Dynamic Behaviour of Earth Dams for Variation of Earth Material Stiffness

8/7/2019 Dynamic Behaviour of Earth Dams for Variation of Earth Material Stiffness

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Abstract This paper presents a numerical analysis of the

seismic behaviour of earth dams. Analysis is conducted for thesolid phase. It may correspond to the response of the dambefore water filling. Analysis is conducted for a simple casewhich concerns the elastic response of the dam. Numericalanalyses are conducted using the FLAC D program. Thebehaviour of the Shell and core of the dam and the foundation

behaviour is assumed to be elastic. Result shows the influenceof the variation of the shear modulus of the core and shell onthe seismic amplification of the dam. It can be observed thatthe variation of the shearing modulus of the core leads to amoderate increase in the dynamic amplification and theincrease in the shell shearing modulus leads to a significantincrease in the dynamic amplification.

Keywords Numerical, earth dam, seismic, dynamic, core,FLAC D.

I.

INTRODUCTION

s eed et al [ ] reported that the seismic performance of embankment dam has been good in general, except whenliquefaction or unusual circumstances have been involved.They noted that a well-built compacted embankment dam canwithstand moderate earthquake shaking, with peak accelerations of g and more, with no detrimental effects.The efficiency of modern compacted embankment dams wasfurther demonstrated in when the Los AngelesReservoir, was severely shaken by the Northridge Earthquake[]. The seismic performance of embankment dams has beenclosely related to the nature and state of compaction of the fill

material [ , ]. Well-compacted modern dams can withstandsubstantial earthquake shaking with no detrimental effects.

F. Y. Parish, Ministry of Energy - The Institute for Energy and Hydro

Technology (IEHT) ,P.O. Box , Taavon Blvd. Shahr-e Ziba,Tehran, IRAN & Azerbaijan Higher Education Research Center, P.O. Box - , Tabriz Iran, e-mail: [email protected]

S. F. Najaei abadi, Ministry of Energy Water and Wastewater Companyof East Azerbaijan, Bahman Blvd, Tabriz Iran, e-mail:fah_ @yahoo.com

The most common method used in engineering practice toassess the seismic stability of earth fill dams consists on apseudo static approach where the earthquake effect on apotential soil mass is represented by means of equivalent statichorizontal force equal to the soil mass multiplied by a seismiccoefficient. This approach is based on several simplifiedassumptions neglecting the soil deformability, misestimatingtherefore of the earthquake effects on dams. Since the

San Fernando earthquake in California [ ], major progress hasbeen achieved in the understanding of earthquake action ondams. Progress in the area of geotechnical computation offersinteresting facilities for the analysis of the dam response inconsidering complex issues such as the soil plasticity, theevolution of the pore pressure during the dam constructionprocedure and real earthquake records.

This paper presents numerical study of the seismicbehaviour of earthfill dams. Analysis is conducted for thesolid phase using the finite difference program FLAC D [].It corresponds to the response of the dam before water filling.

The behaviour of the Shell and core of the dam isdescribed by equivalent-linear method. The equivalent-

linear method is common in earthquake engineering for modeling wave transmission in layered sites and dynamic soil-structure interaction. Since this method is widely used, and thefully nonlinear method embodied in FLAC D is not, it isworth pointing out some of the differences between the twomethods. In the equivalent-linear method (Seed and Idriss ), a linear analysis is performed, with some initial valuesassumed for damping ratio and shear modulus in the variousregions of the model.

The use of this model is justified by the difficulty toobtain constitutive parameters for more advanced constitutiverelations including both isotropic and kinematic hardening. Aparametric study is conducted for the investigation of the

mechanical role of shell and core and their interaction under adynamic loading.

II.

PROBLEM UNDER CONSIDERATION

The selected example is a simplified representation of typical earth dam geometry. The dam section assumed in thepresent survey is a symmetric zone section with clay core andfoundation as shown in Figure . The behaviour of the Shelland core of the dam is described by equivalent-linearmethod, while the foundation behaviour is assumed to beelastic and very stiff (E= MPa). Geotechnical properties

Dynamic Behaviour of Earth Dams for Variation of Earth Material Stiffness

Y. Parish and F. Najaei abadi


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used in the analyses are presented in Table for foundationsoil and earth dam materials. The materials properties thoughare chosen more close to reality. Numerical analyses areconducted using the finite difference FLAC D program basedon a continuum finite difference discretization using theLangrangian approach. Dynamic loading is applied at the baseof the foundation layer as a velocity excitation (Figure ). Theearth dam is subjected to earthquake loading representative of

the Kocaeli earthquake in Turkey witha magnitude Mw= ]]. The estimated peak velocity isapproximately cm/sec (peak acceleration g), and theduration is approximately sec. The record for baseacceleration, velocity, and displacement waves are shown inFigure a-b-c. Fourier analysis of the earthquake velocityrecord results in a power spectrum depicted in Figure d. Thevelocity spectrum reveals a dominant frequency of about Hz.

The natural frequencies of the foundation-dam systemwere determined by a Fourier analysis of the free response of the dam (Figure ). It shows a fundamental frequency f = Hz which is close to dominant frequency of seismic loading

(f= Hz); the second frequency is close to f = Hz.

Fig. Geometry of dam and the shape of zones (units inmeter)

TABLE IPROPERTIES FOR FOUNDATION AND EARTH DAM SOILS

Parameter Units Core Shell Foundation

Dry density ( ) (kg/m )

Youngs modulus (E) (MPa)

Poissons ratio ( )

Elastic shear modulus (G) (MPa)

Bulk modulus (K) (MPa)

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30

Time(sec)

Displacement (cm)

-40-30

-20-10

01020304050

0 5 10 15 20 25 30Time(sec)

Velocity (cm/sec)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 5 10 15 20 25 30Time(sec)

Acceleration (g)

0E+005E-05

1E-04

2E-04

2E-04

3E-04

3E-04

4E-04

0 0 .2

0 .4

0 .6

0 .8

1 1 .2

1 .4

1 .6

1 .8

2 2 .2

frequency(HZ)

spectral velocity (m/s)

Fig. Kocaeli earthquake record ( ) : a) Displacement, b)Velocity, c) Acceleration, d) Fourier Spectra of VelocityComponent


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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.7 1.4 2.1 2.8 3.5 4.2

frequency(HZ)

spectral velocity(m/s)

Fig. Response spectra of design free surface motion of thedam

III.

NALYSIS OF THE SEISMIC INDUCED RESPONSE IN THE DAM

The response of the dam at the maximum excitation ispresented in figure . It shows an increase in the lateralvelocity with the distance from the dam foundation. Thevariation of the lateral velocity in the horizontal directionseems to be low.

Figure shows the velocity amplification in the axis of thedam. It can be observed that the amplification increases withthe distance from the foundation; it attains at the top of the dam. Figure shows the variation of the lateralamplification in the horizontal direction at the middle heightof the dam and the crest. In the first section, we observe avariation in the dynamic amplification between and . Atthe crest, we observe a uniform distribution of theamplification (close to ).

Fig. Dam deformation at the maximum of excitation(Kocaeli earthquake record),(U max = m at the dam crest)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

v / V

h / H

Fig. Velocity amplification in the dam axis (Kocaeliearthquake record)


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0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1l / L

v / V

(Middle height)

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

l / L

v / V

(Dam crest)

Fig. Variation of the amplification in the horizontaldirection: a) At the middle height b) At the dam crest

IV.

MECHANICAL ROLE OF CORE AND SHELL

Analyses were also conducted for the Kocaeli earthquakerecord for:

Three values of the Youngs modulus of the core: E= , and MPa; G = ( , and MPa).

Three values of the Youngs modulus of the shell: E= , and MPa; G = ( , and MPa).

Three values of the Youngs modulus of thefoundation: E = , and MPa; G = ( , and MPa).

G=15 MPa G=23 MPa G=31 MPa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

v / V

h / H

(Velocity)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

a / A

h / H

(Acceleration)

Fig. Influence of the core stiffness on the seismic responseof the dam, (Kocaeli earthquake record)


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Figure shows the influence of the variation of the shear modulus of the core on the seismic amplification of the dam.It can be observed that this variation leads to a moderateincrease in the dynamic amplification. This increase resultsfrom the increase of the fundamental frequency of the damstowards the dominate frequency of the loading. The influenceof the variation of the shearing modulus of the shell on theseismic amplification in the dam is illustrated in figure . It

can be observed that the increase in the shell shearingmodulus leads to a significant increase in the dynamicamplification. This result is also expected, because theincrease in the shell shearing modulus leads to an increase inits fundamental frequency towards the frequency of the major peak of the input motion.

The influence of the variation of the shear modulus of thefoundation on the dynamic amplification is depicted in figure. It can be observed that an important variation of thisparameter ( ) slightly affects the seismic response of thedam.

G=11 MPa G=15 MPa G=23 Mpa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4

v / V

h / H

(Velocity)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

a / A

h / H

(Acceleration)

Figure : Influence of the shell stiffness on the seismicresponse of the dam , (Kocaeli earthquake record)

G=400 MPa G=300 MPa G=200 Mpa


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

v / V

h / H

(Velocity)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3

a / A

h / H

(Acceleration)

Fig. influence of the foundation stiffness on the seismicresponse of the dam , (Kocaeli earthquake record)

V.

CONCLUSIONS

This paper included a numerical analysis of the seismicbehaviour of earth dams. It corresponds to the response of thedam before water filling. Numerical simulations were

performed for real earthquake records using equivalent-linear method.

Elastic analyses show an increase in the lateral velocitywith the distance from the dam foundation. The variation of the lateral velocity in the horizontal direction seems to be low.Also, it can be observed that the amplification increases withthe distance from the foundation.

It can be observed that variation of the shear modulus of

the core on the seismic amplification of the dam leads to amoderate increase in the dynamic amplification. This increaseresults from the increase of the fundamental frequency of thedams towards the dominate frequency of the loading. Also,the increase in the shell shearing modulus leads to asignificant increase in the dynamic amplification. This resultis also expected, because the increase in the shell shearingmodulus leads to an increase in its fundamental frequencytowards the frequency of the major peak of the input motion.

R EFERENCES [ ]

[ ] H. B. Seed, F. I. Makdisi, P. De Alba, Performance of Earth DamsDuring Earthquakes, Journal of Geotechnical Engineering, AmericanSociety of Civil Engineers, Vol, , No. GT , pp. - , .

[ ]

[ ] H. B. Seed, Considerations in the Earthquake-Resistant Design of Earth and Rockfill Dams, th Rankine Lecture of the BritishGeotechnical Society, Geotechnique, Vol XXIX, No. , pp. - , .

[ ]

[ ] C.A. Davis, M.M. Sakado, Response of the Van Norman Complex tothe Northridge Earthquake, Association of Dam Safety OfficialsConference Proceedings, Boston, MA, pp - , .

[ ]

[ ] USCOLD (U.S. Committee on Large Dams), Observed Performanceof Dams during Earthquakes, Committee on Earthquakes, July, Denver,CO, .

[ ]

[ ] USCOLD (U.S. Committee on Large Dams), Observed Performanceof Dams during Earthquakes, vol. II, Committee on Earthquakes,October, Denver, CO, .

[ ]

[ ] HY. Ming, Li XS, Fully coupled analysis of failure and remediationof lower San Fernando dam, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, ( ), , .

[ ]

[ ] Itasca Consulting Group, FLAC: Fast Lagrangian Analysis of Continua, vol. I. User's Manual, vol. II. Verification Problems and Example Applications, Second Edition (FLAC D Version ),Minneapolis, Minnesota USA, .

[ ]

[ ] W.F. Chen, C. Scawthorn, Earthquake Engineering Handbook, CRC Press LLC, .

Dynamic Behaviour of Earth Dams for Variation of Earth Material Stiffness

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