- Email: [email protected]
Seismic performance assessment of different fibers reinforced concrete columns using incremental dynamic analysis
Construction and Building Materials 203 (2019) 241–257
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Seismic performance assessment of different fibers reinforced concrete columns using incremental dynamic analysis Yutao Pang, Li Cai, Hui Ouyang ⇑, Xiaoyong Zhou Faculty of Engineering, China University of Geosciences, Lumo Road 388, Wuhan, China
h i g h l i g h t s Seismic behavior of different fiber-reinforced concrete columns was compared. Nonlinear finite element models were built to present the behavior of columns. Seismic capacity of columns was evaluated through the nonlinear pushover analysis. Incremental dynamic analyses were conducted using 20 near-fault ground motions. Seismic fragility curves were obtained based on the maximum drift of columns.
a r t i c l e
i n f o
Article history: Received 1 September 2018 Received in revised form 6 January 2019 Accepted 12 January 2019
Keywords: Fiber-reinforced concrete Bridge columns Incremental dynamic analysis Nonlinear static analyses Seismic performance Ground motions
a b s t r a c t Different fiber-reinforced concrete (FRC) has been widely used in the recent decades, which can improve the mechanical behavior and dynamic performance of reinforced concrete (RC) columns remarkably. This paper aims to compare the seismic behavior of columns constructed with different FRC material, namely steel fibers reinforced concrete (SFRC), polypropylene fibers reinforced concrete (PFRC) and steelpolypropylene hybrid fiber reinforced concrete (HySPFRC). 3-D nonlinear finite element models have been built to represent the seismic behavior of different FRC columns, which are calibrated with the available experimental results of quasi-static tests. The seismic capacity of bridge columns with different FRC material are assessed based on four flexural damage states through the nonlinear static pushover analysis, such as a) yielding of longitudinal steels; b) core concrete crushing; c) buckling and d) fracture of longitudinal of steels. Incremental dynamic analyses (IDA) are conducted using the selected suite of 20 nearfault as-recorded ground motions to evaluate the inelastic seismic responses of different bridge columns. IDA curves are generated based on the intensity measure, namely peak ground acceleration (PGA) in this paper and seismic demands (i.e. maximum drift, residual drift, displacement ductility and curvature ductility) through nonlinear dynamic time-history analysis. It can be concluded from the IDA results that the SFRC, PFRC and HySPFRC are all effective to enhance the seismic performance, thus reducing the anticipated damage of the bridge columns. Moreover, SFRC and HySPFRC are more effective to improve the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective at the extensive and complete damage states. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Various reinforced concrete (RC) bridges are widely built in China over the last 40 years. The RC columns in these bridges may not fully achieve adequate seismic resistance and deformation capacity which is required by the seismic codes of bridges [1]. In recent strong earthquakes, such as Mw 8.0 Wenchuan 2008 and Mw 7.1 Yushu 2010 in China, many bridges suffered severe damage ⇑ Corresponding author. E-mail address: [email protected] (H. Ouyang). https://doi.org/10.1016/j.conbuildmat.2019.01.087 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
and plastic hinges were developed at the column base. This is partly due to the inherent disadvantages of plain concrete material, which has the drawbacks of inadequate flexural strength, being brittle, low toughness and low energy absorption ability [2–4]. Thus, it is of importance to improve these concrete features in order to enhance the overall seismic capacity of bridges. In traditional methods, the concrete properties can be improved by increasing the density of transverse stirrups in the bridge columns [5,6]. The closely spaced transverse stirrups can improve the core concrete confinement, thus restraining the crack propagation and reducing the strength degradation of RC columns [7].
242
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 1. Bridge column dimensions and reinforcement details.
However, insufficient concrete pouring quality may be caused by the large amount of transverse stirrups during the construction process. Due to this problem, the implement of fiber-reinforced concrete (FRC) has been recognized as a good alternative for enhancing the inherent properties of plain concrete. In the FRC material, different fiber types (e.g. steel fiber [8–10], polypropylene fiber [11] and other fibers [12,13]) can be used in the concrete mixtures. The randomly distributed fibers in the concrete matrix can increase the static properties (i.e. tensile strength, toughness and flexural strength) of plain concrete [14–17], and also show some attractive properties of the improved ductility and energy dissipation capacity in seismic loadings [18,19].
Various previous researches have been proposed to study the effect of fiber types and fiber content (volume fraction) on seismic performance of different FRC bridge columns. Nowadays, there are three main FRC column types, namely columns with inclusion of only steel fibers (SFRC), the columns with only polypropylene fibers or other synthetic fibers (PFRC) and the columns with combined different types of fibers (HyFRC). Stephen et al. [8,20] used some experimental tests to investigate the effect of steel fibers on the seismic behavior of RC columns. The results showed that the ductility and loading capacity of SFRC columns was improved compared to non-fiber concrete specimens. Lee et al. [21] studied the influence of addition of steel fibers into concrete on seismic performance of RC columns under earthquakes. It was observed from the experimental data that the optimal volume fraction for SFRC is 1.5% for improving the shear strength. Meanwhile, Zhao [22] and Laura et al. [11] investigated the seismic behavior of PFRC columns, indicating that polypropylene fibers could also improve the ductility capacity and energy absorption ability of RC columns. With regard to the seismic behavior of HyFRC columns, Huang et al. [23] evaluated the seismic behavior of hybrid steelpolypropylene fiber reinforced concrete (HySPFRC) columns through the experimental studies. Compared to RC columns, it showed that HySPFRC columns with a higher axial compression ratio established a significant effect on the dynamic capacity. Chi et al. [24] presented the experimental study on HySPFRC concrete subjected to uniaxial compression. It was found that in comparison to reinforced concrete with single fibers, HySPFRC showed more ductility at post-peak behavior. All these previous studies have proved that using FRC can achieve remarkable improvement in the mechanic and seismic performance of RC columns. It should be noted that since the damage in RC column is a complex and gradual process, different fiber types may have limited effective ranges. Thus, it is important to compare the seismic behavior of different FRC columns to see whether an optimal performance can be obtained when single fiber or fiber combination is used in the concrete. In the procedures of the performance-based earthquake engineering (PBEE) framework, estimation of both seismic demands and capacity of structures are required in order to present the comprehensive assessment of seismic structural behavior. The interrelationship between the demands and capacity can provide an inference of the expected level of damage at a given intensity level
Fig. 2. Schematic of bridge columns with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
243
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257 Table 1 Summary of the material properties. Material
Diameter (mm)
Length (mm)
Density (g/cm3)
Tensile/compressive strength (MPa)
Elastic modulus (GPa)
Concrete Longitudinal steel Hoop steel Polypropylene fibers Steel fibers
– 32 12 0.048 0.55
– – – 19 35
2.6 7.8 7.8 1.2 7.8
40 400 335 400 1143
30 200 200 43 200
Table 2 Main parameters for different bridge columns. Column No.
Type
Compressive strength (MPa)
Steel fiber content
Polypropylene fiber content
1 2 3 4
Normal RC SFRC PFRC HySPFRC
47 65 61 67
– 1.50% – 1.50%
– – 0.15% 0.15%
Fig. 3. Scheme to establish the FE model of bridge columns with fiber elements and bond-slip model.
Table 3 Mechanical properties used for bond-slip model. Column Type
c/db
fy (MPa)
Sy (mm)
umax (MPa)
Normal RC SFRC PFRC HySPFRC
1.5 1.5 1.5 1.5
400 400 400 400
0.85 0.92 1.06 0.98
6.2 8.9 9.1 9.8
of ground motions. In order to predict the structural responses in large nonlinear range, Luco and Cornell [25] and Vamvatsikos and Cornell [26] proposed a new computational based methodology called incremental dynamic analysis (IDA). IDA requires various nonlinear time-history analyses of a finite element model of a specific structure at different levels of ground intensities. The results of IDA cover the entire range of structural responses, from elastic behavior through yielding to dynamic instability, which can give a clear indication of relationship between the seismic capacity and demands. From IDA curves, the probability of exceed-
ing a specified limit state for a given intensity measure (IM) (known as seismic fragility) can be calculated. Therefore, the aim of this study is to compare the seismic performance of bridge columns reinforced with different FRC material, namely SFRC, PFRC and HySPFRC. The 3-D nonlinear fiber-based finite element models have been built to represent the seismic behavior of different FRC bridge columns, which are first calibrated with the available experimental results. The seismic capacity of bridge columns with different FRC material are assessed using four flexural damage states, a) yielding of longitudinal reinforcements; b) core concrete crushing; c) buckling and d) fracture of longitudinal reinforcements. These four flexural damage states can be obtained using the nonlinear static pushover analysis (NSPA). Moreover, the incremental dynamic analysis (IDA) is conducted to investigate the inelastic seismic demands of the FRC bridge columns under strong ground motions. In the IDA method, a suite of 20 near-fault ground motions is chosen as seismic input to 3-D nonlinear finite element models and scaled to different intensity levels. The results of IDA are shown as IDA curves in terms of the
244
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 4. Comparison of experimental and numerical results of different bridge columns: (a, b) normal RC column (Zhang et al. [28]; Zhang et al. [5]), (c, b) SFRC column (Zhang et al. [28]; Zhang et al. [5]), (e, f) PFRC column (Huang et al. [23]; Liang et al. [36]) and (g, h) HySPFRC columns (Huang et al. [23]).
relationship between the engineering demand parameter (EDP) of structures and IM of ground motions. In this paper, the peak
ground acceleration (PGA) is used as the IM. Various EDPs of the bridge columns, such as the maximum drift, residual drift, dis-
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 5. Pushover curves for bridge columns with different FRC material.
placement ductility and curvature ductility demands, have been selected and recorded during the IDA analysis. Finally, the seismic fragility curves are developed and compared to study the effect of different FRC material on the seismic performance of bridge columns
245
Fig. 6. Moment-curvature analysis of sections with different FRC material.
performance of different FRC columns in this paper is evaluated and compared based on the specified optimal volume ratios recommended by the above studies for different fibers. 3. Modeling of different FRC columns 3.1. Finite element modeling
2. Details of bridge columns In this study, the selected bridge column is located in Sichuan Province in China. This bridge column was designed following the seismic design guidelines for highway bridges in China [27]. The detail dimensions of this column are given in Fig. 1, which is a 1.2 m square, reinforced with 20 longitudinal steel bars with diameter 32 mm (reinforcement ratio of 1.3%). The prototype column has a height of 9.2 m and a cover thickness of 50 mm. The pile cap has the dimension of 2.5 2.5 1.5 m. square transverse stirrups has a diameter of 12 mm and the spacing is 300 mm. The longitudinal reinforcements in the bridge column have the yield strength of 400 MPa, while the compressive strength of the concrete is 40 MPa. Four different bridge columns with normal RC and different FRC material (SFRC, PFRC and HySPFRC) have been implemented in the columns. Fig. 2 illustrates the bridge columns with normal RC and different FRC material in this study. The SFRC bridge column has been adopted from Zhang et al [28], in which the steel fibers have a tensile strength of 1143 MPa, elastic modulus of 200 GPa and density of 7.8 g/cm3 as shown in Table 1. The steel fibers with hooks at both ends have a diameter of 0.55 mm and length of 35 mm. The average aspect ratio (length divided by diameter) equals 64. As excessive steel fibers (e.g. 2.0% volume ratio) may cause the workability reduction of concrete mix and introduce the unwanted defects of concrete members, a volume fraction of 1.5% (117 kg/m3) steel fibers are in the SFRC columns, which is recommended by many previous studies [21,23,28] due to the maximum enhancement of the strength, ductility and energy dissipation. The PFRC bridge column has been used from Huang et al [23], in which the polypropylene fibers have a tensile strength of 400 MPa, elastic modulus of 43 GPa and density of 1.2 g/cm3. The polypropylene fibers have the average aspect ratio l/d = 396 with 0.048 mm diameter and 19 mm length. A volume fraction of 0.15% (1.37 kg/m3) polypropylene fibers are included in the PFRC columns. In the HySPFRC column, the optimal volume ratios of hybrid fibers for improving the concrete strength is the combination of 1.5% steel fibers and 0.15% polypropylene fiber, which are recommended by Xu et al. [29] and Huang et al [23]. Table 2 depicts the main parameters for the different FRC bridge columns. It should be noted that different volume ratios of fibers may influence the seismic behavior of different FRC columns. The seismic
The numerical models of columns with normal RC and FRC material are built using the 3-D nonlinear fiber-based finite element models in the open-source software OpenSees [30] as shown in the Fig. 3. NSPA and IDA analyses are conducted to investigate the seismic performance of columns with different FRC material. In order to account for the material inelasticity of FRC material, 3-D fiber-based displacement-based inelastic beam-column elements have been applied for modeling of the bridge columns. Four integration points have been verified to be adequate for fiberbased beam-column elements to capture the seismic behavior accurately. This fiber-based beam-column element has the ability to represent the distribution of material nonlinearity along the column height. The cross-section of the column is modeled as fiber sections. Each section is divided into about 400–600 fibers. In these fiber sections, each fiber has a suitable uniaxial stress-strain hysteretic relationship to represent the unconfined concrete, confined concrete and longitudinal reinforcements. To develop the nonlinear fiber-based finite element models, the Chang and Mander uniaxial reinforcing steel model [31] in the OpenSees is used to simulate the longitudinal reinforcements, considering the compression buckling, mechanical effects of strain softening and tensile fracture of steel bars. In this Chang and Mander reinforcing steel model, the Coffin-Manson equation for plastic strain amplitude is considered for the effect of fatigue. The yield strength, strain hardening and elasticity modulus of longitudinal reinforcements are 400 MPa, 0.5% and 2 105 MPa, respectively. The cyclic behavior of FRC concrete is simulated by the Chang and Mander concrete model (labeled as ‘concrete070 model in the OpenSees) with simplified unloading and reloading curves. The compressive strength 40 MPa and tensile strength 2.1 MPa of plain concrete have been used. In the bridge columns, different FRC material has different influence on the peak bond strength and bond degradation of RC columns under the seismic loadings. So the compressive strength, the tensile strength, ultimate strength, compressive strain and ultimate strain for different FRC material will be different and can be calculated using the equations in the following section 3.2. In order to account for bond degradation, a nonlinear rotational link element with zero length is employed to simulate the bond-slip rotations at the column-foundation interface. Different bond-slip models are used for different FRC columns, which is also introduced in the following Section 3.2.
246
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Table 4 Relative difference of base shear and displacement at yielding, crushing, buckling and fracture limit states. Material
Steel yielding
Normal RC SFRC PFRC HySPFRC
Concrete crushing
Steel buckling
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
0.091 0.086 0.083 0.084
793 876 884 911
0.263 0.289 0.271 0.274
891 985 1032 1086
0.725 0.732 0.736 0.744
783 996 1018 1132
0.779 0.783 0.782 0.787
760 1005 1011 1147
qffiffiffiffiffiffiffi2 smax ¼ s1 exp 1:8 umax =2:57 f frc 1 for SFRC
3.2. Material property The peak compressive strength of FRC, ffrc, is calculated using the following equation:
f frc ¼ K frc K s f c
ð1Þ
in which is fs is the compressive strength of plain concrete; Kfrc is the modification factor due to the addition of fibers; Ks is the confinement factor to consider the effect of stirrups. The modification factor, Kfrc, can be calculated by Eq. (2), which has been calibrated by the test results in the literature [32].
K frc ¼ 1 þ 0:206ksf þ 0:388kpf
ð2Þ
where ksf is the characteristic parameter for steel fibers; kpf is the characteristic parameter for polypropylene fibers. The characteristic parameters ksf and kpf can be determined by Eq. (3):
ksf ¼
psf lsf ppf lpf and kpf ¼ dsf dpf
ð3Þ
in which psf and ppf are the volume fraction of steel fibers and polypropylene fibers respectively; lsf and lpf are the length of steel and polypropylene fibers; dsf and dpf are the diameter of steel and polypropylene fibers. The confinement factor, Ks, can be derived from the Park model [33] as
Ks ¼ 1 þ
qt f sy K frc f c
efrc ¼ ec ð1 þ 0:705ksf þ 0:364kpf Þ
ð5Þ
in which ec is the peak strain of the plain concrete. The tensile strength of FRC material, ft, can be calculated using the square root of compressive strength according to the recommendation [34]
qffiffiffiffiffiffiffi f t ¼ 0:45 f frc
ð9Þ
" #! qffiffiffiffi2 umax =2:57 f c 1
smax ¼ s1 exp 3:3ln
qffiffiffiffi þ s0 2:57 f c =umax for RC
ð10Þ
in which Atr is the area of transverse hoops; db is the diameter of the reinforcements; c is the thickness of concrete cover; st is the spacing of the transverse stirrups; ns is the number of spliced tension bars in the section; s1 equals 0.15c0 (c0 is the clear distance between the ribs of the reinforcing bars); s0 equals 0.4 mm. The above Harajli model [34] was proposed with limitation to hooked steel fibers. Due to the reason that the aspect ratio (lf/df) of polypropylene fibers is four to six times larger than that of the hooked steel fibers, thus, the Harajli model cannot be used for PFRC concrete. Therefore, a bond-slip model for PFRC proposed by Chao et al. [32] is introduced to determine the bond strength of PFRC. This model is developed from a series of pullout experiments and the equations for the bond strength model are shown in the following:
" umax ¼ 20
rp ðf frc Þ1=4
#
db
ð11Þ
ð4Þ
where fsy is the strength of stirrups; qt is the stirrups ratio. The peak strain of fiber-reinforced concrete, efrc, can be determined by the following equation:
ð6Þ
3.3. Bond-slip model The bond-slip model for SFRC is developed by Harajli [35] from a series of beam experiments of fiber reinforced concrete with various hooked steel fibers at different volume fractions. This model can be also used for normal RC and HySPFRC columns with transverse hoops. Maximum bond strength, umax, and maximum reinforcement slip, smax, can be computed as follows:
qffiffiffiffiffiffiffi c þ 0:45cp l =d 2=3 sf sf sf umax ¼ 0:78 f frc ð Þ for SFRC db
ð7Þ
qffiffiffiffiffiffiffi c þ 7:0A =s n 2=3 tr t s ¼ 0:78 f frc ð Þ for RC db
ð8Þ
umax
Steel fracture
smax ¼
215umax db f frc
ð12Þ
where rp is the tensile stress where tensile softening begins. Table 3 shows the main mechanical properties for bond-slip models for different FRC columns using the above equations. 3.4. Model calibration with experimental results In this section, the finite element models of bridge columns with different FRC material have been calibrated and validated using the existing experimental data from previous literature [5,23,28,36]. Fig. 4 illustrates the comparison of experimental data and numerical results from finite element models using the cyclic pushover analysis. From Fig. 4, it can be observed that the finite element models can simulate the initial stiffness, post stiffness and ultimate capacity accurately when compared to test results. In summary, the developed finite element models of four bridge columns with normal RC and different FRC material are shown to provide the sufficient accuracy. 4. Nonlinear static pushover analysis In order to conducted the NSPA, weight permanent load (340 kN) was included and the superstructure load (780 kN) is applied at the top of the column in the finite element model, Thus, the bridge columns had a ratio of 0.02 fcAc axial load (fc = concrete
247
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
strength; Ac = sectional area). In the NSPA, the incremental lateral load is only set at the top of column with the displacement control method. The results from the NSPA are expressed as the pushover curves which are the relationship between lateral displacement and the base shear. The pushover curves of bridge columns with normal RC and different FPC material, namely SFRC, PFRC and HySPFRC are shown in Fig. 5. It is evident from Fig. 5 that the capacity of all the FRC bridge columns was increased considerably when comparing to that of normal RC bridge column. The HySPFRC bridge column has the maximum enhancement of seismic capacity, while SFRC and PFRC column ranked second and third. Moreover, when the lateral displacement was small, the variations of pushover curves between the SFRC, PFRC and HySPFRC were small. This is due to the reason that elastic modulus of SFRC, PFRC and HySPFRC column was nearly the same. When the lateral displacement was large, the variations between the SFRC and PFRC were small. It is because the compressive strength of concrete improved by SFRC and PFRC was similar. In general, all the FRC material can improve the seismic capacity in an adequate way. In order to study the influence of the FRC material on the seismic capacity of column sections, the moment-curvature analysis was also conducted in this paper. Fig. 6 illustrates the moment-curvature curves. It can be seen from Fig. 6 that all the sectional seismic capacity can be improved by FRC material.
In the seismic performance evaluations of bridge columns, the flexural damage states can be used as performance criteria. In this paper, four flexural damage states (slight, moderate, extensive and collapse) are considered: a) yielding of longitudinal steels; b) crushing of core concrete; c) buckling and d) fracture of longitudinal steel bars. The limit values for these four flexural damage states can be calculated by the strain limits of both core concrete and longitudinal steels. The yielding of longitudinal steels is assumed to take place when the steel strain reached the ratio of yield stress and elastic modulus of steel bars. The core concrete crushing is assumed to be happened when the strain of core concrete changed normally from 0.015 to 0.05 according to the suggestion given by Paulay and Priestley [37]. In this paper, a median value of concrete strain, 0.033, was used as the reference value. Moreover, the tensile strain of longitudinal reinforcements determined by the Berry and Eberhard [38] equations can be used to predict the buckling and fracture of steel bars. Table 4 illustrates the difference of displacement and base shear at four flexural damage states from the pushover curves. From Table 4, it can be observed that different FRC material develop different displacement and base shear of bridge columns. For steel yielding limit state, the yielding of longitudinal steels started at the same level displacement in the all the bridge columns. The base shear at steel yielding for normal RC was 793 kN which was 9.5%, 11.5% and 14.9% lower than that of SFRC, PFRC and HySPFRC respectively. For concrete crushing limit state, the SFRC, PFRC and HySPFRC
Table 5 selected ground motions used in IDA. No.
Earthquake Name
Year
Station Name
Magnitude
Rrup (km)
Vs30 (m/sec)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Helena_ Montana Helena_ Montana Parkfield Managua_ Nicaragua Gazli_ USSR Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Mammoth Lakes
1935 1935 1966 1972 1976 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1980
Carroll College Helena Fed Bldg Cholame-Shandon #5 Managua_ ESSO Karakyr Aeropuerto Mexicali Agrarias Bonds Corner Chihuahua EC Center FF El Centro MG El Centro #10 El Centro #4 El Centro #5 El Centro #6 El Centro #7 El Centro #8 El Centro D Holtville PO Convict Creek
6.0 6.0 6.2 6.2 6.8 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.1
2.9 2.9 9.6 4.1 5.5 0.3 0.7 2.7 7.3 7.3 0.1 8.6 7.1 4.0 1.4 0.6 3.9 5.1 7.5 6.6
593.4 551.8 289.6 288.8 259.6 259.9 242.1 223.0 242.1 192.1 264.6 202.9 208.9 205.6 203.2 210.5 206.1 202.3 202.9 382.1
Fig. 7. 20 selected as-recorded ground motions: a) spectral acceleration and b) percentiles of spectral acceleration.
248
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 8. Dynamic pushover points and static pushover curve for bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
increased the displacement by 9.9%, 3.1% and 4.2% and increased the base shear by 10.5%, 15.8% and 21.9% when comparing to that of normal RC column. For steel buckling and fracture limit states, the displacement in the all bridge columns changed a little by the FRC material. The base shear could be improved by almost 30% for SFRC, PFRC and HySPFRC bridge column respectively. 5. Incremental dynamic analysis While the nonlinear pushover analysis can be used to evaluate the static responses of bridge columns under lateral load, nonlinear time-history analysis (NTHA) can be applied to obtain the dynamic time-history responses of bridge columns. Due to the reason that structures experience the dynamic lateral load during an earthquake in the reality, the NTHA can give the accurate prediction of seismic demands. The IDA method developed by Luco and Cornell [25] and Vamvatsikos and Cornell [26] is based on the NTHA, in order to estimate the large inelastic responses of structures. IDA requires a series of NTHAs of a well-calibrated finite element model of the considered structure for a suite of selected asrecorded or artificial ground motions with different levels of intensities. The different intensity levels are set by adjusting the IM of ground motions in order to study the full range of seismic behavior, from elastic responses to structural collapse. From various NTHAs, IDA curves can be obtained, which expresses the relationship between the selected EDPs and IM of ground motions. 5.1. Ground motions In this paper, a total of 20 near-fault ground motions with moment magnitude Mw between 6.0 and 8.0 are selected from
the PEER strong ground motion database and applied in the assessment of the seismic performance of bridge columns with normal RC and different FRC material as shown in Table 5. These selected near-fault ground motions are records from soil site classes that have shear wave velocities Vs between 200 m/s and 600 m/s in the upper 30 m. The closest site-to-fault distances of the records vary from 0.1 to 10 km. Fig. 7 shows the spectral accelerations of the 20 selected as-recorded ground motions with 5% damping ratio. It is illustrated from Fig. 7 that these selected ground motions can represent the medium to strong earthquakes well. 5.2. IDA analysis In order to conduct the IDA, the PGA is selected as IM. PGA is recognized as an optimal IM by Nielson and DesRoches [39], Padgett et al. [40] and Zelaschi et al. [41] and for sufficiency and efficiency in the seismic assessment of bridges. It is worth mentioning that further studies may be necessary to study whether or not the PGA is a sufficient and efficient IM to be used in similar studies as the present paper especially when dealing with the seismic damage analysis of FRC columns. It is authors’ opinion that PGA is a simple but robust IM that can be reliably utilized as the IM and it is more convenient to implement the scaling of selected ground motions than the spectral acceleration of structures. In the present paper, PGA is adjusted from 0.1 g to final PGA value with an increment 0.01 g to cover a large range (elastic and inelastic) of seismic behavior. This final PGA value is determined by the collapse point [42] of finite element model in which the finite element models experiences the globe dynamic instability and causes a large and unreal maximum drift ratio of top columns. In order to form the IDA curves, four EDPs are selected and monitored during the IDA
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
249
Fig. 9. IDA curves for maximum drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Fig. 10. Median and percentiles of IDA curves for maximum drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
250
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
analysis, namely maximum drift, residual drift, displacement ductility and curvature ductility demands of bridge columns. These four EDPs adopted in this paper have been considered by previous studies [40,43–50] as important parameters, which are considered sufficient and adequate to characterize the seismic performance of the analyzed bridge columns. In this paper, the IDA analyses are conducted for all the bridge columns using the selected suite of 20 near-fault ground motions presented in Table 5. Due to the rare results of shaking table tests in the literatures, the IDA analysis is only calibrated by comparing the static pushover curves with dynamic pushover points generated from IDA curves with as shown in Fig. 8. From Fig. 8, it can be found that the dynamic pushover points coincide with the static pushover curves well although the dynamic pushover points show higher base shear than the static pushover curves. 5.2.1. Maximum drift demand The maximum drift (%) is defined as the ratio of the peak displacement of the top bridge column to the column height under single ground motion with certain intensity level, which can be used to develop one IDA curve. Fig. 9 depicts the maximum drift (%) IDA curves for normal RC, SFRC, PFRC and HySPFRC columns. From Fig. 9, it can be observed that all the IDA curves have a linear part and a nonlinear part, which shows the sign of the elastic and inelastic behavior. In the inelastic region, the IDA curves display the stiffness degradation or a softening behavior until the column collapse takes place. Due to the inherent uncertainty of ground motions, the scattering and variability of IDA curves can also be observed. Moreover, it can be illustrated by Fig. 9 that the FRC bridge columns show relatively higher elastic stiffness than the normal RC bridge column. It can be attributed to the reason that the FRC material can improve the elastic modulus of core concrete.
The FRC bridge columns also show higher maximum drift when comparing to that of the normal RC bridge column in the inelastic range of behavior, indicating a good seismic performance. Because the IDA curves display the diversity and scattering property, it is of important to implement the statistical method for evaluation. In this paper, the 16th, 50th and 84th fractile values of IDA curves are calculated and summarized in order to produce more reliable data for evaluating the seismic behavior of FRC bridge columns. Fig. 10 shows median and percentiles of maximum drift (%) IDA curves for bridge columns with normal RC and different FRC material. It should be noted that when the PGA is large, the remaining number of IDA is so small that it is not suitable for statistical calculation, thus, the PGA range used for fractile IDA curves is smaller than that of original IDA curves. By comparing the fractile IDA curves with the allowable drift at certain damage state, it is convenient to assess the seismic performance of columns. For instance, given the design PGA = 1.0 g at high seismic zones, 16% IDA curve depicts the maximum drift (%) 1.81%, 1.85%, 1.56% and 1.78%; 50% IDA curve depicts the maximum drift (%) 3.89%, 3.15%, 2.94% and 3.02%; 84% IDA curve depicts the maximum drift (%) 5.95%, 4.14%, 4.08% and 4.03% for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that SFRC, PFRC and HySPFRC are all effective to improve the seismic capacity and reduce the seismic demands of the bridge column. The difference of the improvement from different FRC material is within 5%. Previous studies [43,44] have suggested the permissible drift values for the serviceability and collapse damage states. According to these papers, 1.9% is used to indicate the loss serviceability, and 5.0% for global collapse of bridge column. From the above results, it can depict that the maximum drift (%) of all the FRC bridge columns do not exceed the collapse range, indicating that the seismic capacity of all the FRC bridge column are improved.
Fig. 11. IDA curves for residual drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
5.2.2. Residual drift demand Due to the accumulation damage during the earthquakes, a RC structure may experience a large permanent displacement or deformation which may cause the traffic closure and increase the repair cost after the seismic loading. In the PBEE framework, the residual drift has been considered as an important EDP by many researchers [45,46]. Thus, it is of importance to use the residual drift for seismic performance assessment of structures. In this paper, the fiber-based nonlinear beam-column elements are used in the finite element models, which has calibrated and verified by several researchers [47,48] that the fiber-based elements can estimate the residual displacement or deformation quite accurately. The residual drift (%) is defined as the ratio of the residual displacement of the top column to the column height. Fig. 11 shows the residual drift (%) IDA curves plotted for four bridge columns. From Fig. 11, it can be observed that the residual drift IDA curves are different for different FRC bridge columns. By comparing the IDA curves, it can be seen that the FRC bridge columns experience lower residual drift than the normal RC bridge column. It is due to the reason that FRC bridge columns have higher stiffness compared to the normal RC bridge columns. Moreover, PFRC and HySPFRC bridge columns have lower residual drift than the SFRC and normal RC bridge columns. This may be because the steel fibers not only increase the column stiffness, but also increase larger additional weight than the polypropylene fibers, which may increase the inertial force under seismic loading. The 16th, 50th, and 84th fractile IDA curves are also summarized in this section to assess the residual drift demand of FRC bridge columns. Fig. 12 illustrates the median and percentiles of residual drift (%) IDA curves for columns with normal RC and different FRC material. For example, given the design PGA = 1.0 g at
251
high seismic zones, 16% of IDA curves produces the residual drift (%) 0.02%, 0.13%, 0.07% and 0.04%; 50% of IDA curves produces the residual drift (%) 0.27%, 0.32%, 0.19% and 0.13%; 84% of IDA curves depicts the residual drift (%) 0.48%, 0.53%, 0.34% and 0.22% for normal RC, SFRC, PFRC and HySPFRC, respectively. In the previous studies, 1.75% is used as residual drift limit for collapse state, which is concluded after the Kobe earthquake. After the Kobe earthquake [49], a larger number of RC bridge columns are demolished even though they did not collapse, when the residual drift of bridge columns reaches 1.75%. In this case, the FRC bridge columns do not exceed this drift limit when the PGA is smaller than 2.0 g, indicating that the FRC material is effective for reducing the residual drift. 5.2.3. Displacement ductility demand Displacement ductility is defined as the ratio of maximum displacement of bridge columns to the yield displacement, which is usually considered as an important EDP for seismic performance evaluation of bridge column. This displacement ductility demand can be used as the indication of global deformation of the bridge columns. Thus, in this paper, the displacement ductility is also used to assess the seismic performances of the four FRC bridge columns. Fig. 13 presents the IDA curves in terms of displacement ductility of columns. From Fig. 13, it can be observed that the IDA curves plotted using the displacement ductility demands are different for different FRC bridge columns. The FRC material can be effective for reducing the displacement ductility demands at different PGA levels. Fig. 14 summarizes the 16%, 50%, and 84% fractile IDA curves. By comparing the fractile IDA curves of different FRC bridge columns, displacement ductility demand of FRC bridge columns can be evaluated. For instance, given the design PGA = 1.0 g at high
Fig. 12. Median and percentiles of IDA curves for residual drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
252
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 13. IDA curves for ductility demand of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Fig. 14. Median and percentiles of IDA curves for ductility demand of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
253
Fig. 15. IDA curves for curvature ductility of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
seismic zones, 16% IDA curve presents the displacement ductility 1.04, 1.01, 0.93 and 0.87; 50% IDA curve presents the displacement ductility 2.21, 1.73, 1.71 and 1.69; 84% IDA curve presents the displacement ductility 3.41, 2.49, 2.54 and 2.45 for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that the HySPFRC column can be more effective for reducing the displacement ductility than SFRC and PFRC. In the previous studies, many researchers have proposed different values for four damage limit states (slight, moderate, extensive and complete) based on the displacement ductility. Hwang et al. [50] proposed four displacement ductility ratios (1.0, 1.2, 1.76 and 4.76) for four damage states for bridge columns. By comparing with these damage limit values, it can be found that all these FRC bridge columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g). At a high level of intensity (PGA = 2.0 g), different FRC bridge columns do not encounter the complete (collapse) damage. 5.2.4. Curvature ductility demand Curvature ductility is defined as the ratio of maximum curvature to the yield curvature of sections at the column base. In the seismic performance evaluation of bridges, the curvature ductility is usually adopted as an important EDP for developing the seismic fragility of bridge components. Therefore, the curvature ductility is also adopted to assess the seismic behavior of the four FRC bridge columns. Fig. 15 depicts the curvature ductility IDA curves of bridge columns with different FRC material, namely normal RC, SFRC, PFRC and HySPFRC. From Fig. 15, it can be found that the FRC material can be effective for reducing the curvature ductility demands at different PGA levels. Fig. 16 presents the 16%, 50%, and 84% fractile IDA curves. The fractile IDA curves of different
FRC bridge columns are compared to evaluate the curvature ductility demands of FRC bridge columns. For example, given the design PGA = 1.0 g at high seismic zones, 16% IDA curve illustrates the curvature ductility 1.91, 1.25, 1.37 and 1.31; 50% IDA curve illustrates the curvature ductility 4.12, 2.38, 2.45 and 2.36; 84% IDA curve illustrates the curvature ductility 6.21, 3.89, 4.02 and 3.85 for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that the HySPFRC column can be more effective for reducing the curvature ductility than SFRC and PFRC. In the seismic fragility analysis of bridges, the damage limits for four damage limit states (slight, moderate, extensive and complete) are based on the sectional curvature ductility. Padgett et al. [40] proposed four curvature ductility ratios (1.0, 2.0, 4.0 and 7.0) for four damage states for bridge columns. Compared to the displacement ductility demands, similar conclusions can be obtained. All these FRC bridge columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g) and do not encounter the complete (collapse) damage at a high level of intensity (PGA = 2.0 g). 5.3. Mean seismic capacity The seismic capacity can also be expressed as the PGA values, which can be computed based on the IDA curves to link the PGA with the four flexural damage states considered in Section 4. As mentioned in the above section, the four flexural damage states are associated with the strain of both core concrete and longitudinal steels. Thus, each flexural damage state has one specific PGA for any IDA curve. Fig. 17 shows the bar chart of the calculated mean PGA for maximum drift IDA curves. It should be noted that lower mean PGA value of bridge column means lower seismic capacity
254
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 16. Median and percentiles of IDA curves for curvature ductility of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
compared to higher mean PGA values. It can be found from Fig. 17 that the FRC columns have higher mean PGA values compared to that of normal RC bridge column, indicating that the FRC material can enhance the seismic capacity of RC columns. Moreover, SFRC and HySPFRC are more effective for enhancing the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective for the extensive and complete damage states.
5.4. Seismic fragility Seismic fragility analysis is usually used for evaluating the seismic vulnerability of RC bridges. The results obtained from the fragility analysis are in terms of fragility curves, which express the relationship between the conditional damage probabilities of exceeding a damage state with a specified IM of ground motions. Two main methods are usually used to derive the fragility functions, namely the cloud approach and the IDA method. Compared to the cloud approach, the IDA method can be more effective to create sufficient data for fragility functions [51]. When using IDA method, the fragility functions can be developed using Eq. (13) as a lognormal cumulative distribution function (CDF):
lnðx=cÞ Pf ðDamagejIM ¼ xÞ ¼ U b
ð13Þ
in which Pf represents the damage probability, x is a specific conditional value of IM. U(.) is the CDF of standard normal distribution, c is the median intensity of the fragility curves, and b is the standard
deviation. The parameters c and b can be estimated by a simplified fitting method proposed by Baker [52]. In this paper, four damage states (slight, moderate, extensive and collapse) are adopted which have been already defined in the above section. The maximum drift (%) is used to measure these damage states as shown in Table 6. Based on Eq. (13), the results from the IDA curves of the maximum drift (%) of top column are used to generate the analytical fragility curves of different FRC columns. Fig. 18 shows the seismic fragility curves of different FRC columns for four limit states. As stated earlier, it can be seen from Fig. 18 that the FRC columns have lower damage probability compared to that of normal RC bridge column, indicating that the FRC material can be effective to improve the seismic performance. This can be attributed to the difference in strength and ductility properties of FRC material, which has been discussed earlier. Moreover, the PFRC and HySPFRC have a lower damage probability for the extensive and complete damage states, while SFRC and HySPFRC have a lower damage probability for moderate damage state. Interestingly, the normal RC column has similar damage probability as the SFRC column, which may be attributed to the similar behavior of normal RC and SFRC bridge column in the pre-yield behavior level. This is in agreement with previous study [28].
6. Conclusion This paper proposed a comprehensive study to investigate the seismic performance of normal RC and different FRC bridge columns. A 3-D fiber-based finite element model of different FRC columns are firstly built by using proper cyclic constitutive laws
255
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 17. Mean seismic capacity of bridges column with four limit states: a) yielding of longitudinal steel; b) crushing of confined concrete; c) buckling of steel bars; d) fracture of steel bars.
Table 6 Limit state capacity of different bridge columns in terms of maximum drift (%). Damage state
Slight Moderate Extensive Collapse
Performance level
Steel yielding Crushing of core concrete Steel buckling Steel fracture
Normal RC
SFRC
PFRC
HySPFRC
Median
Dispersion
Median
Dispersion
Median
Dispersion
Median
Dispersion
0.98 2.78 7.74 8.35
0.2 0.2 0.46 0.46
0.93 3.14 7.96 8.51
0.2 0.2 0.46 0.46
0.90 2.95 8.01 8.49
0.2 0.2 0.46 0.46
0.91 2.99 8.09 8.56
0.2 0.2 0.46 0.46
Fig. 18. Seismic fragility curves of different FRC columns for four limit states.
of FRC concrete, and then calibrated using the experimental results. In this study, four flexural damage states are evaluated through the static pushover analysis. Then the IDA analyses are conducted for all the FRC bridge columns using the selected suite of 20 near-fault ground motions. Four EDPs, namely maximum drift, residual drift, displacement ductility and curvature ductility demands, are selected and monitored to evaluate the comparative seismic behavior of different FRC bridge columns. Based on the results from the NSPA and IDA analysis, the following conclusions can be drawn: 1) Different FRC material has different influence on the displacement and base shear of bridge columns. The displacement does not change too much by the FRC material except when crushing of concrete occurred. The concrete crushing increases the displacement by 9.9%, 3.1% and 4.2% for SFRC, PFRC and HySPFRC respectively. The base shear is improved by about 10% for SFRC, 15% for PFRC and 20% for HySPFRC columns respectively.
256
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
2) The SFRC, PFRC and HySPFRC are all effective to improve the seismic capacity and reduce the seismic demands of the bridge column. The difference of the improvement from SFRC, PFRC and HySPFRC columns is within 5%. The maximum drift (%) of all the FRC bridge columns do not exceed the collapse range 5.0%, indicating that the seismic capacity of all the FRC bridge column are improved. 3) By comparing IDA curves in terms of the residual drift, it can be concluded that the FRC bridge columns experience lower residual drift than the normal RC bridge column. PFRC and HySPFRC bridge columns have lower residual drift than the SFRC and normal RC bridge columns. The FRC bridge columns do not exceed this drift limit of 1.75% when the PGA is smaller than 2.0 g, indicating that the FRC material is effective for reducing the residual drift. 4) HySPFRC column can be more effective for reducing the displacement and curvature ductility demands than SFRC and PFRC. All the FRC columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g) and do not encounter the complete (collapse) damage at a high level of intensity (PGA = 2.0 g). 5) It can be concluded that the FRC columns have higher mean PGA values compared to that of normal RC bridge column, indicating that the FRC material can enhance the seismic capacity of RC columns. Moreover, SFRC and HySPFRC are more effective for enhancing the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective for the extensive and complete damage states. 6) The FRC columns have lower damage probability compared to that of normal RC bridge column, indicating that the FRC material can be effective to improve the seismic performance. The PFRC and HySPFRC have a lower damage probability for the extensive and complete damage states, while SFRC and HySPFRC have a lower damage probability for moderate damage state. Conflict of interest There is no conflict of interest. Acknowledgements This research is supported by Natural Science Foundation of China under Grant No. 51708527 and China Postdoctoral Science Foundation under Grant No. 2016M592407. References [1] Z.F. Wang, A preliminary report on the great Wenchuan earthquake, Earthquake Eng. Eng. Vibr. 7 (2008) 225–234. [2] A. Zsarnóczay, L.G. Vigh, L.P. Kollár, Seismic performance of conventional girder bridges in moderate seismic regions, J. Bridge Eng. 19 (5) (2014) 04014001. [3] M. Shinozuka, S.H. Kim, S. Kushiyama, J.H. Yi, Fragility curves of concrete bridges retrofitted by column jacketing, Earthq. Eng. Eng. Vib. 1 (2) (2002) 195–205. [4] D.S. Gu, Y.F. Wu, G. Wu, Z.S. Wu, Plastic hinge analysis of FRP confined circular concrete columns, Constr. Build. Mater. 27 (2012) 223–233. [5] Y.Y. Zhang, K.A. Harries, W.C. Yuan, Experimental and numerical investigation of the seismic performance of hollow rectangular bridge piers constructed with and without steel fiber reinforced concrete, Eng. Struct. 48 (2013) 255– 265. [6] M.A. Dagenais, B. Massicotte, Tension lap splices strengthened with ultrahigh performance fiber-reinforced concrete, J. Mater. Civil Eng. 27 (7) (2015) 04014206. [7] Z.L. Wang, Y.S. Liu, R.F. Shen, Stress–strain relationship of steel fiber-reinforced concrete under dynamic compression, Constr. Build. Mater. 22 (2008) 811– 819. [8] J. Stephen, M. Mario, Strength and ductility of fiber-reinforced high-strength concrete columns, J. Struct. Eng. 127 (2001) 28–34. [9] P. Joao, Behaviour of fiber reinforced concrete columns in fire, Compos. Struct. 92 (2010) 1263–1268.
[10] C. Röhm, B. Novák, S. Sasmal, Behaviour of fibre reinforced beam-column subassemblages under reversed cyclic loading, Constr. Build. Mater. 36 (2012) 319–329. [11] I. Laura, P. Patrick, E. Rami, P. Jean, Seismic behavior of synthetic fiberreinforced circular columns, ACI Mater. J. 111 (2014) 189–200. [12] Z. Hashem, R. Yuan, Short vs. long column behavior of pultruded glass-fiber reinforced polymer composites, Constr. Build. Mater. 15 (2001) 369–378. [13] O. Ozcan, B. Binici, G. Ozcebe, Improving seismic performance of deficient reinforced concrete columns using carbon fiber-reinforced polymers, Eng. Struct. 30 (2008) 1632–1646. [14] American Concrete Institute (ACI), State-of-the-art report on fiber reinforced concrete, ACI 1R-82, Detroit, 1982. [15] M. Hsie, C.J. Tu, P.S. Song, Mechanical properties of polypropylene hybrid fiberreinforced concrete, Mater. Sci. Eng. 494 (2) (2008) 153–157. [16] Y.N. Ding, Z. You, S. Jalali, Hybrid fiber influence on strength and toughness of RC beams, Compos. Struct. 92 (2010) 2083–2089. [17] V. Gribniak, G. Kaklauskas, A.K.H. Kwan, Deriving stress-strain relationships for steel fiber concrete in tension from tests of beams with ordinary reinforcement, Eng. Struct. 42 (2012) 387–395. [18] G. Kotsovos, C. Zeris, M. Kotsovos, The effect of steel fibers on the earthquakeresistant design of reinforced concrete structures, Mater. Struct. 40 (2007) 175–188. [19] N. Ganesan, P. Indira, M. Sabeena, Behavior of hybrid fiber reinforced concrete beam-column joints under reverse cyclic loads, Mater. Des. 54 (2014) 686– 693. [20] J. Stephen, On behavior of high-strength concrete columns: cover spalling, steel fibers and ductility, ACI Struct. J. 8 (2001) 583–589. [21] H. Lee, Shear strength and behavior of steel fiber reinforced concrete columns under seismic loading, Eng. Struct. 29 (2007) 1253–1262. [22] H. Zhao, Experimental and theoretical research on seismic performance of concrete frame with special-shaped columns reinforced with polypropylene fiber, Tianjin University, Tianjin, 2008. [23] L. Huang, L.H. Xu, Y.Xu.H. Chi, Experimental investigation on the seismic performance of steel–polypropylene hybrid fiber reinforced concrete columns, Constr. Build. Mater. 2015 (87) (2015) 16–27. [24] Y. Chi, L.H. Xu, Y.Y. Zhang, Experimental Study on Hybrid Fiber-Reinforced Concrete Subjected to Uniaxial Compression[, J. Mater. Civ. Eng. 26 (2) (2014) 211–218. [25] N. Luco, C.A. Cornell, Effects of random connection fractures on the demands and reliability for a three-story pre-Northridge (SMRP) structure, in: Proc sixth US Natl. conf Earthq. eng, Earthq. Eng. Res. Inst., Oakland, California; 1998. [26] D. Vamvatsikos, C.A. Cornell, Incremental dynamic analysis, Earthq. Eng. Struct. Dyn. 31 (2002) 491–514. [27] JTG, T,, B02–01-2008. Guidelines for seismic design of highway bridges, China: Department of Transportation (2008). [28] Y. Zhang, D. Dias-da-Costa, Seismic vulnerability of multi-span continuous girder bridges with steel fiber reinforced concrete columns, Eng. Struct. 150 (2017) 451–464. [29] L.H. Xu, H.R. Xu, Y. Chi, Y.Y. Zhang, Experimental study on tensile strength of steel–polypropylene hybrid fiber reinforced concrete, Adv. Sci. Lett. 4 (2011) 911–916. [30] F. McKenna, M.H. Scott, G.L. Fenves, et al., Open system for earthquake engineering simulation (OpenSees), Pacific Earthquake Engineering Research Center (2008). [31] G. Chang, J. Mander, Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part I – Evaluation of Seismic Capacity, NCEER Technical Report 940006, 1994. [32] S.H. Chao, A.E. Naaman, G.J. Parra-Montesinos, Local bond stress-slip models for reinforcing bars and prestressing strands in high-performance fiberreinforced cement composites, ACI SP 272 (2010) 151–172. [33] R. Park, M. Priestley, W. Gill, Ductility of square-confined concrete columns, J. Struct. Div. 108 (1982) 929–950. [34] 318–05., Building code requirements for reinforced concrete and commentary, America: American Concrete Institute (2005). [35] M.H. Harajli, Bond stress slip model for steel bars in unconfined or steel, FRC, or FRP confined concrete, J. Struct. Eng. 135 (5) (2009) 509–518. [36] X.W. Liang, J. Xu, P.T. Xing, Experimental study and numerical simulation on the seismic behavior of fiber-reinforced concrete columns, Eng. Mech. 33 (8) (2016) 66–76. [37] T. Paulay, M.J.N. Priestley, Seismic design of reinforced concrete and masonry buildings, J. Wiley, New York, 1992. [38] M.P. Berry, M.O. Eberhard, Performance modeling strategies for modern reinforced concrete bridge columns. PEER Report 2007/07 Pacific Earthquake Engineering, Research Center, College of Engineering, University of California, Berkeley, USA, 2007. [39] B.G. Nielson, R. DesRoches, Seismic fragility methodology for highway bridges using a component level approach, Earthquake Eng. Struct. Dyn. 36 (6) (2007) 823–839. [40] J.E. Padgett, B.G. Nielson, R. DesRoches, Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios, Earthquake Eng. Struct. Dyn. 37 (5) (2008) 711–725. [41] C. Zelaschi, R. Monteiro, M. Marques, Pinho Rr, Comparative analysis of intensity measures for reinforced concrete bridges, Second European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey, August 25 29, 2014.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257 [42] B. Shafei, F. Zareian, D.G. Lignos, A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems, Eng. Struct. 33 (2011) 1107–1116. [43] M.J. Kowalsky, Deformation limit states for circular reinforced concrete bridge columns, J. Struct. Eng. 126 (8) (2000) 869–878. [44] M. Liu, B. Lu, B. Liu, Study on performance index of reinforced concrete bridge column, Adv. Intell. Soft Comput. 114 (2012) 189–198. [45] S.R. Uma, S. Pampanin, C. Christopoulos, Development of probabilistic framework for performance-based seismic assessment of structures considering residual deformations, J. Earthq. Eng. 14 (7) (2010) 1092–1111. [46] A.H.M.M. Billah, M.S. Alam, Seismic fragility assessment of concrete bridge piers reinforced with superelastic shape memory alloy, Earthq. Spectra 31 (3) (2014) 1515–1541. [47] M.M. Hachem, S.A. Mahin, J.P. Moehle, Performance of circular reinforced concrete bridge columns under bidirectional earthquake loading, PEER report
[48]
[49] [50] [51]
[52]
257
2003/06, Pacific Earthquake Engineering Research Center, University of California, Berkeley, California. J. Sakai, S.A. Mahin, Analytical investigations of new methods for reducing residual displacements of reinforced concrete bridge columns. PEER-2004/02, Pacific Earthq. Engrg. Res. Center, Univ. of California at Berkeley, California; 2004 K. Kawashima, G. MacRae, J. Hoshikuma, K. Nagaya, Residual displacement response spectrum, J. Struct. Eng. 124 (5) (1998) 523–530. H. Hwang, J.B. Liu, Y.H. Chiu, Seismic fragility analysis of highway bridges. MAEC report: project MAEC RR-4. Mid-America Earthquake Center, Urbana; 2001 A.R. Bhuiyan, M.S. Alam, Seismic vulnerability assessment of a multi-span continuous highway bridge fitted with shape memory alloy bars and laminated rubber bearings, Earthq. Spectra 28 (2012) 1379–1404. J.W. Baker, Efficient analytical fragility function fitting using dynamic structural analysis, Earthq. Spectra 31 (2015) 579–599.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Seismic performance assessment of different fibers reinforced concrete columns using incremental dynamic analysis Yutao Pang, Li Cai, Hui Ouyang ⇑, Xiaoyong Zhou Faculty of Engineering, China University of Geosciences, Lumo Road 388, Wuhan, China
h i g h l i g h t s Seismic behavior of different fiber-reinforced concrete columns was compared. Nonlinear finite element models were built to present the behavior of columns. Seismic capacity of columns was evaluated through the nonlinear pushover analysis. Incremental dynamic analyses were conducted using 20 near-fault ground motions. Seismic fragility curves were obtained based on the maximum drift of columns.
a r t i c l e
i n f o
Article history: Received 1 September 2018 Received in revised form 6 January 2019 Accepted 12 January 2019
Keywords: Fiber-reinforced concrete Bridge columns Incremental dynamic analysis Nonlinear static analyses Seismic performance Ground motions
a b s t r a c t Different fiber-reinforced concrete (FRC) has been widely used in the recent decades, which can improve the mechanical behavior and dynamic performance of reinforced concrete (RC) columns remarkably. This paper aims to compare the seismic behavior of columns constructed with different FRC material, namely steel fibers reinforced concrete (SFRC), polypropylene fibers reinforced concrete (PFRC) and steelpolypropylene hybrid fiber reinforced concrete (HySPFRC). 3-D nonlinear finite element models have been built to represent the seismic behavior of different FRC columns, which are calibrated with the available experimental results of quasi-static tests. The seismic capacity of bridge columns with different FRC material are assessed based on four flexural damage states through the nonlinear static pushover analysis, such as a) yielding of longitudinal steels; b) core concrete crushing; c) buckling and d) fracture of longitudinal of steels. Incremental dynamic analyses (IDA) are conducted using the selected suite of 20 nearfault as-recorded ground motions to evaluate the inelastic seismic responses of different bridge columns. IDA curves are generated based on the intensity measure, namely peak ground acceleration (PGA) in this paper and seismic demands (i.e. maximum drift, residual drift, displacement ductility and curvature ductility) through nonlinear dynamic time-history analysis. It can be concluded from the IDA results that the SFRC, PFRC and HySPFRC are all effective to enhance the seismic performance, thus reducing the anticipated damage of the bridge columns. Moreover, SFRC and HySPFRC are more effective to improve the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective at the extensive and complete damage states. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Various reinforced concrete (RC) bridges are widely built in China over the last 40 years. The RC columns in these bridges may not fully achieve adequate seismic resistance and deformation capacity which is required by the seismic codes of bridges [1]. In recent strong earthquakes, such as Mw 8.0 Wenchuan 2008 and Mw 7.1 Yushu 2010 in China, many bridges suffered severe damage ⇑ Corresponding author. E-mail address: [email protected] (H. Ouyang). https://doi.org/10.1016/j.conbuildmat.2019.01.087 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
and plastic hinges were developed at the column base. This is partly due to the inherent disadvantages of plain concrete material, which has the drawbacks of inadequate flexural strength, being brittle, low toughness and low energy absorption ability [2–4]. Thus, it is of importance to improve these concrete features in order to enhance the overall seismic capacity of bridges. In traditional methods, the concrete properties can be improved by increasing the density of transverse stirrups in the bridge columns [5,6]. The closely spaced transverse stirrups can improve the core concrete confinement, thus restraining the crack propagation and reducing the strength degradation of RC columns [7].
242
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 1. Bridge column dimensions and reinforcement details.
However, insufficient concrete pouring quality may be caused by the large amount of transverse stirrups during the construction process. Due to this problem, the implement of fiber-reinforced concrete (FRC) has been recognized as a good alternative for enhancing the inherent properties of plain concrete. In the FRC material, different fiber types (e.g. steel fiber [8–10], polypropylene fiber [11] and other fibers [12,13]) can be used in the concrete mixtures. The randomly distributed fibers in the concrete matrix can increase the static properties (i.e. tensile strength, toughness and flexural strength) of plain concrete [14–17], and also show some attractive properties of the improved ductility and energy dissipation capacity in seismic loadings [18,19].
Various previous researches have been proposed to study the effect of fiber types and fiber content (volume fraction) on seismic performance of different FRC bridge columns. Nowadays, there are three main FRC column types, namely columns with inclusion of only steel fibers (SFRC), the columns with only polypropylene fibers or other synthetic fibers (PFRC) and the columns with combined different types of fibers (HyFRC). Stephen et al. [8,20] used some experimental tests to investigate the effect of steel fibers on the seismic behavior of RC columns. The results showed that the ductility and loading capacity of SFRC columns was improved compared to non-fiber concrete specimens. Lee et al. [21] studied the influence of addition of steel fibers into concrete on seismic performance of RC columns under earthquakes. It was observed from the experimental data that the optimal volume fraction for SFRC is 1.5% for improving the shear strength. Meanwhile, Zhao [22] and Laura et al. [11] investigated the seismic behavior of PFRC columns, indicating that polypropylene fibers could also improve the ductility capacity and energy absorption ability of RC columns. With regard to the seismic behavior of HyFRC columns, Huang et al. [23] evaluated the seismic behavior of hybrid steelpolypropylene fiber reinforced concrete (HySPFRC) columns through the experimental studies. Compared to RC columns, it showed that HySPFRC columns with a higher axial compression ratio established a significant effect on the dynamic capacity. Chi et al. [24] presented the experimental study on HySPFRC concrete subjected to uniaxial compression. It was found that in comparison to reinforced concrete with single fibers, HySPFRC showed more ductility at post-peak behavior. All these previous studies have proved that using FRC can achieve remarkable improvement in the mechanic and seismic performance of RC columns. It should be noted that since the damage in RC column is a complex and gradual process, different fiber types may have limited effective ranges. Thus, it is important to compare the seismic behavior of different FRC columns to see whether an optimal performance can be obtained when single fiber or fiber combination is used in the concrete. In the procedures of the performance-based earthquake engineering (PBEE) framework, estimation of both seismic demands and capacity of structures are required in order to present the comprehensive assessment of seismic structural behavior. The interrelationship between the demands and capacity can provide an inference of the expected level of damage at a given intensity level
Fig. 2. Schematic of bridge columns with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
243
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257 Table 1 Summary of the material properties. Material
Diameter (mm)
Length (mm)
Density (g/cm3)
Tensile/compressive strength (MPa)
Elastic modulus (GPa)
Concrete Longitudinal steel Hoop steel Polypropylene fibers Steel fibers
– 32 12 0.048 0.55
– – – 19 35
2.6 7.8 7.8 1.2 7.8
40 400 335 400 1143
30 200 200 43 200
Table 2 Main parameters for different bridge columns. Column No.
Type
Compressive strength (MPa)
Steel fiber content
Polypropylene fiber content
1 2 3 4
Normal RC SFRC PFRC HySPFRC
47 65 61 67
– 1.50% – 1.50%
– – 0.15% 0.15%
Fig. 3. Scheme to establish the FE model of bridge columns with fiber elements and bond-slip model.
Table 3 Mechanical properties used for bond-slip model. Column Type
c/db
fy (MPa)
Sy (mm)
umax (MPa)
Normal RC SFRC PFRC HySPFRC
1.5 1.5 1.5 1.5
400 400 400 400
0.85 0.92 1.06 0.98
6.2 8.9 9.1 9.8
of ground motions. In order to predict the structural responses in large nonlinear range, Luco and Cornell [25] and Vamvatsikos and Cornell [26] proposed a new computational based methodology called incremental dynamic analysis (IDA). IDA requires various nonlinear time-history analyses of a finite element model of a specific structure at different levels of ground intensities. The results of IDA cover the entire range of structural responses, from elastic behavior through yielding to dynamic instability, which can give a clear indication of relationship between the seismic capacity and demands. From IDA curves, the probability of exceed-
ing a specified limit state for a given intensity measure (IM) (known as seismic fragility) can be calculated. Therefore, the aim of this study is to compare the seismic performance of bridge columns reinforced with different FRC material, namely SFRC, PFRC and HySPFRC. The 3-D nonlinear fiber-based finite element models have been built to represent the seismic behavior of different FRC bridge columns, which are first calibrated with the available experimental results. The seismic capacity of bridge columns with different FRC material are assessed using four flexural damage states, a) yielding of longitudinal reinforcements; b) core concrete crushing; c) buckling and d) fracture of longitudinal reinforcements. These four flexural damage states can be obtained using the nonlinear static pushover analysis (NSPA). Moreover, the incremental dynamic analysis (IDA) is conducted to investigate the inelastic seismic demands of the FRC bridge columns under strong ground motions. In the IDA method, a suite of 20 near-fault ground motions is chosen as seismic input to 3-D nonlinear finite element models and scaled to different intensity levels. The results of IDA are shown as IDA curves in terms of the
244
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 4. Comparison of experimental and numerical results of different bridge columns: (a, b) normal RC column (Zhang et al. [28]; Zhang et al. [5]), (c, b) SFRC column (Zhang et al. [28]; Zhang et al. [5]), (e, f) PFRC column (Huang et al. [23]; Liang et al. [36]) and (g, h) HySPFRC columns (Huang et al. [23]).
relationship between the engineering demand parameter (EDP) of structures and IM of ground motions. In this paper, the peak
ground acceleration (PGA) is used as the IM. Various EDPs of the bridge columns, such as the maximum drift, residual drift, dis-
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 5. Pushover curves for bridge columns with different FRC material.
placement ductility and curvature ductility demands, have been selected and recorded during the IDA analysis. Finally, the seismic fragility curves are developed and compared to study the effect of different FRC material on the seismic performance of bridge columns
245
Fig. 6. Moment-curvature analysis of sections with different FRC material.
performance of different FRC columns in this paper is evaluated and compared based on the specified optimal volume ratios recommended by the above studies for different fibers. 3. Modeling of different FRC columns 3.1. Finite element modeling
2. Details of bridge columns In this study, the selected bridge column is located in Sichuan Province in China. This bridge column was designed following the seismic design guidelines for highway bridges in China [27]. The detail dimensions of this column are given in Fig. 1, which is a 1.2 m square, reinforced with 20 longitudinal steel bars with diameter 32 mm (reinforcement ratio of 1.3%). The prototype column has a height of 9.2 m and a cover thickness of 50 mm. The pile cap has the dimension of 2.5 2.5 1.5 m. square transverse stirrups has a diameter of 12 mm and the spacing is 300 mm. The longitudinal reinforcements in the bridge column have the yield strength of 400 MPa, while the compressive strength of the concrete is 40 MPa. Four different bridge columns with normal RC and different FRC material (SFRC, PFRC and HySPFRC) have been implemented in the columns. Fig. 2 illustrates the bridge columns with normal RC and different FRC material in this study. The SFRC bridge column has been adopted from Zhang et al [28], in which the steel fibers have a tensile strength of 1143 MPa, elastic modulus of 200 GPa and density of 7.8 g/cm3 as shown in Table 1. The steel fibers with hooks at both ends have a diameter of 0.55 mm and length of 35 mm. The average aspect ratio (length divided by diameter) equals 64. As excessive steel fibers (e.g. 2.0% volume ratio) may cause the workability reduction of concrete mix and introduce the unwanted defects of concrete members, a volume fraction of 1.5% (117 kg/m3) steel fibers are in the SFRC columns, which is recommended by many previous studies [21,23,28] due to the maximum enhancement of the strength, ductility and energy dissipation. The PFRC bridge column has been used from Huang et al [23], in which the polypropylene fibers have a tensile strength of 400 MPa, elastic modulus of 43 GPa and density of 1.2 g/cm3. The polypropylene fibers have the average aspect ratio l/d = 396 with 0.048 mm diameter and 19 mm length. A volume fraction of 0.15% (1.37 kg/m3) polypropylene fibers are included in the PFRC columns. In the HySPFRC column, the optimal volume ratios of hybrid fibers for improving the concrete strength is the combination of 1.5% steel fibers and 0.15% polypropylene fiber, which are recommended by Xu et al. [29] and Huang et al [23]. Table 2 depicts the main parameters for the different FRC bridge columns. It should be noted that different volume ratios of fibers may influence the seismic behavior of different FRC columns. The seismic
The numerical models of columns with normal RC and FRC material are built using the 3-D nonlinear fiber-based finite element models in the open-source software OpenSees [30] as shown in the Fig. 3. NSPA and IDA analyses are conducted to investigate the seismic performance of columns with different FRC material. In order to account for the material inelasticity of FRC material, 3-D fiber-based displacement-based inelastic beam-column elements have been applied for modeling of the bridge columns. Four integration points have been verified to be adequate for fiberbased beam-column elements to capture the seismic behavior accurately. This fiber-based beam-column element has the ability to represent the distribution of material nonlinearity along the column height. The cross-section of the column is modeled as fiber sections. Each section is divided into about 400–600 fibers. In these fiber sections, each fiber has a suitable uniaxial stress-strain hysteretic relationship to represent the unconfined concrete, confined concrete and longitudinal reinforcements. To develop the nonlinear fiber-based finite element models, the Chang and Mander uniaxial reinforcing steel model [31] in the OpenSees is used to simulate the longitudinal reinforcements, considering the compression buckling, mechanical effects of strain softening and tensile fracture of steel bars. In this Chang and Mander reinforcing steel model, the Coffin-Manson equation for plastic strain amplitude is considered for the effect of fatigue. The yield strength, strain hardening and elasticity modulus of longitudinal reinforcements are 400 MPa, 0.5% and 2 105 MPa, respectively. The cyclic behavior of FRC concrete is simulated by the Chang and Mander concrete model (labeled as ‘concrete070 model in the OpenSees) with simplified unloading and reloading curves. The compressive strength 40 MPa and tensile strength 2.1 MPa of plain concrete have been used. In the bridge columns, different FRC material has different influence on the peak bond strength and bond degradation of RC columns under the seismic loadings. So the compressive strength, the tensile strength, ultimate strength, compressive strain and ultimate strain for different FRC material will be different and can be calculated using the equations in the following section 3.2. In order to account for bond degradation, a nonlinear rotational link element with zero length is employed to simulate the bond-slip rotations at the column-foundation interface. Different bond-slip models are used for different FRC columns, which is also introduced in the following Section 3.2.
246
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Table 4 Relative difference of base shear and displacement at yielding, crushing, buckling and fracture limit states. Material
Steel yielding
Normal RC SFRC PFRC HySPFRC
Concrete crushing
Steel buckling
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
Displacement (m)
Base shear (kN)
0.091 0.086 0.083 0.084
793 876 884 911
0.263 0.289 0.271 0.274
891 985 1032 1086
0.725 0.732 0.736 0.744
783 996 1018 1132
0.779 0.783 0.782 0.787
760 1005 1011 1147
qffiffiffiffiffiffiffi2 smax ¼ s1 exp 1:8 umax =2:57 f frc 1 for SFRC
3.2. Material property The peak compressive strength of FRC, ffrc, is calculated using the following equation:
f frc ¼ K frc K s f c
ð1Þ
in which is fs is the compressive strength of plain concrete; Kfrc is the modification factor due to the addition of fibers; Ks is the confinement factor to consider the effect of stirrups. The modification factor, Kfrc, can be calculated by Eq. (2), which has been calibrated by the test results in the literature [32].
K frc ¼ 1 þ 0:206ksf þ 0:388kpf
ð2Þ
where ksf is the characteristic parameter for steel fibers; kpf is the characteristic parameter for polypropylene fibers. The characteristic parameters ksf and kpf can be determined by Eq. (3):
ksf ¼
psf lsf ppf lpf and kpf ¼ dsf dpf
ð3Þ
in which psf and ppf are the volume fraction of steel fibers and polypropylene fibers respectively; lsf and lpf are the length of steel and polypropylene fibers; dsf and dpf are the diameter of steel and polypropylene fibers. The confinement factor, Ks, can be derived from the Park model [33] as
Ks ¼ 1 þ
qt f sy K frc f c
efrc ¼ ec ð1 þ 0:705ksf þ 0:364kpf Þ
ð5Þ
in which ec is the peak strain of the plain concrete. The tensile strength of FRC material, ft, can be calculated using the square root of compressive strength according to the recommendation [34]
qffiffiffiffiffiffiffi f t ¼ 0:45 f frc
ð9Þ
" #! qffiffiffiffi2 umax =2:57 f c 1
smax ¼ s1 exp 3:3ln
qffiffiffiffi þ s0 2:57 f c =umax for RC
ð10Þ
in which Atr is the area of transverse hoops; db is the diameter of the reinforcements; c is the thickness of concrete cover; st is the spacing of the transverse stirrups; ns is the number of spliced tension bars in the section; s1 equals 0.15c0 (c0 is the clear distance between the ribs of the reinforcing bars); s0 equals 0.4 mm. The above Harajli model [34] was proposed with limitation to hooked steel fibers. Due to the reason that the aspect ratio (lf/df) of polypropylene fibers is four to six times larger than that of the hooked steel fibers, thus, the Harajli model cannot be used for PFRC concrete. Therefore, a bond-slip model for PFRC proposed by Chao et al. [32] is introduced to determine the bond strength of PFRC. This model is developed from a series of pullout experiments and the equations for the bond strength model are shown in the following:
" umax ¼ 20
rp ðf frc Þ1=4
#
db
ð11Þ
ð4Þ
where fsy is the strength of stirrups; qt is the stirrups ratio. The peak strain of fiber-reinforced concrete, efrc, can be determined by the following equation:
ð6Þ
3.3. Bond-slip model The bond-slip model for SFRC is developed by Harajli [35] from a series of beam experiments of fiber reinforced concrete with various hooked steel fibers at different volume fractions. This model can be also used for normal RC and HySPFRC columns with transverse hoops. Maximum bond strength, umax, and maximum reinforcement slip, smax, can be computed as follows:
qffiffiffiffiffiffiffi c þ 0:45cp l =d 2=3 sf sf sf umax ¼ 0:78 f frc ð Þ for SFRC db
ð7Þ
qffiffiffiffiffiffiffi c þ 7:0A =s n 2=3 tr t s ¼ 0:78 f frc ð Þ for RC db
ð8Þ
umax
Steel fracture
smax ¼
215umax db f frc
ð12Þ
where rp is the tensile stress where tensile softening begins. Table 3 shows the main mechanical properties for bond-slip models for different FRC columns using the above equations. 3.4. Model calibration with experimental results In this section, the finite element models of bridge columns with different FRC material have been calibrated and validated using the existing experimental data from previous literature [5,23,28,36]. Fig. 4 illustrates the comparison of experimental data and numerical results from finite element models using the cyclic pushover analysis. From Fig. 4, it can be observed that the finite element models can simulate the initial stiffness, post stiffness and ultimate capacity accurately when compared to test results. In summary, the developed finite element models of four bridge columns with normal RC and different FRC material are shown to provide the sufficient accuracy. 4. Nonlinear static pushover analysis In order to conducted the NSPA, weight permanent load (340 kN) was included and the superstructure load (780 kN) is applied at the top of the column in the finite element model, Thus, the bridge columns had a ratio of 0.02 fcAc axial load (fc = concrete
247
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
strength; Ac = sectional area). In the NSPA, the incremental lateral load is only set at the top of column with the displacement control method. The results from the NSPA are expressed as the pushover curves which are the relationship between lateral displacement and the base shear. The pushover curves of bridge columns with normal RC and different FPC material, namely SFRC, PFRC and HySPFRC are shown in Fig. 5. It is evident from Fig. 5 that the capacity of all the FRC bridge columns was increased considerably when comparing to that of normal RC bridge column. The HySPFRC bridge column has the maximum enhancement of seismic capacity, while SFRC and PFRC column ranked second and third. Moreover, when the lateral displacement was small, the variations of pushover curves between the SFRC, PFRC and HySPFRC were small. This is due to the reason that elastic modulus of SFRC, PFRC and HySPFRC column was nearly the same. When the lateral displacement was large, the variations between the SFRC and PFRC were small. It is because the compressive strength of concrete improved by SFRC and PFRC was similar. In general, all the FRC material can improve the seismic capacity in an adequate way. In order to study the influence of the FRC material on the seismic capacity of column sections, the moment-curvature analysis was also conducted in this paper. Fig. 6 illustrates the moment-curvature curves. It can be seen from Fig. 6 that all the sectional seismic capacity can be improved by FRC material.
In the seismic performance evaluations of bridge columns, the flexural damage states can be used as performance criteria. In this paper, four flexural damage states (slight, moderate, extensive and collapse) are considered: a) yielding of longitudinal steels; b) crushing of core concrete; c) buckling and d) fracture of longitudinal steel bars. The limit values for these four flexural damage states can be calculated by the strain limits of both core concrete and longitudinal steels. The yielding of longitudinal steels is assumed to take place when the steel strain reached the ratio of yield stress and elastic modulus of steel bars. The core concrete crushing is assumed to be happened when the strain of core concrete changed normally from 0.015 to 0.05 according to the suggestion given by Paulay and Priestley [37]. In this paper, a median value of concrete strain, 0.033, was used as the reference value. Moreover, the tensile strain of longitudinal reinforcements determined by the Berry and Eberhard [38] equations can be used to predict the buckling and fracture of steel bars. Table 4 illustrates the difference of displacement and base shear at four flexural damage states from the pushover curves. From Table 4, it can be observed that different FRC material develop different displacement and base shear of bridge columns. For steel yielding limit state, the yielding of longitudinal steels started at the same level displacement in the all the bridge columns. The base shear at steel yielding for normal RC was 793 kN which was 9.5%, 11.5% and 14.9% lower than that of SFRC, PFRC and HySPFRC respectively. For concrete crushing limit state, the SFRC, PFRC and HySPFRC
Table 5 selected ground motions used in IDA. No.
Earthquake Name
Year
Station Name
Magnitude
Rrup (km)
Vs30 (m/sec)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Helena_ Montana Helena_ Montana Parkfield Managua_ Nicaragua Gazli_ USSR Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Imperial Valley Mammoth Lakes
1935 1935 1966 1972 1976 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1980
Carroll College Helena Fed Bldg Cholame-Shandon #5 Managua_ ESSO Karakyr Aeropuerto Mexicali Agrarias Bonds Corner Chihuahua EC Center FF El Centro MG El Centro #10 El Centro #4 El Centro #5 El Centro #6 El Centro #7 El Centro #8 El Centro D Holtville PO Convict Creek
6.0 6.0 6.2 6.2 6.8 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.1
2.9 2.9 9.6 4.1 5.5 0.3 0.7 2.7 7.3 7.3 0.1 8.6 7.1 4.0 1.4 0.6 3.9 5.1 7.5 6.6
593.4 551.8 289.6 288.8 259.6 259.9 242.1 223.0 242.1 192.1 264.6 202.9 208.9 205.6 203.2 210.5 206.1 202.3 202.9 382.1
Fig. 7. 20 selected as-recorded ground motions: a) spectral acceleration and b) percentiles of spectral acceleration.
248
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 8. Dynamic pushover points and static pushover curve for bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
increased the displacement by 9.9%, 3.1% and 4.2% and increased the base shear by 10.5%, 15.8% and 21.9% when comparing to that of normal RC column. For steel buckling and fracture limit states, the displacement in the all bridge columns changed a little by the FRC material. The base shear could be improved by almost 30% for SFRC, PFRC and HySPFRC bridge column respectively. 5. Incremental dynamic analysis While the nonlinear pushover analysis can be used to evaluate the static responses of bridge columns under lateral load, nonlinear time-history analysis (NTHA) can be applied to obtain the dynamic time-history responses of bridge columns. Due to the reason that structures experience the dynamic lateral load during an earthquake in the reality, the NTHA can give the accurate prediction of seismic demands. The IDA method developed by Luco and Cornell [25] and Vamvatsikos and Cornell [26] is based on the NTHA, in order to estimate the large inelastic responses of structures. IDA requires a series of NTHAs of a well-calibrated finite element model of the considered structure for a suite of selected asrecorded or artificial ground motions with different levels of intensities. The different intensity levels are set by adjusting the IM of ground motions in order to study the full range of seismic behavior, from elastic responses to structural collapse. From various NTHAs, IDA curves can be obtained, which expresses the relationship between the selected EDPs and IM of ground motions. 5.1. Ground motions In this paper, a total of 20 near-fault ground motions with moment magnitude Mw between 6.0 and 8.0 are selected from
the PEER strong ground motion database and applied in the assessment of the seismic performance of bridge columns with normal RC and different FRC material as shown in Table 5. These selected near-fault ground motions are records from soil site classes that have shear wave velocities Vs between 200 m/s and 600 m/s in the upper 30 m. The closest site-to-fault distances of the records vary from 0.1 to 10 km. Fig. 7 shows the spectral accelerations of the 20 selected as-recorded ground motions with 5% damping ratio. It is illustrated from Fig. 7 that these selected ground motions can represent the medium to strong earthquakes well. 5.2. IDA analysis In order to conduct the IDA, the PGA is selected as IM. PGA is recognized as an optimal IM by Nielson and DesRoches [39], Padgett et al. [40] and Zelaschi et al. [41] and for sufficiency and efficiency in the seismic assessment of bridges. It is worth mentioning that further studies may be necessary to study whether or not the PGA is a sufficient and efficient IM to be used in similar studies as the present paper especially when dealing with the seismic damage analysis of FRC columns. It is authors’ opinion that PGA is a simple but robust IM that can be reliably utilized as the IM and it is more convenient to implement the scaling of selected ground motions than the spectral acceleration of structures. In the present paper, PGA is adjusted from 0.1 g to final PGA value with an increment 0.01 g to cover a large range (elastic and inelastic) of seismic behavior. This final PGA value is determined by the collapse point [42] of finite element model in which the finite element models experiences the globe dynamic instability and causes a large and unreal maximum drift ratio of top columns. In order to form the IDA curves, four EDPs are selected and monitored during the IDA
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
249
Fig. 9. IDA curves for maximum drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Fig. 10. Median and percentiles of IDA curves for maximum drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
250
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
analysis, namely maximum drift, residual drift, displacement ductility and curvature ductility demands of bridge columns. These four EDPs adopted in this paper have been considered by previous studies [40,43–50] as important parameters, which are considered sufficient and adequate to characterize the seismic performance of the analyzed bridge columns. In this paper, the IDA analyses are conducted for all the bridge columns using the selected suite of 20 near-fault ground motions presented in Table 5. Due to the rare results of shaking table tests in the literatures, the IDA analysis is only calibrated by comparing the static pushover curves with dynamic pushover points generated from IDA curves with as shown in Fig. 8. From Fig. 8, it can be found that the dynamic pushover points coincide with the static pushover curves well although the dynamic pushover points show higher base shear than the static pushover curves. 5.2.1. Maximum drift demand The maximum drift (%) is defined as the ratio of the peak displacement of the top bridge column to the column height under single ground motion with certain intensity level, which can be used to develop one IDA curve. Fig. 9 depicts the maximum drift (%) IDA curves for normal RC, SFRC, PFRC and HySPFRC columns. From Fig. 9, it can be observed that all the IDA curves have a linear part and a nonlinear part, which shows the sign of the elastic and inelastic behavior. In the inelastic region, the IDA curves display the stiffness degradation or a softening behavior until the column collapse takes place. Due to the inherent uncertainty of ground motions, the scattering and variability of IDA curves can also be observed. Moreover, it can be illustrated by Fig. 9 that the FRC bridge columns show relatively higher elastic stiffness than the normal RC bridge column. It can be attributed to the reason that the FRC material can improve the elastic modulus of core concrete.
The FRC bridge columns also show higher maximum drift when comparing to that of the normal RC bridge column in the inelastic range of behavior, indicating a good seismic performance. Because the IDA curves display the diversity and scattering property, it is of important to implement the statistical method for evaluation. In this paper, the 16th, 50th and 84th fractile values of IDA curves are calculated and summarized in order to produce more reliable data for evaluating the seismic behavior of FRC bridge columns. Fig. 10 shows median and percentiles of maximum drift (%) IDA curves for bridge columns with normal RC and different FRC material. It should be noted that when the PGA is large, the remaining number of IDA is so small that it is not suitable for statistical calculation, thus, the PGA range used for fractile IDA curves is smaller than that of original IDA curves. By comparing the fractile IDA curves with the allowable drift at certain damage state, it is convenient to assess the seismic performance of columns. For instance, given the design PGA = 1.0 g at high seismic zones, 16% IDA curve depicts the maximum drift (%) 1.81%, 1.85%, 1.56% and 1.78%; 50% IDA curve depicts the maximum drift (%) 3.89%, 3.15%, 2.94% and 3.02%; 84% IDA curve depicts the maximum drift (%) 5.95%, 4.14%, 4.08% and 4.03% for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that SFRC, PFRC and HySPFRC are all effective to improve the seismic capacity and reduce the seismic demands of the bridge column. The difference of the improvement from different FRC material is within 5%. Previous studies [43,44] have suggested the permissible drift values for the serviceability and collapse damage states. According to these papers, 1.9% is used to indicate the loss serviceability, and 5.0% for global collapse of bridge column. From the above results, it can depict that the maximum drift (%) of all the FRC bridge columns do not exceed the collapse range, indicating that the seismic capacity of all the FRC bridge column are improved.
Fig. 11. IDA curves for residual drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
5.2.2. Residual drift demand Due to the accumulation damage during the earthquakes, a RC structure may experience a large permanent displacement or deformation which may cause the traffic closure and increase the repair cost after the seismic loading. In the PBEE framework, the residual drift has been considered as an important EDP by many researchers [45,46]. Thus, it is of importance to use the residual drift for seismic performance assessment of structures. In this paper, the fiber-based nonlinear beam-column elements are used in the finite element models, which has calibrated and verified by several researchers [47,48] that the fiber-based elements can estimate the residual displacement or deformation quite accurately. The residual drift (%) is defined as the ratio of the residual displacement of the top column to the column height. Fig. 11 shows the residual drift (%) IDA curves plotted for four bridge columns. From Fig. 11, it can be observed that the residual drift IDA curves are different for different FRC bridge columns. By comparing the IDA curves, it can be seen that the FRC bridge columns experience lower residual drift than the normal RC bridge column. It is due to the reason that FRC bridge columns have higher stiffness compared to the normal RC bridge columns. Moreover, PFRC and HySPFRC bridge columns have lower residual drift than the SFRC and normal RC bridge columns. This may be because the steel fibers not only increase the column stiffness, but also increase larger additional weight than the polypropylene fibers, which may increase the inertial force under seismic loading. The 16th, 50th, and 84th fractile IDA curves are also summarized in this section to assess the residual drift demand of FRC bridge columns. Fig. 12 illustrates the median and percentiles of residual drift (%) IDA curves for columns with normal RC and different FRC material. For example, given the design PGA = 1.0 g at
251
high seismic zones, 16% of IDA curves produces the residual drift (%) 0.02%, 0.13%, 0.07% and 0.04%; 50% of IDA curves produces the residual drift (%) 0.27%, 0.32%, 0.19% and 0.13%; 84% of IDA curves depicts the residual drift (%) 0.48%, 0.53%, 0.34% and 0.22% for normal RC, SFRC, PFRC and HySPFRC, respectively. In the previous studies, 1.75% is used as residual drift limit for collapse state, which is concluded after the Kobe earthquake. After the Kobe earthquake [49], a larger number of RC bridge columns are demolished even though they did not collapse, when the residual drift of bridge columns reaches 1.75%. In this case, the FRC bridge columns do not exceed this drift limit when the PGA is smaller than 2.0 g, indicating that the FRC material is effective for reducing the residual drift. 5.2.3. Displacement ductility demand Displacement ductility is defined as the ratio of maximum displacement of bridge columns to the yield displacement, which is usually considered as an important EDP for seismic performance evaluation of bridge column. This displacement ductility demand can be used as the indication of global deformation of the bridge columns. Thus, in this paper, the displacement ductility is also used to assess the seismic performances of the four FRC bridge columns. Fig. 13 presents the IDA curves in terms of displacement ductility of columns. From Fig. 13, it can be observed that the IDA curves plotted using the displacement ductility demands are different for different FRC bridge columns. The FRC material can be effective for reducing the displacement ductility demands at different PGA levels. Fig. 14 summarizes the 16%, 50%, and 84% fractile IDA curves. By comparing the fractile IDA curves of different FRC bridge columns, displacement ductility demand of FRC bridge columns can be evaluated. For instance, given the design PGA = 1.0 g at high
Fig. 12. Median and percentiles of IDA curves for residual drift (%) of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
252
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 13. IDA curves for ductility demand of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Fig. 14. Median and percentiles of IDA curves for ductility demand of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
253
Fig. 15. IDA curves for curvature ductility of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
seismic zones, 16% IDA curve presents the displacement ductility 1.04, 1.01, 0.93 and 0.87; 50% IDA curve presents the displacement ductility 2.21, 1.73, 1.71 and 1.69; 84% IDA curve presents the displacement ductility 3.41, 2.49, 2.54 and 2.45 for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that the HySPFRC column can be more effective for reducing the displacement ductility than SFRC and PFRC. In the previous studies, many researchers have proposed different values for four damage limit states (slight, moderate, extensive and complete) based on the displacement ductility. Hwang et al. [50] proposed four displacement ductility ratios (1.0, 1.2, 1.76 and 4.76) for four damage states for bridge columns. By comparing with these damage limit values, it can be found that all these FRC bridge columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g). At a high level of intensity (PGA = 2.0 g), different FRC bridge columns do not encounter the complete (collapse) damage. 5.2.4. Curvature ductility demand Curvature ductility is defined as the ratio of maximum curvature to the yield curvature of sections at the column base. In the seismic performance evaluation of bridges, the curvature ductility is usually adopted as an important EDP for developing the seismic fragility of bridge components. Therefore, the curvature ductility is also adopted to assess the seismic behavior of the four FRC bridge columns. Fig. 15 depicts the curvature ductility IDA curves of bridge columns with different FRC material, namely normal RC, SFRC, PFRC and HySPFRC. From Fig. 15, it can be found that the FRC material can be effective for reducing the curvature ductility demands at different PGA levels. Fig. 16 presents the 16%, 50%, and 84% fractile IDA curves. The fractile IDA curves of different
FRC bridge columns are compared to evaluate the curvature ductility demands of FRC bridge columns. For example, given the design PGA = 1.0 g at high seismic zones, 16% IDA curve illustrates the curvature ductility 1.91, 1.25, 1.37 and 1.31; 50% IDA curve illustrates the curvature ductility 4.12, 2.38, 2.45 and 2.36; 84% IDA curve illustrates the curvature ductility 6.21, 3.89, 4.02 and 3.85 for normal RC, SFRC, PFRC and HySPFRC, respectively. Thus, it can be concluded that the HySPFRC column can be more effective for reducing the curvature ductility than SFRC and PFRC. In the seismic fragility analysis of bridges, the damage limits for four damage limit states (slight, moderate, extensive and complete) are based on the sectional curvature ductility. Padgett et al. [40] proposed four curvature ductility ratios (1.0, 2.0, 4.0 and 7.0) for four damage states for bridge columns. Compared to the displacement ductility demands, similar conclusions can be obtained. All these FRC bridge columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g) and do not encounter the complete (collapse) damage at a high level of intensity (PGA = 2.0 g). 5.3. Mean seismic capacity The seismic capacity can also be expressed as the PGA values, which can be computed based on the IDA curves to link the PGA with the four flexural damage states considered in Section 4. As mentioned in the above section, the four flexural damage states are associated with the strain of both core concrete and longitudinal steels. Thus, each flexural damage state has one specific PGA for any IDA curve. Fig. 17 shows the bar chart of the calculated mean PGA for maximum drift IDA curves. It should be noted that lower mean PGA value of bridge column means lower seismic capacity
254
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 16. Median and percentiles of IDA curves for curvature ductility of bridge column with different FRC material: a) normal RC; b) SFRC; c) PFRC and d) HySFRC.
compared to higher mean PGA values. It can be found from Fig. 17 that the FRC columns have higher mean PGA values compared to that of normal RC bridge column, indicating that the FRC material can enhance the seismic capacity of RC columns. Moreover, SFRC and HySPFRC are more effective for enhancing the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective for the extensive and complete damage states.
5.4. Seismic fragility Seismic fragility analysis is usually used for evaluating the seismic vulnerability of RC bridges. The results obtained from the fragility analysis are in terms of fragility curves, which express the relationship between the conditional damage probabilities of exceeding a damage state with a specified IM of ground motions. Two main methods are usually used to derive the fragility functions, namely the cloud approach and the IDA method. Compared to the cloud approach, the IDA method can be more effective to create sufficient data for fragility functions [51]. When using IDA method, the fragility functions can be developed using Eq. (13) as a lognormal cumulative distribution function (CDF):
lnðx=cÞ Pf ðDamagejIM ¼ xÞ ¼ U b
ð13Þ
in which Pf represents the damage probability, x is a specific conditional value of IM. U(.) is the CDF of standard normal distribution, c is the median intensity of the fragility curves, and b is the standard
deviation. The parameters c and b can be estimated by a simplified fitting method proposed by Baker [52]. In this paper, four damage states (slight, moderate, extensive and collapse) are adopted which have been already defined in the above section. The maximum drift (%) is used to measure these damage states as shown in Table 6. Based on Eq. (13), the results from the IDA curves of the maximum drift (%) of top column are used to generate the analytical fragility curves of different FRC columns. Fig. 18 shows the seismic fragility curves of different FRC columns for four limit states. As stated earlier, it can be seen from Fig. 18 that the FRC columns have lower damage probability compared to that of normal RC bridge column, indicating that the FRC material can be effective to improve the seismic performance. This can be attributed to the difference in strength and ductility properties of FRC material, which has been discussed earlier. Moreover, the PFRC and HySPFRC have a lower damage probability for the extensive and complete damage states, while SFRC and HySPFRC have a lower damage probability for moderate damage state. Interestingly, the normal RC column has similar damage probability as the SFRC column, which may be attributed to the similar behavior of normal RC and SFRC bridge column in the pre-yield behavior level. This is in agreement with previous study [28].
6. Conclusion This paper proposed a comprehensive study to investigate the seismic performance of normal RC and different FRC bridge columns. A 3-D fiber-based finite element model of different FRC columns are firstly built by using proper cyclic constitutive laws
255
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
Fig. 17. Mean seismic capacity of bridges column with four limit states: a) yielding of longitudinal steel; b) crushing of confined concrete; c) buckling of steel bars; d) fracture of steel bars.
Table 6 Limit state capacity of different bridge columns in terms of maximum drift (%). Damage state
Slight Moderate Extensive Collapse
Performance level
Steel yielding Crushing of core concrete Steel buckling Steel fracture
Normal RC
SFRC
PFRC
HySPFRC
Median
Dispersion
Median
Dispersion
Median
Dispersion
Median
Dispersion
0.98 2.78 7.74 8.35
0.2 0.2 0.46 0.46
0.93 3.14 7.96 8.51
0.2 0.2 0.46 0.46
0.90 2.95 8.01 8.49
0.2 0.2 0.46 0.46
0.91 2.99 8.09 8.56
0.2 0.2 0.46 0.46
Fig. 18. Seismic fragility curves of different FRC columns for four limit states.
of FRC concrete, and then calibrated using the experimental results. In this study, four flexural damage states are evaluated through the static pushover analysis. Then the IDA analyses are conducted for all the FRC bridge columns using the selected suite of 20 near-fault ground motions. Four EDPs, namely maximum drift, residual drift, displacement ductility and curvature ductility demands, are selected and monitored to evaluate the comparative seismic behavior of different FRC bridge columns. Based on the results from the NSPA and IDA analysis, the following conclusions can be drawn: 1) Different FRC material has different influence on the displacement and base shear of bridge columns. The displacement does not change too much by the FRC material except when crushing of concrete occurred. The concrete crushing increases the displacement by 9.9%, 3.1% and 4.2% for SFRC, PFRC and HySPFRC respectively. The base shear is improved by about 10% for SFRC, 15% for PFRC and 20% for HySPFRC columns respectively.
256
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257
2) The SFRC, PFRC and HySPFRC are all effective to improve the seismic capacity and reduce the seismic demands of the bridge column. The difference of the improvement from SFRC, PFRC and HySPFRC columns is within 5%. The maximum drift (%) of all the FRC bridge columns do not exceed the collapse range 5.0%, indicating that the seismic capacity of all the FRC bridge column are improved. 3) By comparing IDA curves in terms of the residual drift, it can be concluded that the FRC bridge columns experience lower residual drift than the normal RC bridge column. PFRC and HySPFRC bridge columns have lower residual drift than the SFRC and normal RC bridge columns. The FRC bridge columns do not exceed this drift limit of 1.75% when the PGA is smaller than 2.0 g, indicating that the FRC material is effective for reducing the residual drift. 4) HySPFRC column can be more effective for reducing the displacement and curvature ductility demands than SFRC and PFRC. All the FRC columns suffered slight and moderate damage under design level earthquake intensity (PGA = 1.0 g) and do not encounter the complete (collapse) damage at a high level of intensity (PGA = 2.0 g). 5) It can be concluded that the FRC columns have higher mean PGA values compared to that of normal RC bridge column, indicating that the FRC material can enhance the seismic capacity of RC columns. Moreover, SFRC and HySPFRC are more effective for enhancing the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective for the extensive and complete damage states. 6) The FRC columns have lower damage probability compared to that of normal RC bridge column, indicating that the FRC material can be effective to improve the seismic performance. The PFRC and HySPFRC have a lower damage probability for the extensive and complete damage states, while SFRC and HySPFRC have a lower damage probability for moderate damage state. Conflict of interest There is no conflict of interest. Acknowledgements This research is supported by Natural Science Foundation of China under Grant No. 51708527 and China Postdoctoral Science Foundation under Grant No. 2016M592407. References [1] Z.F. Wang, A preliminary report on the great Wenchuan earthquake, Earthquake Eng. Eng. Vibr. 7 (2008) 225–234. [2] A. Zsarnóczay, L.G. Vigh, L.P. Kollár, Seismic performance of conventional girder bridges in moderate seismic regions, J. Bridge Eng. 19 (5) (2014) 04014001. [3] M. Shinozuka, S.H. Kim, S. Kushiyama, J.H. Yi, Fragility curves of concrete bridges retrofitted by column jacketing, Earthq. Eng. Eng. Vib. 1 (2) (2002) 195–205. [4] D.S. Gu, Y.F. Wu, G. Wu, Z.S. Wu, Plastic hinge analysis of FRP confined circular concrete columns, Constr. Build. Mater. 27 (2012) 223–233. [5] Y.Y. Zhang, K.A. Harries, W.C. Yuan, Experimental and numerical investigation of the seismic performance of hollow rectangular bridge piers constructed with and without steel fiber reinforced concrete, Eng. Struct. 48 (2013) 255– 265. [6] M.A. Dagenais, B. Massicotte, Tension lap splices strengthened with ultrahigh performance fiber-reinforced concrete, J. Mater. Civil Eng. 27 (7) (2015) 04014206. [7] Z.L. Wang, Y.S. Liu, R.F. Shen, Stress–strain relationship of steel fiber-reinforced concrete under dynamic compression, Constr. Build. Mater. 22 (2008) 811– 819. [8] J. Stephen, M. Mario, Strength and ductility of fiber-reinforced high-strength concrete columns, J. Struct. Eng. 127 (2001) 28–34. [9] P. Joao, Behaviour of fiber reinforced concrete columns in fire, Compos. Struct. 92 (2010) 1263–1268.
[10] C. Röhm, B. Novák, S. Sasmal, Behaviour of fibre reinforced beam-column subassemblages under reversed cyclic loading, Constr. Build. Mater. 36 (2012) 319–329. [11] I. Laura, P. Patrick, E. Rami, P. Jean, Seismic behavior of synthetic fiberreinforced circular columns, ACI Mater. J. 111 (2014) 189–200. [12] Z. Hashem, R. Yuan, Short vs. long column behavior of pultruded glass-fiber reinforced polymer composites, Constr. Build. Mater. 15 (2001) 369–378. [13] O. Ozcan, B. Binici, G. Ozcebe, Improving seismic performance of deficient reinforced concrete columns using carbon fiber-reinforced polymers, Eng. Struct. 30 (2008) 1632–1646. [14] American Concrete Institute (ACI), State-of-the-art report on fiber reinforced concrete, ACI 1R-82, Detroit, 1982. [15] M. Hsie, C.J. Tu, P.S. Song, Mechanical properties of polypropylene hybrid fiberreinforced concrete, Mater. Sci. Eng. 494 (2) (2008) 153–157. [16] Y.N. Ding, Z. You, S. Jalali, Hybrid fiber influence on strength and toughness of RC beams, Compos. Struct. 92 (2010) 2083–2089. [17] V. Gribniak, G. Kaklauskas, A.K.H. Kwan, Deriving stress-strain relationships for steel fiber concrete in tension from tests of beams with ordinary reinforcement, Eng. Struct. 42 (2012) 387–395. [18] G. Kotsovos, C. Zeris, M. Kotsovos, The effect of steel fibers on the earthquakeresistant design of reinforced concrete structures, Mater. Struct. 40 (2007) 175–188. [19] N. Ganesan, P. Indira, M. Sabeena, Behavior of hybrid fiber reinforced concrete beam-column joints under reverse cyclic loads, Mater. Des. 54 (2014) 686– 693. [20] J. Stephen, On behavior of high-strength concrete columns: cover spalling, steel fibers and ductility, ACI Struct. J. 8 (2001) 583–589. [21] H. Lee, Shear strength and behavior of steel fiber reinforced concrete columns under seismic loading, Eng. Struct. 29 (2007) 1253–1262. [22] H. Zhao, Experimental and theoretical research on seismic performance of concrete frame with special-shaped columns reinforced with polypropylene fiber, Tianjin University, Tianjin, 2008. [23] L. Huang, L.H. Xu, Y.Xu.H. Chi, Experimental investigation on the seismic performance of steel–polypropylene hybrid fiber reinforced concrete columns, Constr. Build. Mater. 2015 (87) (2015) 16–27. [24] Y. Chi, L.H. Xu, Y.Y. Zhang, Experimental Study on Hybrid Fiber-Reinforced Concrete Subjected to Uniaxial Compression[, J. Mater. Civ. Eng. 26 (2) (2014) 211–218. [25] N. Luco, C.A. Cornell, Effects of random connection fractures on the demands and reliability for a three-story pre-Northridge (SMRP) structure, in: Proc sixth US Natl. conf Earthq. eng, Earthq. Eng. Res. Inst., Oakland, California; 1998. [26] D. Vamvatsikos, C.A. Cornell, Incremental dynamic analysis, Earthq. Eng. Struct. Dyn. 31 (2002) 491–514. [27] JTG, T,, B02–01-2008. Guidelines for seismic design of highway bridges, China: Department of Transportation (2008). [28] Y. Zhang, D. Dias-da-Costa, Seismic vulnerability of multi-span continuous girder bridges with steel fiber reinforced concrete columns, Eng. Struct. 150 (2017) 451–464. [29] L.H. Xu, H.R. Xu, Y. Chi, Y.Y. Zhang, Experimental study on tensile strength of steel–polypropylene hybrid fiber reinforced concrete, Adv. Sci. Lett. 4 (2011) 911–916. [30] F. McKenna, M.H. Scott, G.L. Fenves, et al., Open system for earthquake engineering simulation (OpenSees), Pacific Earthquake Engineering Research Center (2008). [31] G. Chang, J. Mander, Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part I – Evaluation of Seismic Capacity, NCEER Technical Report 940006, 1994. [32] S.H. Chao, A.E. Naaman, G.J. Parra-Montesinos, Local bond stress-slip models for reinforcing bars and prestressing strands in high-performance fiberreinforced cement composites, ACI SP 272 (2010) 151–172. [33] R. Park, M. Priestley, W. Gill, Ductility of square-confined concrete columns, J. Struct. Div. 108 (1982) 929–950. [34] 318–05., Building code requirements for reinforced concrete and commentary, America: American Concrete Institute (2005). [35] M.H. Harajli, Bond stress slip model for steel bars in unconfined or steel, FRC, or FRP confined concrete, J. Struct. Eng. 135 (5) (2009) 509–518. [36] X.W. Liang, J. Xu, P.T. Xing, Experimental study and numerical simulation on the seismic behavior of fiber-reinforced concrete columns, Eng. Mech. 33 (8) (2016) 66–76. [37] T. Paulay, M.J.N. Priestley, Seismic design of reinforced concrete and masonry buildings, J. Wiley, New York, 1992. [38] M.P. Berry, M.O. Eberhard, Performance modeling strategies for modern reinforced concrete bridge columns. PEER Report 2007/07 Pacific Earthquake Engineering, Research Center, College of Engineering, University of California, Berkeley, USA, 2007. [39] B.G. Nielson, R. DesRoches, Seismic fragility methodology for highway bridges using a component level approach, Earthquake Eng. Struct. Dyn. 36 (6) (2007) 823–839. [40] J.E. Padgett, B.G. Nielson, R. DesRoches, Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios, Earthquake Eng. Struct. Dyn. 37 (5) (2008) 711–725. [41] C. Zelaschi, R. Monteiro, M. Marques, Pinho Rr, Comparative analysis of intensity measures for reinforced concrete bridges, Second European Conference on Earthquake Engineering and Seismology (2ECEES), Istanbul, Turkey, August 25 29, 2014.
Y. Pang et al. / Construction and Building Materials 203 (2019) 241–257 [42] B. Shafei, F. Zareian, D.G. Lignos, A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems, Eng. Struct. 33 (2011) 1107–1116. [43] M.J. Kowalsky, Deformation limit states for circular reinforced concrete bridge columns, J. Struct. Eng. 126 (8) (2000) 869–878. [44] M. Liu, B. Lu, B. Liu, Study on performance index of reinforced concrete bridge column, Adv. Intell. Soft Comput. 114 (2012) 189–198. [45] S.R. Uma, S. Pampanin, C. Christopoulos, Development of probabilistic framework for performance-based seismic assessment of structures considering residual deformations, J. Earthq. Eng. 14 (7) (2010) 1092–1111. [46] A.H.M.M. Billah, M.S. Alam, Seismic fragility assessment of concrete bridge piers reinforced with superelastic shape memory alloy, Earthq. Spectra 31 (3) (2014) 1515–1541. [47] M.M. Hachem, S.A. Mahin, J.P. Moehle, Performance of circular reinforced concrete bridge columns under bidirectional earthquake loading, PEER report
[48]
[49] [50] [51]
[52]
257
2003/06, Pacific Earthquake Engineering Research Center, University of California, Berkeley, California. J. Sakai, S.A. Mahin, Analytical investigations of new methods for reducing residual displacements of reinforced concrete bridge columns. PEER-2004/02, Pacific Earthq. Engrg. Res. Center, Univ. of California at Berkeley, California; 2004 K. Kawashima, G. MacRae, J. Hoshikuma, K. Nagaya, Residual displacement response spectrum, J. Struct. Eng. 124 (5) (1998) 523–530. H. Hwang, J.B. Liu, Y.H. Chiu, Seismic fragility analysis of highway bridges. MAEC report: project MAEC RR-4. Mid-America Earthquake Center, Urbana; 2001 A.R. Bhuiyan, M.S. Alam, Seismic vulnerability assessment of a multi-span continuous highway bridge fitted with shape memory alloy bars and laminated rubber bearings, Earthq. Spectra 28 (2012) 1379–1404. J.W. Baker, Efficient analytical fragility function fitting using dynamic structural analysis, Earthq. Spectra 31 (2015) 579–599.