static and dynamic analysis of rockiill dam using finite...

Pertanika J. Sci. & Techno!. 13(1): 31 - 42 (2005)ISSN: 0128-7680

© Universiti Putra Malaysia Press

Static and Dynamic Analysis of RockIill Dam UsingFinite-inrmite Element Method

IJ. Noorzaei, 2M. Karami, IWaleed A. Thanoon & 1M. S. Jaafar/Civil Engineering Department, Faculty of Engineering

Universiti Putra Malaysia, 43400 UPM, Selangor, Malaysia2post Graduate Student, Civil Engineering Department, Engineering College

University of Shahid Chamran, Ahvaz, Iran

Received: 5 May 2003

ABSTRAK

Dalam kertas ini, sebuah empangan dan tanah di bawahnya telah dimodelkandengan menggunakan unsur tergabung terhingga-tak terhingga dalam keadaanterikan satah. Tegasan statik yang teIjadi pada sistem empangan-asas disebabkanoleh beban-beban graviti dan hidrostatik telah dinilai. Analisis seismik kenyalplastik sistem tersebut kemudiannya dilakukan dengan menggunakan kriteriaDrucker-Prager untuk ketidakurusan bahan. Kesamaan gerakan diselesaikanmelalui kaedah pengamiran tokokan masa Newmark. Kajian menekankankelakuan struktur sistem empangan-asas yang dikenakan dengan gegaran gempabumi. Kelakuan dalam bentuk kontur pesongan, agihan tegasan dan ragamkegagalan dibentangkan.

ABSTRACT

In this paper, the dam body and the underneath soil were modeled usingcoupled finite-infinite elements under plane strain conditions. Initially, staticstresses developed in the dam-foundation system due to gravity and hydrostaticloads are evaluated. Elasto-plastic seismic analysis of the dam-foundationsystem is next carried out by adopting the Drucker-Prager criterion for thematerial nonlinearity. The equation of motion is solved by Newmark incrementaltime integration technique. The study focuses on the structural behaviour ofthe dam-foundation system under earthquake excitations. The behaviour interms of displacement contours, stress distributions and the failure mode arepresented.

Keywords: Finite-inImite elements, static, elasto-plastic seismic analysis

INTRODUCTION

The rockfill dam has been used in many parts of the world with increasingfrequency in recent years. This type of the dam is one of the most attractive typefor the consulting engineers because of its good adaptability, convenience ofconstruction, good performance during the past earthquakes, safety and economywith the development of the technologies of construction and the applicationof new structural materials. Rock fill dams having different heights have beenused in different parts of the world. As an example Kuzuryu dam"which is 128 mhigh was constructed in Japan (Nose et at. 1980), Masjeid Soleyman dam whichis 170 m high was built up in Iran (Jafarzadeh et al. 1998), and Messochara dam

J. oorzaei, M. Karami, Waleed A. Thanoon & M. S. Jaafar

which is 150 m high was completed in Greece (Thanopoulos et al. 1998). Tostudy the variation of stresses in the body of the dams subjected to static anddynamic loading, the finite element technique has been widely used.

Skermer et al. (1973) analysed a rockfill dam with impervious core using athree-dimensional finite element model. A hyperbolic model was used toaccount for material nonlinearity. The comparisons between the results obtainedfrom the finite element analysis with the results measured in the rockfin damat site showed good agreement. Seed et al. (1985) reported a set of conventionalfinite element analyses aimed at estimating the magnitude of sliding deformationsof typical concrete faced rockfin dams subjected to base accelerations with apeak acceleration amplitude (PGA) of 0.5 g. It is concluded that in high seismicactive area, the geometry of the dam body and abutments should be 1.6H :IVor flatter. Bureau et at. (1985) presented a study dealing with the seismicperformance of rockfin dams in general and the possible modes of failure ofconcrete faced rockfin dams in particular. The permanent deformation obtaineddirectly using DSAGE software is based on finite difference method. SayedKhaleed et al.(1990) used incremental and interface elements to discretise theCethana concrete-faced rockfin dam assuming plain strain condition.

Gazetas et at. (1992, 1995) have studied the 3D seismic response of an actual120 m tall concrete-faced rockfill dam, and concluded that tall concrete-facedrockfin dams in narrow canyons of solid rock may experience extremely intenseshaking at mid crest during strong seismic motions. Roa et al. (1996) studiedthe Santa Juana dam under static and earthquake excitation having peakacceleration of 0.3 g. The deformation in the dam body and stresses in theconcrete slab are obtained using the finite element method. Mircerska etat. (1998) analysed a rockfin dam for linear and nonlinear cases using ProcessSoftware under plane strain condition. The linear and nonlinear behaviour ofthe dam in terms of displacement, acceleration and stress histories werepresented and discussed.

In the present study which is the continuation of the author's previous work(Noorzaei et at. 1999, 2000, 2002) the material nonlinearity of Kavar rockfilldam have been taken into consideration by employing the Drucker Prager yieldcriteria. The behaviour of the dam with respect to accelerations, displacementsand stresses in the dam body has been discussed. Moreover, an attempt hasbeen made to find out the mode of failure in the dam.

Static and Dynamic Anatysis

Static stresses developed in the dam-foundation system due to gravity andhydrostatic loads are evaluated using usual finite element procedure availablein many finite element textbooks. The nonlinear dynamic analysis of rockfilldams involves the solution of the well-known dynamic Equation of motion(Zeinkeiwicz et al. 1972; Owen and Hinton 1980):

32

[M]I u} + [c]l it.} + [k]l u} = - [M]I u(g) }

PertanikaJ. Sci. & Techno!. Vo!. 13 No.1, 2005

(1)

Static and Dynamic Analysis of Rockfill Dam Using Finite-infinite Element Method

Using the Newmark step-by-step integration method the solution of Eqn. (1)can be expressed by:

(2)

(3)

The record of the earthquake is divided into definite steps and in each step,the displacement vector determined from which the strains and stresses at eachtime step are calculated.

Drucker-Prager failure criteria was used to investigate the yielding of thematerials in the dam-foundation systeql using:

( )

0.5

!=a1,+ 12 -K

where,], and.h' are first and second stress invariants,

(4)

2sin¢a = ---;==-;---'---;-

.J3(3 -sin¢)and K = 6Ccos¢

.J3(3-sin¢)

At each time step, a check on material yielding is performed for all Gausspoints using Eqn.(4). If the state of stress at a specific Gauss point exceeds theyielding stress, the effective stress and residual stress are calculated as:

1tJ.f,} = f[BY" 1<J}dy - If,}y

(5)

By comparing the effective stress with that obtained in the previous iteration,loading or unloading status at a specified Gauss point will be known. Theportion of stress level that is greater than yield value must be brought back tothe yield surface by iteration processes within each time step. This procedureis useful in earthquake analysis when accelerograms are used to characterise theground motion when structural nonlinear effects are present.

ANALYSIS OF ROCKFILL DAM

Finite-Infinite Modeling

The numerical example selected to illustrate the structural behaviour of rockfilldam is the Kavar rockfill in southern part of Iran. The dam has been proposedand designed by the consulting engineers ( oorzaei et al. 1999, 2000). TheFinite element discretisation of the dam-foundation system is shown in Fig. 1.The total number of the nodal points is equal to 533. The number of finite andinfinite elements are 160 and 8 respectively. The software used for the analysisof the dam is a multi-element and general purpose two-dimensional finite

PertanikaJ. Sci. & Technol. Vol. 13 No.1, 2005 33

J. Noorzaei, M. Karami, Wa1eed A. Thanoon & M. S. Jaafar

element package developed by the author (Noorzaei et al. 2002). Appendix Ashows the different types of elements such as eight-noded finite and five-nodedinfinite isoparametric element along with their shape function used for theidealization of the dam section. The berm in the upstream (shown in Fig. 1) hasbeen added to enhance the stability of the dam. Different materials have beenused for the main body of the dam and the berm.

40

450

0.30.25

1000Rock

E

v10m

,A \ a]

~ 45

..~.......-Ilf \\V

Berm //1/1 \'\~.7//11 \\\

///11 \\\////1 \ \ ..... ne.at

EIII

E13 Free

All the base node are fixed in both direction

Fig. 1: Finite-infinite element discretisation oj rockfill dam

Static Analysis

Initially static analysis of the dam for the dead weight has been performed. Thecorresponding static stress vector and load vector are stored for the earthquakeanalysis of the dam. Fig. 2 shows the contours of vertical and horizontal

~i~~O @!:I.,...----- ~ '\:: - ~ -----

a) Horizontal Displacement

~-----~ ~-----b) Vertical Settlements

Fig. 2: Contour lines oj maximum horizontal and vertical settlement due to static load

34 PertanikaJ. Sci. & Techno\. Vo\. 13 o. 1,2005


settlements obtained form static analysis. The contours indicate that there is anincrease in the vertical displacement as the height of the dam is increased andhas a maximum value of 9.5 cm at the crest level of the dam. On the otherhand, there is negligible movement in the horizontal direction.

The distributions of the static stresses throughout the body of the dam interm and the contours of maximum and minimum principle stresses are shownin Fig. 3. It is clear from this plot that highest values of principal stresses aredeveloped at the centre of the lower portion of the dam and their values aredecreasing with the increase of the height of the dam. The contours also showthat both maximum and minimum principle stresses are in compression.

a) Maximum Principle Stresses

b) Minimum Principle Stresses

Fig. 3: Contour lines of maximum and minimum principw stresses due to static wad

Dynamic Analysis

The dam-foundation system has been analysed for the earthquake excitationhaving PGA=0.27g and duration time equal 6.1 seconds [DBL record] as shownin Fig. 4. By using the direct ewmark integration technique, the record ofearthquake is divided into 1220 steps. Damping of 5% has been assumed for theanalysis.

52

3r-----:--------------------

Fig. 4: Horizontal earthquake excitation record

PertanikaJ. Sci. & Technol. Vol. 13 No. 1,2005 35

J. oorzaei, M. Karami, Waleed A. Thanoon & M. S. Jaafar

The time history for the horizontal acceleration and displacement at threenodal points selected along the vertical central axis of the dam are shown inFigs. 5 and 6 respectively. ode 204 is selected at the ground level while nodes326 and 439 are chosen to be at the berm and crest level of the damrespectively. Both acceleration and displacement increase with the increase ofthe height of the dam. The absolute horizontal acceleration at the top of thedam is found to be 10.7 m/s2

, with an amplification factor (AF) of 3.96, whilethe peak absolute displacement at the top of the dam is found to be 3.03centimeters.

Fig. 7 shows the time history of principle stresses and maximum shear stressat selected critical Gauss points in the dam section. The location of the selectedGauss point is shown in the same figure. This figure indicates that themaximum principal stress (JI is occurred near the ground level while theminimum principal, (J3 is located at either sides of the dam. Fig. 8 shows thepeak absolute main stress contours ( (Jl ' (J3 ) in the dam cross-sections. AJ;, itcan be seen in these figures, the peak absolute main stresses ( (Jl ' (J3 ) aremostly located at the foundation level. Fig. 8 shows the plastification zone in thedam body at the end of earthquake record which also indicates the mode offailure of the dam. The failure will be in the form of wedges occurring atupstream and down stream of the dam.

CONCLUSIONS

The main conclusions that can be drawn from this work are:(i) In static conditions, the maximum settlement occurred at the crest of the

dam while the principal stresses reached their highest value in lowerportions along the central core of the dam.

(ii) The damage of rockfill dam, resulting from earthquake, is in the form ofwedge failure occurring upstream and downstream of the dam.

(iii) The maximum principal stress (Jj occurred near the ground level while theminimum principal, (J3 occurred at either sides of the dam.

(iv) The maximum and minimum main stresses are much higher in theupstream side compared to those found in the downstream side of thedam.

[B] = strain displacement matrix

if) = external load vector

(l1f) = residual force vector

= damping matrix= first stress invariants= second stress invariants= angle of internal friction= cohesion= stress vector

NOTATIONS

[c]

.Ith'If>c(o"}

[M] = mass matrix[k] = stiffness matrixaB ewmark integration constantI1t = increment of time stepUn = displacement at marching step n

il. = velocity at marching step n

u. = acceleration at marching step n

{ill ..", = velocity at time t+l1t

36 PertanikaJ. Sci. & Techno!. Vol. 13 No.1, 2005


ry

.. l.=:=:NOdO No -204

"20

15

i " I----•

"• . A

I .. --

)""·15

...20 ._-

J."-"." I--- --- .._--..., f----.-.- -_.. . .._-...•S<>

• , 2 , . • .T1•• 10.0)

a Acceleration time histo at Node 204

I- -..i '; r"I

I ., 1-" II

1"" -." -

.. .20I...... --...-

I :::.-_-_._ --'j

b) Acceleration time history at ode 326

.. ~ T....:_=-_•....:Oo.N°"'·ll

i~ -=11i ~ -_- 1j:::

I r~ 111

TI",. (ue)

c) Acceleration time history at Node 439

Fig. 5: Horizontal acceleration at Node 204, 326 and 439

PertanikaJ. Sci. & Techno!. Vo!. 13 No.1, 2005 37

J. Noorzaei, M. Karami, Wa1eed A. Thanoon & M. S. Jaafar

-------------- ----

I---

1--Ho•• NO.,04

00• .------------------------======='==i10.02$

00' +------····-----------------------110.011 +-------------------------------11

i 001

I.: ::: t_./"""'\"'_:..._""'~\Jz~"_\-v_';:;rv~~~.A_\v-l_>.l· ~~~v~.::v~.,p.J.I\""'vrl'<>",,""~-\v---f,--),f\~r.;P"''rtV ''O:>'<I7'....,.°d....,.'''''',l-f':,.:L----H

1·;:-:;.. 0' +---------------------------------11

-0.026 +-------------·-------------------11-00' 1---- ----- --------- ----------------11

-tlOU 1--- ·····---------------------------il-004 L- ---' I

~I-

a) Displacement time history at Node 204

------------'1

'\TIM. ( •• c)

~--NOct.Ho -U8 ~

------- i'

-jl

-jI

OD'

0025

002

OOHI

! 001

10.00:

-0005

1-0:::i -002

-0025

"D'.0.035

-00.

b) Displacement time history at Node 326

--Node No....3i

OD,

ODZ'

0.02

0.015

I i 0::I 0

I:::1-0.015

i ~.o2-0.025

-oD'-0.035

-0.04

- - ~ --- - ---- I

A- A 1\ n ~I-

f\ - - f\i1 - l- Ii A f\ --~

V :~I\ ~f - - - --I- -V \

y V'- '--

- -- __v -- -

-- - -- ----- - --------

3. ~

Time (sec)

c) Displacement time history at ode 439

Fig. 6: Horizontal displacement at Node 204, 326 and 439

38 PertanikaJ. Sci. & Techno!. Vo!. 13 No.1, 2005

Static and Dynamic Analysis of Rockfill Dam sing Finite-infinite Element Method

• •T1oMl..,

'llDO r---------------- --,IOII~~~~~~~_______ ~

iI ....r--~~--~~~~-~ -1000

a) History of stresses in Gauss point No. 257

0.' ....

~s:EIlllDO

100

iI ....

,'000 ---·'100 ----

0 • •T1oMl_1

---- ....~----~

0.350

GINo.....'

IllDO

100

iI ....

·'llDO

·IlOO0 • •

TIoMl_)

b) History of stresses in Gauss point

c) History of stresses in Gauss point No. 447

0"'_'llDO .----------

---1---I_~-

ij -1-----

·'000.,!IOll 1- _

o

d) History of stresses in Gauss point o. 481

Fig. 7: Principle and shear stresses at critical G.P in the dam body

PertanikaJ. Sci. & Techno!. Vol. 13 o. 1,2005 39

J. Noorzaei, M. Karami, Waleed A. Thanoon & M_ S. Jaafar

a) Minimum Principle Stresses

~ ,> - 250-.-- "~~." -1£\" ".', \/<." .!~ ---. ._ \_\d~•. _

"_ ---/ ~50 500 --. '-- ~-- -= --.- .../ I / ....: --:-:..::.- -:.- -.:-

b) Maximum Principle Stresses

Fig. 8: Contours of peak absolute maximum and minimum principal stress (KPa)

Fig. 9: Mod of failure

REFERENCES

BREAU, G., R.L. VOLPE, W.H. ROTH and T. UDAKA. 1985. Seismic analysis of concrete facerockfill dams. In Proc. of Symp. on Concrete - Face Rockfill Dams - Design, Construction,and Performance, p. 479-508, ASCE, New York.

GAlETAS, G. and N. UDDIN. 1995. Dynamic response of concrete face rockfill dams tostrong seismic excitation. Journal of Geotechnical Engrg, ASCE 121(2): 185- 197.

GAlETAS, G. and P. DAKOULAS. 1992. Seismic analysis and design of rockfill dams: state ofthe art. Soil Dynamic and Earthquake Engg. 2: 27-6l.

JAFARZADA, F. and A. YAGHUBI. 1998. 3D dynamic behaviour of zoned rockfill dams withemphasis on real case study. In Proced. Int. Symposium on New Trends & Guidelines onDams Safety, II: 817-824.

KHALm, S., B. SINGH, G.C. AYAK and O.P. JAIN. 1990. onlinear analysis of concrete facerockfill dam. Journal Geotechnical Engrg. ASCE 116(5).

MIRCEVSKA, V. and V. BICKOVSKI. 1998. Two-dimensional nonlinear dynamic analysis ofrockfill dam. Intenational Symposium on Dam Safety 2: 859-866.



OORZAEI, j. and E. MOHAMMADlAN. 1999. Dynamic behavior of the Kavar CFRD III

southern Iran. Int Joumal of Hydropower and Dams (6): 70-73.

NOORZAEI,j. and E. MOHAMMADlAN. 2000. Modeling of concrete face rockfill dam via finiteinfinite and interface elements. In Proc. Int. Symp. on CFRD, p. 361-370, 18 Sept,Beijing.

NooRZAEI, j., M. KARAMI, T.A. WALEED and M.S. JAFAAR. 2002. Elasto-plastic seismicresponse of Kavar rockfilJ dam. In 1Zlo International Symposium in Earthquake Engineering,I.l.T, Roorkee, India, Dec. (To be presented).

NOSE M. and K. BABA. 1980. Dynamic behaviour of rockfill dams. In Proceedings ofConference on "Dams & Earthquake", p. 69-78, Oct 1-2, London.

OWEN, D.RJ and E. HI!\'TON. 1980. Finite Elements in Plasticity: Theory and Practice. UK:Pineridge Press Limited.

ROA, F.R. and L.A. GAMBOA. 1996. Seismic analysis of concrete - faced gravel-fill dams.In Proceedings of the Int Symposium on Seismic and Environmental Aspects ofDams Design,I, Santiago, Chile.

SKERMER, .A. 1973. Finite element analysis of el infiernillo dam. Can. Geotech. Joumal10(2).

SEED, H.B., R.B. SEED, S.S. LA! and B. KHAMENEHPOUR. 1985. Seismic design of concrete face rockfill dams. In Proc of Symp. on Concretejace &ckfill Dams - Design, Censtructionand Performance, p.459-478, ASCE, ew York.

THANOPOULOS, j. and j. TICOB. 1998. Erosion problems of concrete faced rockfill damsduring construction. In Proced. Int. Symposum on New Trends & Guidelines on DamsSafety, II: 967-974.

ZIENKIEWlCZ, D.C. and C.c. AYAK. 1972. Elasto - plastic stress analysis, a generalization forvarious constitutive relation including strain softening. IntJoumal Num. Meth. Energy.5(1): 113-135.

PertanikaJ. Sci. & Techno!. Vo!. 13 No.1, 2005 41

J. Noorzaei, M. Karami, Waleed A. Thanoon & M. S. Jaafar

APPENDIX A

Shape functions for two-dimensional serendipity types of finite and infiniteelements

Type of element Element figure Shape functions

Eight-nodes 7 6 5 For corner nodes:finite element

804

1N, ="4(1 + ~~,)(1 + 1]1],)(~~, + 1]1], -1)

For midside nodes:a) ~ = 0.0

1 2 3 1N, =2(1- ~')(1 + 1]1],)

b) 1] = 0.0

1N, =2(1- ~~,)(1+ 1]')

Five-nodes 4 6 3 ~1](1-1J) -~1](1 + 1J)

5L N= N=infinite element I (1- ~). (1- ~)

N=(l + ~)(1 -1])

N=-2W-1]'),

2(1-~s (1- ~)

N = (1 + ~)(1 + 1])1 2 3 2(1-~)


static and dynamic analysis of rockiill dam using finite...

Documents