamic Analysis(in time domain)

                      

Effective Stress Based Numerical Analysis

60

660

712

150

440

46 46

LS-h1

LS-h2

LVDT

Laser sensor

ACC3ACC7 ACC6

ACC2

PPT3PPT7

PPT1

PPT2

PPT6

ACC1

1:2 1:2

Laser sensor

Unit: mm

CMC solution

Camera

ACCb-X,Y,ZACCb1-X

ACC5PPT5 PPT4ACC4

1040

5050

120 120

75 75

X

Z

Pore Water Pressure

0 0.5 1 1.5 2Tim e, s ec

0

20

40

60

80

Por

e P

ress

ure,

kP

a

M o de l E2 0 .13 g

P P T 1

P P T 2

P P T 7

P P (5 ,4 )

P P (5 ,5 )

P P (5 ,6 )

0 0.4 0.8 1.2 1.6 2Tim e, s ec

- 8

- 4

0

4

8

Acc

eler

atio

n, g

S im uM o d e l E2 0 .1 3 g

In p u t

Acceleration

0 0.5 1 1.5 2T im e, s ec

-12

-8

-4

0

4

8

12

Acc

eler

atio

n, g

M o d e l E2 0 .1 3 gA C C 1

0 0.4 0.8 1.2 1.6 2Tim e, s ec

-12

-8

-4

0

4

8

12

Acc

eler

atio

n, g

M o d e l E2 0 .1 3 gs im u A C C (5 ,3 )

0 0.4 0.8 1.2 1.6 2Tim e, s ec

-12

-8

-4

0

4

8

12

Acc

eler

atio

n, g

M o d e l E2 0 .1 3 gA C C 2

0 0.4 0.8 1.2 1.6 2Tim e, s ec

-12

-8

-4

0

4

8

12

Acc

eler

atio

n, g

M o d e l E2 0 .1 3 gs im u A C C 2

Settlement

0 0.4 0.8 1.2 1.6 2T im e, s ec

-0 .5

0

0.5

1

1.5

2

Set

tlem

ent,

mm

M o de l E2 0 .1 3gL V D T 2

L V D T 1

Y d isp (5 ,7 )

Application in Li-Yu-Tan Dam

Li-Yu-Tan Dam A well instrumented earth dam. Data was successfully recorded in Chi-Chi earthquake

Input motion in numerical simulation Using the recorded bedrock acceleration in Chi-Chi

earthquake Comparison of the numerical results and the

recorded data in Chi-Chi earthquake

Mesh

Vertical Stress

Horizontal Stress

Vertical Deformation

HorizontalDeformation

Results of Static Analysis

Pore WaterPressure

Steady-state Flow

Vertical Stress

Horizontal Stress

Vertical Deformation

HorizontalDeformation

Results of Dynamic AnalysisPore Water

Pressure

Vertical Stress

Horizontal Stress

Vertical Deformation

HorizontalDeformation

Acceleration history in bedrock & Crest

m/sec2

sec

Comparison of Numerical Results and Recorded Data

Maximum settlement Recorded settlement < 10 cm Calculated settlement ~10cm

Horizontal deformation Downstream slope moves toward

downstream, and vice versa Agree with the trend of instrumented data

Amplification of acceleration About 3 times at crest Close to the recorded data

Conclusions Heavily compacted fill in an earth dam behaves

like a very dense soil. An effective stress based constitutive model for

compacted fill was proposed. This model takes into account

Progressive degradation Stress-level dependency Effects of stress history & Stress history Pore water pressure build-up

Conclusions (con’d) A numerical model for an effective stress based

analysis was developed for dynamic analysis of earth dam verified by the results of centrifuge tests

Effective stress analysis for a well instrumented earth dam

using the Chi-Chi earthquake data numerical and instrumented results were consistent

Thank youfor

Attention