the effect of concrete slab–rockfill interface behavior on the earthquake performance of a cfr dam
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The effect of concrete slab–rockfill interface behavior on the earthquake performance of a CFR damTRANSCRIPT
International Journal of Non-Linear Mechanics 46 (2011) 35–46
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International Journal of Non-Linear Mechanics
0020-74
doi:10.1
n Corr
E-m
journal homepage: www.elsevier.com/locate/nlm
The effect of concrete slab–rockfill interface behavior on the earthquakeperformance of a CFR dam
Alemdar Bayraktar a, Murat Emre Kartal b,n, Suleyman Adanur a
a Karadeniz Technical University, Department of Civil Engineering, 61080 Trabzon, Turkeyb Zonguldak Karaelmas University, Department of Civil Engineering, 67100 Zonguldak, Turkey
a r t i c l e i n f o
Article history:
Received 14 June 2009
Received in revised form
23 June 2010
Accepted 6 July 2010
Keywords:
Concrete-faced rockfill dam
Dam–reservoir interaction
Drucker–Prager model
Friction contact
Interface element
The Lagrangian approach
62/$ - see front matter & 2010 Elsevier Ltd. A
016/j.ijnonlinmec.2010.07.001
esponding author. Tel.: +90 372 257 4010; fa
ail address: [email protected]
a b s t r a c t
Earthquake response of the concrete slab is mostly depended upon its conjunction with rockfill. This
study aims to reveal the effect of concrete slab–rockfill interface behavior on the earthquake
performance of a concrete-faced rockfill dam considering friction contact and welded contact. Friction
contact is provided by using interface elements with five numbers of shear stiffness values. 2D finite
element model of Torul concrete-faced rockfill dam is used for this purpose. Linear and materially
non-linear time-history analyses considering dam–reservoir interaction are performed using ANSYS.
Reservoir water is modeled using fluid finite elements by the Lagrangian approach. The Drucker–Prager
model is preferred for concrete slab and rockfill in non-linear analyses. Horizontal component of 1992
Erzincan earthquake with peak ground acceleration of 0.515g is used in analyses. The maximum and
minimum displacements and principal stresses are shown by the height of the concrete slab and
earthquake performance of the dam is investigated considering different joint conditions for empty
and full reservoir cases. In addition, potential damage situations of concrete slab are evaluated.
& 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Concrete-faced rockfill (CFR) dams are considered to be safeunder seismic excitations because of two following origins [1].First, porewater development and strength descent do not occurbecause the entire CFR dam embankment is waterless during anearthquake. Second, CFR dams provide more stability with theirwhole rockfill mass than earth core rockfill (ECR) dams, since CFRdams do not permit water to penetrate inside the dam on theother hand only downstream rockfill mass of the ECR dams mayresist for stability under seismic excitations.
CFR dams involve fluid–structure interaction problems. Hydro-dynamic pressures resulted from earthquakes considerably affectdynamic response of dams. The hydrodynamic pressure effects ondynamic response of dams have been started to be researched inthe 1930s [2–4]. Dynamic response of dam–reservoir systemsusing the Eulerian and the Lagrangian approaches has beeninvestigated by many researchers [5–14]. In the last years,Bayraktar et al. [13–15] paid attention on hydrodynamicpressures on concrete slab of CFR dams.
Earthquake analysis of CFR dams subjected to strong groundmotion was carried out and published in the literature by variousresearchers [1,13–22]. In addition, a new approach based on
ll rights reserved.
x: +90 372 257 4023.
(M.E. Kartal).
scaled boundary-finite element method was used to obtainscattered motion along a prismatic canyon with trapezoidal crosssection [23]. The authors performed three-dimensional dynamicanalysis of a typical CFR dam including dam-face slab–abutmentsinteraction using scaled boundary-finite element method.Ghannad [24] performed numerical (finite element method) andanalytical analyses of a CFR dam, which is located in a highseismicity region of Iran, and compared the results. The effect ofnon-linearity and time-dependent deformation on the separationof the concrete slab from the cushion layer was examined usingcontact analysis method [25]. Beyond these studies, there islimited research related to earthquake performance of CFR dams.Particularly, performance analysis of a CFR dam includingdam–reservoir interaction and slippage–separation in concreteslab–rockfill interface is rarely seen in the literature.
Interface elements have a wide range of use to describe theinteraction between different media [26–31]. Various researchersinvestigated discrete joints in non-linear analyses [32–38]. Inter-face elements were used to determine the effect of discontinuitieson the response of circular tunnels established in layeredgeological media by Lee and Zaman [39]. The seismic responseof rigid highway bridge abutments, retaining and founded on drysand was examined considering sliding and debonding/recontactbetween the wall and the soil [40]. Toki et al. [41,42] used jointelements for dynamic analysis of soil–structure interactionsystems to simulate time-dependent sliding and separation alongthe soil–structure interface. The interface behavior in reinforced
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–4636
embankments on soft grounds was researched considering slipbetween soil and reinforcement according to Mohr–Coulombstrength criterion with interface elements [43]. Nam et al. [44]used elasto-plastic interface element to predict static anddynamic behaviors of underground RC structures. Proposedinterface model was quiet well in agreement to describe theinteraction between the underground RC structure and thesurrounding soil media. Uddin [45,46] performed dynamicanalyses using interface elements for the potential sliding inter-face in embankment of an ECR dam and also for the interaction ofconcrete slab–rockfill in a CFR dam.
This study investigates the effect of interface behaviorbetween concrete slab and rockfill on the earthquake responseand performance of a CFR dam including hydrodynamic effects.For this purpose, two-dimensional dam and dam–reservoir finiteelement models are used. Hydrodynamic pressure is taken intoconsideration by the Lagrangian approach using two-dimensionalfluid finite elements. Both material and connection non-linearityare considered in finite element analyses. Drucker–Prager modelis used for concrete slab and rockfill in materially non-linearanalyses. Welded and friction contact is considered in concreteslab–rockfill interface. Friction is considered with interfaceelements. Earthquake response and performance of Torul CFRDam are investigated considering different joint conditionsbetween concrete and rockfill. All numerical analyses areperformed using ANSYS [47].
2. Formulation of dam–reservoir interaction by theLagrangian approach
The formulation of the fluid system based on the Lagrangianapproach is presented as following [48,49]. In this approach, fluidis assumed to be linearly compressible, inviscid and irrotational.For a general three-dimensional fluid, pressure–volumetric strainrelationships can be written in matrix form as follows:
P
Px
Py
Pz
8>>><>>>:
9>>>=>>>;¼
C11 0 0 0
0 C22 0 0
0 0 C33 0
0 0 0 C44
266664
377775
ev
wx
wy
wz
8>>><>>>:
9>>>=>>>;
ð1Þ
where P, C11, and ev are the pressures which are equal to meanstresses, the bulk modulus and the volumetric strains of the fluid,respectively. Since irrotationality of the fluid is considered likepenalty methods [50,51], rotations and constraint parameters areincluded in the pressure–volumetric strain equation (Eq. (1)) ofthe fluid. In this equation, Px, Py and Pz, are the rotational stresses;C22, C33 and C44 are the constraint parameters and wx, wy and wz
are the rotations about the cartesian axis x, y and z, respectively.In this study, the equations of motion of the fluid system are
obtained using energy principles. Using the finite elementapproximation, the total strain energy of the fluid system maybe written as
pe ¼1
2UT
f Kf Uf ð2Þ
where Uf and Kf are the nodal displacement vector and thestiffness matrix of the fluid system, respectively. Kf is obtained bythe sum of the stiffness matrices of the fluid elements as follows:
Kf ¼X
Kef
Kef ¼
ZV
BeTf Cf Be
f dVe ð3Þ
where Cf is the elasticity matrix consisting of diagonal terms inEq. (1). Be
f is the strain–displacement matrix of the fluid element.
An important behavior of fluid systems is the ability todisplace without a change in volume. For reservoir and storagetanks, this movement is known as sloshing waves in which thedisplacement is in the vertical direction. The increase inthe potential energy of the system because of the free surfacemotion can be written as
ps ¼1
2UT
sf Sf Usf ð4Þ
where Usf and Sf are the vertical nodal displacement vector andthe stiffness matrix of the free surface of the fluid system,respectively. Sf is obtained by the sum of the stiffness matrices ofthe free surface fluid elements as follows:
Sf ¼P
Sef
Sef ¼ rf g
RAhT
s hs dAe
9=; ð5Þ
where hs is the vector consisting of interpolation functions of thefree surface fluid element. rf and g are the mass density of thefluid and the acceleration due to gravity, respectively. Besides,kinetic energy of the system can be written as
T ¼1
2_UT
f Mf_Uf ð6Þ
where _U f and Mf are the nodal velocity vector and the massmatrix of the fluid system, respectively. Mf is also obtained by thesum of the mass matrices of the fluid elements as follows:
Mf ¼P
Mef
Mef ¼ rf
RV HT H dVe
9=; ð7Þ
where H is the matrix consisting of interpolation functions of thefluid element. If (Eqs. (2), (4) and (6)) are combined using theLagrange’s equation [52]; the following set of equations isobtained:
Mf€Uf þK*
f Uf ¼ Rf ð8Þ
where K*f , Uf, Uf and Rf are the system stiffness matrix including
the free surface stiffness, the nodal acceleration and displacementvectors and time-varying nodal force vector for the fluid system,respectively. In the formation of the fluid element matrices,reduced integration orders are used [48].
The equations of motion of the fluid system (Eq. (8)), have asimilar form with those of the structure system. To obtain thecoupled equations of the fluid–structure system, the determina-tion of the interface condition is required. Since the fluid isassumed to be inviscid, only the displacement in the normaldirection to the interface is continuous at the interface ofthe system. Assuming that the structure has the positive faceand the fluid has the negative face, the boundary condition at thefluid–structure interface is
U�n ¼Uþn ð9Þ
where Un is the normal component of the interface displacement[53]. Using the interface condition, the equation of motion of thecoupled system to ground motion including damping effects aregiven by
Mc€UcþCc
_UcþKcUc ¼Rc ð10Þ
in which Mc, Cc, and Kc are the mass, damping and stiffnessmatrices for the coupled system, respectively. Uc, _Uc , Uc and Rc arethe vectors of the displacements, velocities, accelerations andexternal loads of the coupled system, respectively.
12
3 4
l
h
h
12
3 4
l
h
u
h
Δh=ε
h
Δu=γ
y
x
12
3 4
u1
v1
u2
v2
u3
v3
u4
v4
l
hξ
η
Fig. 2. (a) Interface finite element, (b) normal strain and (c) shear strain.
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–46 37
3. Drucker–Prager model
There are many criteria for determination of yield surface oryield function of materials. Drucker–Prager criterion is widelyused for frictional materials such as rock and concrete. Druckerand Prager [54] obtained a convenient yield function to determineelasto-plastic behavior of concrete smoothing Mohr–Coulombcriterion. This function is defined as
f ¼ aI1þffiffiffiffiJ2
p�k ð11Þ
where a and k are constants which depend on cohesion (c) andangle of internal friction (f) of the material given by
a¼ 2 sin fffiffiffi3pð3�sin fÞ
k¼6c cos fffiffiffi3pð3�sin fÞ
ð12Þ
in Eq. (11), I1 is the first invariant of stress tensor (sij)
I1 ¼ s11þs22þs33 ð13Þ
and J2 is the second invariant of deviatoric stress tensor (sij)
J2 ¼1
2sijsij ð14Þ
where sij is the deviatoric stresses as given below
sij ¼ sij�dijsm ði,j¼ 1,2,3Þ ð15Þ
In Eq. (15), dij is the Kronecker delta, which is equal to 1 fori¼ j; 0 for ia j, and sm is the mean stress and obtained as follows:
sm ¼I1
3¼s11þs22þs33
3¼sii
3ð16Þ
If the terms in Eq. (15) are obtained by the Eq. (16) and replaced inEq. (14), the second invariant of the deviatoric stress tensor can beobtained as follows:
J2 ¼1
6ðs11�s22Þ
2þðs22�s33Þ
2þðs33�s11Þ
2h i
þs212þs
213þs
223
ð17Þ
It is observed from Fig. 1 that a smooth surface is obtainedremoving Coulomb corner spots [55].
4. Interface element formulation
The formulation of the stiffness matrix of two-dimensionalinterface element is presented in this section. The geometry of theinterface element is shown in Fig. 2(a). Since the interfaceelement represents the interaction characteristics between two
−σ1
−σ3
Hydrostatic Axis(σ11 = σ22 = σ33)
Failure Surface of Drucker-Prager
Failure Surface of Coulombc Cotφ
−σ2
Fig. 1. Failure criteria for Coulomb, Drucker–Prager and von Mises [55].
different materials and is not a material itself, there exist only anormal stress and shear stress [56].
Displacements in the upper and lower faces are independentlyinterpolated as follows:
uupp ¼N1u1þN2u2, vupp ¼N1v1þN2v2
ulow ¼N3u3þN4u4, vupp ¼N3v3þN3v4ð18Þ
Ni ¼1
4ð17xiÞð17ZiÞ ð19Þ
With reference to Fig. 2, strains are computed from Eq. (20) asshown in Fig. 2(b)
feg ¼gyx
ey
( )¼
uupp�ulow
vupp�vlow
( )�h ð20Þ
in which ey and gyx represents the normal and tangential (shear)strains as shown in Fig. 2(c).
Stresses are obtained from strains and constitutive law as
fsg ¼tyx
sy
( )¼ ½D�feg ð21Þ
in which [D] is the elastic constitutive matrix given by
½D� ¼d11 0
0 d22
" #ð22Þ
From Eqs. (18) and (20), strains are written as
feg ¼ ½B�fdg ð23Þ
in which fdg and [B] are the nodal displacement vector and thestrain–displacement matrix given by
fdgT¼ u1 v1 u2 v2 u3 v3 u4 v4
n oð24Þ
B½ � ¼ B1½I� B2½I� �B3½I� �B4½I�� �
ð25Þ
with [I] being the identity matrix of order two.
00.030.060.090.120.150.180.210.240.27
0.30.330.36
1 2
Cum
ulat
ive
Dur
atio
n (s
) May require nonlinear analysis to estimate damage
Acceptable damage based on linear analysis
1.91.81.71.61.51.41.31.21.1
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–4638
On minimizing the potential energy of the element, we obtainthe stiffness matrix, [K], of the interface element in the localcoordinates. Thus
½K� ¼
ZZ½B�T ½D�½B� dx dy ð26Þ
This area integral can be easily computed if a change in thevariables is carried out by writing
dx dy¼Det½J� dx dZ ð27Þ
in which [J] is the Jacobian matrix. The element thickness is oftenassumed to be zero [57].
Demand-Capacity Ratio
Fig. 3. Accepted performance curve for CFR dams [59].
Fig. 4. Torul Dam [60]: (a) empty reservoir case and (b) full reservoir case.
5. Structural performance and damage criteria for dams
Linear time-history analysis is used to formulate a systematicand rational methodology for qualitative estimate of the level ofdamage. In linear time-history analysis, where accelerationtime-histories are the seismic input, deformations, stresses andsection forces are computed in accordance with elastic stiffnesscharacteristics of various components in time domain. A systematicevaluation of these results in terms of the demand–capacity ratios(D/C), cumulative inelastic duration, spatial extent of overstressedregions, and consideration of possible failure modes comprise thebasis for approximation and appraisal of probable level of damage.The damage for structural performance amounts to cracking ofthe concrete, opening of construction joints, and yielding of thereinforcing steel. If the estimated level of damage falls below theacceptance curve for a particular type of structure, the damage isconsidered to be low and linear time-history analysis will besufficient. Otherwise the damage is considered to be severe in whichcase non-linear time-history analysis would be required to estimatedamage more accurately [58].
5.1. Performance criteria for linear and non-linear analysis
The dam response to the maximum design earthquake isconsidered to be within the linear elastic range of behavior withlittle or no possibility of damage if computed demand–capacityratios are less than or equal to 1.0. The stage of non-linearresponse or opening and cracking of joints is considered accept-able if demand–capacity ratio is less than 2, overstressed region isless than 15% of the dam surface area, and the cumulativeinelastic duration falls below the performance curve given inFig. 3. Cumulative duration has not been defined for the concreteslab of CFR dams till now; therefore the performance curve forconcrete gravity dams is used in this study [59].
5.2. Demand–capacity ratios
The demand–capacity ratios for CFR dams can be defined asthe ratio of the computed principal tensile stresses to tensilestrength of the concrete. As discussed previously demand–capacity ratio is limited to 2.0, thus permitting stresses up totwice the static or at the level of dynamic apparent tensilestrength of the concrete, as long as the overstressed region is lessthan 15% of the dam surface area. The cumulative durationbeyond a certain level of demand–capacity ratio is obtained bymultiplying number of stress values exceeding that level of tensilestrength by the time-step of the time-history analysis. Thecumulative duration in Fig. 3 refers to the total duration of allstress excursions beyond a certain level of demand–capacityratio. Although tensile strength of concrete is affected by therate of seismic loading, the acceptance criteria employ stabletensile strength in computation of the demand–capacity ratios.
The reason for this is to account for the lower strength of the liftlines and provide some level of conservatism in estimation ofdamage using the results of linear elastic analysis.
6. Numerical model of Torul CFR dam
6.1. Torul dam
Torul CFR Dam (Fig. 4) is sited on Harsit River andapproximately 14 km northwest of Torul, Gumushane, Turkey.The dam construction was completed in 2007 by the GeneralDirectorate of State Hydraulic Works [60]. The main goal of the
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–46 39
reservoir is power generation. The volume of the dam body is4.6 hm3 and the lake area of the dam at the normal water levelis 3.62 km2. The annual total power generation capacity is322.28 GW. The length of the dam crest and the wide of thedam crest are 320 and 12 m, respectively. Besides, the maximumheight and base width of the dam are 142 and 420 m, respec-tively. The thickness of the concrete slab is 0.3 m at the crest leveland 0.7 m at the foundation level. The concrete slab has highseepage resistance. The two-dimensional largest cross section andthe dimensions of the dam are shown in Fig. 5.
6.2. Material properties
The Torul Dam body consists of concrete face slab and fiverockfill zones: 2A, 3A, 3B, 3C, 3D, respectively, from upstream todownstream. Rockfill zones were arranged from thin granules tothick particles in upstream–downstream direction. Table 1 showsthe material properties of the dam and reservoir water used inlinear and non-linear analyses. Performed materially non-linearanalysis procedure is based on the Drucker–Prager model. Thecohesion and the angle of internal friction of the dam body areassumed as 1.225 MPa and 451, respectively. The concrete slabhas tensile strength of 1.6 MPa and compression strength of20 MPa [61]. The bulk modulus of reservoir water and density areassumed as 2.07�103 MPa and 1000 kg/m3.
6.3. Finite element model
The two-dimensional dam–reservoir finite element modelused in analyses is shown in Fig. 6. In this model, dam body has592 solid finite elements, reservoir water has 495 fluid finiteelements and 16 interface elements are defined between concreteslab and rockfill. The solid elements used in the analyses have fournodes and 2�2 integration points and the fluid elements havefour nodes and 1�1 integration point. Element matrices arecomputed using the Gauss numerical integration technique [48].The damping ratio of 5% is used in finite element analyses.Coupling length is chosen as 1 mm at reservoir–dam interfaceand 15 numbers of couplings are defined in dam–reservoir model.
Fig. 5. The largest cross section of Torul Dam body [60].
Table 1Material properties of Torul CFR Dam.
Material aDmax (mm) Material proper
Modulus of ela
Concrete – 3.420E+07
2A (sifted rock or alluvium) 150 1.400E+07
3A (selected rock) 300 1.350E+07
3B (filling with quarry rock) 600 1.250E+07
3C (filling with quarry rock) 800 1.150E+07
3D (selected rock) 1000 1.000E+07
a Maximum particle size.
The main objective of the couplings is to hold equal the displace-ments between two reciprocal nodes in normal direction to theinterface. The length of the reservoir is taken as three times ofthe dam height to adequately consider reservoir water effects.
6.4. Concrete slab–rockfill interface
The earthquake response of the concrete slab is mostlydepended upon its conjunction to the rockfill. Welded contactand friction contact models can be used in this joint (Fig. 7).In fact, concrete slab does not directly contact with the rockfill.According to this observation, the use of interface element infinite element analysis can procure more realistic results.Concrete slab may slide over the surface of the rockfill by usingthis element. This element provides ability for transverse sheardeformation. This study assumes that concrete slab and rockfilldam body are independent deformable bodies by using interfaceelements and also dependent deformable bodies consideringwelded contact.
The interface element used in this study has four node andtwo integration points (Fig. 8). Normal stiffness of the interfaceelement is considered as 20�103 MPa/m. Five numbers oftransverse shear stiffness values of the interface element areused as 1.8, 3.6, 18, 180 and 1800 MPa/m in the numericalanalyses.
7. Earthquake response of Torul CFR Dam
This study investigates the earthquake response of Torul CFRDam subjected to strong ground motion is. Empty and fullreservoir cases are taken into account in the numerical solutions.The horizontal component of the 1992 Erzincan earthquakewith peak ground acceleration (pga) 0.515g is utilized in analyses.
ties
sticity (kN/m2) Poisson’s ratio Mass density (kg/m3)
0.18 2395.5
0.26 2905.2
0.26 2854.2
0.26 2833.8
0.26 2803.3
0.26 2752.3
Fig. 6. The two-dimensional finite element model including reservoir of
Torul Dam.
ConcreteSlab
Rockfill Zones
ConcreteSlab
Rockfill Zones
InterfaceInterface allowing slippage
2A 3A 3B
2A 3A 3B
Concrete Slab
TransitionZones
Transition Zones
2A
3A3B 3C
3D
2A
3A3C
3D
3B
Concrete Slab
Transition Zones: 2A, 3ARockfill Zones: 3B, 3C
Fig. 7. (a) Welded and (b) friction contact in concrete slab–rockfill interface.
x
y
i
l
kj
i-j and l-k surfacesare the contact surfaces
Fig. 8. The view of two-dimensional interface element in local coordinates [47].
Fig. 9. The location of Torul Dam [60].
-3-2-10123456
0 3 6 9 12 15 18 21 24
Time (s)
Acc
eler
atio
n (m
/s2 )
t = 3.235s
pga = 5.054 m/s2
pga = 0.0 m/s2
t = 2.75spga = 0.0 m/s2
t = 2.9s
Fig.10. 1992 Erzincan earthquake acceleration record [62].
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–4640
This earthquake record is preferred because Torul Dam is close toErzincan where severe strong ground motions occurred in lastdecades (Fig. 9) and its foundation has similar characteristics withthe place ground motion recorded. Earthquake analyses areperformed during 21.31 s (Fig. 10) and used acceleration recordis available at the PEER Strong Motion Database [62]. The timeinterval of the acceleration record is 0.005 s. Displacement andprincipal stress components by the height of the concrete slab arecompared.
7.1. Displacements
This section presents the horizontal displacements obtainedfrom linear time-history analyses by the height of the concreteslab considering different material properties of the interfaceelement. The analysis results are shown in Figs. 11–14 for emptyand full reservoir cases. It is obviously seen from Figs. 11–14 thathydrodynamic pressure of the reservoir water increases the
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–46 41
displacements for all joint conditions. Displacements decreasewith the decrease of shear stiffness of the interface element inempty reservoir case. However, those increase with the decrease
0
30
60
90
120
150
-40 0
Displacement (mm)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m
180 MPa/m 1800 MPa/m Welded Contact
-35 -30 -25 -20 -15 -10 -5
Fig. 11. The minimum horizontal displacements by the dam height in empty
reservoir case.
0
30
60
90
120
150
0 5 10Displacement (mm)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m
180 MPa/m 1800 MPa/m Welded Contact
15 20 25
Fig. 12. The maximum horizontal displacements by the dam height in empty
reservoir case.
0
30
60
90
120
150
0
Displacement (mm)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m18 MPa/m180 MPa/m
1800 MPa/m Welded Contact
-50 -45 -40 -35 -30 -25 -20 -15 -10 -5
Fig. 13. The minimum horizontal displacements by the dam height in full
reservoir case.
0
30
60
90
120
150
0 5 20
Displacement (mm)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m180 MPa/m 1800 MPa/m Welded Contact
25 301510
Fig. 14. The maximum horizontal displacements by the dam height in full
reservoir case.
of shear stiffness of the interface element if hydrodynamicspressure effects are included. In addition, displacements obtainedfrom finite element models including high shear stiffness of theinterface element come close to the ones obtained from the modelincluding welded contact.
Some deflected shapes of Torul Dam during the time intervalof 2.75 and 3.235 s are given in Fig. 15. According to Fig. 15,
Fig. 15. The deflected shapes of Torul Dam between 2.75 and 3.235 s: (a) the
deflected shape on second 2.750 (acceleration is equal to zero); (b) the deflected
shape on second 2.900 (pga is equal to 0.515g); (c) the deflected shape on
second 2.975 (minimum displacement at the crest); (d) the deflected shape on
second 3.200 (excessive deformations in downstream side) and (e) the deflected
shape on second 3.235 (acceleration is equal to zero).
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–4642
the minimum displacement of the crest does not occur on second2.9 in which the maximum ground acceleration of the earthquakeexists. The deflected shape, where the minimum horizontaldisplacement occurs, shown in Fig. 15c cannot be adequatelydistinguished because of relatively high vertical displacements ofreservoir water. Relatively excessive deformations at downstreamside near foundation and besides separation and transverse sheardeformation of the concrete slab appear on second 3.20 as shownin Fig. 15d.
7.2. Stresses
This section presents the principal tensile and compressionstresses occurred in the concrete slab by the dam height. Figs. 16and 17 refer that maximum and minimum principal stressesdecrease with the decrease of the shear stiffness of the interfaceelement in empty reservoir case. Besides, those increase with thedecrease of the shear stiffness of the interface element in fullreservoir case as shown in Figs. 18 and 19. If the analysis ignores
0
30
60
90
120
150
0
Stress (kPa)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m
180 MPa/m 1800 MPa/m Welded Contact
-7000 -6000 -5000 -4000 -3000 -2000 -1000
Fig. 16. The principal compression stresses by the dam height in empty
reservoir case.
0
30
60
90
120
150
0
Stress (kPa)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m
180 MPa/m 1800 MPa/m Welded Contact
500 1000 1500 2000 2500 3000 3500 4000 4500
Fig. 17. The principal tensile stresses by the dam height in empty reservoir case.
0
30
60
90
120
150
0
Stress (kPa)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m180 MPa/m 1800 MPa/m Welded Contact
-9000 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000
Fig. 18. The principal compression stresses by the dam height in full reservoir
case.
reservoir water effects and considers friction in concreteslab–rockfill interface, concrete slab may behave itself easilyand avoid unnecessary stress intensity resulting from rockfill.However, in full reservoir case, hydrodynamic pressure causesadditional stress density in the concrete slab.
8. Performance analysis of Torul CFR Dam
This part of the study presents earthquake performanceanalysis of Torul CFR Dam. The main objective of this study is toreveal the effect of concrete slab–rockfill interface on the earth-quake performance of a CFR dam. Therefore, this study considersfive shear stiffness values of the interface element for empty andfull reservoir cases. Time-history analyses are performed accord-ing to north–south component of 1992 Erzincan earthquakerecord shown in Fig. 10.
The demand–capacity ratios, which are evaluated between1 and 2, are considered for the principle tensile stresses occurred inthe concrete slab. The principal tensile stress cycles obtained fromlinear time-history analyses are given for different shear stiffnessvalues of the interface element in Fig. 20. As seen from Fig. 20,principal tensile stresses exceed the tensile strength of the concretenumerous times in full reservoir case even if D/C is equal to 2.Besides, the tensile stresses exceed the tensile strength of theconcrete several times in empty reservoir case as well. Fig. 20 refersthat reservoir water increases the principal tensile stresses. But,this increase is more evident in the case that shear stiffness of theinterface element is lower. For the higher shear stiffness values ofthe interface element, hydrodynamic pressure effects on theconcrete slab are relatively low. In addition to this, numericalresults of the concrete slab for the maximum shear stiffness of theinterface element are fairly close to ones of the dam includingwelded contact in concrete slab–rockfill interface.
The performance curves are drawn to determine the earth-quake performance of the concrete slab of Torul CFR Damaccording to linear time-history analyses. Those frequentlyexceed the acceptable level in empty reservoir case andcompletely exceed it by the effect of the reservoir water. Theearthquake performance of the dam involving hydrodynamicpressure effects is lower for the shear stiffness of 1.8 and3.6 MPa/m than the other ones, which are relatively close toearthquake performance of the dam modeled with welded contactin concrete–rockfill interface. Nevertheless, these shear stiffnessvalues have the increase effect on earthquake performance whenhydrodynamic pressure effects are ignored. In this conditions,earthquake performance curve fall below the acceptable level into1.5–1.8D/C interval for the shear stiffness of 1.8 MPa/m, and1.7–1.8D/C interval for 3.6 MPa/m. The performance curve for18 MPa/m is a bit lower than the curves drawn for 1.8 and3.6 MPa/m. Figs. 21 and 22 indicate that the use of higher shear
0
30
60
90
120
150
0
Stress (kPa)
Hei
ght (
m)
1.8 MPa/m 3.6 MPa/m 18 MPa/m
180 MPa/m 1800 MPa/m Welded Contact
5001000
15002000
25003000
35004000
45005000
5500
Fig. 19. The principal tensile stresses by the dam height in full reservoir case.
0
800
1600
2400
3200
4000
4800
5600
0 3 6 9 12 15 18 21 24
Stress D/C=1 D/C=2
0
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5600
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
Stress D/C=1 D/C=2
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5600
Stress D/C=1 D/C=2
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Stress D/C=1 D/C=2
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5600
Stress D/C=1 D/C=2
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800
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5600
Stress D/C=1 D/C=2
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0
800
1600
2400
3200
4000
4800
5600
Stress D/C=1 D/C=2
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Stress D/C=1 D/C=2
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Stress D/C=1 D/C=2
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Stress D/C=1 D/C=2
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5600
Stress D/C=1 D/C=2
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5600
Stress D/C=1 D/C=2
Fig. 20. The principal tensile stress cycles according to linear analyses: (a) shear stiffness is 1.8 MPa/m in empty reservoir case; (b) shear stiffness is 1.8 MPa/m in full
reservoir case; (c) shear stiffness is 3.6 MPa/m in empty reservoir case; (d) shear stiffness is 3.6 MPa/m in full reservoir case; (e) shear stiffness is 18 MPa/m in empty
reservoir case; (f) shear stiffness is 18 MPa/m in full reservoir case; (g) shear stiffness is 180 MPa/m in empty reservoir case; (h) shear stiffness is 180 MPa/m in full
reservoir case; (i) shear stiffness is 1800 MPa/m in empty reservoir case; (j) shear stiffness is 1800 MPa/m in full reservoir case; (k) welded contact in empty reservoir case
and (l) welded contact in full reservoir case.
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–46 43
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–4644
stiffness causes the earthquake performance closer to the oneof the dam including welded contact. The decrease of the shearstiffness of the interface element increases the earthquakeperformance in empty reservoir case and reduces it in full
00.15
0.30.45
0.60.75
0.91.05
1.21.35
1 2
Demand-Capacity Ratio
Cum
ulat
ive
Dur
atio
n (s
) 1.8 kPa 3.6 kPa 18 kPa 180 kPa
1800 kPa Welded Contact Acceptance Curve
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Fig. 21. Performance assessment of the dam in empty reservoir case.
00.15
0.30.45
0.60.75
0.91.05
1.21.35
1 2
Demand-Capacity Ratio
Cum
ulat
ive
Dur
atio
n (s
) 1.8 MPa 3.6 MPa 18 MPa 180 MPa
1800 MPa Welded Contact Acceptance Curve
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Fig. 22. Performance assessment of the dam in full reservoir case.
0
800
1600
2400
3200
4000
4800
5600
Time (s)
Stre
ss (
kN/m
2 )St
ress
(kN
/m2 )
Stress D/C=1 D/C=2
0
800
1600
2400
3200
4000
4800
5600Stress D/C=1 D/C=2
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
Fig. 23. The principal tensile stress cycles according to non-linear analyses: (a) shear sti
reservoir case; (c) welded contact in empty reservoir case and (d) welded contact in fu
reservoir case. According to linear analyses, performance curvesare usually over the acceptance curve in both cases so damage inconcrete appears inevitable.
The estimation of the earthquake performance of the damimplies non-linear analysis to predict realistic earthquakeperformance of the dam. Hence, non-linear analyses are per-formed to estimate the essential performance of the dam for onlywelded contact and shear stiffness of 1.8 MPa/m of the interfaceelement because the most critical tensile stresses are obtained inthese contact situations.
The maximum principle tensile stresses obtained from non-linear analyses are entirely small from the maximum tensilestrength of the concrete in empty and full reservoir cases asshown in Fig. 23. Non-linear analyses point out that principletensile stresses occurred in concrete slab are less than tensilestrength of the concrete during earthquake, so performance curveis not required to draw. According to non-linear analysis results,crack formation does not appear in the concrete slab; thereforedamage does not occur in concrete.
9. Conclusions
This paper presents the effect of the interface element, whichrepresents the friction contact in concrete slab–rockfill interface,on the earthquake response and earthquake performance of TorulCFR Dam considering dam–reservoir interaction. The reservoirwater is modeled using two-dimensional fluid finite elements bythe Lagrangian approach. The Drucker–Prager model is used innon-linear time-history analyses.
The reservoir water has an obvious effect on the earthquakeresponse of the dam. According to linear analyses hydrodynamicpressure increases the displacements and principle stresses andthis increase is more evident for low shear stiffness of the
Stre
ss (
kN/m
2 )St
ress
(kN
/m2 )
0
800
1600
2400
3200
4000
4800
5600
Stress D/C=1 D/C=2
0
800
1600
2400
3200
4000
4800
5600
Stress D/C=1 D/C=2
Time (s)
0 3 6 9 12 15 18 21 24
Time (s)
0 3 6 9 12 15 18 21 24
ffness is 1.8 MPa/m in empty reservoir case; (b) Shear stiffness is 1.8 MPa/m in full
ll reservoir case.
A. Bayraktar et al. / International Journal of Non-Linear Mechanics 46 (2011) 35–46 45
interface element. The numerical results for higher shear stiffnessvalues are close to ones of the model including welded contact.
Earthquake performance assessment of Torul CFR Damindicates that significant damages will occur in the concrete slabaccording to linear time-history analyses for each reservoir case.The hydrodynamic pressure has also considerable influence onthe earthquake performance of the dam especially for low shearstiffness of the interface element. The linear analysis resultsindicate that hydrodynamic pressure increases the damage level.So materially non-linear time-history analyses are performed andanalysis results refer that damage formation will not appear inboth reservoir cases.
As a consequence of this study, some suggestions may bearranged as follows:
�
The more realistic CFR dam models may be achievedconsidering friction contact in the joints. � In earthquake performance assessment of a CFR dam, interfaceelements should be used in concrete slab–rockfill interface.
� The hydrodynamic pressure should be considered in earth-quake performance analyses to obtain more critical results.
� The materially non-linear analyses should be performed toevaluate reliable earthquake performance of a CFR dam.
Acknowledgement
The authors would like express heartfelt thanks to Dr. YaseminBayram working at General Directorate of State HydraulicWorks, 22, Regional Directorate, Trabzon, for her contributionsto this study.
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