Seismic fragility analysis of concrete bridge piers reinforced by steel fibers

Abstract

Seismic fragility analyses of eight bridge piers, made of steel fiber–reinforced concrete or conventional reinforced concrete, were conducted to reasonably analyze the seismic performance of concrete piers reinforced by steel fibers. The pier specimens were constructed with different steel fiber contents, stirrup ratios, and lengths of the steel fiber–reinforced concrete region. The cyclic load tests on the specimens were carried out to obtain the characteristic values of structural capacity for five damage states. The nonlinear time history analyses of the piers under a suite of selected ground motions were performed to obtain the probabilistic characteristics of structural demand. Using the data related to structural capacity and seismic demand, the fragility curves of these piers were constructed based on an assumed lognormal distribution. The fragility results indicate that (1) the seismic vulnerability of the concrete piers is reduced with the increase in steel fiber content in a certain range, (2) the reinforced concrete pier with a higher stirrup ratio is found to be more vulnerable than the steel fiber–reinforced concrete pier with a relatively lower stirrup ratio, and (3) the fragility of piers adopting steel fiber–reinforced concrete locally and suitably is similar to that of the piers adopting steel fiber–reinforced concrete wholly.

Keywords

bridge piers fragility curves seismic vulnerability steel fiber–reinforced concrete

Introduction

As an excellent composited material, steel fiber–reinforced concrete (SFRC) has been used at an increasing rate in recent years, particularly for the structures located at the meizoseismal area (Tang et al., 1992; Wang and Dai, 2013). It has been demonstrated that the addition of steel fibers to concrete can not only improve the static behaviors (e.g. the compressive, tensile, shear and flexural strength) of structures (Bencardino et al., 2008; Dancygier and Savir, 2011; Robins et al., 2001; Singh and Sharma, 2007) but also enhance their dynamic performances under seismic or cyclic action, such as ductility, toughness, and energy absorption capacity (Banthia and Sappakittipakorn, 2007; Buyle-Bodin and Madhkhan, 2002; Kotsovos et al., 2007). The seismic behavior of various SFRC members (e.g. SFRC beams, columns, piles, and beam–column joints) has been studied by many researchers (Germano et al., 2013; Lee et al., 2013; Shannag et al., 2003), and the seismic capacity of hollow bridge piers constructed with SFRC has also been investigated in our previous study (Zhang et al., 2013). However, few researches focused on the seismic demand of SFRC piers and their seismic vulnerability, which are crucial for the seismic risk evaluations of the bridge systems with SFRC piers.

The seismic vulnerability of a structure is usually presented in the form of fragility curves, which express the probability of a structure being damaged beyond a specific damage state for various levels of ground motions (Choi et al., 2004). Several methodologies for generating seismic fragility curves for bridge structures have been recently developed. Generally, they can be broadly classified into three groups: expert opinion–based (Applied Technology Council (ATC), 1991), empirically based (Basoz and Kiremidjian, 1999; Shinozuka et al., 2000), and analytical methods (Nielson and DesRoches, 2007a; Noroozinejad Farsangi et al., 2014). Since there are limitations (e.g. the subjectivity in defining damage states and the requirements of large amount of recorded damage data) inherent in expert-based and empirically based fragility curves, the analytical fragility curves have been extensively studied (Hwang et al., 2001; Zhang and Huo, 2009). For this reason, the analytical method will also be employed in this study to generate the fragility curves of bridge piers.

In this article, the fragility curves of eight RC or SFRC bridge piers were developed based on the cyclic load tests and the nonlinear time history analyses. These piers were designed with respect to three main parameters, including steel fiber content, stirrup ratio, and the length of SFRC region. The test results on the pier specimens were used to obtain the characteristic values of structural capacity corresponding to five damage states. The nonlinear time history analyses, using OpenSees (Mazzoni et al., 2008), were conducted to investigate the probabilistic characteristics of structural demand. With the data related to the structural capacity and seismic demand, the fragility curves of these piers were then established as a function of peak ground acceleration (PGA). Furthermore, the influences of the three parameters on the fragility curves of the SFRC piers were discussed in detail.

Experimental program and structural capacity

Generally, five major parts are included in the analytical method for bridge structures (Choi et al., 2004; Hwang et al., 2001): the establishment of an appropriate bridge model, the acquisition of the characteristic values of structural capacity for different damage states, the simulation of ground motions applied to the structures, seismic response analyses of the bridges, and the generation of fragility curves by regression analysis of the obtained data. For the specificity of the bridge piers reinforced by steel fibers, their characteristic values of structural capacity for different damage states were obtained from a series of tests in this study, as they cannot be acquired by the existing design standards.

Test overview

Eight solid rectangular SFRC pier specimens (numbered by S1–S8) were tested to investigate their seismic capacity. These specimens were constructed with different stirrup ratios, steel fiber contents, and lengths of SFRC region. The material details of the specimens are given in Table 1.

Table 1.

Main parameters of test specimens.

Specimen number	Concrete applied in specimen	Volumetric ratio of stirrup ρ_v (%)	Steel fiber content ρ_f (%)	Length of SFRC region h_f (mm)	Concrete strength (MPa)
S1	RC	1.5	0.0	0	38.7
S2	SFRC	1.5	0.5	800	40.9
S3	SFRC	1.5	1.0	800	43.1
S4	SFRC	1.5	1.5	800	45.3
S5	SFRC	1.0	1.5	800	45.3
S6	RC and SFRC	1.5	1.0	100	38.7/43.1
S7	RC and SFRC	1.5	1.0	200	38.7/43.1
S8	RC and SFRC	1.5	1.0	300	38.7/43.1

RC: reinforced concrete; SFRC: steel fiber–reinforced concrete.

Four longitudinal reinforcing bars with diameters of 14 mm (yield strength: 335 MPa) were arranged for all piers. A series of closed 8-mm diameter ties with yield strength of 235 MPa were placed in these specimens. As shown in Table 1, the stirrups in S5 were spaced at 110 mm on center vertically and its volumetric transverse reinforcing ratio (ρ_v) is 1.0%, while in other specimens, the stirrup spaces were 70 mm and ρ_v is 1.5%. For these eight specimens, the steel fiber volume fractions (ρ_f) ranged from 0.0% (RC pier) to 1.5%. The round steel fibers (tensile strength: 1150 MPa) had a diameter of 0.55 mm and length of 35 mm with hooks at both ends (Figure 1(a)), and they would be softened and separated on contact with water (Figure 1(b)). For specimens S6–S8, it should be noted that the SFRC was only used in the potential plastic hinge region (pier bottom), and the length of this region (h_f) ranged from 100 to 300 mm. The concrete compressive strength of each specimen was tested by 150 × 150 × 150 mm cubic specimen and is presented in Table 1, which is used to calculate the nominal axial capacity of each specimen and to construct the numerical model.

Figure 1.

Steel fibers used in the SFRC specimens: (a) initial state and (b) pouring state.

As illustrated in Figure 2, each pier specimen was 200 × 200 × 800 mm and was cast monolithically with a 700 × 700 × 300 mm foundation block and 700 × 700 × 250 mm loading block. Thus, the height of the entire specimen was 1350 mm. The specimens were tested in an inverted position to accommodate test frame details. The lateral cyclic loading history and constant axial loading were applied to the loading block through the steel clevis seen at the bottom of each specimen, as shown in Figure 3. The pseudo-static lateral load was applied under displacement control. Loading constituted three cycles at subsequently increasing lateral displacements of 5, 10, 15, 20, 30, 40, 50, 60, and 75 mm. Each pier was subjected to a constant axial load equal to 10% of its nominal axial capacity. Linear variable differential transducers (LVDTs) and electrical resistance strain gages were placed to measure the displacements at key locations along the pier specimens, as well as the strain of reinforcing steel.

Figure 2.

Geometry and reinforcing details of pier specimens (unit: mm)

Figure 3.

Photographs of specimens installed in the pseudo-static test system: (a) S1 and (b) S8.

Load–displacement results

Based on the data measured by the LVDTs on the top of piers, the horizontal load–displacement hysteretic curves of eight specimens can be obtained. The skeleton curves, drawn through the peak responses of the hysteresis curves, contain important indices to measure the seismic capacity of structures (Zhang et al., 2013). Figure 4(a) to (c), respectively, demonstrates the influence of the steel fiber content, stirrup ratio, and the length of SFRC region on the skeleton curves.

Figure 4.

Skeleton curves of eight pier specimens: (a) different steel fiber contents, (b) different stirrup ratios, and (c) different lengths of SFRC region.

As shown in Figure 4(a), the SFRC piers exhibit a higher bearing capacity and an improved behavior with respect to maintaining its peak capacity over the RC pier. Also, these enhancements of SFRC piers increase with the increase in the steel fiber volume ratio. By analyzing Figure 4(b) and comparing it with Figure 4(a), it can be observed that the peak capacity of S4 (ρ_v = 1.5%, ρ_f = 1.5%) is higher than that of S5 (ρ_v = 1.0%, ρ_f = 1.5%), while they both have a greater carrying capacity than S1 (ρ_v = 1.5%, ρ_f = 0.0%). Moreover, the post-peak deterioration of S5 is less pronounced than that of S1, which indicates that the addition of steel fibers to the RC pier can substitute for stirrup to some extent. As shown in Figure 4(c), the skeleton curves of S7 (h_f = 200 mm) and S8 (h_f = 300 mm) are similar to those of S3 (h_f = 800 mm). This indicates that adopting SFRC locally and suitably (at the plastic hinge region) is capable of producing a similar enhancement effect to adopting SFRC wholly.

In order to quantitatively analyze the seismic capacity of specimens, some key parameters (e.g. the ultimate displacement ductility ratio) are defined herein. The ultimate displacement ductility ratio µ_cu is defined as the ratio of the displacement at the ultimate load, P_u, to that at yield, P_y: µ_cu = Δ_u/Δ_y. The ultimate load P_u is defined as the post-peak load having fallen 15% from the maximum load P_max. The yield displacement Δ_y is defined following the method used by Shannag et al. (2003). The characteristic points of the skeleton curves in both positive and negative directions are presented in Table 2. The average absolute values of the ultimate displacement ductility ratios (µ_cu), derived from the ductility ratios in positive and negative directions, are listed in the last column of Table 2 and used for the following analyses.

Table 2.

Characteristic values of test specimens.

Specimen number	P_y (kN)		Δ_y (mm)		P_max (kN)		P_u (kN)		Δ_u (mm)		µ_cu
Specimen number	Pos.	Neg.	Pos.	Neg.	Pos.	Neg.	Pos.	Neg.	Pos.	Neg.	Ave.
S1	27.12	27.64	8.17	8.39	32.88	34.54	27.95	29.37	37.94	34.20	4.36
S2	27.31	29.41	7.69	8.59	35.09	36.69	29.83	31.11	45.03	43.21	5.42
S3	28.36	34.08	7.86	7.44	38.02	40.16	32.32	34.14	63.20	57.22	7.87
S4	31.28	32.40	8.74	8.30	40.64	42.96	34.54	36.52	61.75	61.61	7.24
S5	26.68	29.98	7.18	7.42	35.23	37.21	29.95	31.61	46.88	46.30	6.38
S6	26.98	28.30	6.87	7.15	33.72	36.14	28.66	30.72	44.42	43.40	6.26
S7	29.23	31.47	6.58	6.88	36.53	37.17	31.05	31.23	53.41	51.51	7.79
S8	31.05	31.65	7.80	7.98	37.46	38.38	31.84	32.62	59.97	58.89	7.53

P_y: yield load; Δ_y: yield displacement; P_max: maximum load; P_u: ultimate load; Δ_u: displacement at the ultimate load; µ_cu: ultimate displacement ductility ratio; Pos.: positive direction; Neg.: negative direction; Ave.: average value.

The yield displacements of eight specimens listed in Table 2 are similar to each other. However, the ultimate displacements of specimens are quite different, resulting in the large differences of their ultimate ductility ratios (µ_cu varies from 4.36 to 7.87). Two regularities can be observed from the variation in µ_cu: (1) µ_cu basically increases with the increase in the steel fiber content, except for S4 and (2) µ_cu of S7 and S8, with local use of SFRC in the piers, is almost the same as the result of S3.

Structural performance levels

The structural capacity can be defined as the maximum displacement, force, velocity, or acceleration that a structure can withstand without exceeding a prescribed performance level (Sathish, 2006). In this article, the most widely used damage index (DI) proposed by Park et al. (1985) was employed. It consists of a simple linear combination of normalized deformation and energy absorption. The DI can be expressed as

D I = \frac{δ_{m}}{δ_{u}} + \frac{β}{Q_{y} δ_{u}} \int d E

(1)

where δ_m is the maximum response deformation, δ_u is the ultimate deformation under monotonic loading, Q_y is the calculated yield strength, dE is the incremental dissipated hysteretic energy, and β is the cyclic loading factor that can be obtained by the equation suggested by Park and Aug (1985) as follows

β = (- 0.447 + 0.073 \frac{l}{d} + 0.24 n_{0} + 0.314 ρ_{t}) \cdot 0 . 7^{ρ_{w}}

(2)

where l/d is the shear span ratio, n₀ is the normalized axial force, ρ_t is the reinforcement ratio for longitudinal steel, and ρ_w is the reinforcement ratio for confining steel. The ρ_w for the SFRC piers in this study is the nominal transverse reinforcement ratio, in which the enhancement of the steel fibers in transverse reinforcement needs to been considered, and the values of ρ_w for SFRC piers with different steel fiber contents can be found in Zhang (2013).

The DI for the damage assessment of the bridge piers can also be expressed as follows (Karim and Yamazaki, 2001)

DI = \frac{μ_{c} + β μ_{ch}}{μ_{cu}}

(3)

where µ_c is the displacement ductility ratio of the piers; µ_cu is the ultimate displacement ductility ratio as mentioned above; µ_ch is the cumulative energy ductility ratio, defined as the ratio of the hysteretic energy to the energy at yield point; and β is the same as equation (1) and calculated by equation (2).

The DIs can be calibrated to obtain the relationship between the DI and damage rank (DR) (Karim and Yamazaki, 2001). The DR can be classified by the observed seismic damage (e.g. bond failure and spalling). The classifications and definitions of DRs (Karim and Yamazaki, 2001; Vosooghi and Saiidi, 2012; Williams and Sexsmith, 1995) are shown in Table 3. The structural states of plastic hinge region of a typical specimen (S3) at each DR are illustrated in Figure 5.

Table 3.

Classifications and definitions of DRs.

DR	DI	Degree of damage	Definition
1	0.00 < DI < 0.14	Slight	Localized minor cracking
2	0.14 ⩽ DI < 0.40	Minor	Light cracking throughout
3	0.40 ⩽ DI < 0.60	Moderate	Severe cracking, localized spalling
4	0.60 ⩽ DI < 1.00	Extensive	Concrete crushing, reinforcement exposed
5	1.00 ⩽ DI	Complete	Total or partial collapse

DR: damage rank; DI: damage index.

Figure 5.

Structural states of plastic hinge region of S3 at each damage rank (DR)

Based on the minimum DI given in Table 3, the minimum µ_c for each specimen can be obtained by equation (3) and is presented in Table 4, which would be used to determine the seismic capacity of each pier. In order to consider the uncertainties in estimating back bone curves (e.g. uncertainties in material properties, specimen dimensions and test measurements), the displacement ductility ratio (µ_c) for each specimen is described by a lognormal distribution, as recommended by Feng (2009), where the logarithmic standard deviation (β_c) for µ_c is determined to be 0.3.

Table 4.

Minimum displacement ductility ratio (µ_ci) of specimens for each DR.

Specimen number	µ_c₂ (DR = 2)	µ_c₃ (DR = 3)	µ_c₄ (DR = 4)	µ_c₅ (DR = 5)
S1	0.50	1.61	2.37	4.32
S2	0.71	2.09	3.23	5.38
S3	1.03	3.03	4.66	7.83
S4	0.97	2.92	4.35	7.19
S5	0.84	2.50	3.79	6.34
S6	0.81	2.46	3.74	6.23
S7	1.02	2.97	4.54	7.74
S8	1.01	2.88	4.43	7.49

DR: damage rank.

Analytical model and seismic demand of the piers

In this section, the analytical models of the piers corresponding to the above tests were constructed first. Then, nonlinear dynamic time history analyses of the piers subjected selected ground motions were conducted to obtain their probabilistic seismic demand, which would be used to calculate the probabilities that the structural demand exceeds the structural capacity and construct the fragility curves of the piers.

Analytical model

A suite of 50 ground motion records from the Pacific Earthquake Engineering Research Center (PEER) Strong Motion Database (http://peer.berkeley.edu/smcat) was used in this study. The propagation of seismic waves is closely related to the site types of seismic record, and the amplification effects of different type sites on seismic waves are different. Thus, the characteristics of main site types in China (Feng, 2009) were considered in the selection of ground motions. The uncertainties in ground motion records (Choi et al., 2004) that a bridge may encounter were also taken into account. Consequently, the moment magnitudes of the selected ground motions ranged from 6.0 to 7.5, and the epicentral distances ranged from 10 to 100 km, where other parameters were not specified. The response spectra (RS) with 5% damping ratio of the selected 50 ground motions are shown in Figure 6.

Figure 6.

Response spectra of the selected ground motions.

The numerical models of the piers mentioned above were developed using OpenSees to analyze seismic response of the structures subjected to earthquakes. The nonlinearities of the pier models were incorporated into the nonlinear fiber model using beam–column and zero-length elements. Figure 7 shows the pier model and cross-sectional meshing in this article.

Figure 7.

Schematic diagram of the pier model and cross-sectional meshing.

For the numerical model shown in Figure 7, the concrete07 material model (Mazzoni et al., 2008) was used to simulate the confined and unconfined concrete. The reinforcing steel material model was adopted to simulate the reinforcing bars. The bond_sp01 material model was applied to simulate the differences in bond–slip response between the RC and SFRC piers. A zero-length section element using the bond_sp01 model was arranged at the intersection of the pier shaft and foundation. The element fiber cross sections are also presented in Figure 7. The mechanical properties adopted in the above material models and other details can be found in Zhang et al. (2013).

Random samples of four modeling parameters (e.g. compressive strength of concrete, compressive strain of concrete, yield strength of reinforcing steel, and elastic modulus of reinforcing steel) were combined with the eight pier samples, to represent the inherent variability in the material properties of the piers (Nielson and DesRoches, 2007b). These parameters were taken as random variables with a mean and standard deviation. A set of 50 pier models were developed for each pier sample using the Latin-hypercube sampling technique. Each pier model was divided into several beam–column and zero-length elements, where the mass of the superstructure was lumped on the uppermost node and the pier mass was lumped averagely on the distributed nodes (Figure 7). The pier base was fixed and the earthquake excitations were applied to the uppermost node.

Seismic demand

The pier models were randomly matched with the 50 ground motions, resulting in a total of 50 earthquake-pier samples for each pier type. Then nonlinear dynamic time history analyses were conducted to obtain the seismic demand of the piers. As recommended by Nielson and DesRoches (2007b), the PGA is a good intensity measure when analyzing bridge structures. Thus, the PGA was selected as the intensity parameter in this study.

The seismic response of these piers was measured by displacement ductility ratio µ_d, which was similar to µ_cu defined above but corresponds to the seismic demand. Take S1 for example, the displacement ductility ratio µ_d was plotted versus PGA on a log–log scale (50 data points), as shown in Figure 8. A regression analysis was then performed to establish a relationship between the expected damage and the PGA of seismic records. Thus, the median value of structural demand µ_d, the variance R², and the logarithmic standard deviation β_d of each pier specimen can be determined and tabulated in Table 5.

Figure 8.

Regression analysis of displacement ductility ratio versus PGA (S1)

Table 5.

Probabilistic seismic demand models for eight pier responses.

Specimen number	ln(µ_d)	R ²	β_d
S1	1.756 + 1.620 × ln(PGA)	0.890	0.365
S2	0.943 + 1.329 × ln(PGA)	0.684	0.438
S3	1.232 + 0.966 × ln(PGA)	0.953	0.577
S4	1.864 + 0.857 × ln(PGA)	0.521	0.230
S5	0.794 + 1.235 × ln(PGA)	0.796	0.496
S6	2.018 + 1.036 × ln(PGA)	0.663	0.605
S7	1.530 + 0.953 × ln(PGA)	0.711	0.513
S8	1.497 + 1.034 × ln(PGA)	0.679	0.455

µ_d: median value of structural demand; R²: variance; β_d: logarithmic standard deviation; PGA: peak ground acceleration.

Fragility curves

The fragility curves of these eight piers express the probabilities for the DRs that quantified in terms of pier displacement ductility ratios. Generally, the probability that the structural demand exceeds the structural capacity, P_f, can be given as

P_{f} = P [\frac{S_{d}}{S_{c}} \geq 1]

(4)

where S_d and S_c are the structural demand and capacity, respectively. In this article, the structural capacities of the piers are obtained by the test results listed in section “Experimental program and structural capacity,” while their seismic demands are derived from the simulation results shown in section “Analytical model and seismic demand of the piers.”

The demand and capacity of piers were both assumed to follow lognormal distributions, in this study, as recommended by Hwang et al. (2001). Thus, the conditional probability of reaching or exceeding a specified DR at a PGA, $P_{f} (DR \geq i | PGA)$ , can be determined by

P_{f} (DR \geq i | PGA) = Φ [\frac{\ln (S_{d} / S_{c})}{{({β_{d}}^{2} + {β_{c}}^{2})}^{1 / 2}}]

(5)

where Φ is the standard normal distribution, i is the DR, and β_d and β_c are the logarithmic standard deviation for the demand and capacity, respectively. Since the displacement ductility of piers was selected for the measure of structural demand and capacity in this article, equation (5) can be expressed as

P_{f} (DR \geq i | PGA) = Φ [\frac{\ln (μ_{d} / {μ_{c}}_{i})}{{({β_{d}}^{2} + {β_{c}}^{2})}^{1 / 2}}]

(6)

where µ_d and µ_ci are the displacement ductility ratios corresponding to the seismic demand and structural capacity, respectively. Using equation (6) and Tables 4 and 5, the probability of reaching or exceeding Rank 4 (take Pier S1 as an example) can be obtained by

P_{f} (DR \geq 4 | PGA) = Φ {\frac{\ln [5.789 {(PGA)}^{1.620} / 2.37]}{{({0.365}^{2} + {0.3}^{2})}^{1 / 2}}}

(7)

Based on the data of the calculated probabilities, the fragility curves of these piers for each DR can be obtained and plotted in Figure 9. Since the probabilities of reaching or exceeding Rank 1 are always 100%, the fragility curves of the piers for slight damage (DR = 1) are not presented.

Figure 9.

Fragility curves of eight piers for each damage rank: (a) minor damage (DR = 2), (b) moderate damage (DR = 3), (c) extensive damage (DR = 4), and (d) complete damage (DR = 5).

Results and discussions

Figure 9 shows the fragility curves of eight piers for each DR. Generally, the fragility curves of piers become lower with the increase in the DR. In other words, the probability of reaching or exceeding damage decreases as the DR increases. In order to make it easier to compare the piers’ vulnerability, the median value of the exceeding probability is determined for each DR. The median PGA (with 50% exceeding probability) for each pier at each DR is listed in Table 6.

Table 6.

Fragility curve median values of pier specimens for PGA.

Specimen number	Minor damage (DR = 2) (g)	Moderate damage (DR = 3) (g)	Extensive damage (DR = 4) (g)	Complete damage (DR = 5) (g)
S1	0.22	0.50	0.68	0.93
S2	0.23	0.52	0.72	1.10
S3	0.24	0.62	0.92	1.58
S4	0.28	0.68	0.89	1.54
S5	0.23	0.60	0.82	1.38
S6	0.25	0.59	0.80	1.23
S7	0.27	0.70	1.00	1.69
S8	0.25	0.65	0.93	1.62

DR: damage rank.

For the minor DR (DR = 2), the fragility curves of the pier specimens are similar to each other. As presented in Table 6, the median PGAs of the piers range from 0.22 to 0.28 g when DR = 2, while the values of median PGA of eight piers are more distinct when DR > 2. This is mainly due to the fact that the behavior of the RC and SFRC piers is essentially the same at pre-yield displacement levels, while the effects of the steel fibers controlling the cracking and eventual spalling are gradually enhanced at the post-yield phase. Thus, the safety of the concrete piers subjected to moderately strong earthquakes is improved with the addition of steel fibers.

For the moderate DR (DR = 3), the median PGA ranges from 0.50 to 0.70 g. Pier S1 (RC pier) is the most vulnerable structure, and the piers become less vulnerable with the increase in the steel fiber content, up to 1.5% fiber volume ratio, as shown in Figure 9(b) and Table 6. Figure 9 also shows that the fragility curves of S3 (ρ_f = 1.0%) are basically in coincidence with those of S4 (ρ_f = 1.5%). This means that a greater amount of SFRC in S4 does not attain a better seismic performance. It is mainly because the concrete workability may become worse when the addition of steel fibers reaches a certain level. Hence, the pier with the fiber volume ratio of 1.0% may be the most cost-effective.

For the extensive DR (DR = 4), the damage exceeding probability of S5 (ρ_v = 1.0%, ρ_f = 1.5%) is smaller than that of S1 (ρ_v = 1.5%, ρ_f = 0.0%), and the median PGA is 0.82 g for the former and 0.68 g for the latter. This indicates that adding steel fibers appropriately to RC piers can substitute part of the transverse reinforcement’s role of seismic resistance, which is particularly useful for the concrete members with congested reinforcing details.

For each DR, the fragility curves of S7 (h_f = 200 mm) and S8 (h_f = 300 mm) are similar to that of the S3 (h_f = 800 mm), while the fragility curve of S6 (h_f = 100 mm) is higher than the above. For the complete DR (DR = 5), the median PGA is approximately 1.69 g for S7 and 1.62 g for S8, which are both greater than that 1.23 g for S6. This shows that the seismic vulnerability of piers adopting SFRC locally and suitably (at the plastic hinge region) is close to those adopting SFRC wholly, because the plastic hinge region always bears greater stress when subjected to earthquakes.

Conclusion

Based on the cyclic load tests and nonlinear time history analyses, the analytical fragility curves of eight pier specimens for five DRs were developed. The influences of steel fiber content, stirrup ratio, and length of SFRC region on the seismic vulnerability of the piers were analyzed.

For most specimens tested, the seismic vulnerability of SFRC piers was reduced with the increase in the steel fiber content, up to 1.5% fiber volume ratio, and the fiber volume ratio of 1.0% was relatively more suitable for the seismic enhancement of bridge piers. The differences of fragility curves between the RC and SFRC piers were not significant until the structures reach the moderate DR. This indicates that the effect of the steel fibers on the piers’ seismic safety is more pronounced under moderate strong earthquakes.

The damage exceeding probabilities of the SFRC pier with a lower stirrup ratio were smaller than those of the RC pier with a higher stirrup ratio, indicating a better seismic performance of the former. Moreover, the seismic vulnerability of piers with the local use of SFRC was similar to that of piers with the whole use of SFRC. This observation can be used to reduce the amount of steel fibers in SFRC piers for seismic design, and then the construction cost of the SFRC piers would be reduced.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 30915011329).

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