Engineering Structures 38 (2012) 142–152

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Engineering Structures

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Analysis of segmental piers consisted of concrete filled FRP tubes

Mohamed A. ElGawady a,⇑, Haitham M. Dawood b,1

a Washington State University, 405 Spokane Street, Sloan 101, PO Box 642910, Pullman, WA 99164-2910, United Statesb Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0002, United States

a r t i c l e i n f o

Article history:Received 24 June 2011Revised 12 December 2011Accepted 2 January 2012Available online 18 February 2012

Keywords:PiersSeismicFRP tubesBridgesSegmentedRockingFinite elementPost-tensioning

0141-0296/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.engstruct.2012.01.001

⇑ Corresponding author. Tel.: +1 509 288 1642; faxE-mail address: melgawady@wsu.edu (M.A. ElGaw

1 Research Assistant, Virginia Polytechnic Institutegraduate student, Washington State University.

a b s t r a c t

Precast segmental construction technique is an excellent candidate for economic rapid bridge construc-tion in highly congested urban environments and environmentally sensitive regions. This paper presentsthree dimensional nonlinear finite element models using ABAQUSnStandard for evaluating the behaviorof segmental precast post-tensioned piers under lateral loads. The piers were constructed by stackingprecast concrete filled fiber reinforced polymer tube segments one on top of the other and then connect-ing the assembly structurally with vertical post-tensioning tendons passing through ducts located in theprecast segments. A stress–strain relationship for confined concrete was used to model the concrete. Thepost-tensioning tendons were modeled with beam elements. The model was able to predict the backbonecurves for two piers subjected to cyclic loads. A parametric study indicated that increasing the appliedpost-tensioning force increases nominal strength. Finally, the model showed that the pier aspect ratio,cross sectional diameter size, pier size, and confinement have significant effects on the performance ofthe investigated piers.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Significant number of existing reinforced concrete (RC) struc-tures including bridges were built under the current prevailingcapacity design concept in combination with ductile design whichpermits structures to dissipate the input seismic energy in prede-fined plastic hinge regions. In the case of a strong earthquake,the energy that is dissipated in plastic hinge regions causes exten-sive damage and permanent drifts that is generally expensive to re-pair or irreparable at all and may leave the bridge unserviceable.One alternative solution to avoid residual displacements andextensive damage in design of RC structures is to use base isola-tion. However, such alternative is quite expensive and requiresadvanced dynamic analysis.

Several ancient ‘‘multi-drum’’ Greek columns have withstoodnumerous strong earthquakes with limited, if any, damage [1].The Greek columns are made by carefully fitted stone blocks‘‘drums’’ which placed on top of each other without mortar (dryjoints). During an earthquake ground motion, the blocks rock backand forth and dissipate the input seismic energy through radiationdamping, sliding, and minimal damage.

Segmental precast post-tensioned (PPT) concrete bridge piersare constructed by stacking precast concrete segments one on

ll rights reserved.

: +(509) 335-7632.ady).and State University. Former

top of the other and then connecting the assembly structurallywith vertical post-tensioning tendons passing through ducts lo-cated in the precast segments. Hence, it represents a modern andimproved version of the multi-drum Greek columns. The tendonsare anchored in the concrete foundation and in the cap beam. Asegmental PPT bridge pier will rock back and forth during groundmotion excitation and the inelastic deformations are accommo-dated within the interface joints between the segments. Fig. 1shows a schematic drawing of a rocking pier indicating stressesand strains at different heights of the pier. As shown in the figure,during ground motion excitation, the interface joint at the base willopen and stretch the tendon leading to increase in the post-ten-sioning force. If the tendon is unbonded, the increase in the axialstrain will be uniformly distributed over the whole length of thetendon and the tendon remains elastic at large displacements.Thus, the pier will remain nearly elastic and re-center uponunloading as a result of the restoring nature of the applied post-tensioning force.

The use of precast segmental construction for concrete bridges inthe United States has increased in recent years due to the demandfor shortened construction periods and the desire for innovativedesigns that yield safe, economical and efficient structures. Re-cently, New Jersey Department of Transportation (NJDOT) reducedthe construction duration of the Victory Bridge by at least 1 yearusing precast segmental construction for the superstructure andsubstructure. Such reduced construction time saved NJDOT millionsof dollars [2]. Examples of bridges constructed with segmental piersinclude Louetta Road Overpass (SH-249, Texas), Linn Cove Viaduct

List of symbols

f 0c concrete unconfined compressive stress,f 0c concrete ultimate compressive strength,ecu ultimate concrete strain,E1 modulus of elasticity of the unconfined concrete,Ej modulus of elasticity of FRP tubetj thickness of FRP tubefj hoop strength of the FRP

D concrete core diameterAR pier aspect ratioft the maximum permissible tension stress in the concreteUx, Uy, and Uz degrees of freedom in the x, y, and z directionDL axial stresses due to applied axial load, normalized by f 0cPT axial stresses due to post-tensioning forces, normalized

by f 0c

Displacementor force

Sec. 1

Sec. 2

Decompressedregion

Sec. 1

Sec. 2

Fig. 1. A schematic drawing of a rocking pier indicating stresses and strains atdifferent heights of the pier.

Post-tensioned bar

381

381

381

254

203

51

B B

SectionB-B

Post-tensioned bar

1524

254

B B

M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152 143

(Grandfather Mountain, North Carolina), Sunshine Skyway Bridge(I-275, Florida), Varina-Enon Bridge (I-295, Virginia), John T. Collin-son Rail Bridge (Pensacola, Florida), Seven Mile Bridge (Tallahassee,Florida), and the Chesapeake and Delaware Canal Bridge (St.Georges, Delaware). However, knowledge of the behavior andperformance of segmental precast bridges during earthquakes islacking, and consequently their widespread use in seismic regionssuch as California is yet to be realized. Recent tests showed thatsegmental PPT piers can safely resist lateral cyclic forces withoutexperiencing significant or sudden loss of strength [3–11].

A typical rocking pier will have an equivalent viscous dampingof about 5% even at higher drift ratios. To overcome this drawback,researchers supplied post-tensioned precast piers with simpleyield-dampers. Both internal mild steel at the interface jointsand/or external fuses were used to increase the system energy dis-sipation. However, the provided mild steel increased the residualdisplacements and damage compared to piers without mild steel[3,5,6,8–11].

Since the 1980s, concrete filled fiber reinforced polymer tubes(CFFTs) were used as piles for bridges. These piles have two mainstructural components: a fiber reinforced polymer (FRP) shell anda concrete infill. The FRP shell provides a stay-in-place concreteform, confinement to the concrete, shear reinforcement, and corro-sion protection. The continuous confinement by the jacket signifi-cantly improves the ductility and the strength of the concrete [12].In addition, CFFT has been successfully used as bridge piers, gird-ers, and piles in different field applications by several United StateDepartments of Transportation.

Several studies investigated the seismic behavior of reinforcedconcrete piers encased in FRP tubes [13,14]. Various constructiondetails between the piers and foundations were investigated. Thereinforced CFFT piers behaved similarly to conventional reinforcedconcrete piers. An experimental study investigated the cyclic per-formance of six CFFT beams under four-point bending and foundthat CFFT beams can be designed with a ductility level comparableto conventional reinforced concrete beams. Adding a moderateamount of steel reinforcement improved the cyclic performanceof the beams [15].

This paper presents a three dimensional finite element modelfor bridge piers constructed out of segmental precast post-ten-sioned concrete filled fiber reinforced polymer tubes (PPT-CFFTs).The model was first validated against the results of experimentalinvestigations on two PPT-CFFT piers. Then, the effects of the ap-plied post-tensioning force, load combination, pier aspect ratio,pier size, pier cross sectional diameter size, and pier confinementon the lateral performance of the piers were investigated.

203 381

610

457

203

610

457

Fig. 2. Schematic drawings of piers FRP1 and FRP4 [mm].

2. Experimental investigation

In this section the cyclic behavior of two PPT-CFFT piers,namely, FRP1 and FRP4 is presented [4]. Fig. 2 shows the dimen-sions of the two piers. Each pier had a diameter of 203 mm [8 in]and a clear height of 1524 mm [60 in]. The actuator for lateral

loading was attached to a 254 mm [10 in] reinforced concreteloading stub placed atop of the pier. The lateral load was appliedhalfway up the loading stub giving a total height above the topof the footing for the load application of 1651 mm [65 in]. PierFRP1 was constructed using a single segment of CFFT while pierFRP4 was constructed using four segments of CFFT each having aheight of 381 mm [15 in].

The circular tubes were made by filament-winding techniquewith ±55� glass fiber orientation with respect to the longitudinalaxis of the tube. The tube had a nominal wall thickness of3.18 mm [0.125 in] and interior diameter of 203 mm [8 in]. Thiswall thickness was designed to avoid brittle shear failure underthe anticipated ultimate lateral load of the piers [4].

144 M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152

The post-tensioning force was applied on each pier using32 mm [1.25 in] diameter Dywidag bar grade 270 passing througha 51 mm [2 in] polyvinyl chloride (PVC) duct located within thesegments (Fig. 2). Two strain gauges were mounted on the barand were used to monitor the strains in the bar during the post-tensioning and the cyclic tests. The effective strain in the bar afterpost-tensioning was approximately 1550 le, corresponding to165 kN [37 kips] or 30% of the ultimate strength of the post-ten-sioning bar .

The RC foundations of the test specimens were post-tensionedto the laboratory strong floor (Fig. 3). The specimens were sub-jected to reverse cyclic lateral loading with increasing levels of lat-eral displacements. The loading pattern for the specimensconsisted of three cycles at drift angle levels of approximately±0.6%, ±1.2%, ±1.8%, ±2.4%, ±3.0%, ±4.6%, ±5.8%, and ±7%. Then,due to the actuator limitations, the piers were subjected to half-cy-cles where the piers were pushed to the required displacement andretracted to the zero position. Specimen FRP1 was subjected to alateral drift of approximately +15%. Specimen FRP4 was subjectedto three half-cycles at drift levels of +9%, +12%, and +15%.

3. Experimental results

Both specimens were able to sustain the peak lateral load forseveral cycles at higher drifts of approximately 15% with minordamage at the edge of the FRP tube due to bearing of the FRP tubeagainst the concrete foundation. Microcracks in the concrete core

Actuator

HorizontalStays

SegmentalPier

Strong Floor

Base

LoadingFrame

LoadingHead

Fig. 3. Test setup.

Fig. 4. Hysteretic curves of spec

were also observed by the end of the test. Testing of both speci-mens was stopped once the actuator reached its displacementcapacity. Fig. 4 shows the lateral force vs. the piers lateral drift an-gles measured at the middle of the loading stubs for specimensFRP1 and FRP4 [4].

Specimen FRP1 attained its lateral drift capacity through rigidbody rotation of the whole pier around its toe due to opening ofthe interface joint at the bottom of the pier (Fig. 5).

Specimen FRP4 behaved very similar to specimen FRP1 until driftof approximately 7%. Beyond that slight opening in the second inter-face joint locating above the first segment (Fig. 6). The measuredrotations at the different cross sections of pier FRP4, at ultimatedisplacement, revealed that approximately 75% of the pier rotationsresulted from opening of the first interface joint while theremaining rotations occurred approximately due to opening of thesecond interface joint. In addition, the deformations through the dif-ferent segments were minimal i.e. the piers mainly rotated as rigidbodies. It should be noted that Priestley et al. [16] recommendeddrift level of 4.5% for collapse prevention in bridge piers since driftsbeyond that level will cause damage in other elements in the bridge.Hence, results from this experimental work beyond 4.5% drift donot have significant importance for practical applications.

The envelopes of the hysteretic loops of the tested specimensare shown in Fig. 7. As shown in the figure, both specimens exhib-ited approximately the same initial stiffness and behaved linearuntil opening of the interface joints at the bottom of the piers lead-ing to softening in the lateral stiffness. While increasing the lateralload, the neutral axis continued to move through the pier’s crosssection towards its geometric centroid, and the opening of theinterface joint between the bottommost segment and the founda-tion increased. Once the neutral axis reached the geometric cen-troid of the pier’s cross section, the tendon elongated and thepost-tensioning force increased with increasing the applied dis-placement. Such increment in the post-tensioning force led to rel-atively higher post-elastic stiffness compared to a conventionalreinforced concrete pier. Both specimens reached a lateral drift an-gle of 15% and the test was stopped. Specimen FRP1 reached a lat-eral strength of approximately 19 kN [4.3 kips] slightly higher thanspecimen FRP4 which reached a lateral strength of 17 kN [3.8 kips].More details about the experimental results are available inElGawady et al. [4].

4. Finite element modeling

This paper presents a three dimensional nonlinear finiteelement (FE) models, using ABAQUS/Standard [17], to predict thelateral force-lateral displacement of the piers presented in theexperimental work section.

imen (a) FRP1 and (b) FRP4.

Fig. 5. Uplift of pier FRP-1 during testing.

Fig. 6. Deformed shape of specimen FRP4 during the experimental work.

0

5

10

15

20

25

0 5 10 15 20

Lat

eral

Loa

d (k

N)

Drift (%)

Experimental FRP1Experimental FRP4FE Model FRP1FE Model FRP4

Fig. 7. Experimental and predicted backbone curves for piers FRP1 and FRP4.

M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152 145

4.1. Constitutive theories and mesh

Standard eight-node, fully integrated, 3D linear stress/displace-ment continuum brick elements (C3D8) were used for modelingthe core concrete, foundation, FRP tube, loading stub. The pierswere meshed such that each element height was approximately25.4 mm [1 in]. The element length in the pier radial directionwas also 25.4 mm [1 in] (Fig. 8). Standard linear space shear flexi-ble beam elements (B31) were used to model the post-tensioningbar with an approximate element length of 50 mm [2 in].

4.1.1. ConcreteThe concrete damaged plasticity model was used to define the

behavior of the concrete. Five parameters are required to definethe yield surface, flow potential, and viscosity parameters for theconcrete damaged plasticity constitutive model: the dilation anglein degrees, the flow potential eccentricity, the ratio of initial equi-biaxial compressive yield stress to initial uniaxial compressiveyield stress, the ratio of the second stress invariant on the tensilemeridian to that on the compressive meridian, and the viscosityparameter that defines visco-plastic regularization. The aforemen-tioned parameters were set to 1�, 0.1, 1.16, 0.66, and 0,respectively.

The compression behavior of the concrete was defined by con-crete compressive stress and corresponding inelastic strain data.For the concrete stress–strain relationship, the concrete core expe-riences a higher level of confinement, due to restraining action ofthe FRP tube [18]. Therefore, a stress–strain model of confinedconcrete is required. Several models for confined concrete areavailable in the literature. A stress–strain relationship for concreteconfined using FRP is used in this manuscript [19].

Fig. 8. FE model for pier FRP1. (a) Boundary conditions and applied loads and (b) mesh and parts of the pier.

Fig. 9. A stress strain curve for concrete having f 0c of 13.8 MPa.

146 M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152

To define the stress strain of a confined concrete using thismodel, the following parameters are required: the concrete uncon-fined compressive stress f 0c , modulus of elasticity of the unconfinedconcrete E1, modulus of elasticity of FRP tube Ej, thickness of FRPtube tj, hoop strength of the FRP fj, concrete core diameter D. Themeasured unconfined concrete compressive strength and elasticmodulus were 13.8 MPa [2000 psi], and 13,617 MPa [1975 ksi],respectively. The tube had a compressive strength and elastic mod-ulus of 192 MPa [27.875 ksi], and 16,600 MPa [2410 ksi], respec-tively; and tensile strengths and elastic tensile strengths andelastic tensile modulus of the FRP are 110 MPa, and 13848 MPa[2000 ksi] respectively. The used stress–strain model assumes thatthe axial stress–strain of the confined concrete is approximately bi-linear and can be calculated using Eq. (1). The concrete ultimatestrain ecu and ultimate stress fcu can be evaluated using Eqs. (2)–(6). Note that Eqs. (2)–(6) use imperial units [19].

fcðecÞ ¼ðE2 � E1Þecf 0cu � fo

1þ ðE1 � E2Þ ecfo

h i1:5� � 1

1:5þ E2ec ð1Þ

f 0cu ¼ f 0c þ 3:38f 0:7r ð2Þ

fr ¼2f jtj

Dð3Þ

ecu ¼f 0cu � fo

E2ð4Þ

E2 ¼ 52:4f 00:2c þ 1:3Ejtj

Dð5Þ

fo ¼ 0:872f 0c þ 0:371f r þ 0:908 ð6Þ

The stress strain of the confined concrete, used in the construc-tion of FRP1 and FRP4, were calculated using Eqs. (2)–(6) and pre-sented in Fig. 9. The concrete constitutive law was prescribed bytabular data which specifies the stress and corresponding valuesof plastic strain. The concrete for the loading stub and foundationwas modeled using a linear elastic concrete definition since dur-ing the experimental work they did not suffer any damage orcracking.

Concrete tension stiffening was prescribed using tabular formas a function of the cracking strain. Eq. (7) is used to calculatethe maximum permissible tension stress in the concrete [20].

ft ¼ 7:5ffiffiffiffif 0c

qð7Þ

4.1.2. Post-tensioning barThe post-tensioning bar had a diameter of 32 mm [1.25 in] and

the classical metal plasticity model was used to define the behav-ior of the post-tensioning bar material. Material properties for thebar, including elastic modulus of 204,774 MPa [29,700 ksi], yieldstress of 874 MPa [126.8 ksi], Poisson ratio of 0.3, ultimate strainof 10%, ultimate stress of 1110 MPa [160.9 ksi], were provided bythe bar manufacturer. The post-tensioning bar was embedded inthe loading stub and foundation using an embedded regionconstraint type.

4.2. Boundary and initial conditions

To simulate a cantilevered structure, the Ux, Uy, and Uz degreesof freedom (DOF) (Fig. 8) were constrained for all the nodes at thebottom surface of the foundation while the Ux and Uy DOF at the

M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152 147

top of the column were unrestrained to simulate a free end. A sym-metry (ZSYMM) boundary condition was also applied to the em-ployed plane of symmetry.

4.3. Behavior at contact

When the post-tensioning bar, PVC tube, FRP tube, or concretesurface come into contact with each other, a contact interface algo-rithm is used to transmit stresses between different contacted sur-faces. Separated surfaces come into contact when the clearancebetween them reduces to zero. The used contact algorithm has afinite sliding formulation where the contact area and pressures ata specific interface is estimated from the deformed shape of thestructural elements. Master and slave formulation was used to de-fine the form of contact between the different surfaces. Shear stres-ses between contacted surfaces were transmitted tangentially byCoulomb friction model i.e. proportional to the normal stress atthe interface. The normal direction of the contact surface is definedusing hard contact i.e. coupling of the displacements using con-straint equations and node to surface discretization method. Usinghard contact allows for enforcing exact constraints which does notallow the nodes from the slave surface to penetrate the master sur-face and do not provide any tensile strength [17].

The normal stresses reach zero when a gap exist between thedifferent surfaces and some value when contact occur betweenany two surfaces. The contact formulation is implemented usingLagrange multiplier method and is solved using the Newton–Raph-son iteration method. The Lagrange multiplier method increasesthe number of degrees of freedom leading to potential convergenceissues. For tangential components of the contact surfaces, coeffi-cients of frictions of 0, 0.5, and 0.1 were selected for post-tension-ing bar/PVC tube, concrete/concrete and concrete/FRP tubesurfaces, respectively.

4.4. Model loading

Loading of the pier in the finite element analysis was a two-stepprocess. First, a post-tensioning force after elastic shortening of

Fig. 10. Deformed shape o

approximately 165 kN [37 kips] was applied. Then, the pier waslaterally loaded in a displacement control. The lateral displacementwas applied at the middle of the loading stub (Fig. 1) and it was in-creased monotonically until failure of the pier was observed. In thisstudy, failure was defined as the displacement at which the FEmodel can’t proceed any further.

5. Model results

The model was able to capture the general behavior of the testspecimens quite well. Figs. 6 and 10 show the pier deformed shapeobtained from the experimental tests and the FE analysis. Asshown in the figure, the FE model predicted the general deformedshape with the opening of the interface joints at the base. However,beyond a drift of 7% the opening of the second interface joint in theexperimental work was slightly higher than those predicted usingthe finite element analysis. Fig. 7 shows the backbone curves ob-tained from the FE models plotted on the same graph with theexperimental results. As shown in the figure, under small lateralforce, the FE analysis showed a linear response of the pier. Whenthe applied lateral force caused decompression stress at the healof the pier a limited geometrical nonlinearity started correspond-ing to opening of the interface joint between the bottommost seg-ment and the foundation. Beyond that and by increasing theapplied lateral displacement, the extension of the interface jointopening increased until it reached the location of the post-tension-ing bar leading to increase in the post-tensioning force. The FEmodel slightly overestimated the resistance of the piers until driftof 7% for multi-segment pier. Beyond that the finite element pre-dicted a slightly stiffer behavior since the opening of the secondinterface joint was generally smaller in the finite element com-pared to the experimental results. For single-segment pier, the fi-nite element prediction was generally in a good agreement withthe experimental results since the size of the bottommost interfacejoint opening during the experimental work was very close to thatpredicted by the finite element analysis. In addition, the modelshowed that the piers will reach their ultimate displacement at alateral drift angle of approximately 25%. At this drift limit the toe

f multi-segment pier.

Fig. 11. Damage to the piers at failure. (a) Single-segment pier and (b) multi-segment pier.

148 M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152

of each pier was subjected to very high stress concentration lead-ing to truncation of the analysis (Fig. 11).

It is worth noting that the experimental work was stoppedbecause the actuator reached its displacement capacity withoutfailure of the piers. For a typical bridge pier in real service, defor-mations of more than 4.5% drift limits are beyond the anticipatedperformance drifts at collapse prevention limit state. Hence, thedeveloped finite element model within this range is consideredadequate to predict the backbone curve for this type of piers andto carry out parametric studies to study the effects of differentdesign parameters on the backbone curves of PPT-CFFT piers.

6. Parametric study

The piers in this parametric study have f 0c ¼ 41:4 MPa[6000 psi], a FRP confining tube thickness = 19 mm [0.75 in], theFRP characteristics were similar to those used in piers FRP1 andFRP4. Two sets of piers were investigated in this parametric study:set ‘‘L’’ including piers that have a large diameter of 1220 mm[48 in] while set ‘‘S’’ including piers that have a small diameterof 610 mm [24 in]. The post-tensioning tendons had nominaldiameters of 176 mm [6.92 in] and 93 mm [3.68 in] for ‘‘S’’ and‘‘L’’ series, respectively. The piers have variable heights rangingfrom 1830 mm [72 in] to 9145 mm [360 in]. All the piers were sub-jected to external gravity load corresponding to an axial stresses,normalized by f 0c , (DL) of 5%, unless otherwise mentioned. The pierswere subjected to variable post-tensioning forces corresponding toaxial stresses, normalized by f 0c , (PT), ranging from 10% to 30%.These variations in the applied post-tensioning forces wereachieved by increasing the stresses in the tendons from 20% to60% of the yield stresses of the tendons, respectively.

6.1. Effects of applied post-tensioning force

Fig. 12 shows the effects of changing the applied post-tension-ing force on the backbone curves of three different piers of the S-set . The piers have three different aspect ratios (ARs) of 3, 6, and9, where the AR is the height of the pier measured from its bottomto the point of the applied lateral load divided by the diameter ofthe pier . As shown in the figure, increasing PT from 10% to 30% in-creased the piers nominal strengths. The rate of increase in thenominal strength is higher for slender piers compared to squatpiers. For a given aspect ratio, increasing the post-tensioning stres-ses in the tendon led to early yielding of the tendon. Yielding of thetendon is characterized by softening in the backbone curve due todegradation in the lateral strength and stiffness. Under earthquakeexcitation, yielding of the tendon leads to losses in the post-ten-

sioning forces. However, for all cases presented in the figure, theearliest yielding in a tendon occurred at a drift of approximately7% for pier having an AR = 3 and PT = 30%. A typical bridge pierwould be anticipated to reach a drift of approximately 4.5% underthe maximum credible earthquake.

6.2. Load combination effects

Fig. 13 shows the backbone curves for three piers of S serieshaving AR of 3, 6, and 9. Each pier was subjected to a sum of DLand PT of 25%. However, two different load combinations wereinvestigated. Case I has PT = 15% and DL = 10% while case II hasPT = 20% and DL = 5% i.e. the sum of the PT and DL in each case is25%. As shown in the figure, for drift angles smaller than approxi-mately one-half the ultimate drift angle of each pier, the backbonecurves are not sensitive to the loading combinations. However, be-yond such drift angle, piers having higher PT yielded at smallerdrift angles compared to those having smaller PT. Relatively earlyyielding of the tendon in the case of piers having higher PT led tosmaller ultimate resistance. Hence, for practical application andwithin drift angles of 4.5% or smaller, it seems appropriate for a de-sign model to consider the effect of the total axial stresses ratherthan distinguish the effects of the axial stresses due to gravityloads and post-tensioning forces.

6.3. Effects of pier aspect ratio

Fig. 14 shows the backbone curves for four different piers of theS series having AR = 3, 6, 9, and 15. Each pier had PT = 20% andDL = 7%. As shown in the figure, decreasing the aspect ratio of a pierincreased the pier initial stiffness, nominal strength, and ultimatestrength. However, such increase in the ultimate strength cam-paigned by a significant decrease in the pier deformation capacity.In addition, yielding of the tendons occurred at small drift anglesfor squat piers. Yielding of the tendon occurred at drifts rangedfrom 10% for AR = 3 to 30% for AR = 15.

6.4. Pier size effects

Fig. 15 shows the backbone curves for two piers: one pier fromthe S set and the other one from the L set . Each pier has an aspectratio of 3. The piers were investigated under two values of PT of10% and 30%. The applied lateral loads on both piers were normal-ized by the cross sectional areas of each pier. As shown in the fig-ure, for the same PT value both piers have the same shear stressesfor a given drift angle until opening of the interface joints at thebases of the piers. Once the interface joints opened, the shear stres-ses for the smaller pier are higher than those of the larger pier at a

0

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800

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Loa

d (k

N)

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PT=10%

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d (k

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PT=10%

PT=15%

Pt=20%

PT=30%

(a) (b)

(c)

Fig. 12. Effects of changing the applied post-tensioning forces on the backbone curves of piers having aspect ratios of: (a) 3, (b) 6, and (c) 9 (note the different scales in thegraphs).

0

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Loa

d (k

N)

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PT=20%+DL=5%PT=15%+DL=10%

(a) (b)

(c)

Fig. 13. Effects of different combinations of axial stresses for piers having AR = (a) 3, (b) 6, and (c) 9 (note the different scales in the graphs).

M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152 149

given drift angle. Finally, the smaller pier reached yielding of thetendon at smaller drift angle compared to the larger pier. The ten-don yielded at drift angles ranged from approximately 7% forPT = 30% to 10% at PT = 10%. The corresponding values for largepiers are 10% and 15%, respectively.

6.5. Diameter size effects

Fig. 16 shows the backbone curves for six different piers repre-senting three different groups. Each group includes one pier of theS set and one from the L set. The piers in each group has identical

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AR=3.00AR=6.00AR=9.00AR=15.00

(a) (b)

Fig. 14. Effects of piers aspect ratios on the lateral drift angles vs. (a) lateral load and (b) lateral load normalized by the cross sectional area.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20

Lat

eral

Stre

ss(N

/mm

2 )

Drift (%)

Dia=610 mmDia=1220 mm

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20

Lat

eral

Stre

ss(N

/mm

2 )

Drift (%)

Dia=610 mmDia=1220 mm

(a) (b)

Fig. 15. Backbone curves for two piers having AR = 3 and different sizes for (a) PT = 10%, and (b) PT = 30%.

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25

Lat

eral

Str

es s

(N/m

m2 )

Drift (%)

AR=3.00AR=6.00

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30

Lat

era

lStr

ess

(N/m

m2 )

Drift (%)

AR=4.50AR=9.00

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40

Lat

eral

Str

ess

(N/m

m2 )

Drift (%)

AR=7.50AR=15.00

(a) (b)

(c)

Fig. 16. Backbone curves for piers from the S series (dashed line) and L series (solid line) having heights of: (a) 3660, (b) 5490, and (c) 9150 mm.

150 M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152

height of 3660 mm [144 in], 5490 mm [216 in], or 9150 mm[360 in]. The lateral forces were normalized by the piers cross sec-

tional areas and presented as lateral (shear) stresses. As shown inthe figure, the pier diameter size has a significant effect on the

H HD1 D2

Fig. 17. An approximate mechanism for rocking of two piers having the sameheight but with different cross sectional diameter.

M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152 151

shear stresses and limited effects on the lateral drift angle capacity.Piers of the L set consistently were able to resist higher stressescompared to those of the S set at the same drift angle. For the samepier height, increasing the piers diameter by 100% increased thelateral shear stresses by approximately 100%. Fig. 17 shows anapproximate mechanism for rocking of two piers having the same

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25

Lat

eral

Loa

d (k

N)

Drift (%)

PT=10%

PT=15%

Pt=20%

PT=30%

(a) (b

Fig. 18. Backbone curves for piers of the L series con

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30

Lat

eral

Loa

d (k

N)

Drift (%)

PT=10%PT=15%Pt=20%PT=30%

(a) (

Fig. 19. Backbone curves for piers of the S series con

0

10

20

30

40

50

60

70

80

90

0.000 0.005 0.010 0.015 0.020 0.025

Stre

ss (

MP

a)

Strain (mm/mm)

Diameter= 610mmDiameter=1220mm

(a) (

Fig. 20. The stress–strain relationships for piers from the S and L

height but with different cross sectional diameters. As shown inthe figure, for the same drift angle, increasing the pier cross sec-tional diameter increases the lever arm between the compressionforces in the concrete toe and the tension forces in the tendon. Inaddition, moving the tendon far from the rocking pivot increasesthe stretch in the tendon leading to higher post-tensioning stressesand higher lateral resistance. Finally, increasing the diameter sizeslightly reduced the displacement capacity of the piers. However,all the piers reached lateral drift angles significantly higher than4.5%.

6.6. Confinement effects

Figs. 18 and 19 show the backbone curves for four piers: twofrom the S set and two from the L set . Each pier has a height of5487 mm [216 in]. The piers were subjected to PT ranged from10% to 30%. The piers were constructed with two different FRP

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25

Lat

eral

Loa

d (k

N)

Drift (%)

PT=10%

PT=15%

Pt=20%

PT=30%

)

structed using (a) weak FRP and (b) strong FRP.

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30

Lat

eral

Loa

d (k

N)

Drift (%)

PT=10%PT=15%PT=20%PT=30%

b)

structed using (a) weak FRP and (b) strong FRP.

0

10

20

30

40

50

60

70

80

90

0.000 0.005 0.010 0.015 0.020 0.025

Stre

ss (

MP

a)

Strain (mm/mm)

Diameter= 610mmDiameter=1220mm

b)

series confined using (a) weak FRP and (b) strong FRP tubes.

152 M.A. ElGawady, H.M. Dawood / Engineering Structures 38 (2012) 142–152

tubes. Both tubes have the same thickness of FRP but the secondtube having a tensile stress of 275.79 MPa [40 ksi] and E modulusof 24,821 MPa [3600 ksi] representing a stronger and stiffer FRPtubes available in the market. Fig. 20 shows the stress–strainbehavior for the S set and L set confined using the different FRPmaterials. As shown in Figs. 18 and 19, increasing the modulus ofelasticity and tensile strength of the tubes significantly increasedthe strengths and the post-elastic stiffness of the piers. The in-crease in the strength and post-elastic stiffness is more significantin the case of the piers from the S series.

7. Summary and conclusions

Based on the results of the presented finite element analyses,the following conclusions and findings are drawn:

� The FE model was able to capture the general performance ofthe PPT-CFFT piers. Both the model and experimental resultsconfirmed that PPT-CFFT pier can safely and effectively resistlateral forces. The piers were capable of undergoing large non-linear displacements without experiencing significant or sud-den loss of strength.� The level of the applied post-tensioning forces has significant

effects on the backbone of PPT-CFFT piers. Increasing theapplied post-tensioning force increased the nominal strengthof the piers. However, increasing the post-tensioning stressesin the tendons combined with decreasing the pier’s height ledto yielding of the tendon at relatively small drift angles.� For the parameters chosen for this study and within the feasible

drift angle for a pier, the analysis was sensitive to the totalapplied axial loads rather than the ratio of the applied post-ten-sioning to gravity loads.� Increasing the piers aspect ratios, decreased the initial stiffness,

ultimate strength, nominal strength but increased the deforma-tion capacity. In addition tendons in squat piers tend to yield atsmall drift angles compared to relatively slender piers.� The analysis carried out in this study showed that the pier size

played an important role in the behavior of the piers once theinterface joint opened. However, before the interface jointopening, the performance of the piers depended on the piersaspect ratios.� For the same pier height, increasing the pier diameter size sig-

nificantly increased the pier shear stress capacity and has min-imal effects on the deformation capacity of the pier.� Increasing the tensile strength and E-modulus of the confining

tube significantly improved the strength and post-elastic stiff-ness of the piers. However, it did not have significant effect onthe deformation capacity of the piers.

Within the scope of this research, earlier experimental research[3,4], and anticipated drift limits under strong ground motions itseems that both multi-segment and single-segment piers behavedvery similar. Using multi-segment piers allow easier delivery of

segments to a construction site and do not require heavy cranesfor erecting the segments. However, having single-segment piermay accelerate the construction since alignment is required forsmaller number of interface-joints. Finally, it should be noted thathaving multi-interface joints in a multi-segment pier may resultedin higher damping effects since rocking will take place across sev-eral interface-joints. Such likelihood needs to be investigated usingdynamic tests.

Acknowledgement

This research was funded from Transportation Northwest(TransNow) under Contract No. 463258.

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