earthquake engineering and engineering vibration

12
Vol.7, No.4 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION December, 2008 Earthq Eng & Eng Vib (2008) 7:403-414 DOI: 10.1007/s11803-008-1006-5 Experimental research and nite element analysis of bridge piers failed in exure-shear modes Sun Zhiguo 1† , Si Bingjun 2‡ ; Wang Dongsheng and Guo Xun 3 § 1. Institute of Road and Bridge Engineering, Dalian Maritime University, Dalian 116026, China 2. School of Civil & Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China 3. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China Abstract: In recent earthquakes, a large number of reinforced concrete (RC) bridges were severely damaged due to mixed exure-shear failure modes of the bridge piers. An integrated experimental and nite element (FE) analysis study is described in this paper to study the seismic performance of the bridge piers that failed in exure-shear modes. In the rst part, a nonlinear cyclic loading test on six RC bridge piers with circular cross sections is carried out experimentally. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers are studied and compared with each other. The experimental results suggest that all the piers exhibit stable exural response at displacement ductilities up to four before exhibiting brittle shear failure. The ultimate performance of the piers is dominated by shear capacity due to signicant shear cracking, and in some cases, rupturing of spiral bars. In the second part, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The inuences of the shear retention coefcients between concrete cracks, the Bauschinger effect in longitudinal reinforcement, the bond-slip relationship between the longitudinal reinforcement and the concrete and the concrete failure surface on the simulated hysteretic curves are discussed. Then, a modied analysis model is presented and its accuracy is veried by comparing the simulated results with experimental ones. This research uses models available in commercial FE codes and is intended for researchers and engineers interested in using ANSYS software to predict the hysteretic behavior of reinforced concrete structures. Keywords: RC bridge piers; exure-shear failure; seismic behavior; nite element; ANSYS software Correspondence to: Wang Dongsheng, Institute of Road and Bridge Engineering, Dalian Maritime University, 1 Linghai Road, Dalian 116026, China Tel: 86-411-84725098 E-mail: [email protected] PhD; Associate Professor; § Professor Supported by: National Natural Science Foundation of China Under Grant No. 50878033 and National Special Foundation of Earthquake Science of China Under Grant No.200808021 Received September 22, 2008; Accepted October 15, 2008 1 Introduction In recent earthquakes, including the 1995 Kobe earthquake (Hashimoto et al., 2005), 1999 Chi-Chi earthquake (Chang et al., 2000) and 2008 Wenchuan earthquake, a large number of bridges were severely damaged as a result of a mixed exure-shear failure of the RC (reinforced concrete) bridge piers. Figure 1 shows some examples of this kind of failure for the Baihua Bridge and Huilan Overpass Bridge. For the latter bridge, four piers suffered from severe exure- shear mode damage and minor-to-moderate exure- shear cracks were observed in many other piers. The bridge piers that are susceptible to exure-shear failure are short columns with a shear span/depth ratio between 1.5–2.5, and their ultimate performance are dominated by brittle shear capacity. Therefore, it is important to investigate their seismic performance to advance seismic assessment and retrotting techniques. Even though an increasing amount of research is becoming available on the seismic performance of RC bridge piers (Priestley and Park, 1987; Jaradat et al., 1998, 1999; Wehbe et al., 1999; Yeh et al., 2002; Lehman et al., 2004), studies on exure-shear dominated RC bridge piers is scare. The number of test specimens available for exure-shear dominated cantilever RC columns in the PEER (Pacic Earthquake Engineering Research Center) database is only eight (Berry ., 2004). In this paper, a nonlinear cyclic loading test on six RC bridge piers with exure-shear failure mode was carried out. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers, are studied and compared with each other. Then, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The inuences of the shear retention coefcients between concrete cracks,

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  • Vol.7, No.4 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION December, 2008

    Earthq Eng & Eng Vib (2008) 7:403-414 DOI: 10.1007/s11803-008-1006-5

    Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes

    Sun Zhiguo1, Si Bingjun2; Wang Dongsheng1 and Guo Xun3

    1. Institute of Road and Bridge Engineering, Dalian Maritime University, Dalian 116026, China2. School of Civil & Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China

    3. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China

    Abstract: In recent earthquakes, a large number of reinforced concrete (RC) bridges were severely damaged due to mixed fl exure-shear failure modes of the bridge piers. An integrated experimental and fi nite element (FE) analysis study is described in this paper to study the seismic performance of the bridge piers that failed in fl exure-shear modes. In the fi rst part, a nonlinear cyclic loading test on six RC bridge piers with circular cross sections is carried out experimentally. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers are studied and compared with each other. The experimental results suggest that all the piers exhibit stable fl exural response at displacement ductilities up to four before exhibiting brittle shear failure. The ultimate performance of the piers is dominated by shear capacity due to signifi cant shear cracking, and in some cases, rupturing of spiral bars. In the second part, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The infl uences of the shear retention coeffi cients between concrete cracks, the Bauschinger effect in longitudinal reinforcement, the bond-slip relationship between the longitudinal reinforcement and the concrete and the concrete failure surface on the simulated hysteretic curves are discussed. Then, a modifi ed analysis model is presented and its accuracy is verifi ed by comparing the simulated results with experimental ones. This research uses models available in commercial FE codes and is intended for researchers and engineers interested in using ANSYS software to predict the hysteretic behavior of reinforced concrete structures.

    Keywords: RC bridge piers; fl exure-shear failure; seismic behavior; fi nite element; ANSYS software

    Correspondence to: Wang Dongsheng, Institute of Road and Bridge Engineering, Dalian Maritime University, 1 Linghai Road, Dalian 116026, ChinaTel: 86-411-84725098 E-mail: [email protected]

    PhD; Associate Professor; ProfessorSupported by: National Natural Science Foundation of China

    Under Grant No. 50878033 and National Special Foundation of Earthquake Science of China Under Grant No.200808021

    Received September 22, 2008; Accepted October 15, 2008

    1 Introduction

    In recent earthquakes, including the 1995 Kobe earthquake (Hashimoto et al., 2005), 1999 Chi-Chi earthquake (Chang et al., 2000) and 2008 Wenchuan earthquake, a large number of bridges were severely damaged as a result of a mixed fl exure-shear failure of the RC (reinforced concrete) bridge piers. Figure 1 shows some examples of this kind of failure for the Baihua Bridge and Huilan Overpass Bridge. For the latter bridge, four piers suffered from severe fl exure-shear mode damage and minor-to-moderate fl exure-shear cracks were observed in many other piers.

    The bridge piers that are susceptible to fl exure-shear failure are short columns with a shear span/depth ratio

    between 1.52.5, and their ultimate performance are dominated by brittle shear capacity. Therefore, it is important to investigate their seismic performance to advance seismic assessment and retrofi tting techniques.

    Even though an increasing amount of research is becoming available on the seismic performance of RC bridge piers (Priestley and Park, 1987; Jaradat et al., 1998, 1999; Wehbe et al., 1999; Yeh et al., 2002; Lehman et al., 2004), studies on fl exure-shear dominated RC bridge piers is scare. The number of test specimens available for fl exure-shear dominated cantilever RC columns in the PEER (Pacifi c Earthquake Engineering Research Center) database is only eight (Berry ., 2004).

    In this paper, a nonlinear cyclic loading test on six RC bridge piers with fl exure-shear failure mode was carried out. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers, are studied and compared with each other. Then, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The infl uences of the shear retention coeffi cients between concrete cracks,

  • 404 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    (a) Baihua Bridge

    (b) Huilan Overpass Bridge

    Fig. 1 Flexure-shear failure of RC piers

    Fig. 2 Details of the pier specimens

    Specimens A1, A2, A5 and A6 Specimen A3 Specimen A4

    Lateral load

    Constant axial load Constant axial load Constant axial load

    Lateral load Lateral load

    600m

    m

    5

    50m

    m

    700

    mm

    450m

    m

    7

    00m

    m

    550

    mm

    400m

    m

    850

    mm

    750m

    m

    6@80

    814

    300mm

    6@80

    1014

    300mm

    6@60

    1014

    300mm

    6@60

    1014

    300mm

    6@60

    1214

    300mm

    6@40

    1214

    300mm

    Specimen A1 Specimen A2 Specimen A3

    Specimen A4 Specimen A5 Specimen A6

  • No.4 Sun Zhiguo et al.: Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes 405

    Table 1 Pier design parameters

    Specimen Diameter,D (mm)

    Aspect ratio,M/VD

    fc(MPa)

    Longitudinal reinforcement Spiral reinforcement Axial load ratio,

    P/Agfc

    Quantity t (%) s (mm) s (%)

    A1 300 2 29.4 814 1.74 80 0.51 0.15A2 300 2 32.2 1014 2.18 80 0.51 0.15A3 300 1.5 29.4 1014 2.18 60 0.67 0.10A4 300 2.5 30.1 1014 2.18 60 0.67 0.10A5 300 2 27.3 1214 2.61 60 0.67 0.15A6 300 2 32.2 1214 2.61 40 1.01 0.10

    the Bauschinger effect in longitudinal reinforcement, the bond-slip relationship between the longitudinal reinforcement and the concrete, and the concrete failure surface on the simulated results are discussed. Finally, a modifi ed analysis model is presented and its accuracy is verifi ed by experimental results.

    2 Experimental study

    2.1 Specimen description

    Six RC bridge pier specimens representing about 1/3 scale of the prototype bridge piers are designed and constructed, which are designated as specimen A1, A2, A3, A4, A5 and A6, respectively. The details of the specimens are shown in Fig. 2 and their design parameters are listed in Table 1. Measured yield strengths of the 14 longitudinal bars and 6 spiral bars are 327.6 MPa and 511 MPa, respectively.

    The confi ning reinforcement requirements of AASHTO LRFD 2005, Caltrans 2001 and Eurocode 8 1994 code provisions for circular RC bridge piers are expressed by Eqs. (1), (2), and (3), respectively. Table 2 presents spiral reinforcement ratios obtained by these expressions for the specimens. It is concluded that only specimen A6 satisfi es all these provisions.

    s = 0 45 1.

    AA

    ff

    g

    c

    c

    yh

    but not less than s cyh

    = 0 12. ff

    (1)

    s gc

    c

    yh c

    g

    = +0 45 1 0 5 1 25. ( ) ( . . )AA

    ff

    Pf A

    (2)

    w wwwd,rg

    cc k + 2 436 0 009 0 17 0 098. ( . . ) . ,min

    AA

    (3)

    where s is the spiral reinforcement ratio, Ag is the gross area of pier section, Ac is the cross-sectional area of the concrete core, fyh is the yield strength of the spiral bars, P is the applied axial load, c is the required curvature ductility factor, 13 for ductile piers and 7 for limited ductile piers, k is the axial load ratio, wwd,r is the

    mechanical reinforcement ratio defi ned as

    wwd,r syh

    c

    = ff

    (4)

    wwd,r 0.12 for ductile pier and wwd,r 0.08 for limited ductile pier.

    Table 2 Required spiral reinforcement ratios of the pier specimens

    Specimen s,exp/s,AASH s,exp/s,Caltr s,exp/s,EuroA1 0.62 0.89 0.77A2 0.57 0.82 0.70A3 0.82 1.31 1.01A4 0.80 1.26 0.98A5 0.88 1.26 1.08A6 1.12 1.80 1.39

    2.2 Testing setup and loading sequence

    The testing setup for each of the specimens is shown in Fig. 3. The specimen bottom is bolted to a strong

    Fig. 3 Testing setup

    Rolling shaft

    Vertical actuator

    Load cell

    Hinge

    Horizontal actuator

    SpecimenReaction

    frame

    Specimen bolted to strong fl oor

  • 406 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    reinforced concrete foundation, and its top is held by one vertical actuator to provide a constant axial load. Also, the lateral force is applied at the top of the specimen by two horizontal actuators which are mounted to the reaction frame.

    The lateral loading history presented in Fig. 4 is applied to all the specimens. The loading cycles are divided into two phases: load control and displacement control. The load control phase is used to defi ne the piers experimental yield displacement y; Besides, a displacement control loading sequence is used. The displacement controlled loading history includes three complete cycles each for u

    ,,exp=1, 2, 3, , until the shear capacity of the piers declined and to 85% of the peak loads. Here, u

    , exp is the ratio of the applied lateral

    displacement at the top of the piers over the yield displacement y.

    As shown in Fig. 4 (a), the fi rst three cycles of the lateral load is applied to 70% of the theoretical yield load Fy, which is calculated based on fi ber model and measured material properties. The yield displacement y is determined by extrapolating a straight line from the origin through the measured point corresponding to 0.7Fy to the theoretical yield load Fy. The average of the displacement values in both positive and negative loading directions is used as the yield displacement y.

    2.3 Observed damage states

    The progression of damage was similar for all the

    specimens. Flexural cracks perpendicular to the pier axis developed fi rst in regions close to the bottom of the specimens. At later stages of loading, the fl exural cracks became inclined and extended into the neutral axis of the specimens due to the infl uence of shear. Then, initial spalling of the concrete cover was observed, once the cover concrete had completely spalled and the spiral and longitudinal reinforcement was exposed, longitudinal bar buckling and concrete core crushing initiated within the next displacement cycles. The ultimate performance of the piers is dominated by shear capacity due to signifi cant shear cracking and in some cases rupturing of spiral bars. Figure 5 shows the fi nal damage states of the specimens at the end of the tests. Note that the initial yielding of the longitudinal and spiral reinforcement was also measured using a strain gauge, as shown in Table 3.

    It is useful to study key damage states of the piers as each damage state may be associated with one or more engineering limit state. In this study, the fi rst occurrence of each key damage state, such as longitudinal reinforcement yielding, initial spalling of the concrete cover, spiral reinforcement yielding, exposing of spiral and longitudinal reinforcement, longitudinal reinforcement buckling, spiral fracture, is identifi ed in

    0.7Fy

    Fy

    Lateral force

    Displacement

    -0.7Fy

    -Fy

    b -

    + a

    DisplacementLoad

    Number of cycles

    0.7Fy-0.7Fy

    654321

    123456

    (a) Experimental defi nition of yield displacement (b) Loading sequence

    Fig. 4 Lateral loading sequence for pier specimens

    y a b=+

    2

    aa

    FK

    =y b

    b

    FK

    =y

    KF

    a = +

    0 7. y

    KF

    b =

    0 7. y

    +

    +

    =

    =

    jj 1

    3

    3

    =

    =

    jj 1

    3

    3

    max

    y

    Table 3. The lateral force-displacement responses of all

    specimens are shown in Fig. 19. In these fi gures, indicates lateral displacement at the top of the pier and F is the lateral force acting on the specimen.

    The concrete crack widths are of some importance in assessing the damage level of bridge piers. In this study, the fl exural and shear crack widths are measured using a reading microscope during the tests. Fig. 6 shows the measured maximum crack widths at each displacement ductility level as defi ned in Fig.8. In general, the fl exural and shear crack widths are almost the same at small displacement levels. At large displacement levels, shear cracks grow faster than fl exural cracks, and this may be an important feature of fl exure-shear dominated RC bridge piers.

    In the 1995 Kobe earthquake, bridge piers with residual inclination R (the displacement at zero lateral force divided by the height of the pier) larger than 1 were demolished, since it makes placing girders diffi cult and causes visual uneasiness (Fujino et al., 2005). The residual inclinations R at each displacement ductility level for each specimen are plotted in Fig. 7. It is obvious from the fi gure that the residual inclinations

  • No.4 Sun Zhiguo et al.: Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes 407

    A1 A2 A3

    A4 A5 A6

    Fig. 5 Failure patterns of the pier specimens at the end of the tests

    increase linearly with the displacement ductility factors, and Specimens A5 and A6 have the largest longitudinal reinforcement ratios and biggest residual inclinations at each displacement level.

    2.4 Ductility and dissipated energy

    In this study, the ductility parameters suggested by Sheikh and Khoury (1993), and Lgeron and Paultre

    (2000) are used to evaluate the seismic performance of the specimens. Fig. 8 describes various ductility parameters including displacement ductility factors , cumulative displacement ductility ratios N

    , normalized

    dissipated energy EN, work index IW, and work damage indicator W. The

    and N

    represent the deformability

    of the member, the EN and IW are used to assess energy dissipation capabilities, whereas W estimates toughness. Table 4 lists the ductility parameters for all

    Table 3 The damage parameters of the pier specimens

    SpecimenLongitudinal reinforcement Spiral reinforcement

    Concrete cover spalling Exposing of reinforcementYielding Buckling Yielding FractureA1 4.07 mm / 0.8 33.0 mm / 6.5 / 2 16.7 mm / 3.3 11.1 mm / 2.2 / 3 27.5 mm / 5.4 / 1A2 3.05 mm / 0.7 32.8 mm / 7.3 / 1 12.8 mm / 2.8 36.0 mm / 8.0 / 1 12.8 mm / 2.8 / 3 24.5 mm / 5.4 / 1A3 2.37 mm / 0.7 22.1 mm / 6. 1/ 3 9.4 mm / 2.6 9.4 mm / 2.6 / 3 16.3 mm / 4.5 / 3A4 5.62 mm / 0.8 50.6 mm / 7.5 / 1 16.6 mm / 2.5 16.6 mm / 2.5 / 1 33.0 mm / 4.9 / 3A5 5.30 mm / 0.9 36.5 mm / 6.0 / 1 15.8 mm / 2.6 41.6 mm / 6.8 / 3 10.7 mm / 1.8 / 3 26.4 mm / 4.3 / 3A6 4.00 mm / 0.6 44.4 mm / 7.0/ 3 16.8 mm / 2.7 49.5 mm / 7.8 / 2 11.4 mm / 1.8 / 3 38.9 mm / 6.2 / 3

    Note: In expression a mm / b / c, a denote the displacement at the top of the specimen, b is the displacement ductility factor defi ned in Fig.8, and c is the cycle number, if applicable.

  • 408 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    tested specimens. Note that the ductility factors of the tested specimens are in the range from 5.14 to 7.48, and Specimen A6 with most transverse reinforcement has the largest ductility and dissipated energy related parameters.

    2.5 Stiffness degradation

    For every three cycles under the same displacement

    amplitude, , the stiffness for the piers is defi ned as

    KK K

    =

    ++

    2 (5)

    K Fj

    j j + +

    = =

    = ,max /1

    3

    1

    3

    j

    + , K Fjj j

    =

    =

    = ,max /1

    3

    1

    3

    j (6)

    where Fj,max is the maximum lateral load and j is the corresponding displacement within a cycle at the displacement .

    For comparison, the calculated stiffness for each displacement is normalized with respect to the stiffness of the fi rst three cycles. The normalized stiffness versus the displacement ductility factor for the specimens is shown in Fig. 9, where indicates the ratio of the stiffness for a subsequent displacement ductility level to that for an initial displacement ductility level and indicates displacement ductility factor. Note that

    the stiffness degradation rate for all specimens is very similar.

    2.6 Shear strength

    Four approaches to estimate the shear strength of RC bridge piers were used in this study: Caltrans 2001

    6 5 4 3 2 1 0 1 2 3 4 5 6

    3.0

    2.5

    2.0

    1.5

    1.0

    0.5

    0

    (m

    m)

    Flexural cracksShear cracks

    A1

    7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

    3.0

    2.5

    2.0

    1.5

    1.0

    0.5

    0

    (m

    m)

    Flexural cracksShear cracks

    A2

    7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

    5.55.04.54.03.53.02.52.01.51.00.5 0

    (m

    m) Flexural cracks

    Shear cracks

    A3

    7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

    3.5

    3.0

    2.5

    2.0

    1.5

    1.0

    0.5

    0

    (m

    m) Flexural cracks

    Shear cracks

    A4

    7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

    5.55.04.54.03.53.02.52.01.51.00.5 0

    (m

    m) Flexural cracks

    Shear cracks

    A5

    8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

    5.04.54.03.53.02.52.01.51.00.5 0

    (m

    m) Flexural cracks

    Shear cracks

    A6

    Fig. 6 Crack width vs. displacement ductility level of the specimens

    9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9

    3.5

    3.0

    2.5

    2.0

    1.5

    1.0

    0.5

    0.0

    R (%

    )

    Fig. 7 Residual inclinations vs. displacement ductility level of the specimens

    A1A2A3A4A5A6

  • No.4 Sun Zhiguo et al.: Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes 409

    model, Eurocode 8 1994 model, Priestley model (1994), and Bi model (2004).

    The fi rst model is based on Caltrans shear design equation, which is expressed as

    V V Vn c s= + (7)

    V v Ac c g= ( . )0 8 (8)

    v f fc c

    c

    = 1 2 0 33. (9)

    0 025 0 08 0 305 0 083 0 251. . . . . = + 0 1. (15)

    Fig. 9 Stiffness degradation with increasing displacement ductility level of the bridge piers

    Fig. 8 Defi nition of the ductility and dissipated energy parameters of the bridge piers

    Table 4 Results of ductility and energy dissipation related parameters

    Specimen 1(mm) u(mm) N EN IW WA1 5.1 34.4 6.75 48.6 95.0 43.7 240.3A2 4.5 31.2 6.93 73.3 125.0 67.3 425.6A3 3.6 18.5 5.14 53.1 98.0 84.2 411.8A4 6.7 48.9 7.30 86.7 158.1 79.1 579.7A5 6.1 37.6 6.16 69.3 110.7 63.0 384.7A6 6.3 47.1 7.48 100.2 147.3 92.7 779.6

    F

    Fmax0.85Fmax0.75Fmax

    -0.75Fmax-0.85Fmax-Fmax

    u 1

    1+ u

    +

    K1

    F

    Fi+

    Ki+

    i+

    i

    Fi

    Ki

    Area wi

    11 1

    2=

    ++

    u u u= ++

    2

    K K K1 1 12=

    ++

    i i i=++

    2

    FF F

    ii i

    ,max =++

    2

    KK K

    ii i

    =

    ++

    2

    = u

    1

    N ii

    i m

    ==

    = 11

    IFFw

    i i

    i

    i m

    =

    =

    = ,maxmax

    11

    EF

    wN ii

    i m

    =

    =

    =11 1max

    WF

    wKKii

    i mi i

    =

    =

    =11 1 1 1

    2

    max

    1.4

    1.2

    1.0

    0.8

    0.6

    0.4

    0.2

    0

    0 1 2 3 4 5 6 7 8

    A1A2A3A4A5A6 u

  • 410 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    = ( )P A f/ c c (16)

    V A s Dfs b yh= ( )/ .0 9 (17)

    whereDsp is the spiral diameter, D is circular column

    diameter. The third model, the one proposed by Priestley et al., is expressed as

    V V V Vn c p s= + + (18)

    V k f Ac c

    g= ( . )0 8 (19)

    V D c

    aPp =

    2 (20)

    VA f D

    ssb yh

    =

    230

    cot (21)

    where Vp is the shear resistance provided by the axial load; k is the deterioration factor for concrete; c is the depth of the compressive zone in a column; a=M/V, is the ratio of moment to shear at critical section.

    The fourth model, proposed by Bi (2004), is expressed as

    V C C f AA f

    sDn c

    g

    b yh= +0 15 0 8

    21 2. ( . ) (22)

    C s1 1 2 2= + . k (23)

    C21

    2 0=

    + . (24)

    A comparison of the measured shear strength-displacement ductility relationship and the predicted values obtained by using different models is given in Fig. 10, where the shear strength Fshear is defi ned as Fshear=F, max, F, max is the lateral force of the specimen corresponding to the lateral displacement in the fi rst cycle, and the lateral force in the last cycle must be equal or less than 0.85F

    , max. The shear strength Fshear for each specimen is indicated in Fig.10 by symbol X.

    Note that for specimens A1 and A5, except for the Priestley model that yields much larger shear capacity than the test results, the other three models predict the shear capacity with acceptable accuracy. Also, all four models predict the shear capacity well for specimen A2, but overestimate the shear capacity of specimen A6. For specimen A3, all models predict the shear capacity very well except for the Eurocode 8 model, from which the specimen may fail in shear with much lower strength than in the test results. For Specimen 4, the Eurocode 8 model yields shear capacity very close to the maximum shear force from the tests, but the remaining three models give greater shear capacity than in the test results.

    Fig. 10 Shear strength-displacement ductility relationship for all specimens

    2402101801501209060300

    F (k

    N)

    2402101801501209060300

    F (k

    N)

    2702402101801501209060300

    F (k

    N)

    0 1 2 3 4 5 6 7 8 9 10

    TestCaltransEurocode 8PriestleyBi & Fan

    A1

    TestCaltransEurocode 8PriestleyBi & Fan

    A42702402101801501209060300

    F (k

    N)

    TestCaltransEurocode 8PriestleyBi & Fan

    A5

    2702402101801501209060300

    F (k

    N)

    TestCaltransEurocode 8PriestleyBi & Fan

    A3A2

    0 1 2 3 4 5 6 7 8 9 10

    0 1 2 3 4 5 6 7 8 9 10

    0 1 2 3 4 5 6 7 8 9 10

    0 1 2 3 4 5 6 7 8 9 10

    0 1 2 3 4 5 6 7 8 9 10

    3603303002702402101801501209060300

    F (k

    N)

    TestCaltransEurocode 8PriestleyBi & Fan

    A6

    TestCaltransEurocode 8PriestleyBi & Fan

  • No.4 Sun Zhiguo et al.: Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes 411

    3 Numerical study

    Next the capability of the commercially available fi nite element analysis software ANSYS (2004) to model the hysteretic behavior of RC bridge piers is evaluated. The software ANSYS was used in the fi nite element (FE) analysis of the pier specimens. First, a series of FE models for specimen A3 are constructed using the ANSYS software to evaluate the infl uence of material models and their associated parameters on the hysteretic response. Then, a modifi ed analysis model is presented and the model accuracy was verifi ed by comparing the calculated hysteretic curves with the experimental results.

    Solid 65 elements which have crushing (compressive) and cracking (tensile) capabilities were used to model the concrete. All reinforcements were modelled using Link 8 truss elements. Solid 45 elements were used for the steel plates at the support and under the load. The effect of bond-slip at the interface between concrete elements and truss elements was simulated using Combin 39 elements.

    To account for the confi nement effect, the Mander model (Mander et al., 1988) for confi ned stress-strain relationship with an assumption of perfectly plastic after ultimate compression strength is used to defi ne the constitutive relationship of the concrete. Meanwhile, the multilinear kinematic hardening relationship, using the von Mises yield criterion, was also adopted. In addition, the Willam and Warnke fi ve parameter model is used as the failure criterion of concrete under multiaxial stress conditions, in which the failure surface is defi ned by at least two constants: the concrete ultimate uniaxial tensile strength, ft , and the ultimate uniaxial compressive strength, fc

    .Taking advantage of the symmetry of the geometry

    and the reinforcement of the specimen, only half of the specimens are modelled. Figure 11 shows the FE model of specimen A3.

    3.1 Infl uence of shear retention coeffi cient

    After cracking, the tension stress in the concrete

    element is set to zero in the direction normal to the crack plane. The shear transfer coeffi cient t for open cracks and c for closed cracks determine the amount of shear transferred across the cracks. The value of the shear transfer coeffi cient ranges from 0 to 1.0, with 0 representing no shear transfer at a crack section and 1.0 representing full shear transfer. In this study, the shear transfer coeffi cient t for open cracks is assumed to be 0.2, 0.3 and 0.5, while for closed cracks the shear transfer coeffi cient c is assumed to be 0.5, 0.7 and 0.95, respectively. As shown in Fig. 12, the simulated hysteretic curves using different shear transfer coeffi cients are almost the same. Therefore, it could be concluded that the shear transfer coeffi cient does not have an obvious infl uence on the simulated hysteretic response in this study. This may be because the fi xed crack model used in the ANSYS software could not precisely refl ect the shear transfer capability across concrete cracks.

    3.2 Infl uence of Bauschinger effect

    To investigate the Bauschinger effect for the longitudinal reinforcement in simulating the hysteretic behavior of the pier specimen, two models are used:the bilinear kinematic hardening (BKH) model without Bauschinger effect (model 1), and the multilinear kinematic hardening (MKH) model with Bauschinger effect (model 2) (see Figs. 13 (a) and (b)). Figure 14 depicts the simulated hysteretic curves given by models 1 and 2. Note that the Bauschinger effect in the longitudinal reinforcement has a signifi cant infl uence on the pinching effect in the hysteretic response.

    3.3 Infl uence of bond-slip effect

    To investigate the effect of bond-slip between longitudinal reinforcement and concrete on the simulated hysteretic response of the pier specimen, two FE models are used: model 3 and model 4. In model 3, perfect bond between the concrete and the longitudinal reinforcement is assumed, whereas in model 4 the bond-slip is incorporated. As illustrated in Fig. 15, the bond-

    Fig. 12 Infl uence of the shear retention coeffi cients on the hysteretic behaviorFig. 11 FE model for specimen A3

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  • 412 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    slip model for the interface element has a simplifi ed linear relationship to the slip strength c with a constant stress after the critical slip displacement c. Experimental results of the bond-slip relationship between the concrete and the longitudinal reinforcement were not available at the time of this modelling. Therefore, representative values for c and c are selected as 10 MPa and 0.1 mm. Fig.16 depicts the simulated hysteretic curves by model 3 and 4. It is recognized that a certain degree of bond-slip may have contributed to the pinching effect in the hysteretic response. Also, model 4 predicts a low lateral load at large lateral displacement as a result of the bond-slip effect.

    3.4 Infl uence of failure surface for concrete

    It has been reported in the literature that if both cracking and crushing capabilities for Solid 65 element are activated in the ANSYS software, fi ctitious crushing of the concrete may be caused due to the coupling of excessive cracking strains to the orthogonal uncracked directions through Poissons effect. This may be one of the reasons that cause divergence of the solution at later stages (Zhou et al., 2004). Therefore, in most previous literature, the crushing capability of the concrete is turned off and the crushing failure of the concrete is ignored (Si et al., 2007).

    Obviously, the FE model in which the crushing capability of the concrete is turned off cannot predict all the failure features of the specimens. However, it is also found in this study that if fc

    is used to defi ne the concrete failure surface, the FE model fails prematurely (Fig. 17).

    In order to simulate the crushing failure of the concrete in the conducted experiments, an enlarged failure surface is adopted, i.e., 1.22 times of fc

    are used to defi ne the failure surface, but the normal stress-strain curves are still used to defi ne the constitutive relationship of the concrete. Figure 18 illustrates the simulated hysteretic response by enlarged failure

    Fig. 13 Two constitutive models for longitudinal reinforcement

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    Fig. 14 Infl uence of constitutive models of reinforcing steel on the hysteretic behavior

    (a) Bilinear kinematic hardening model (b) Multilinear kinematic hardening model

    fs

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    Fig. 15 Relationship of the bond-slip between the longitudinal reinforcement and concrete

    Fig. 16 Infl uence of the bond-slip between the longitudinal reinforcement and concrete on the hysteretic behavior

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  • No.4 Sun Zhiguo et al.: Experimental research and fi nite element analysis of bridge piers failed in fl exure-shear modes 413

    Fig. 19 Comparisons of the experimental and simulated hysteretic curves

    surface for concrete. It is concluded that the model using an enlarged failure surface of concrete predicts the piers load-displacement relationship well.

    3.5 Modifi ed FE model

    A modifi ed FE model is presented based on the above analysis. In this model, a multilinear kinematic hardening model is used to include the Bauschinger effect in the longitudinal reinforcement under cyclic

    loading, the bond-slip relationship between longitudinal reinforcement and concrete is accounted for by using combin 39 element, and an enlarged failure surface for concrete is used to simulate the crushing of concrete in the tests, which can also prevent fi ctitious crushing of the concrete in the simulation. The simulated hysteretic curves are compared with the experimental results, as illustrated in Fig. 19, where it is seen that the calculated hysteretic curves correspond well with the experimental ones.

    Fig. 17 Infl uence of the crushing for concrete to the hysteretic curves

    Fig. 18 Infl uence of enlarged failure surface for concrete to the hysteretic behavior

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  • 414 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.7

    4 Conclusions

    An integrated experimental and FE analysis study is described in this paper to study the seismic performance of bridge piers that failed in fl exure-shear modes. In the fi rst part, a nonlinear cyclic loading test on six RC bridge piers with circular cross sections was performed, and all the piers failed in the fl exure-shear mode. In the second part, modeling approaches describing the hysteretic behavior of the piers were investigated by using ANSYS software. A set of models with different parameters was selected and evaluated through comparison with experimental results. Then, a modifi ed analysis model is presented and its accuracy was verifi ed by comparing the simulated results with the experimental ones. Based on the studies presented in this paper, the following conclusions can be made.

    (1) The progression of damage is similar for all the specimens: concrete fl exural cracking, longitudinal reinforcement yielding, concrete shear cracking, concrete cover spalling, spiral reinforcement yielding, reinforcement exposing, longitudinal reinforcement buckling, and concrete core crushing. The ultimate performance of the specimens is dominated by shear capacity due to signifi cant shear cracking, and in some cases, rupturing of spiral bars.

    (2) The observed fl exural and shear crack widths are almost the same at small displacement levels, but at large displacement levels, the shear cracks grow faster than the fl exural cracks. The displacement ductility factors of the tested specimens range from 5.14 to 7.48, and Specimen A6 with most transverse reinforcement has the largest ductility and dissipated energy parameters. All the specimens have similar stiffness degradation rates. The predicted accuracy of the current shear strength model for the specimens with fl exure-shear failure modes needs to be further improved.

    (3) Simulated hysteretic behavior of the pier is strongly infl uenced by the Bauschinger effect in longitudinal reinforcement, bond-slip relationship between longitudinal reinforcement and concrete, and choice of concrete failure surface. However, the hysteretic response is not signifi cantly affected by the shear transfer coeffi cient between concrete cracks for the considered pier specimens.

    (4) The modifi ed FE model using ANSYS software predicts the piers hysteretic response well.

    References

    AASHTO LRFD (2005), AASHTO LRFD Bridge Design Specifi cations, American Association of State Highway and Transportation Offi cials, Washington, D.C.ANSYS (2004), ANSYS Users Manual, ANSYS, Inc., Canonsburg, Pennsylvania, USA.Berry M, Parrish M and Eberhard M (2004), PEER Structural Performance Database Users Manual, Version 1.0, University of California, Berkeley.Bi Guiping (2004), Research on the Key Problems for Seismic Behavior of Large-scale Complicated Overcross Engineering, PhD. Dissertation, Tongji University. (in Chinese) Caltrans (2001), Seismic Design Criteria, California Department of Transportation, Sacramento, California.

    Chang KC, Chang DW, Tsai MH and Sung YC (2000), Seismic Performance of Highway Bridges, Earthquake Engineering and Engineering Seismology, 2(1): 5577.Eurocode 8 (1994), Design Provisions for Earthquake Resistance of Structures-Part 2: Bridges, European Committee for Standardization, Brussels.Fujino Y, Hashimoto S and Abe M (2005), Damage Analysis of Hanshin Expressway Viaducts During 1995 Kobe Earthquake. I: Residual Inclination of Reinforced Concrete Piers, Journal of Bridge Engineering, ASCE, 10(1): 4553.Hashimoto S, Fujino Y and Abe M (2005), Damage Analysis of Hanshin Expressway Viaducts During 1995 Kobe Earthquake. II: Damage Mode of Single Reinforced Concrete Piers, Journal of Bridge Engineering, ASCE, 10(1): 5460.Jaradat OA, Mclean DI and Marsh ML (1998), Performance of Existing Bridge Columns Under Cyclic Loading-Part 1: Experimental Results and Observed Behavior, ACI Structural Journal, 95(6): 695704.Jaradat OA, Mclean DI and Marsh ML (1999), Performance of Existing Bridge Columns Under Cyclic Loading-Part 2:Analysis and Comparisons with Theory, ACI Structural Journal, 96(1): 5767.Lgeron F and Paultre P (2000), Behavior of High-strength Concrete Columns Under Cyclic Flexure and Constant Axial Load, ACI Structural Journal, 97(4): 591601.Lehman D, Moehle J, Mahin S, Calderone A and Henry L (2004), Experimental Evaluation of the Seismic Performance of Reinforced Concrete Bridge Columns, Journal of Structural Engineering, ASCE, 130(6): 869879.Mander JB, Priestley MJN and Park R (1988), Theoretical Stress-strain Model for Confi ned Concrete, Journal of Structural Engineering, ASCE, 114(8): 18041826.Priestley MJN and Park R (1987), Strength and Ductility of Concrete Bridge Columns Under Seismic Loading, ACI Structural Journal, 84(1): 5175.Priestley M J N, Verma R and Xiao Y (1994), Seismic Shear Strength of Reinforced Concrete Columns, Journal of Structural Engineering, ASCE, 120(8): 23102329.Sheikh S A and Khoury S S (1993), Confi ned Concrete Columns with Stubs, ACI Structural Journal, 90(4): 414431.Si Bingjun, Sun Zhiguo and Ai Qinghua (2007), Application of Solid65 Element in the Finite Element Analysis of Concrete Structures, Industrial Construction, 37(1): 8792. (in Chinese)Wehbe NI, Saiidi MS and Sanders DH (1999), Seismic Performance of Rectangular Bridge Columns with Moderate Confi nement, ACI Structural Journal, 96(2): 248258.Yeh YK, Mo YL and Yang CY (2002), Full-scale Tests on Rectangular Hollow Bridge Piers, Materials and Structures, 35(2): 117125Zhou S, Rizos DC and Petrou MF (2004), Effects of Superstructure Flexibility on Strength of Reinforced Concrete Bridge Decks, Computers & Structures, 82(1): 1323.

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