Soil Dynamics and Earthquake Engineering 31 (2011) 792–804

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Soil Dynamics and Earthquake Engineering

0267-72

doi:10.1

n Corr

E-m

URL

journal homepage: www.elsevier.com/locate/soildyn

Three-dimensional nonlinear seismic analysis of concrete faced rockfill damssubjected to scattered P, SV, and SH waves considering the dam–foundationinteraction effects

Ali Seiphoori a,n, S. Mohsen Haeri b, Masoud Karimi c

a Ecole Polytechnique Federale de Lausanne (EPFL), Laboratory of Soil Mechanics (LMS), Lausanne, Switzerlandb Civil Engineering Department, Sharif University of Technology, Tehran, Iranc Iranian Offshore Engineering and Construction Company (IOEC), Tehran, Iran

a r t i c l e i n f o

Article history:

Received 29 July 2010

Received in revised form

6 January 2011

Accepted 9 January 2011Available online 16 February 2011

61/$ - see front matter & 2011 Elsevier Ltd. A

016/j.soildyn.2011.01.003

esponding author.

ail address: ali.seiphoori@epfl.ch (A. Seiphoor

: http://personnes.epfl.ch/ali.seiphoori (A. Sei

a b s t r a c t

In this study, the nonlinear seismic analysis of a typical three-dimensional concrete faced rockfill dam

is reported. Three components of the Loma Prieta (Gilroy 1 station) earthquake acceleration time

history are used as input excitation. The dam under study is considered as if it were located in a

prismatic canyon with a trapezoidal cross-section. A nonlinear model for the rockfill material is used,

and contact elements with Coulomb friction law are utilized at the slab–rockfill interface. Vertical joints

in the face slab are also considered in the finite element model. A substructure method, in which the

unbounded soil is modelled by the scaled boundary finite element method (SBFEM), is used to obtain

the scattered motion and interaction forces along the canyon. The dam is subjected to spatially variable

P, SV, and SH waves, and the effect of dam–foundation interaction and the reservoir water effects are

considered. The results are compared with the non-scattered input motion analysis. Results of the

analyses indicate that due to applying the scattered motion to the canyon the response of the dam and

concrete face slab significantly increases. The reservoir water pressure affects the tensile stresses

induced in the face slab by reducing the uplift movement of the concrete panels.

Large horizontal axial forces are induced in the face slab due to out-of-phase and out-of-plane

motions of the abutments. Although the normal movements of vertical joints are reduced due to the

reservoir water confinement, the opening movements are still significant, and the local failure of

construction joints is inevitable.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The number of concrete faced rockfill (CFR) dams under designand construction is increasing in many parts of the world.Complete usage of local embankment materials, simple construc-tion methods and short construction duration are some advan-tages of CFR dams. CFR dams are inherently safer than other typesof dams, as the earthquake ground motion cannot lead to pore-water pressure buildup and strength reduction [29].

The performance of CFRDs under static loading conditions iswell known, while static analysis of this type of dam can be carriedout in a similar way to that of other types of earth and rockfill dams.Static design of CFR dams can be verified by available data fromexisting dams [20,18,24]. Seismic analysis of CFR dams in strongground motion has been studied and published in the literature byvarious researchers [28,7,29,16,10,33,34,15,17,12]. The above

ll rights reserved.

i).

phoori).

studies indicate that the rockfill dam body is safe enough understrong earthquake conditions. However, damage can occur in theconcrete slab due to the high axial forces and/or the repeated upliftand downfall of the slab on the dam body.

In addition, Bayraktar and Kartal [4] recently performed aseries of 2D finite element analyses of Torul CFR dam consideringdam–reservoir interaction. The horizontal component of 1992Erizincan Earthquake was used in these analyses. The linear andnonlinear response of the dam in seismic excitation, and the effectof reservoir water were investigated. Bayraktar et al. [5] used thesame model this time to study the effect of concrete slab–rockfillinterface behaviour considering both friction and welded con-tacts. In the same direction, Kartal et al. [21] investigated thefailure probability of the concrete slab on CFR dams with weldedand friction contact under earthquake effects by the reliabilityanalysis. They used the same model reported by Bayraktaret al. [4] considering the deconvolution of the free-field surfacerecord to obtain the ground motion for the foundation baserock. In their study, the probability of failure of the most criticalpoints in the concrete slab was obtained regarding various slabthicknesses.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 793

One of the common assumptions made in the above studies isthat the concrete slab of the CFR dam has been modelled as acontinuous shell, or the existence of vertical joints have beenignored. Particularly in two dimensions, where it is not possible tosee the vertical joints behaviour in the model. However, the slabis generally placed in vertical panels, where the panels may beconnected together by steel reinforcements. Therefore, themechanical response of these panels has to be studied through3D models. Besides, these analyses are also based on the assump-tion that all points along the canyon experience uniform groundmotion. However, most CFR dams are built in the canyons of finitesize where borders and geometry play an important role on theseismic response of the dam–foundation system.

During an earthquake, incoming waves are reflected at the freesurface of the canyon in which the dam is constructed, leading toa nonuniform movement of the foundation of the dam. This iscalled the scattering problem. In addition, the movement of thefoundation acts as an excitation of the dam but it is alsoinfluenced by the vibration of the dam. This is called the inter-action problem [31]. Therefore, the effect of spatial variation ofthe ground motion and dam–foundation interaction effects areimportant details to consider in the seismic analysis of CFR damsbuilt in canyons.

The effect of the spatially varying ground motion on theresponse of fill dams have been investigated in past few years[31,9,23,1,13,26,3,11,6].

Among recent studies, a new approach introduced by Haeriand Karimi [13] for the evaluation of scattered P, SV, and SHwaves exciting arbitrary cross-sections. This approach was uti-lized to solve scattering problems in two dimensions, which isalso applicable to prismatic canyons. The output of this two-dimensional scattering solution could be used for the excitation ofthe three-dimensional structures as proposed by Szczesiak et al.[31]. They studied the effect of scattered motion and out of phasemovement of the abutments on the response of CFR damstructure. The inertial effect of dam and the water effect werenot considered in their analyses. They concluded that applyingthe spatial variable motion on the canyon increases the peakdisplacements and accelerations in the dam body and the faceslab considerably. Later on, Haeri and Karimi [14] improved theformulation to consider the dam–foundation interaction effectson overall response of CFR dams. They mentioned that the dam–foundation interaction effects reduce dam and slab responses, andapplying the scattered motion without dam–foundation interac-tion analysis is unrealistically conservative.

This study investigates the nonlinear seismic response of athree-dimensional CRF dam and the concrete slab using the sameapproach as reported by Haeri and Karimi [14]. The spatiallyvarying ground motion including the scattering of the incident P,SV, and SH waves by the canyon. The dam–foundation interactioneffects are also formulated in the analysis. A new finite elementmodel for concrete slab is used to study the vertical jointsmovement and the distribution of the induced stresses in theface slab. Finally, the effects of reservoir water on the concreteface slab and vertical joint movement are investigated inthis study.

2. Basic of the analysis

2.1. Spatial variation of the ground motion

Wave scattering is the most important aspect of a realisticearthquake input excitation for the dams built in the canyons.The effect of local site amplifications in terms of border and geo-

metry (topographical effects) can produce huge ground motion

amplification during the earthquake. In addition to scatteringproblem and delay of wave arrivals between the base of the damand points higher along the abutments, the incoherence effectwhich arises from scattering of waves in heterogeneous medium,and their differential superpositioning when arriving from anextended source, and the site-response effect due to difference inthe local soil conditions at different stations are the otherphenomena that give rise to the spatial variability of earth-quake-induced ground motion [22].

In this research, the canyon is considered to be excavatedin an elastic and homogeneous medium. Therefore, the spatialvariation of the ground motion resulting from the wave scatteringand diffraction of waves by the canyon is considered.

To formulate this reaction, a half space without the canyonis assumed, and a three-dimensional earthquake excitation isselected as a control motion. It is assumed that only a certainpoint in the canyon will experience this control motion duringexcitation—the ‘control point.’ The control point can be locatedanywhere, but is generally selected on the ground surface orbedrock.

The time history of the control motion is indeed the accel-erograms at a point on the ground surface, which is the combina-tion of incoming and reflected waves. Therefore, the controlmotion can be decomposed to a number of assumed components.For this purpose, the three-dimensional excitation is divided intotwo sets of waves:

1.

Out of plane component (E–W direction): SH wave 2. In plane components (N–S direction): SV and P waves.

Decomposing formulation is discussed in detail by Wolf [35].For decomposing purposes, excitation is assumed to be a combi-nation of body waves. Free-field motion (uf) and soil stresscomponents along the canyon are calculated in the next step(Fig. 1, top and middle). This calculation can be made via theelastic wave propagation formulation, as detailed by Wolf [35].

If the canyon is excavated in a half space, soil stresses willappear as tractions along the canyon surface by

ti ¼X

sijnj i,j¼ 1,2,3 ð1Þ

where t is the traction, s is the soil stress component, and n is theunit normal vector. To achieve a free traction surface along thecanyon, the same traction with a negative sign shall be applied tothe canyon. These negative tractions, or equivalent forces, causenew motion along the canyon, which is a scattered wave (ub)(Fig. 1, bottom). The total ground motion along the canyon (ug)can be calculated as

ug ¼ uf þub ð2Þ

The most important key in the above calculation is theprediction of the scattered wave, ub, from the surface traction,or force, which requires knowledge of the dynamic stiffness ofthe media.

Szczesiak et al. [31] obtained scattered motion for an arbitrarycross-section canyon via two-dimensional dynamic stiffness matrixcalculated using the complementary domain method (CDM).

In this study, a new method is considered for the calculation ofthe dynamic stiffness matrix of the material involved in thecanyon based on the scaled boundary finite element methodestablished by Wolf and Song [37] and Wolf [38].

The force–acceleration relationship of the unbounded mediumis expressed as

fRðtÞg ¼

Z t

0½Mgðt�tÞ�f €uðtÞgdt ð3Þ

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804794

where Mg(t) is the acceleration unit-impulse response matrix inthe time domain developed based on the scaled boundary finiteelement method. The scaled boundary finite element method

-5

-3

-1

1

3

5

Acc

eler

atio

n (m

/sec

2 )

N-S components

-5

-3

-1

1

3

5

Acce

lera

tion

(m/s

ec2 )

E-W component

-2.5

-1.5

-0.5

0.5

1.5

2.5

0

Acce

lera

tion

(m/s

ec2)

time (sec)

Vertical component

1 2 3 4 5 6 7 8 9 10

Fig. 2. Three components of the recorded time history of the Loma Prieta

P,SV and SH-Waves

P,SV and SH-Waves

-ti

ti

uf

ub

Fig. 1. Solution for scattering problem.

proposed by Wolf [36], Wolf and Song [37], and Wolf [38] is exactin the radial direction, converges to an exact solution in thecircumferential direction, and is rigorous in both space and time.Haeri and Karimi [13] established a FORTRAN basis programmecalled ‘‘Similar1’’ for the calculation of acceleration unit-impulseresponse matrix.

2.1.1. Verification

The scaled boundary finite element method and relative unit-impulse response matrices have been verified using benchmarkproblems [37,38]. However, in this respect, the response of acanyon subjected to earthquake excitation is examined in timedomain. A semi-circular canyon with a radius of 100 m isconsidered, as illustrated in Fig. 3. The first 10 s of the recordedtime history at the Gilroy 1 station (E–W component) during theLoma Prieta earthquake is used as the out of plane (SH) excitation.Displacement time history of this control motion is shown inFig. 2. The ‘‘control point’’ is selected at the centre of the virtualcanyon at the ground surface. The elastic half space shear wave

-5

-3

-1

1

3

5

Dis

plac

emen

t (cm

) N-S component

-6-4-202468

Dis

plac

emen

t (cm

) E-W component

-10

-5

0

5

10

Dis

plac

emen

t (cm

)

time (sec)

Vertical component

0 1 2 3 4 5 6 7 8 9 10

earthquake (Station Gilroy 1): (a) acceleration and (b) displacement.

Fig. 3. Semi-cylindrical canyon cross-section.

Fig. 4. Comparison of scattered displacement time history for semi-circular

canyon excited with SH wave with those obtained based on closed form by

Trifunac [32]. Top: point 1, Middle: point 2, Bottom: point 3 (refer to Fig. 3).

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 795

velocity is 220 m/s and the excitation angle is 301 to the vertical.Scattering of plane SH waves through a semi-circular canyon hasbeen studied by Trifunac [32] in the closed form. The total motionalong the semi-circular canyon with radius a, and subjected to aharmonic SH excitation with a frequency of o and an incidentangle of g in polar coordinate system (r, y) is expressed as

ut ¼ uiþurþuR ð4Þ

uiþur ¼ 2J0ðkrÞþ4X1n ¼ 1

ð�1ÞnJ2nðkrÞcos2ngcos2ny

�4iX1n ¼ 0

ð�1ÞnJ2nþ1ðkrÞsinð2nþ1Þgsinð2nþ1Þy ð5Þ

K ¼o=b ð6Þ

uR ¼X1n ¼ 0

½anHð2Þ2n ðkrÞcos2nyþbnHð2Þ2nþ1ðkrÞsinð2nþ1Þy� ð7Þ

The coefficients a0, b0, an, and bn are defined as follows:

a0 ¼�2J1ðkaÞ

Hð2Þ1 ðkaÞð8Þ

b0 ¼ 4ising kaJ0ðkaÞ�J1ðkaÞ

kaHð2Þ0 ðkaÞ�Hð2Þ1 ðkaÞð9Þ

For n¼1,2, y

an ¼ 4ð�1Þn cos2ng kaJ2n�1ðkaÞ�2nJ2nðkaÞ

kaHð2Þ2n�1ðkaÞ�2nHð2Þ2n ðkaÞð10Þ

bn ¼ 4ið�1Þn sinð2nþ1Þg kaJ2nðkaÞ�ð2nþ1ÞJ2nþ1ðkaÞ

kaHð2Þ2n ðkaÞ�ð2nþ1ÞHð2Þ2nþ1ðkaÞð11Þ

In the absence of a canyon, ui and ur are incident and reflectedwaves, respectively. In other words, parameter (ui+ur) is the same asthe free field motion (uf). The displacement uR represents thescattered and diffracted waves reflected from the semi-circularcanyon boundary, which is the same as ub. Jp(x) is the Bessel functionof the first kind with the argument x and the order of p, and H2

p(x) isthe Hankle function of the second kind with the argument x and theorder of p. To solve the problem in closed form the time history of theexcitation shall be transferred to the frequency domain.

Fig. 4 shows the total scattered motion at three differentpoints along the semi-circular canyon, computed by the proposedmethod, and is compared with the closed form solution proposedby Trifunac [32]. In this regard, time history of the motion istransferred to frequency domain at first calculations, based onTrifunac’s proposed method, and is carried out in frequencydomain. The results are then transferred to time domain again.The results of the proposed method are in good agreement withthe theory, as can be observed in Fig. 4.

2.2. Soil–structure interaction

The dynamic equilibrium equation of the dam super-structurein time domain can be expressed as

Mss Msb

Mbs Mbb

" #€ut

s

€utb

!þ

Css Csb

Cbs Cbb

" #_ut

s

_utb

!þ

Kss Ksb

Kbs Kbb

" #ut

s

utb

!¼

0

�rb

!þ

Ps

Pb

!

ð12Þ

where M, C, and K are mass, damping, and stiffness matrix ofthe dam, respectively; u, u, and u are displacement, velocity, andacceleration vectors, respectively; P is externally applied forcevectors; and rb is the interaction force vector applied in the dam–foundation interface. In the above equation, subscripts b and s

refer to nodes on the dam–base interface and remaining nodes ofthe structure (dam). The superscript t denotes the total motion ofthe dam. As shown, dynamic response of the dam can be obtainedfrom Eq. (12) if the interaction force vector rb is known. Theinteraction force vector rb can be formulated as proposed byWolf [36]:

rbðtÞ ¼

Z t

0½Mg

bbðt�tÞ�ðf €utbðtÞ� €u

gbðtÞgÞdt ð13Þ

where Mg(t) is the acceleration unit-impulse response matrix.Mg(t) indicates the foundation stiffness matrix as an unboundedmedium, and ug indicates the scattered ground motion alongthe canyon in the absence of the dam. In the following formulas,the superscript g denotes the ground without the dam. As ut is themain unknown variable, scattered ground motion ug and accel-eration unit-impulse response Mg(t) are only required. A timeintegration scheme considering approximation in time [40] isimplemented to solve the basic Eq. (12).

3. Case study

The formulation presented above is now applied to investigatethe effects of soil–structure interaction, scattering and diffraction

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804796

of input motion on the seismic response of a three-dimensionalCFR dam model under strong ground motion. The seismic analysisis performed based on the proposed algorithm using the accel-eration unit-impulse response matrix. All numerical simulationsare performed in ANSYS domain using APDL (ANSYS ParametricDesign Language) programming application.

3.1. Geometry and material modelling of the studied CFR dam

The typical 100 m dam studied in this research is symmetricwith upstream and downstream slopes of 1V:1.5H. The face slabconsists of fifteen 20 m wide panels with a clearance of 100 mmas vertical joints. (The actual width of the middle panels is

A

Foundation, Acceleration unit-impulse response matrix, M (t)

Dam body, Solid Element

g

Incident P, SV, and SH-waves

30°

1

6

11 17 23

100 m100 m

11

Fig. 5. CFRD body and foundation model: (a) two-dimensional canyon to solve the scat

SBFE methods.

therefore 19.9 m.) The thickness of the face and toe slabsis 40 cm and the width of the toe slab is 10 m. The face slab is0.3% reinforced in each direction, and the steel reinforcement isplaced in the middle of slab thickness. However, the reinforce-ment does not continue through the vertical joints. The dam islocated in a prismatic canyon with a trapezoidal cross-section(see Fig. 5). The width of the canyon at the riverbed is 100 m andthe slopes of the abutments are 1:1. The material elastic para-meters of the canyon, concrete slab, and steel reinforcement arelisted in Table 1. The shear wave velocity can then be obtained asvs¼1373.6 m/s, which represents a sort of sedimentary rock forthe canyon bed material.

The mechanical parameters of rockfill, which is divided intofive layers, are estimated including the effect of confinement on

A

Concrete Slabs, Shell Elements

28

33

100 m

100 m

11

tering problem and (b) dam body, concrete slab, and foundation models in FE and

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10

Dis

plac

emen

t (cm

)

Left abutment Right abutmentRelative movement

-202468

10la

cem

ent (

cm)

a

b

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 797

the rockfill modulus. The maximum shear modulus of each layeris calculated based on the following relationship given by Seedet al. [27]:

Gmax ðlb=ft2Þ ¼ 1000K2, max

ffiffiffiffiffiffiffismu

pðlb=ft2

Þ ð14Þ

where s0m is the mean effective stress and K2, max is a coefficientdepending on relative density, which varies from 30 to 75 forsands. Seed et al. [27] suggested that K2, max is 1.35–2.5 timeshigher for gravels as compared to those of sands. Therefore, in thisstudy K2, max is assumed to be 100 (stresses are in lb/ft2), withappropriate unit conversion.

In order to account for the material nonlinearity, a multi-linearkinematic hardening model (MKIN), incorporated in ANSYS soft-ware [2], is considered for the rockfill material. The model uses auniaxial stress–strain curve of the material as input for the multi-linear kinematic hardening model. In this study, a basic stress–strain curve is used for the rockfill material (see Table 2), which isproduced for initial elastic modulus of 200 MPa, and based onpublished rockfill stress–strain behaviour [25].

The stress–strain relationship presented in Table 2 is scaledto maximum initial shear modules (Gmax) for each layer. In thisstudy, separate models are used with different yield surfaces foreach layer in order to insure the relation between confiningpressure, elastic modulus, and the size of the yield surfaces.

Hysteresis damping is involved in the multi-linear kinematichardening model of the ANSYS. However, to account for thematerial damping at a low strain level, Rayleigh type dampinghas been suggested to be used in the analysis [39]. Therefore, inaddition to the hysteretic damping provided by the non-linearstress–strain behaviour of the soil, a small amount (0.01) of massand stiffness proportional damping was introduced. The first

Table 1Material parameters of the canyon concrete and steel of the face slab.

Material Module ofelasticity(GPa)

Poissonratio

Unitweight(kN/m3)

Canyon 12 0.2 26

Concrete 21 0.15 24.5

Steel 200 0.3 78.5

Table 2Rockfill material nonlinear properties (stress–strain relationship).

Stress (kN/m2) 20 188 860 1606.7 5873.3 5873.3

Strain (%) 0.01 0. 1 0. 5 1 5 5.5

0

2

4

6

8

10

12

14

50

distance from center (m)

dist

ance

men

t (cm

)

Peak Scattered Displacement

VerticalN-S directionE-W direction

N-S

-150 -100 -50 0 150100

Fig. 6. Distribution of maximum horizontal and vertical components of scattered motio

plane motion (SH wave): (a) maximum scattered displacement and (b) maximum scat

natural frequency of 1.59 Hz is also obtained based on the modalanalysis.

The Newmark method is used for implicit transient analysis, andthe full solution method solves equation of motion by Newton–Raphson method along with the Newmark assumption [2].

3.2. The finite element modelling of dam, and the input ground motion

As mentioned in Section 2.1, in seismic analysis, the first 10 s ofthe accelerograms recorded during the Loma Prieta earthquake(Station Gilroy 1) are used as input ground motion for calculating

0

2

4

6

8

10

12

14

Acce

lera

tion

(m/s

ec2 )

distance from center (m)

Peak Scattered Acceleration

VerticalN-S directionE-W direction

50-150 -100 -50 0 150100

ns along the canyon for the in plane motion (combined P and SV waves) and out of

tered acceleration.

-8-6-4

Dis

p

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10

Dis

plac

emen

t (cm

)

Time (sec)0 1 2 3 4 5 6 7 8 9 10

c

Fig. 7. Two abutments vertical and horizontal relative movements: (a) N–S

direction, (b) E–W direction, and (c) vertical direction.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804798

the scattered motion along the canyon. The dam axis is assumed to bein the north–south direction, and the waves are assumed to approachthe canyon at an angle of 30o to the vertical from the east forSH-wave, and from the left side for P, and SV waves (see Fig. 5a). Thefirst arrival point for P and SV and SH waves is in the middle of thecanyon section, and the scattered motion of these three componentsis calculated for 33 nodes along the canyon using the methoddescribed in Section 2.1. In this way, the first arrival point for thewaves is node 17.

Distribution of maximum horizontal and vertical componentsof the scattered motion across the canyon for combined P and SVwaves, and for out of plane motion, SH, is shown in Fig. 6. Then,the output of this two-dimensional scattering solution is used for

Fig. 8. Contours of horizontal maximum displacements of dam body during the se

Fig. 9. Contour lines of acceleration magnification factors during the seismic

Fig. 10. Contour lines of maximum horizontal compressive stresses (MPa) in

the three-dimensional model of dam as proposed by Szczesiaket al. [31]. When extended for the three-dimensional model,dynamic stiffness matrix of the foundation is needed. In thisregard, acceleration unit-impulse response matrix, Mg(t), is thenintroduced to ANSYS domain through the substructure analysisapplication.

Considering the nodes along the canyon (for which thescattered motion has been calculated) and also the dam bodygeometry, Mg(t) is defined by a total of 86 eight-node boundaryelements and 303 nodes (Fig. 5b). Including the three degree offreedoms for each node respected to the components of scatteredmotion, Mg(t) has a dimension of 909�909 arrays which is alsoabout the maximum allowed matrix size in ANSYS domain. In

ismic analysis: (a, b) non-scattered excitation and (c, d) scattered excitation.

analysis: (a, b) non-scattered excitation and (c, d) scattered excitation.

the face slab: (a) non-scattered excitation and (b) scattered excitation.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 799

compatible with the boundary elements, the dam body has to bediscretized in 150 twenty-node brick elements. The face and toeslabs are modelled using shell elements. The boundary elementsof Mg(t) matrix, and the finite element model of CFR dam andconcrete slabs are shown in Fig. 5b.

The Mohr–Coulomb friction law is implemented in the inter-face of the face slab and the dam using node to surface contactelements. The performance of the contact elements is based onaugmented Lagrangian method. This method is an iterative seriesof penalty updates to find the Lagrange multipliers (i.e., contacttractions). Compared to the penalty method, the augmentedLagrangian method leads to better conditioning and is lesssensitive to the magnitude of the contact stiffness coefficient [30].

To model the contact between two bodies (dam body andconcrete slab), the surface of one body is conventionally taken asa contact surface (dam body) and the surface of the other body as

Fig. 11. Contour lines of maximum horizontal tensile stresses (MPa) in th

Fig. 12. Contour lines of maximum longitudinal compressive stresses (MPa) i

Fig. 13. Contour lines of maximum longitudinal tensile stresses (MPa) in t

a target surface (concrete slab). The contact and target surfacesconstitute a ‘Contact Pair’ used to represent the contact andsliding between two surfaces.

The contact detection points are the integration point andare located either at nodal points or Gauss points. The contactelements are constrained against penetration into target surfaceat its integration points. However, the target surface can, inprinciple, penetrate through into the contact surface. In thisanalysis the contact element uses Gauss integration points asproposed by Cescotto and Zhu [8], which generally provides moreaccurate results than those using the nodes themselves as theintegration points. Also, the penetration distance is measuredalong the normal direction of contact surface located at integra-tion points to the target surface. Contact occurs when the elementsurface penetrates one of the target segment elements on aspecified target surface. This element allows separation of bonded

e face slab: (a) non-scattered excitation and (b) scattered excitation.

n the face slab: (a) non-scattered excitation and (b) scattered excitation.

he face slab: (a) non-scattered excitation and (b) scattered excitation.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804800

contact to simulate interface delamination [2], which providesrealistic simulation of the slippage, uplifting, and downfall of theslab relative to the dam body.

4. Results of the analysis

The results are presented in two main parts. In the first part,the response CFR dam, concrete slab, and the vertical jointmovements during the seismic analysis are investigated whenthe reservoir is empty. In this part, the effect of scattering isemphasized by comparing the two cases of scattered and non-scattered input motions. In the second part, the effect of reservoirwater pressure on the response of CFR dam and the concrete faceusing the scattered input motion is investigated.

The staged construction of the dam was considered in theanalysis. In this regard, the dam body is supposed to be built infive stages, and when the construction of the dam is completed,the face slab is then casted to the dam body. The initial stressesfrom this procedure are also computed and subsequently appliedin one increment before the seismic analysis. In the case of fullreservoir, the initial stresses induced in the face slab during waterstorage are also calculated and considered in the analysis.

4.1. Effect of scattered non-uniform input motion

The seismic analyses for two different input motions areperformed. In the first case, the Loma Prieta earthquake accelera-tion time history (first 10 s of accelerograms recorded during theearthquake as shown in Fig. 2a) is applied as uniform inputmotion. For the second case, the scattered ground motion of threecomponents of the recorded acceleration time histories is used asnon-uniform input motion.

Fig. 14. Definition of joints movement types: (a) initial situation, (b) opening norma

Fig. 15. Maximum joint opening movement (mm) computed during the sei

4.1.1. The dam body seismic response

Fig. 7 shows the displacement time history of the two pointslocated at the centre of the left and right abutments of the dam. Therelative displacement of the two abutments is also shown. In Fig. 7a,it can be observed that, after 4 s, the two abutments move towardeach other (in the N–S direction) by about 9 cm. The relativedisplacements of the abutments in the E–W and vertical directionsreach to a maximum of 6.4 cm after 3.2 s, and 2 cm after 4 s.

Fig. 8 shows the contours of maximum displacements in thedam body. In the N–S direction (Fig. 8a and c), it can be seen thatthe maximum response in the locations near the left side of thecanyon for scattered motion is significantly higher than theone for uniform input motion. Moreover, a shade zone can berecognized in the area near the right abutment. This is as a resultof the scattering of the waves due to the border of the canyonleading to site amplification and increasing the maximum dis-placement in the dam body by about 50% in the upper left side. Itcan be also concluded that due to wave scattering of the sameearthquake record a completely different seismic response will beexpected in the dam body depending on the observed location.

In Fig. 8b and d, maximum vertical displacement of the dam,when subjected to the out-of-plane motion of the scattered SHwaves, is shown. For the vertical direction, inclination of inputmotion decreases the vertical response of the dam body. Thecontours of the acceleration magnification factor of the dam in thehorizontal and vertical direction are summarized in Fig. 9. It canbe observed that the top third of the dam experiences stronghorizontal shaking by applying the scattered motion. However,the vertical magnification factor in the E–W central longitudinalsection slightly changes by the scattering effect.

4.1.2. Response of the face slab

The face slab experiences considerable axial forces andmoments. In the case of scattered excitation, however, very large

l to joint, (c) shear parallel to joint, and (d) movement normal to concrete face.

smic analysis: (a) non-scattered excitation and (b) scattered excitation.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 801

horizontal forces are applied in the face slab due to the out-of-plane motion of the two opposite abutments. Contour lines ofmaximum axial compressive and tensile stresses induced in theface slab in the horizontal direction are illustrated in Figs. 10and 11. As the face slab is confined between two abutments, theout-of-plane motion of the abutments in the N–S direction canexert considerable horizontal forces in the face slab. Scatteredground input motion has increasing effects on both compressiveand tensile forces due to the out-of-phase and out-of-planemotions of the abutments.

While the excitation in the abutments is uniform, the hor-izontal tensile axial forces in the face slab are negligible. It shouldbe clarified that the high horizontal stresses in the face slab at thelower left abutment are not the result of stress concentration,since this effect could also cause similar high stresses for non-

Fig. 17. Maximum movement normal to concrete face (mm) computed during th

Fig. 18. Maximum joint shear movement (mm) computed during the seism

-8-6-4-202468

1012

Dis

plac

emen

t (cm

)

Time (sec)

Abutment horizontal relative movement

100 m60 m40200 m (riverbed)

0 1 2 3 4 5 6 7 8 9 10

Fig. 16. Two abutments horizontal relative movements at different elevation in

N–S direction.

scattered ground motion input. Rather, the large stresses at thislocation are due to the amplification of horizontal excitation dueto scattering of the waves along the left abutment.

The magnitude of induced axial forces in the face slab dependsalso on the opening of the vertical joints between the adjacentslabs, or on the permitted amount of the relative movement.Haeri and Karimi [13] investigated the effects of initial jointsopening on the induced forces in the face slab. They concludedthat, when the joints are assumed to be rigid and no clearance ispresent between the vertical joints, the relative movements of theabutments exert very high axial forces in the face slab. In fact, thevertical joints between slab panels can absorb a remarkable partof the relative movement of the abutments.

The contour lines of maximum longitudinal axial stresses inthe face slab are shown in Figs. 12 and 13. The longitudinaldirection is defined along the slab panels from the dam crest tothe riverbed or abutment. The slab experiences high axial forcesin the longitudinal direction in which the slab panels are structu-rally continuous. As the tensile strength of the plain concrete isabout 3–4 MPa, such stresses in the location near the riverbedcould lead to tensile failure in the face slab.

4.1.3. Movement of vertical joints

In addition to induced forces in the face slab, movement of thevertical joints is important for slab stability. Three types of jointmovement (opening normal to the joint, shear parallel to thejoint, and movement normal to the concrete slab) are expected invertical joints (illustrated in Fig. 14, schematically).

Fig. 15 shows the maximum joint opening computed in bothcases. As the joint opening is dependent upon the out-of phaselateral movements of the abutments, in the scattered excitation

e seismic analysis: (a) non-scattered excitation and (b) scattered excitation.

ic analysis: (a) non-scattered excitation and (b) scattered excitation.

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804802

case, vertical joint opening movements are greater than thoseobtained for the non-scattered excitation case.

The time history of the relative movement of the abutments atdifferent levels in the N–S direction is depicted in Fig. 16. Asobserved, the maximum joint opening movement increases by anincrease in elevation. It is also evident that higher openingmovements have appeared near the upper side of the leftabutment in which the magnitude of relative lateral movementof the abutments is considerable.

Fig. 17 also indicates the distribution of relative joint move-ments normal to the face slab. The normal movement of verticaljoints is due to the flexural deformation of slab panels resultedfrom repeated uplift and downfall of the slab on the dam body.Distribution of maximum relative shear movement of the verticaljoints on the face slab is also shown in Fig. 18. The magnitudes ofshear movements are larger at the areas close to perimetric joints.However, the shear movements are negligible compared to theopening and normal joint movements.

4.2. Effect of reservoir water on CFR dam and concrete slab seismic

response

In this section, the effects of reservoir water on the seismicresponse of CFR dam considering the non-uniform scattered

Displacement response (mm)

Acceleration response (m/sec2)

Fig. 19. Contours of maximum displacements and accelerations of dam body

during the seismic analysis for empty (dashed line) and full (solid line) reservoir:

(a, c) vertical response in E–W longitudinal section and (b, d) horizontal response

in N–S transverse section.

motion are investigated. For this purpose, the reservoir isassumed filled 90 m. As explained in Section 2.1, Ps in Eq. (12)represents the externally applied forces such as reservoir waterpressure during the seismic analysis. In this analysis, the hydro-static effect of impounded water is considered, and the hydro-dynamic effects are ignored. However, Irani et al. [19] carried outa 2D finite element analysis to study the effects of reservoirhydrodynamic on the seismic behaviour of CFR dams usingLagrangian (displacement based) approach for fluid elements.They noted that the hydrodynamic effect increases the responseof the dam and concrete slab to about 5%.

In Fig. 19, the contour lines of the maximum vertical andhorizontal displacements and accelerations during the seismicanalysis and for the empty and full reservoir are shown. It can beinferred that reservoir confinement hardens the dam body mate-rial, and consequently the horizontal displacement in N–S direc-tion are reduced. However, the horizontal acceleration changesmore slightly in N–S direction. As seen in Fig. 19c, the verticalacceleration in the dam body has increased in middle of the dam.In fact, the reservoir confinement in terms of changing therelative impedance of dam–foundation system can amplify theinteraction response of the dam body.

The distribution of maximum horizontal compressive andtensile stresses in the face slab for empty and full reservoir isdepicted in Figs. 20, and 21. It can be observed that the reservoirwater leads to an increase in horizontal compressive stresses.However, the horizontal tensile stresses have been decreased.The same trend is seen in Figs. 22 and 23 where the longitudinalcompressive and tensile stresses are shown. In Fig. 23b, the distri-bution of tensile stresses for the middle panel of concrete slab is

-0.5

-1

-1.5

-2

-1.5

-1-0.5

-2

-1.5

-0.5

-2

-1.5

-1.5

-.05

-1

-1.5

-1

-0.5

-1

-1

Fig. 20. Contour lines of maximum horizontal compressive stresses (MPa) in the

face slab for empty (dashed line) and full (solid line) reservoir.

1

1.5

0.5

0.50.5

0.5

0.50.50.5

1

1

1

0.5

1.5

Fig. 21. Contour lines of maximum horizontal tensile stresses (MPa) in the face

slab for empty (dashed line) and full (solid line) reservoir.

20

20

20

20

20

40

40

40

60

6060

100

20

20 20

20

20

04

40 40

40

60 100

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804 803

shown for both cases. As seen, in the case of full reservoirthe maximum tensile stresses are reduced to about 60% in theaverage level of the reservoir depth. In general, the tensilestresses in the face slab panels are induced due to repeated upliftand downfall of the slab on the dam body under seismic loading.By applying the reservoir water pressure the uplift movements ofthe slab panels, and consequently the tensile stresses havedecreased during the analysis.

In Fig. 24, the maximum vertical joint opening and normalmovements are shown. It is can be seen that in the case of fullreservoir, the joint movements in general are reduced. This is

1

1

1

22

2

3

1

2

2

3

3

1

020406080

100120140160180

4000

Slab

leng

ht (m

)

Maximum tensile stress (MPa)

Empty Full

0 1000 2000 3000

Fig. 23. (a) Contour lines of maximum longitudinal tensile stresses (MPa) in the

face slab for empty (dashed line) and full (solid line) reservoir. (b) Maximum

longitudinal tensile stresses in the middle slab panel.

20

70

60

50

40

40

30

10 10

50

40

20

60

80

70

60

50

50

10 2030

40

Fig. 24. (a) Maximum joint opening movement (mm) and (b) maximum joint

normal movement (mm) computed during the seismic analysis for empty (dashed

line) and full (solid line) reservoir.

-1

-1

-1

-2

-3

-4

-5

-1

-2

-2 -3

-3-4

-2

Fig. 22. Contour lines of maximum longitudinal compressive stresses (MPa) in the

face slab for empty (dashed line) and full (solid line) reservoir.

more evident for the normal joint movements where reservoirwater confinement has limited the relative uplift of the slabpanels during the earthquake shakings. However, the openingmovements are significant, and the local failure of constrictionjoints in strong ground motions is inevitable.

5. Conclusion

The main purpose of the present study is to evaluate theeffects of the scattering and diffraction of seismic waves on theearthquake response of CFR dams built in the canyons. The scaledboundary finite element method (SBFEM) is used to assessscattered motion and interaction forces along the canyon. Thedam is subjected to spatially variable P, SV, and SH waves, and theinertial effect of dam–foundation interaction is considered. A non-linear model for rockfill material has been used. The Coulombfriction law is applied to describe the behaviour of the slab rockfillinterface, and the vertical joints are modelled between adjacentconcrete panels. The seismic response of CFR dams subjected tonon-scattered and scattered excitations is investigated. The hydro-static effects of reservoir water on the dam body and concrete slabare presented using the scattered input excitation. Finally, thefollowing statements can be concluded:

1.

Wave scattering due to the canyon geometry and dam–foundation interaction effects are the most important aspectsof realistic seismic analysis of CFR dams built in the canyons.Applying the scattered motion on the canyon significantlyincreases the response of the dam and concrete face slab.Due to wave scattering of the same earthquake record, a

A. Seiphoori et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 792–804804

completely different seismic response is anticipated in thedam body and face slab depending on the observed location.Local amplification of displacements and stresses in concreteslab are observed due to wave scattering. Considering thereservoir water pressure considerably affects the amount oftensile stress of the face due to reduction of uplift movementof the concrete panels.

2.

Out-of-plane motion of the opposite abutments causes a largeaxial force in the face slab. This is particularly significant in thedirection in where the dam body is confined by the canyon.The concrete face slab experiences high axial forces in thelongitudinal direction, and is vulnerable to tensile failurewhere requires appropriate reinforcing.

3.

The significant effect of scattered motion on the openingmovement of the vertical joints is observed. Although thenormal movements of vertical joints are reduced due to thereservoir water confinement, the opening movements are stillsignificant. Therefore, the flexibility of vertical joints is animportant problem to address; the joints should be capable ofopening and closing, and to undergo lateral movements,without failure.

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