Comparison study of time-varying seismic fragility of precast segmental and cast-in-place bridge columns in high-speed railway bridges

In recent years, precast segmental bridge columns (PSBCs) have been widely used in high-speed railway bridges, but the lack of long-term seismic performance limits PSBCs application in harsh environments and high-intensity areas. However, the selection of high-speed rail lines in high-intensity offshore areas is inevitable. Therefore, considering the impact of environmental erosion and earthquake, it is necessary to study the seismic performance of PSBC. In order to study the application of PSBCs in offshore high-intensity areas, this paper comprehensively compares the time-varying seismic fragility of PSBCs and cast-in-place bridge columns (CPBCs) in high-speed railway bridges. Based on offshore high-speed railway columns, the finite element models of representative PSBCs and CPBCs are established and verified by experiments. Then, the verified finite models are utilized to implement the time-varying fragility analysis by considering chloride ion erosion under four damage states. The main conclusions are as follows: the exceeding probabilities of PSBCs and CPBCs are close in intact bridges under different damage states and seismic intensities. With the prolongation of bridge service time, the steel bars corrosion rate of PSBCs is faster than that of CPBCs due to the discontinuity of PSBCs segments, the exceeding probabilities of PSBCs increase more rapidly than those of CPBCs. When the columns reach the design working life, the exceeding probability and PGA (Peak Ground Acceleration) median of PSBCs are higher than those of CPBCs under four damage states. Taking the moderate damage state as an example, the maximum exceeding probability of PSBCs and CPBCs were 97.2% and 89.1%, respectively, and the PGA median of PSBCs were 24% lower than that of CPBCs at 100 years. This work provides a theoretical foundation for the better application of PSBCs in offshore high-intensity areas.


Introduction
In recent decades, researchers have shown an increased interest in modular construction of precast structures due to their lower environmental pollution, fast construction speed and reliable component quality. In the field of the bridge engineering, precast segmental construction has been widely used in superstructures and substructures (Kashani et al. 2019). However, the application of precast components in the substructure occurred later than that in the superstructure. PSBCs were first applied to JFK Causeway in Texas in the 1970s, and the bridge community has realized the obvious advantages of prefabricated columns. Compared with CPBCs, the use of PSBCs can improve the engineering quality, and reduce the number of on-site personnel and the environmental impact (Sideris et al. 2014;Zhang 2019). However, the lack of the long-term seismic performance of PSBCs limits its application in high-intensity and offshore environmental areas (Hung et al. 2017). Therefore, the time-varying seismic vulnerability of the PSBCs should be studied and compared with that of the CPBCs in detail.
Seismic vulnerability analysis is widely used for the seismic performance of investigated bridges and is a part of the seismic risk analysis framework of the Pacific Earthquake Engineering Research Center (PEER) (Rao et al. 2016). It quantifies the exceeding probability of structural or component damage in earthquakes. In the offshore environment, corrosion deterioration (especially caused by chloride ions) is considered to be the key factor affecting the quantification of bridge vulnerability. The probability of bridge damage increases with the extension of service time (Liang et al. 2020(Liang et al. , 2021. Meanwhile, many coastal areas are high-intensity zones. The seismic performance of cast-in-place bridges is expected to be significantly lower than their design performance under the combined action of earthquakes and chloride ion corrosion (Ou and Nguyen 2016;Yuan et al. 2017). Numerous studies of the time-varying vulnerability of cast-in-place bridges have been reported considering the accelerated degradation of materials in coastal areas and earthquake impacts in fault zones. Biondini proposed a probabilistic approach to predict the lifetime seismic performance of concrete bridges exposed to aggressive environments (Biondini et al. 2014). Li established a framework for evaluating the time-varying seismic performance of uncertain degraded CPBCs by considering material parameters, corrosion initiation time and uncertainty of ground motion (Li et al. 2018). Cheng proposed a seismic vulnerability analysis method for CPBCs corrosion degradation based on a timevarying estimation of the displacement ratio as the bearing capacity index ( Cheng et al. 2019).Based on the Duracrete model and previous experimental results, Li determined the probability distribution types and statistical characteristics of various environmental and corrosion parameters, and a framework for analyzing the seismic vulnerability of CPBCs subjected to chloride ion erosion was proposed (Li et al. 2020).
PSBCs have different structural components than CPBCs, which includes joints, energy dissipation (ED) bars and unbonded prestressed tendon (PT) strands . Theirs working performance are very different from CPBCs. Due to the discontinuity between segments, the seismic performance of PSBCs is recognized to be weaker than that of CPBCs (Jia et al. 2020). Many researchers have performed many studies on the working performance of PSBCs, such as cyclic load tests , shaking table tests , and impact tests (Do et al. 2019) and so on. The PSBCs are more likely to show quasi-elastic behavior in medium and small earthquakes (Tong et al. 2021). Through the experimental study (Zhanghua et al. 2021), an appropriate slenderness ratio and longitudinal bars can significantly improve the deformation capacity of PSBCs under earthquakes. These studies enable PSBCs to be widely used in low-intensity areas. Some scholars have studied the seismic vulnerability of PSBCs in high-intensity areas. Lee and Billington analyzed the seismic vulnerability of a bridge system supported by PSBCs in the performance-based earthquake engineering (PBEE) framework and evaluated its economic loss (Lee and Billington 2011). Incremental dynamic analysis (IDA) method is often used to evaluate the seismic performance of bridge piers (Shafigh et al. 2020;Ahmadi et al. 2019). And Ehsan Ahmadi used IDA method to generate a vulnerability curve for studying the vulnerability of PSBCs, and the results indicated that low columns are more prone to earthquake collapse than slender columns (Ahmadi and Kashani 2021). However, many high-intensity areas are in coastal areas, and when bridges are built in these areas, the structures are vulnerable to chloride ion corrosion in seawater. Therefore, the coupling effect of material performance degradation and earthquakes should be considered, however, scholars rarely study the time-varying seismic fragility of PSBCs. From the above review, this paper studies the time-varying seismic vulnerability of PSBCs on the basis of predecessors and compares it with that of CPBCs.
This paper makes a comparative study on the long-term seismic vulnerability of PSBCs and CPBCs. First, the bridge model is established according to an example bridge in an offshore high-intensity area in Sect. 2, and then the established model is tested and verified to verify the effectiveness of the modeling method in Sect. 3. In Sect. 4, the seismic resistance analysis of CPBCs and PSBCs are studied based on IDA method. In Sect. 5, the displacement-ductility ratio is selected as fragility damage index, the ground motions which are meet the local site conditions and structure natural vibration characteristics are selected from PEER for probabilistic seismic demand analysis, the fragility curve is drawn, and the median PGA is obtained. The main conclusions are drawn in Sect. 6.

Description of the finite element model of PSBC and CPBC
In this paper, a typical bridge column from five-span continuous rigid frame bridge in high-intensity offshore area is selected for the finite element modelling. The site condition is class 2, the seismic fortification intensity is 8th degree, and the designed service life is 100 years. The concrete grade is C45, and the protective layer thickness is 45 mm. The stirrups in PSBCs and CPBCs are 10 mm HPB300, and the longitudinal reinforcements are 32 mm HRB500, with reinforcement ratios of 0.56% and 0.70%, respectively. In PSBCs, 28 mm HRB500 steel bar is used for ED bars and 1860 steel strand with a diameter of 15.2 mm is used for unbonded PT strands, and ED bars and unbonded PT strands both penetrate through all segments.
The established finite element models of PSBCs and CPBCs are shown in Fig. 1. The models are simulated by using fiber-based nonlinear elements in OpenSees which can effectively simulate the hysterical behavior of columns and dynamic response under earthquake excitation (Pan et al. 2017). PSBCs fiber element model were established based on the traditional simulation method for CPBCs (Ko 2022;Xu et al. 2021). Each segment of PSBCs and the whole body of CPBCs are all simulated by Displacement-Based Beam-Column element, 5 integral points are set along the length direction, the bottom node is consolidated, and the top node is released. Different from CPBCs, in the joint section of PSBCs, the ED bar fibers are decorated. The joint sections between the column segments 1 3 are simulated by Zero-Length-Section element in OpenSees, four joints are arranged at the edge of the joint section, and the joints are rigidly connected with the pier joints. The existing PSBCs test results showed that the joints will open and close under the action of horizontal displacement, and there is basically no shear dislocation between the segments (Chou and Chen 2006;Ou et al. 2007Ou et al. , 2010a. For PSBCs with no shear bond at the segmental joints, the concrete friction force between segments can meet the horizontal bearing capacity of its members. Corotational Truss element is used to simulate unbonded PT strands, the division of Corotational Truss elements corresponds to Displacement-based Beam-Column elements of the column body, the alignment of unbonded PT strands and the prestressed pipe is consistent in the deformation process.

Time-varying material and mechanical properties
Concrete02 is selected to model the constitutive behavior of the concrete, which can better estimate the residual deformation of the concrete (Kent and Park 1990). The reinforcing reinforcements were modelled using the steel02 in OpenSees, which is capable of considering isotropic strain hardening and the Bauschinger effect (Spacone and Filippou 1991). The parameter values in the steel model for longitudinal reinforcement are: f y = 500 MPa, f u = 630 MPa, E s = 1.93 × 10 5 MPa, E sh = 6.0 × 10 3 MPa, ε sh = 0.01, ε su = 0.15, the corresponding values for stirrups are: f y = 300 MPa, f u = 420 MPa, E s = 1.93 × 10 5 MPa, E sh = 6.0 × 10 3 MPa, ε sh = 0.01, ε su = 0.15.
In offshore environments, bridge columns are susceptible to chloride ion corrosion in seawater, which will cause the corrosion of the steel bars in the column. In the service period, compared with the corrosion of concrete, the corrosion of reinforcement has a more significant effect on the seismic performance and seismic vulnerability of bridge columns. In this paper, the influence of steel corrosion on the structure is considered, the initial corrosion time of reinforcing steel bars are: where t i is the beginning corrosion time of the reinforcement (year); c is the thickness of the concrete cover (mm); D c is the diffusivity coefficient of chloride ions (mm 2 /year); erf(.) represents the Gauss error function; M cr is the critical chloride concentration of (1) × 10 −6 + 0.2t 1 Fig. 1 Finite element model of PSBCs and CPBCs reinforcement corrosion (kg/m 3 ); M s is the chloride concentration at the concrete surface (kg/m 3 ); t 1 is the accumulation time for chloride ions to reach a stable value on the concrete surface.
The rust expansion cracking time of the concrete protective layer includes the initial corrosion time of the reinforcement and the migration and diffusion time process of the corrosion products. It can be expressed as follows (Liang et al. 2019): where t cr is the rust expansion cracking time of the concrete cover, t c is the time from steel bar corrosion to concrete cracking.
After the concrete cover cracks, the corrosion rate of reinforcements further accelerates with the deepening of chloride ion erosion, the concrete cover cracks and the corrosion rate of reinforcements accelerates, the time-varying diameter model of corroded reinforcement considering the cracking of concrete cover is as follows (Stewart and Rosowsky 1998): where, d(t) is the time-variant diameter; d0 is the initial diameter of the reinforcement (mm); λ1 is the corrosion rate before the cracking of the concrete cover (mm/year); λ2 is the corrosion rate after the cracking of the concrete cover (mm/year).
The yield strength and ultimate strength of the reinforcement degenerated with the corrosion, and the degradation formula can be expressed as (Du et al. 2005): where f y,corr and f u,corr are the yield strength (MPa) and the ultimate strength (MPa) of the corroded reinforcement; β y and β u are the reduction coefficients of the yield strength and the ultimate strength, which are taken as 0.0049 and 0.0065 respectively considering the field site of the investigated bridge; f y and f u are the yield strength (MPa) and ultimate strength (MPa) of the reinforcement before corrosion; Q corr is the corrosion rate of the reinforcement.
For PSBC with ED bars, the corrosion of ED bars across the joints should be considered. Wet joints and epoxy rubber joints are widely used in the PSBCs joints, the durability degradation coefficient of them are the same. Therefore, the effect of chloride ion erosion on joints is considered in the form of direct wet joints, cement mortar can be equivalent to concrete of a certain thickness according to the following formula: where, C B is the equivalent concrete thickness (mm); f cu,k is the standard value of compressive strength of concrete cube (MPa); C A is the thickness of cement mortar (mm). Due to the deep location of the unbonded PT strands in the engineering example, the equivalent concrete protective layer thickness is 181.72 mm, and the corrosion time of the unbonded PT strands is 207.66 years, so the chloride ion corrosion effect of unbonded PT strands can be ignored.
The relevant parameters of reinforcement corrosion under chloride ion corrosion are shown in Table 1 according to the site conditions of the investigated bridge. Table 1 indicates that the initial corrosion time of longitudinal reinforcements in Row 1 of CPBCs and PSBCs is later than that of stirrup and earlier than that of longitudinal reinforcements in Row 2. PSBCs have joints, and the thickness of concrete protective layer after equivalent cement mortar between PSBCs joints is far less than that of bars in segment. Therefore, the corrosion time of ED bars is earlier than that of other steel bars.
In the whole life cycle, the diameter, yield strength and ultimate strength of the reinforcements decrease with the service time extension. Due to the same concrete cover of PSBCs and CPBCs, the stirrup damage degrees of PSBCs and CPBCs are the same. Compared with the second row of longitudinal reinforcements of CPBCs, the first row of longitudinal reinforcements of CPBCs is easily eroded by chloride ions in seawater, and the mechanical performance of the material decreases the most. The ED bars in PSBCs are most seriously corroded by chloride ions, the corrosion rate of ED bars is also faster than that of other steel bars, especially the first row of ED bars, the mechanical properties of the material decline the fastest. The corrosion conditions with the bridge service time extension of CPBCs and PSBCs are shown in Fig. 2. After 100 years of service, the reinforcement diameter, yield strength and ultimate strength of CPBCs are reduced by 11%, 10%, and 14%, respectively; the reinforcement diameter, yield strength and ultimate strength of PSBCs are reduced by 32%, 26%, and 35%, respectively.

The verification of finite element model
The previous experimental results are used to verify the accuracy of the current modeling method in Sect. 2. Bu compared and analyzed four reduced scale PSBCs specimens with different reinforcement types and one CPBC specimen through experience tests (Bu et al.  Fig. 3a. The piles and column body are cast with C40 concrete. The perforated unbonded PT strands ratio is 0.31%, the initial tension was 252 kN, and the ED bars ratio is 0.71%. The stirrup spacing of the S1 segment is 50 mm, the stirrup ratio is 0.96%, and the stirrup spacing and ratio of the others are 80 mm and 0.6%, respectively. The finite element (FE) model of the selected column was established by using the identical modeling method, and the corresponding model is shown in Fig. 3b. In the experiment, the displacement-controlled method was used for the loading test process, and the controlled draft levels included 0.1%, 0.2%, 0.3%, 0.5%, 0.75%, 1%, 1.5%, 2.0%, 2.5%, 3.0%, 3.5%, 4.0%, 4.5%, 5.0%, 6.0% and 7.0% with two cycles for each drift level. In order to verify the accuracy of the established model, comparisons of the load-displacement hysteretic curve, skeleton curve, vertical displacement of the column bottom joint and stress variation of the PT strands from the simulated and experimental results are shown in Fig. 4. The finite element analysis results are symmetrical in the positive and negative loading. And the finite element analysis results fit well with the test results in the negative loading, while fit poorly in the positive loading, but the trend change of the positive loading is relatively fit. Comparing Fig. 4a, b, the maximum bearing capacity from the  Figure 4c shows that the maximum opening displacements of the column bottom are 15 mm and 13 mm, and the maximum displacements when the joint is closed are both 5 mm. Figure 4d shows that the maximum stress values of the prestressed reinforcement under the positive and negative horizontal displacement angles of the finite element model and the test model are 1495 MPa, 1484 MPa, 1412 MPa and 1550 MPa, respectively. Therefore, the results from FE models and tests under reverse loading process are in a good agreement, the modeling method used is reasonable and that the models established in this paper can be used in the following seismic analysis with reliable calculation.

Seismic performance of PSBCs and CPBCs
The seismic response of CPBCs and PSBCs under typical ground motion excitation was studied firstly regardless of the time-varying effects. The typical seismic wave Imperial (magnitude 6.9, PGA 0.28 g) was selected, and the time history of the seismic wave is as shown in Fig. 5a. The input direction of seismic waves is along the longitudinal direction of bridge. The ground motion is divided into three classes, design ground motion (0.3 g), rare ground motion (0.57 g) and great ground motion (1.0 g) in the reference of (Chen Wei 2020). Therefore, the PGA of the ground motion Imperial was modulated to 0.3 g, 0.57 g and 1.0 g to simulate the different seismic performance of PSBCs and CPBCs under different ground motion intensity. The seismic performance of PSBCs and CPBCs was evaluated based on the IDA method. Taking the amplitude modulation of ground motion Imperial to 1.0 g as an example, the column top displacement time-varying curve is shown in Fig. 5b. It shows that the maximum column top displacement Δ max of CPBCs and PSBCs are 339.72 mm and 387.09 mm, respectively, while the residual displacements Δ r of CPBCs and PSBCs are 19.34 mm and 2.42 mm respectively. The maximum displacement of PSBCs was 14% larger than that of CPBCs, and the residual displacement was 87% smaller than that of CPBCs. The opening and closing of joints resulted in the maximum column top displacement of PSBCs being greater than that of CPBCs. Smaller residual displacement indicates that the PSBCs have a better self-centering capacity than CPBCs due to the unbonded PT strands.
The moment-curvature hysteretic curves of PSBCs and CPBCs changes under different ground motion intensity are shown in Fig. 6. Under the designed ground motion, the PSBCs is in an elastic state, and the moment-curvature hysteretic curve changes linearly. Under the action of rare ground motion and great ground motion, the stiffness degradation of PSBCs is small, the residual displacement is small, the structure has no obvious damage, and the bridge pier is basically in elastic state. The moment-curvature hysteresis curve of CPBCs changes linearly under designed ground motion. And the moment-curvature hysteresis curves of CPBCs show nonlinear changes under the action of rare ground motion and great ground motion. CBPCs have significant plastic deformation with the increase of earthquake intensity, the residual displacement increases, the hysteresis loop increases significantly, the stiffness deforms, and the structure enters the plastic stage. Take the great motion for an example, the maximum bending moment and maximum curvature of PSBCs are 16.2 MN·m and 1.03 × 10 −4 m −1 , and the maximum bending moment and maximum curvature of CPBCs are 20.4 MN·m and 2.58 × 10 −4 m −1 . The maximum bending moment ratio of PSBCs is 20% smaller and the maximum curvature is 60% smaller than that of CPBCs.

Time-varying seismic fragility analysis
The seismic performance of PSBCs and CPBCs provides a basis for the time-varying seismic fragility analysis. The comparison of time-varying seismic fragility analysis between CPBCs and PSBCs is subsequently studied. Seismic fragility is usually defined as a probability function that structure or component exceeds its a certain ultimate condition under given seismic intensity: where, D is the seismic demand; C is the bearing capacity; I M is the seismic intensity parameter; μ C and μ D are the mean values of the bearing capacity and structure seismic demand respectively, β C and β D are the logarithmic standard deviations of the bearing capacity and structure seismic demand respectively. The PGA is selected as the seismic intensity parameter, denoted as I M , √ 2 D + 2 C is 0.5; Ф(·) is the standard normal accumulation distribution function.
A linear correlation between seismic demand (D) and seismic intensity parameter (I M ) on logarithmic scale is usually used, and then seismic demand can be expressed as a function of seismic intensity parameter: where a and b are the coefficients obtained from the structural response simulations under earthquake lading. Therefore, the quantitative formula of conditional failure probability (exceeding probability) can be obtained as:

Ground motion selection
According to the study of Kashani et al. 2017, the nonlinear dynamic response of reinforced concrete columns is significantly affected by different ground motion types. In this paper, ten earthquakes are selected from PEER based on the local site conditions and natural vibration characteristics of the structure, as shown in Table 2. Based on these actual ground motion records and Eq. (11), 10 groups of 150 ground motions are randomly generated in the range of 0.01 g-1.0 g.
where a g (i) (t) is the ground motion record after the first amplitude modulation; a(t) is the original actual ground motion record, and k i is the amplitude modulation coefficient.

Damage index
Damage index is to evaluate the damage state of structures under earthquake action, and the definition of damage index is the basis of seismic fragility analysis of structures. Most damage indexes are converted based on displacement evolution, commonly used damage indexes include maximum curvature, drift ratio, displacement-ductility ratio, curvature ductility, etc. Based on the relevant references (Afsar Dizaj and Kashani 2020; Ebrahim Afsar Dizaj 2022; Hwang et al. 2001), the displacement-ductility ratio can better reflect the mechanical properties of the isobaric bending members of the pier. Therefore, the displacement-ductility ratio is adopted to define the damage index of the bridge piers: where, μ d denotes the displacement-ductility ratio (%), Δ is the relative displacement of the column top under seismic conditions (mm), Δ cy1 is the relative displacement of the column top when the steel bar of the column bottom section yields for the first time (mm).
Seismic damage can be divided into four stages: slight damage, moderate damage, serious damage and complete damage, the corresponding damage indexes of the four damage stages are the displacement-ductility ratio of the steel bar for the first yield time (μ cy1 ), the displacement-ductility ratio of the section equivalent yield (μ cy ), the displacement ductility ratio when the protecting layer strain of the bridge column is 0.004, and the maximum displacement Hulverstone drive pumping station 0.14 7 ductility ratio (μ c4 ), and the maximum displacement ductility ratio (μ cmax ). The definition of the damage state of the columns by the displacement-ductility ratio is shown in Table 3. In order to obtain the damage index, the section moment-curvature is analyzed. Under offshore environments, the RC bridge columns in the service period are heavily affected by chloride ion erosion, and the mechanical properties of the materials will degrade, which can influence the moment-curvature change of the column section. The column moment-curvature curves under different service periods are shown in Fig. 7. In the whole life cycle, the mechanical properties of the reinforced steel are decreased due to the corrosion of the steel bar. The slope degradation rate of PSBCs is greater than that of CPBCs, and the ultimate curvature of PSBCs decreases more obviously with the extension of bridge service time due to the effects of chloride ion erosion. The equivalent and ultimate bending moments of CPBCs and PSBCs decreased by 19%, and 22% and 30%, and 39% respectively when the columns reached their service life.
After the moment-curvature analysis, the displacement-ductility ratio can be calculated as follows: where, Δ cy is the relative displacement of the column top when the column section yields equivalently (mm); Δ c4 is the relative displacement of the column top when the strain of concrete for column protection is 0.004 (mm), Δ p4 is the ideal elastic-plastic displacement (mm), θ p4 is the permissible angle; ϕ y is the equivalent yield curvature of reinforcements; ϕ y` is the first yield curvature of reinforcements; L is the height of the cantilever; L p is the length of the equivalent plastic hinge region (mm). Considering the service environment of the investigated columns and the related parameters in Table 1, the displacement-ductility ratio can be obtained. The time-varying damage indexes of CPBCs and PSBCs are shown in Table 4. In the whole life cycle, the displacement of the column top of CPBCs and PSBCs decrease with the extension of the service time under four damage damages; under the slight damage stage, the damage index remains unchanged, under the moderate damage, severe damage and complete damage stages, the damage index of CPBCs increased with the extension of service time, and the damage index of PSBCs decreased with the extension of service time.

Time-variant fragility analysis
Based on the 150 seismic waves obtained by amplitude modulation, the logarithmic linear regression analysis are executed by using the 150 relative displacement-ductility ratios. Then, the probabilistic seismic demand model between seismic demand (D) and seismic intensity parameter (I M ) is obtained, as shown in Fig. 8. Then the exceeding probability under different damage states in the whole life cycle of the column can be calculated, the time-varying vulnerability curve can be drawn.
In the whole life cycle, the time-variant fragility surfaces of CPBCs and PSBCs are shown in Figs. 9 and 10. The comparison indicates that under the four damage stages, the exceeding probability of PSBCs is higher than that of CPBCs. Under the same stages, the growth rate of the exceeding probability of PSBCs with the extension of service time is greater than that of CPBCs.
In order to directly compare the exceeding probability of PSBCs and CPBCs under different PGAs in the whole life cycle, the time-varying fragility curve and the exceeding probability difference under the four damage states are drawn, as shown in Figs. 11 and 12, respectively.
The exceeding probability curve of CPBCs and PSBCs under the four damage states are shown in Fig. 11. It can be seen that the exceeding probability of PSBCs is always greater than that of CPBCs in the whole life cycle. When the designed service life is reached, the maximum exceeding probabilities of PSBCs and CPBCs are 99.6% and 95.7% under the slight damage stage, the exceeding probability of CPBCs and PSBCs were 0.7% and 4.1% higher than that of the completed bridge, respectively. The maximum exceeding probability of CPBCs and PSBCs were 97.2% and 89.1% in the moderate damage stage, which were 6.5% and 7.2% higher than those in bridge completion, respectively. The maximum exceeding probability of CPBCs and PSBCs was 82.2% and 28.4%, which were 17.3% and 4.8% higher than that of the bridge completed. When the bridge was completely destroyed, the maximum exceeding probability of CPBCs and PSBCs were 25.1% and 2.8%, which increased by 75.6% and 53.6%, compared to the bridge completed, respectively. In the four damage states, the exceeding probability of CPBCs and PSBCs increases with the extension of bridge service time and the increase of PGA. The initial corrosion time of the first row of CPBCs longitudinal reinforcements is 22 years, and that of the second row longitudinal reinforcements -s 50 years. The damage of the CPBCs bridge column is small in 0-25 years, due to the discontinuity between segments, the corrosion time in PSBCs is earlier than that in CPBCs, the first row of ED bars at the PSBCs began to rust in the 8th year, and the second row began to rust in the 14th year. The exceeding probability of PSBCs increased rapidly with the extension of the service time of the bridge. Taking the moderate damage with PGA = 0.5 g as an example, compared with that of the bridge when it has been in service for 25, 50, 75 and 100 years, the exceeding probability of CPBCs increased by 1.25%, 8%, 18% and 33%, and the exceeding probability of PSBCs increased by 5%, 17%, 28% and 46%. Figure 12 shows the exceeding probability difference between CPBCs and PSBCs under four damage states. In the four damage conditions, when PGA is less than 0.3 g, the exceeding probability difference is small. With the increase in PGA, the exceeding probability difference reached the maximum value around PGA = 0.6 g, and the maximum exceeding probability difference was approximately 32%. When PGA = 1.0 g, the exceeding probability difference gradually decreased to approximately 10%. In the severe damage and complete damage condition, the exceeding probability difference increases all the time and reaches the maximum value around PGA = 1.0 g. In the severe damage condition, the exceeding probability difference reaches 54%, and in the complete damage condition, the exceeding probability difference reaches 22%. Supposing that the vulnerability curve follows a logarithmic positive distribution, linear regression analysis was carried out for different exceeding probabilities of PGA to calculate the median PGA, which is defined as the PGA value corresponding to exceeding 50% exceeding probability of specified damage state. The time-varying damage index of the column in different damage states is taken as the mean value of the structural seismic capacity μ C replacing the mean value of the structural seismic demand in Eq. T im e /a Fig. 9 CPBCs time-varying fragility surface the completion of the bridge. Taking the moderate damage state as an example, the median PGA at 50, 75 and 100 years of CPBCs are reduced by approximately 3%, 7% and 12%, respectively, compared with that at the completion of the bridge; the corrosion time of the first row of ED bars of PSBCs is approximately 8 years, while the corrosion time of the second row of ED bars is approximately 14th year, which is far earlier than that of the reinforcement in CPBCs, the durability damage of PSBCs is more serious than that of CPBCs, the median PGA of PSBCs after 0, 25, 50, 75 and 100 years of service are approximately 16%, 18%, 21%, 22% and 24% lower than the corresponding value of CPBCs, respectively.

Conclusions
Based on a comprehensive comparative study of the time-varying seismic fragility analysis of the PSBCs and CPBCs over the whole life cycle, the main conclusions are as follows: (1) In the whole life cycle, considering the influence of chloride ion erosion, the diameter, yield strength and ultimate strength of the reinforcement decrease with the extension of the service time. After 100 years of service, the diameter, yield strength and ultimate strength of the CPBCs reinforcement are reduced by 11%, 10% and 14%, respectively; the diameter, yield strength and ultimate strength of the PSBCs are reduced by 32%, 26% and 35%, respectively. (2) PSBCs have a better self-centering capacity, the residual displacement is smaller, stiffness degradation and plastic damage are reduced under the action of designed ground motion, rare ground motion and great ground motion. The seismic response of PSBCs is significantly lower than that of CPBCs. Take the great ground motion for an example, the maximum displacement of PSBCs is 14% larger than that of CPBCs, the residual displacement is 87% smaller than that of CPBCs, the maximum bending moment is 20% smaller than that of CPBCs, and the maximum curvature is 60% smaller than that of CPBCs. (3) When the bridge is formed, the exceedance probability of PSBCs are similar with that of CPBCs in the four states, and the difference in fragility is small. With the aggravation of the damage state, the exceeding probability decreases gradually. When the damage state was relatively light, there was a small difference between PSBCs and CPBCs exceeding probability. When the damage state was severe, the exceeding probability of PSBC was greater than that of MR due to the discontinuity between PSBCs segments.  (4) In the whole life cycle, the PGA median value of CPBCs and PSBCs decreases with the extension of bridge service time and increases with the aggravation of the damage state. The PGA median value of PSBCs is less than that of CPBCs, and the durability damage of PSBCs is more serious than that of CPBCs. Taking the moderate damage condition as an example, the median PGA of PSBCs is 6%, 18%, 21%, 22% and 24% lower than the corresponding median PGA of CPBCs when the column has been in service for 0, 25, 50, 75 and 100 years.  The comprehensive seismic performance of PSBCs is weaker than that of CPBCs, which is not conducive to popularization and application in moderate-and high -intensity areas. In the follow-up, the influence of adding high-performance materials such as highstrength steel strands and UHPC on the time-varying seismic vulnerability of PSBC should be considered. At the same time, it is also necessary to further study the impact of bridge maintenance on the seismic performance and time-varying seismic vulnerability of PSBCs.