Analysis on the Time-varying Fragility of Offshore Concrete Bridge

For offshore bridges, the most prominent problem in the whole life cycle is that it is in an earthquake prone zone and an offshore corrosion environment at the same time. A nonlinear dynamic analysis model is set up for an offshore multi-span and continuous rigid frame bridge based on the OpenSEES platform. The fragility surface of the bridge pier, bearing, bridge platform and system are established by selecting a reasonable damage constitutive model of the material durability and a damage index analysis that studies the damage of the bridge durability to time-varying seismic fragility of bridge components and the system of the whole life cycle in offshore environment. The results show that: the durability damage will lead to a constant decline in seismic capacity of the pier, and an increase of the seismic demand under earthquake action as well as the probability to reach the ultimate failure state; compared to high piers, a low pier is more vulnerable to the offshore corrosion environment; the seismic fragility of bridge platform is higher than that of simply bearing, and the influence of offshore corrosion on environment is relatively large. With the prolongation of service period, the effect of durability damage on the seismic fragility of bridge system cannot be ignored in the coastal environment and it is necessary to make a reasonable evaluation on the seismic fragility of bridge structure during the whole life period.


INTRODUCTION
So far, the offshore and cross sea bridges have been widely built around the world, such as the Ming Shi channel bridge in Japan, the Waal bridge in Netherland, and the Oakland Harbour Bridge in New Zealand. With a coastline of 18,000 km, China also has carried out the construction of offshore and cross sea bridges so as to promote the economic development of offshore areas, to meet the needs of offshore resources exploration and to maintain maritime sovereignty (Wang et al. 2019;Zhou and Wang 2018 Korea, September 17 -21, 2019 consequent problem is the corrosion of concrete structures under the offshore environment. For the Offshore Bridge, the special geographical environment will seriously corrode the bridge structure material, and make its mechanical properties degenerate, and the most prominent problem is that many bridges are in both the offshore corrosion environment and the earthquake multiple zones. The existing studies (Choe et al. 2009) show that: as the service time of the bridge extends, the concrete carbonization and chloride ion erosion effect will cause durability damage to the bridge structure, and then lead to degradation of the seismic performance.
Seismic fragility analysis is one of the main methods to evaluate seismic performance of the offshore bridges in the whole life cycle. Scholars at home and abroad have made a lot of research achievements. Considering the degradation effect of chloride ion erosion on the properties of reinforcing steel bars, and by analyzing the seismic fragility of a two-span bridge, (Choe et al. 2008) conclude that the corrosion of reinforcing steel bars will have a certain effect on the seismic performance of concrete bridges. A new intensity measure of earthquakes for probabilistic seismic analysis is presented for skewed highway bridges by . (Andre et al. 2015) concerns the development of a new structural robustness definition, and structural robustness and structural fragility indices. (Salimi and Yazdani 2018) have studied that the reliability-based analysis of nonlinear structures using the analytical fragility curves are excited by random earthquake loads. A hybrid fiber reinforced polymer/reinforced concrete bridge was designed and constructed in Texas by (Ziehl et al 2009), which was unique in several respects. In addition, the bid process and results of intermittent live load evaluations that have been conducted over a period of approximately 2 years are presented. The incremental nonlinear dynamic analysis is used to evaluate the seismic performance of steel moment frame structures by (Khorami et al. 2017). (Ghosh and Padgett 2010) proposed a two-model of seismic fragility parameters to discuss the effect of chloride ion erosion on the time variation of bridge and the influence of the deterioration of component performance on seismic fragility of bridges subjected to chloride attack. (Jeon et al. 2017) suggest that the earthquake incidence angle more significantly affects the seismic demand and fragilities of the integral bridge platform bridge than the skewed bridge platform bridge. (Waseem et al. 2017) present seismic vulnerability assessment of three real case simply bearing multi-span reinforced concrete bridges commonly found in northern Pakistan, having one, two and three bents with circular piers. (Simon et al. 2010) take steel corrosion and protective concrete cracking as variables to establish the no damage model, steel corrosion model, protective concrete failure model and reinforcement corrosion and protective concrete failure model of a single pier bridge based on the OpenSEES program to analyze the effect of reinforcement corrosion and protective concrete failure on the fragility of concrete bridge. (Alipour et al. 2011) study the life-cycle performance and cost of reinforced concrete highway bridges subjected to earthquake ground motions when they are continuously exposed to the attack of chloride ions, and provides a multi-hazard framework that will achieve more realistic performance and cost estimates. (Cui et al. 2018) present an improved reinforced concrete reinforcing steel bar deterioration model that incorporates pitting corrosion and considers the change in after-cracking corrosion rate to assess the time-dependent seismic fragility of RC  Korea, September 17 -21, 2019 bridge substructures in marine environments. The calculated time-dependent fragility curves indicate that there is a nonlinear accelerated growth of RC column vulnerability along the service life of highway bridges, especially after twenty-five years' exposure to chlorides. (Deng et al. 2018) reveal that the corrosion-induced deterioration of strain penetration and rebar yield strength significantly increase the seismic fragility of the corroded MSSS bridge.
To sum up, with regard to the effect of steel corrosion on seismic fragility of bridges, relevant research results have been obtained at home and abroad. However, the traditional research often ignores the problem of seismic performance degradation of bridge structures during the whole life cycle. As a result, some bridges cannot reach the design service life and need to be repaired and strengthened to maintain their normal function, thus leading to a lot of economic losses.

THE ESTABLISHMENT OF NONLINEAR FINITE ELEMENT MODEL BASED ON OPENSEES
The OpenSEES analysis platform can be used for structural modal analysis, section analysis, static linear elastic analysis, dynamic nonlinear analysis, and the sensitivity and reliability analysis of structural systems in earthquake (Cui et al. 2018;Deng et al. 2018;Chung 2007). In this paper, a finite element model of bridge is established based on OpenSEES platform.
In this paper, the bridge is a 6 span (6 × 60m = 360 m) prestressed concrete rigid frame continuous girder bridge in which 2 # and 3 # piers are fixed piers, while 1 # , 4 # and 5 # piers are simply-bearing ones. The seismic fortification intensity in the area where the bridge is located is 7 degree, and the earthquake is divided into the first group and the site soil is the class II site. The facade arrangement is shown in Fig. 1(a). According to the soil category of the bridge site, seismic waves are selected from the PEER ground motion database. Considering the uncertainty of the earthquake and structural damage indexes, the seismic fragility analysis is established and the nonlinear finite element modeling of this example is completed.
The deck is one box single chamber box section, and the Elastic Beam Column unit, the fiber element based on the flexibility method-nonlinear Beam Column unit, the nonlinear connection unit, and zero-length element which are used to simulate the deck, the nonlinear characteristics of the pier, the bridge platform ball bearing and bridge platform separately. In addition, the area of deck is A = 9.5 m 2 , Young's modulus of elasticity of deck concrete (C50) is E = 3.45×10 4 MPa, poisson ratio is μ = 0.2, torsional inertia moment of deck section is J = 25.8 m 4 , bending moment of inertia of cross section in z-axis and y-axis direction are I z = 14.3 m 4 and I y = 82.4 m 4 , as shown in Fig. 1(b); the section of pier is shown in Fig. 1(c); in the Fig. 1(d), 1 is lower plate, 2 is spherical F4 Plate,3 is sealed skirt,4 is mid-seat plate, 5 is planar F4 plate,6 is upper slide plate and 7 is upper seat plate and bridge abutment model as shown in Fig. 1(e). The ductility of the pier is mainly reflected by plastic rotation capacity in the plastic hinge of the pier. The concrete in the core area has a particularly higher ultimate compressive strain than the unconstrained concrete before the failure of the compression zone, which can ensure the ductility required by the structure (Toghroli et al. 2016;Mohammadhassani et al. 2013;Xie 2018). Therefore, it is necessary to separate the protective concrete from the core concrete. Unconstrained and constrained concrete materials are simulated by using the Concrete 01 model as shown in Fig. 2, and the stress-strain relationship curve is shown in Fig. 3. And the related parameters for the calculating of stress and strain are shown in Eqs. (1)-(4).
In the formulas, f cc is the axial compressive strength of concrete in core area, and f' cc is the axial compressive strength of unconstrained concrete. f c0 is axial compressive strength of concrete, ε cc is axial compressive strain of concrete in core area, and ε c0 is axial compressive strain of concrete, which is generally -0.002, λ V is stirrup eigenvalue, d is volume radio of reinforcement, which is calculated by the lipid of stirrups, and f yh is yield strength of stirrups. ε cu is ultimate compressive strain of confined concrete, which is generally -0.004, ε su is strain of stirrups under maximum tensile stress, which is generally 0.09, and ρ s is volume reinforcement ratio of stirrups. In the study of existing durability of concrete, carbonation depth is used as a parameter, but the effect of its size in structural section cannot be taken into consideration if putting the depth of carbonization as a parameter of carbonization to concrete performance. In this paper, the carbonation rate (Mohammadhassani et al. 2014;Khanouki 2016) is chosen as the calculation parameter, as shown in Fig. 4, and the calculation of related parameters (Atiş 2003) are shown in Eqs. (5)-(12). And the peak stress, peak strain, and elastic modulus of concrete in the life cycle are shown in Figs In the formulas, x c (mm),t and k ( mm / t ) are the depth, time and coefficient of concrete carbonization respectively. K CO2 is the influence coefficient for concentration of CO 2 , K 1 is the influence coefficient of carbonization position, K kt is the influence coefficient of concrete pouring and maintenance, K ks is the influence coefficient for working stress, K F is the substitution coefficient of flyash, T (℃) is the temperature of concrete, RH is the environmental relative humidity, f cuk (MPa) is the compressive strength of concrete cube, F is the weight ratio of flyash, S is carbonization rate, A c (m 2 ) is the carbonization area and A (m 2 ) is total area of cross section, ζ cp , ε cp , ε cu and E c are peak stress, peak strain, limit strain and elastic modulus of carbonated concrete respectively, also the ζ p , ε p , ε u and E are peak stress, peak strain, limit strain and elastic modulus of the initial concrete and μ is poisson ratio. As shown in Figs. 5-7, we can know that with the increase of service time, the peak stress increases to a certain extent and varies greatly; the elastic modulus increases slightly; and the peak strain decreases slightly for both the C50 and C40 concrete, after carbonization. In addition, as the mechanical properties of C50 concrete becomes better, the rate of carbonization of C40 concrete is higher than that of C50 concrete.

Constitutive relation of reinforcement
The types of longitudinal stirrups and stirrups are HRB335 and R235, whose diameters are 32 mm and 16 mm, and the thickness of protective layer is 0.09 m. In

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 -21, 2019 addition, the location and number of longitudinal reinforcements are shown in Fig. 4 and for 1 # pier, the spacing of stirrups in the range of 7 cm -157 cm, 157 cm -757 cm, 757 cm -968 cm from pier top and 120 cm downward from pier bottom are 10 cm, 20 cm, 10 cm and 40 cm respectively; for 4 # pier, the spacing of stirrups in the range of 7 cm -157 cm, 157 cm -697 cm, 697 cm -917 cm from pier top and 120 cm downward from pier bottom are 10 cm, 20 cm, 10 cm and 40 cm respectively; for 5 # pier, the spacing of stirrups in the range of 7 cm -157 cm, 157 cm -1437 cm, 1437 cm -1655 cm from pier top and 120 cm downward from pier bottom are 10 cm, 20 cm, 10 cm and 40 cm respectively; for 2 # pier, the spacing of stirrups in the range of 7 cm -157 cm, 157 cm -3437 cm, 3437 cm -3644 cm from pier top and 120 cm downward from pier bottom are 10 cm, 20 cm, 10 cm and 40 cm respectively; as for 3 # pier, the spacing of stirrups in the range of 7 cm -157 cm, 157 cm -3297 cm, 3297 cm -3507 cm from pier top and 120 cm downward from pier bottom are 10 cm, 20 cm, 10 cm and 40 cm respectively.
The constitutive relation model of reinforcement adopts the double line reinforcement model-the Steel 01 model as shown in Fig. 8. On the basis of the corrected Giuffré-Menegotto-Pinto reinforcement model, the model can consider the two way Bauschinger effect and isotropic enhancement effect. The parameter values of steel material model are shown in Table 1.   Korea, September 17 -21, 2019 structures (CECS220:2007) gives the estimation formula of the initial corrosion time, the corrosion expansion time and the corrosion rate of reinforcing steel bar in the corrosive environment. The initial corrosion time of reinforcing steel bar t i can be estimated by Eq. (13): In the formula, t i is the accumulation time of the chloride ion concentration on the concrete surface to reach the stable value; the initial corrosion time of reinforcing steel bar can be estimated by Eq. (14) when the time dependence of the chloride diffusion coefficient is not taken into consideration (Seo and Rogers 2017;Duracrete 2000): In the formula, c is the thickness of concrete cover (mm); k is Chloride Erosion coefficient which is calculated according to Eq. (15).  Table 2; k' is the correction factor which can be selected according to Table 3. The calculation results of the initial corrosion time of the reinforcing steel bar in the C40 and C50 concrete bridge piers in the offshore atmosphere are shown in Table 4, according to the environmental conditions of the bridge site.
The correlated calculation of material properties of reinforcing steel bars (longitudinal reinforcement and stirrup) after chloride ion corrosion in its life cycle are shown in Eqs. (17) In the formulas, t cr is rust expansion and cracking time of concrete cover, t c is the time from corrosion of reinforcing steel bars to expansion and cracking of protective coat, δ cr (mm) is critical corrosion depth of reinforcement bars when the protective layer The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 -21, 2019 cracks, c (mm) is thickness of protective layer, d (mm) is diameter of reinforcing steel bar, f cuk (MPa) is compressive strength of concrete, λ cl is average annual corrosion rate of reinforcement bars before cracking of protective layer, i (μA/cm 2 ) is corrosion current density of reinforcement bars, m cl is local environmental coefficient, T ( ℃ ) is temperature of reinforcement bar, M sl (kg/m 3 ) is chloride ion concentration on reinforcing steel bar surface, ρ (KΩ·cm) is resistivity of concrete, M so (kg/m 3 ) is chloride ion content in concrete preparation, k ρ is coefficient, M cl μ (kg/m 3 ) is average chloride ion concentration in concrete protective layer, λ cll is average corrosion rate of reinforcement bar after corrosion expansion and cracking of protective layer, when λ cll < λ cl , λ cll = 1.8 λ cl , f yc and E sc are the yield strength and modulus of elasticity after carbonization, f y and E s are the yield strength and modulus of elasticity for initial concrete.
According to the Eqs. (17)- (26), we can know corrosion rate, diameter, modulus of elasticity and yield strength of longitudinal reinforcement and stirrup for C40 and C50 concrete, in order to save space, we only give the pictures of diameter and modulus of elasticity, as shown in Figs. 9-10. C50 and C40 concrete both decrease with the increase of service time.
In order to simplify the calculation, the corrosion cracking time of the protective layer is taken as the critical life of the concrete failure of the protective layer (Maaddawy and Soudki 2007;Zhang et al. 2010). Therefore, the effect of concrete protection layer on bridge pier is no longer considered from the bridge full life cycle of 30.39 years when the seismic fragility analysis is carried out for example bridges. , μ d is the relative displacement ductility ratio of the pier, Δ is the maximum relative displacement of pier top in seismic response analysis of piers and Δ cy1 is the relative displacement of the pier top of the reinforcing steel bar for the first yield in this formula.
In this paper, the connection between the 2 # , 3 # piers and the deck in the bridge is the consolidation, which regards the 2 # and 3 # piers as rigid piers and assumes that the counter bend point is located at the midpoint of the pier when the damage index is calculated. The calculated damage index of each pier is shown in Table 5. 4.2 Analysis on damage index of bearing Relative displacement of shear strain and displacement ductility are more able to reflect the mechanical properties of the bearing in practical engineering. Generally, the relative displacement is used as the damage index of bearing in the present study, and the bearing damage index is commonly used in existing studies as listed in Table 6. The type of bearing used for example bridge is the spherical bearing resisting to marine atmospheric corrosion that belongs to the movable steel bearing. Therefore, the bearing damage index given by Bryant to analyze the seismic fragility of the bearing is adopted in this paper.

Analysis on damage index of bridge platform
There are few studies focusing on the damage state of bridge platform and there is no uniform method to quantify the damage index of bridge platform at present. The establishment of injury indicators proposed by scholars in various countries is shown in Table 7. In this paper, the relative displacement is used as an index to quantify the seismic damage of bridge platform, and the seismic fragility of bridge platform is analyzed by the bridge platform damage index defined by (Murzewski 2001).

Damage index and uncertainty of different bridge components
The bending moment curvature analysis of bridge piers is carried out by XTRACT (Fu et al. 2016) software to determine the failure state of the bridge's different components and to quantify its damage index. 150 seismic waves are generated by amplitude modulation. The uncertainties of seismic and structural damage indexes are taken into consideration to analyze the damage index S c and uncertainty β c in different damage states of each member under a completion state, as shown in Table 8.

ANALYSIS ON TIME-VARYING FRAGILITY
This paper considers the effect of bridge pier concrete carbonization and steel corrosion on bridge structure dynamic response during service time, in spite of the performance degradation of other components such as deck, bearing and bridge platform. The time-varying effect of the bridge fragility is introduced by modifying the constitutive relation of concrete and reinforcement in the finite element model of the bridge and the ratio of the confinement strength of the stirrup to the concrete in the core area ‗k'.
The key of non-linear problems lies in the establishment of material nonlinearity and the non-linear simulation of bridge system in finite element analysis software, that is, the establishment of non-linear elements. The establishment of material nonlinearity includes the constitutive relationship of concrete and reinforcing steel bar, which have been introduced in chapter 3. As for the establishment of non-linear element, we use -nonlinear Beam Column element‖ to establish the pier to achieve the non-linear simulation, and the command is -lement nonlinear Beam Column $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag‖. And in this command, $eleTag is unique element object tag, $iNode and $jNode are the start and end node respectively. $numIntgrPts is the number of Gauss-Lobatto integration points along the element,

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 -21, 2019 $secTag is identifier for previously-defined section object and $transfTag is identifier for previously-defined coordinate-transformation (CrdTransf) object.
According to this, we establish the nonlinear finite element model of bridge structure by OpenSEES platform, and the seismic fragility curves of components and systems are calculated respectively for 20, 40, 60, 80 and 100 years by inputting the seismic waves selected for nonlinear dynamic analysis and using the functional formula for seismic fragility as the Eq. (27) which uses the damage index parameters in Table 8. And the influence of service time on seismic fragility of offshore bridges is also analyzed.
5.1 Time-varying fragility of pier In order to describe the seismic fragility of concrete beam bridge in offshore environment during the whole life span more intuitively, this paper compares and analyses the fragility curves of pier during service period, and the seismic variation surfaces of 5 piers under four damage conditions are given respectively, the fragility laws of 1 # , 4 # , 5 # and 2 # , 3 # piers are basically the same, so only the curves of 1 # , 2 # piers are given in order to save space, as shown in Figs. 11-12. It is obtained from Figs. 11-12 that in the 100-year service period of the bridge, the seismic fragility of the five piers under the four failure states increases along with the earthquake intensity and the service life of the bridge. The exceeding probability of 1 # pier after 100 years' service under the slight damage, medium damage, serious damage as well as the complete collapse can be maximized by 23%, 21%, 20%, and 17% respectively. Compared with the completion state, the trend of 4 # piers is similar to 1 # pier. The exceeding probability of 5 # pier after 100 years' service under the same conditions can be maximized by 15%, 16%, 15%, 7% respectively. Compared with the completion state, the trend of 2 # and 3 # piers are similar to 5 # pier. In the service period, the probability of the 5 piers to surpass all types of damage states are increased with the erosion of chloride ions in the offshore environment and the carbonization of concrete. Seismic fragility of 1 # and 4 # pier are more susceptible to offshore environment compared with the 2 # , 3 # and 5 # piers With the extension of service time, taking the simply borne pier 1 # as an example, the exceeding probability of minor damage to the 1 # pier during the 100 years' service period is not less than 97%, the exceeding probability of medium damage are 89%, 90%, 92%, 95%, 98% and 100% respectively, the exceeding probability of serious damage are 82%, 82%, 86%, 89%, 93% and 96% respectively, and the exceeding probability of complete collapse are 21%, 22%, 25%, 28%, 31% and 31% respectively when SA is 0.6g; the exceeding probability of minor damage of 3# rigid frame pier at service time of 0 and 100 years are 10% and 13% respectively, the exceeding probability of medium damage are 10% and 15% respectively, the exceeding probability of serious damage are 9% and 13% respectively, and the exceeding probability of complete collapse is less than 1%. with the extension of service time, the The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 -21, 2019 exceeding probability of all the piers under different failure states increases.
According to the results mentioned above, it is found that the seismic fragility of 1 # and 4 # bridge piers are more vulnerable to the impact of the offshore environment compared with 2 # , 3 # and 5 # piers. The exceeding probability of 1 # , 4 # and 5 # piers under four damage states in the first 20 years is significantly less than that in the latter 80 years for the initial corrosion time of the hoop reinforcement is about 14 years and the initial corrosion time of the longitudinal reinforcement about 19 years, which shows that the mechanical behavior of reinforcement is the main factor to affect the seismic performance of piers. The results show that for the bridge subjected to chloride ion erosion, the actual seismic capacity of the pier will be continuously decreasing with the extension of the service life, while the seismic demand for earthquake action and the probability to reach ultimate failure state will all be continuously increasing.

Time-varying fragility of bearing
The degradation of pier's seismic performance is bound to affect the bearing condition under the earthquake action. In this paper, the fragility curves of the bridge bearings in service period are compared and analyzed, what's more, the fragility laws of 1 # , 5 # and 2 # , 3 # , 4 # bearings are basically the same, so only the curves of 1 # , 2 # bearings are given in order to save space, as shown in Figs. 13-14, so as to analyze the impact of the seismic performance degradation of the pier on the seismic performance of the bearing and to describe the seismic fragility of the bridge bearing in the whole life period directly. It is obtained from Figs. 13-14 that the seismic fragility of five bearings under different damage states is continuously increasing with the increase of the earthquake intensity and service life in the 100-year service period of the bridge. The exceeding probability of 1 # and 5 # bearings under the minor damage, medium damage, serious damage and complete collapse can be increased by 22%, 17%, 17% and 15% respectively after 100 years' service compared with the completion state period; the exceeding probability of 4 # bearing under four damage states can be increased by 20%, 7%, 7% and 2% respectively after 100 years' service compared with the completion state period; the exceeding probability of 2 # bearing under four damage states can be increased by 22%, 12%, 11% and 5% respectively after 100 years' service compared with the completion state period, and the trend of 3 # bearing is similar to the 2 # bearing's. In the period of service, the probability of five bearings to surpass all kinds of damage states increases with the erosion of chloride ion on the pier, and the seismic fragility increase of the 1 # and 5 # bearings is the largest. Therefore, we should pay attention to improving the seismic capacity of bearings in the design of offshore bridges.

Time-varying fragility of abutment
When the displacement between superstructure and pier accumulates to the bridge platform, it will result in a collision between the deck and bridge platform under seismic action. In the present work, the fragility curve of bridge platform during service period is compared and analyzed to describe the change of seismic fragility of bridge platform in the life span of offshore bridges. Taking the left bridge platform as an example, it will show the seismic fragility surface of two bridge platforms, as shown in As shown in Fig. 21, the seismic fragility of the two bridge platforms in each state is continuously increasing with the increase of the earthquake intensity and the service life during the 100-year service period. The exceeding probability of two bridge platforms after 100 years' service under the slight damage, medium damage, serious damage and complete collapse can be maximized by 33%, 25%, 18%, 13% The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 -21, 2019 respectively compared with the completion state. The exceeding probability of two bridge platforms under minor and medium damage during the 100 years' service period is no less than 98%, the exceeding probability under serious damage to bridge platform are 70%, 71%, 78%, 84%, 87% and 87% respectively, and the exceeding probability of complete collapse are 31%, 33%, 38%, 43%, 44% and 45% respectively when SA is 0.6g.

Time-varying fragility of bridge system
By using seismic fragility of components, the fragility assessment of bridge system will overestimate the seismic capacity of bridges, so it is necessary to combine the fragility of components and the system of the bridge to make an accurate evaluation when the fragility of offshore bridges is assessed during the whole life cycle. The fragility curve of bridge in service period is compared and analyzed to directly evaluate the seismic fragility of offshore bridge during the whole life cycle. The first order boundary method is used to obtain the upper and lower limit surface of the seismic fragility of the system under four damage states of minor damage, medium damage, serious damage and complete collapse according to the calculation results of the fragility of the piers, bearings and bridge platforms, as shown in Figs In the formulas, P sys is failure probability of full bridge system, P i is failure probability of the component and m is the total number of components; and the Eq. (28) is the formula for calculating the upper limit value of the fragility curve of bridge system.  As shown in Fig. 22, the upper and lower limit exceeding probability of the system under the minor damage, medium damage, serious damage and complete collapse can be maximized by 20% and 11% respectively after 100 years' service compared with the completion state period; the upper and lower limit exceeding probability of the system under the medium damage can be maximized by 20% and 23% respectively after 100 years' service compared with the completion state period; the upper and lower limit exceeding probability of the system under the serious damage can be maximized by 17% and 22% respectively after 100 years' service compared with the completion state period; the upper and lower limit exceeding probability of the system under the complete collapse can be maximized by 12% and 15% respectively after 100 years' service compared with the completion state period. It can be seen that the influence of the offshore environment on the seismic fragility of bridge system cannot be ignored in the service period, in addition, we can know from Fig. 23 that the fragility of the system is lower than that of any component, that is to say, the exceeding probability of the bridge system is higher than that of any component. Therefore, the exceeding probability of the system cannot be evaluated by the fragility curve of any component, otherwise， the seismic performance of the bridge system will be overestimated.
The upper and lower limits of the system fragility curve are continuously increasing with the increase of the earthquake intensity and the service life under the four damage states of minor damage, medium damage, serious damage and complete collapse in the 100-year service period of the bridge. The actual seismic capacity of the bridge members (pier, bearing and bridge platform) will decrease with the increase of the service life of the bridge, which is mainly influenced by the corrosion of the reinforcing steel bars in the pier and the concrete carbonization on the mechanical properties of the bridge structures.

CONCLUSIONS
The probability of pier to exceed all kinds of damage states during service period is increasing affected by chloride ion erosion and concrete carbonation in the offshore environment, that is, the actual seismic capacity of the pier will continue to decrease, while the seismic demand for seismic action and the probability to reach the limit state of failure will be continuously increasing.
The seismic fragility of short pier is more susceptible to the offshore environment compared with high piers. The exceeding probability of unconsolidated pier under four kinds of damage states is obviously smaller than that before reinforcement corrosion, which shows that the mechanical behavior of reinforcement is the main factor to affect the seismic performance of piers.
The time dependent seismic fragility curve of the bearing shows that the probability of the five bearings exceeding the various damage states during the service period is increasing. The seismic fragility of bearings at the bridge platform increases the most and is more vulnerable to the offshore environment compared to other bearings. Attention should be paid to improving the aseismic capacity of bearing at the bridge platform in the future design of offshore bridges.
The upper and lower limits of the fragility curve of the bridge system are increasing with the increase of the earthquake intensity and the service life under four damage states of minor damage, medium damage, serious damage and complete collapse in the 100-year service period of the bridge, and the impact of the offshore environment on the seismic fragility of the bridge system cannot be ignored. It is necessary to make a reasonable evaluation of the seismic fragility of the bridge in the whole life span by combining the fragility of the components and systems.