Seismic Fragility Assessment of RC Columns Exposed to the Freeze-Thaw Damage

Abstract

Freeze–thaw damage is one of the primary causes deteriorating the seismic resistance of reinforced concrete (RC) structures. This paper proposed a freeze–thaw damage deterioration model for C30 concrete, and it can be employed to study the time-varying seismic performance of aging RC columns. Next, this study developed a seismic fragility analysis framework for deteriorating RC columns considering the effect of freeze–thaw damage. Considering the geometric parameters of the case-study bridge, the deterioration characteristics of material, and the uncertainties involved in structural modeling and ground motions, a probabilistic seismic fragility analysis on aging RC columns was conducted. The results indicate that the influence of freeze–thaw damage cannot be ignored in studying the seismic performance of aging RC structures. The seismic fragilities of deteriorating RC columns shown a nonlinear increase trend as the increased of freeze–thaw cycles and severity of the damage state. In the early stage of freeze–thaw cycles, the seismic fragilities of RC columns increased slowly. However, the closer to the later stage of freeze–thaw cycles, the more significant of the increase in the seismic fragilities of the columns.

1. Introduction

Effect of freeze–thaw damage on the seismic behavior of RC structures has attracted an increasing attention. In the northern coastal regions of China, there are numerous cross-sea bridges with RC structures. These regions have long and cold winters, with average temperature below minus 6 degrees, relatively heavy snowfall, and deep snow. Therefore, these bridges are prone to freeze–thaw cycles, which greatly aggravates the damage to RC piers in seawater [1]. A large amount of seismic damage data [2,3,4] shows that the structures after freeze–thaw damage are more prone to damage from the earthquake excitations, which seriously affects their long-term performance and safe operations. Therefore, it is of great importance to explore the deterioration law of the seismic performances of RC structures subjected to freeze–thaw cycling in the northern coastal regions.

Numerous scholars have conducted many studies regarding the reduction in the mechanical properties of concrete and deterioration of the seismic behavior of structures under freeze–thaw cycles. For example, Yu et al. [5] recommended a concrete deterioration model through the rapid freeze–thaw tests. Si et al. [6] have experimentally and numerically investigated the freeze–thaw damage on the mechanical properties of concrete. In addition, Li et al. [7] studied the impacts of different air contents and water–cement ratios on concrete members through a series of freeze–thaw cycle tests. Xu et al. [8] proposed a bond stress–slip constitutive model of concrete in the marine environments through the freeze–thaw tests and numerical simulations. Moreover, Wang and Petru [9] studied the bonding properties of concrete after the rapid freeze–thaw cycles in the fresh and salt water through the pull-out tests, and they also established a simplified trilinear constitutive model. Gong et al. [10] explored the utilization of a multi-scale macroscopic mechanical damage simulation method regarding the performance of concrete via many freeze–thaw cycling and the silicic acid reaction tests.

Furthermore, Liu et al. [11] studied the seismic vulnerabilities of bridge piers and established a probabilistic seismic demand model through freeze–thaw tests and monitoring data. Yu et al. [12] modified the Drucker-Prager (DP) constitutive model and established a constitutive model for concrete via the freeze–thaw tests. Niu et al. [13] explored the variations in the compressive strength, flexural strength, and the relative dynamic elastic modulus of concrete through the extreme freeze–thaw tests. Although many scholars have experimentally explored the effect of freeze–thaw cycling process on the mechanical properties of concrete and seismic performance of RC structures [1,3,14,15,16,17], the constructed freeze–thaw deterioration models are only obtained through several given test results, which may have certain contingency limitations. In addition, dimensions of the specimens are different, and the testing methods are also varied. These factors would lead to the significant variations of the test results reported in the literature. Therefore, to establish a general freeze–thaw deterioration model is crucial, which is of great importance to the investigations on the seismic performance of deteriorating RC structures.

In this paper, a review of the test results of freeze–thaw damage to concrete by several previous researchers was conducted. Analyses regarding the variation laws of concrete constitutive parameters with different freeze–thaw cycles were performed. Combined with the traditional Mander model, a freeze–thaw damage deterioration model of C30 concrete was suggested, which could be used to investigate freeze–thaw cycling on the seismic performance of RC structures. Moreover, by incorporating both the uncertainties in ground motions and the structural-related parameters, this paper proposed a seismic fragility analysis framework for RC columns exposed to freeze–thaw damage, and the seismic fragility curves were developed.

2. The Proposed Deterioration Model of RC Columns

Freeze–thaw cycling could not only deteriorate the performance of concrete, but also affect the seismic resistance of RC columns. At present, the seismic investigations of RC columns are often carried out via nonlinear time history analysis (NTHA), which is often based on a nonlinear fiber-element model. When establishing the nonlinear finite element (FE) models, it is crucial to construct the constitutive models of the cover concrete, confined concrete, and steel bars, respectively. The test results in [1,18,19] indicated that freeze–thaw cycles have little effect on the mechanical properties of steel bars. Therefore, in this paper, freeze–thaw cycling on the material properties of concrete was mainly investigated, whereas that on the properties of steel bars was ignored.

For those bridges in the northern coastal regions, RC columns are generally located in the fluctuation zone of sea-water level, which is in direct contact with the seawater. Therefore, freeze–thaw cycles mainly affect RC columns and it usually has little impact on the bridge superstructure [20]. In addition, C30 concrete is generally used as the main material in the constructions of the columns of the cross-sea bridges in the northern coastal regions China. Therefore, this paper proposed a deterioration model for C30 concrete under different freeze–thaw cycles. This deterioration model includes the traditional Mander constitutive model of the plain and confined concrete. Finally, the established model is used to explore the deterioration effects on the constitutive properties of concrete caused by freeze–thaw damage on the probabilistic seismic demand and seismic capacity, and seismic fragility estimates of RC columns.

2.1. Review of the Experimental Data

In order to fully consider the influence of the uncertainties of raw materials, specimen size, test process, and other factors on the freeze–thaw test results, this paper selected the representative test results from [10,14,21,22,23] to establish the deterioration model of C30 concrete. The basic parameters of different specimens are given in

Table 1. The design parameters of the specimens.

Literature	Shape	Dimensions (mm)	Water-to-Cement Ratio	Compressive Strength (MPa)	Freeze–Thaw Cycles	Object
Gong et al. [10]	Prism	100 × 100 × 100	0.50	36.85	0, 100, 200, 300	Plain concrete
Zhang et al. [14]	Cylinder	d = 100, h = 200	0.50	29.64	0, 50, 100, 200, 300	Plain concrete
Niu et al. [21]	Prism	100 × 100 × 300	0.43	35.42	0, 50, 100, 150, 200	Plain concrete
Duan et al. [22]	Prism	100 × 100 × 300	0.45	30.26	0, 75, 100, 125, 150	Plain and confined concrete
Sun et al. [23]	Prism	100 × 100 × 400	0.50	30.48	0, 50, 100, 150, 200	Plain concrete

.

As seen from Table 1, the freeze–thaw tests were mainly applied to plain concrete, while the freeze–thaw tests applied to RC specimens were relatively less. Meanwhile, there are some differences in the material parameters, specimen size, and test process used by different scholars, which would inevitably lead to the variations in the freeze–thaw test results. As a consequence, it is significant to study the variations of these test results in constructing a more accurate deterioration model for RC columns. Thus, the collected freeze–thaw test results were statistically analyzed and the variation rules of the key constitutive parameters of concrete under different freeze–thaw cycles were studied. Furthermore, combined with the traditional Mander model, the deterioration model was established, which provides a necessary time-varying constitutive model for the subsequent seismic fragility analysis of the bridge.

2.2. Freeze–Thaw Test Results of Plain Concrete

2.2.1. Variation Law of the Peak Stress

The statistical parameters and experimental data of the peak stress of plain concrete listed in Table 1 are drawn in Figure 1. As seen from Figure 1a, the peak stress exhibited an overall downward trend [6,24,25,26]. When freeze–thaw cycles reached 300, the mean value of the peak stress of C30 concrete decreased by 28.93%. Under different freeze cycles, the peak stress fluctuated greatly. For instance, in the early freeze–thaw cycling stages, the discrepancy was relatively small. However, the closer to the later stages of the freeze–thaw cycling, the greater the discrepancy. The range of the variation coefficient was between 0 and 0.33, indicating the strong discrepancy of the test results. Next, the peak stress parameters were fitted, which is shown in Figure 1b, and the compressive strength of plain concrete can be determined by,

$$f_c\left(N\right)=-0.0368\cdot N+30.52$$

(1)

where N is the number of the freeze–thaw cycles.

2.2.2. Variation Law of the Peak Strain

The statistical parameters and experimental data of the peak strain of plain concrete listed in Table 1 are drawn in Figure 2. As seen from Figure 2a, the peak strain of concrete exhibited an overall upward trend [10,27,28]. As freeze–thaw cycles reached 300, the mean value of the peak strain increased by 1.3 times. Under different freeze–thaw cycles, the peak strain fluctuated greatly. For example, in the early stage of freeze–thaw cycling, the discrepancy was relatively small. However, the discrepancy increased significantly in the middle time period. The variation coefficient range was between 0 and 0.41, suggesting the strong discrepancy of the test results. Similarly, the peak strain parameters were fitted, as shown in Figure 2b. The peak strain of plain concrete can be obtained by,

$${\epsilon }_c\left(N\right)=0.000011\cdot N+0.00192$$

(2)

2.2.3. Variation Law of the Elastic Modulus

The statistical parameters and experimental data the elastic modulus of plain concrete listed in Table 1 are shown in Figure 3. As seen from Figure 3a, the elastic modulus of concrete also exhibited a global downward trend [26,29,30,31]. When freeze–thaw cycles reached 300, the mean value of the elastic modulus of concrete decreases by 16.54%. Under different freeze–thaw cycles, the discrepancy of the test results fluctuated greatly. In the early stages of freeze–thaw cycling, the discrepancy was relatively small. The closer the process to the later freeze–thaw period, the greater the discrepancy. After the calculation, the variation coefficient range of the elastic modulus was between 0 and 0.18. Next, the elastic modulus parameters are fitted, which is shown in Figure 3b. The elastic modulus of plain concrete can be acquired by,

$$E_{\mathrm{c}}\left(N\right)=-22.38·N+2.651\times {10}^4$$

(3)

By analyzing the available experimental data listed in Table 1, the time-varying formulas of plain concrete constitutive parameters were obtained, which lays a good foundation for the establishment of deterioration model and seismic vulnerability analyses of the columns.

2.3. Development of the Proposed Deterioration Model

Mander model is currently widely utilized in the seismic analysis of concrete columns [32]. It is not only applicable to circular members, but can also be well applied to rectangular ones. This model essentially considers the influences of the effective area of the confined concrete, volumetric ratio, spacing and yield strength of stirrups on the mechanical properties of the confined concrete. Many scholars compared their freeze–thaw test results with the traditional Mander model [25,32,33]. The results suggested that the traditional Mander model is consistent well with the test results. In addition, Mander model could also better reflect the stress-strain curve of the whole test process. Considering the practicability of Mander model, freeze–thaw cycles (N) is introduced to build a modified Mander model, as given in Equation (4).

$$\sigma \left(N\right)=\frac{f_{cc}\left(N\right)·X·r\left(N\right)}{r\left(N\right)-1+X^{r\left(N\right)}}$$

(4)

where $\sigma \left(N\right)$ is the concrete stress; $f_{cc}\left(N\right)$ is the compressive strength of the confined concrete; $r\left(N\right)$ is the shape parameter; and $X$ is the strain-related coefficient. These parameters can be determined by,

$$f_{{}_{cc}}\left(N\right)=f_{{}_c}\left(N\right)·\left(-1.254+2.254\sqrt{1+\frac{7.94f_l}{f_c\left(N\right)}}-2·\frac{f_l}{f_c\left(N\right)}\right)$$

(5)

$$X=\frac{\epsilon }{{\epsilon }_{cc}\left(N\right)}$$

(6)

$${\epsilon }_{cc}\left(N\right)={\epsilon }_c\left(N\right)·\left[1+5\left(\frac{f_{cc}\left(N\right)}{f_c\left(N\right)}-1\right)\right]$$

(7)

$$r\left(N\right)=\frac{E_c\left(N\right)}{E_c\left(N\right)-E_{sec}}$$

(8)

$$E_{sec}=\frac{f_{cc}\left(N\right)}{{\epsilon }_{cc}\left(N\right)}$$

(9)

where $f_c\left(N\right)$ is the compressive strength of plain concrete; $f_l$ is the effective confining stress of the transverse reinforcements to concrete; ${\epsilon }_{cc}\left(N\right)$ is the peak strain of the confined concrete; ${\epsilon }_c\left(N\right)$ is the peak strain of plain concrete; $\epsilon$ is the concrete strain; $E_c\left(N\right)$ is the elastic modulus; and $E_{sec}$ is the secant modulus. The established deterioration model is based on the material tests. The constitutive model of plain concrete has been verified. However, there are few constitutive models for the confined concrete subjected to the freeze–thaw damage. Further experimental studies should be carried out in future.

2.3.1. Constitutive Model of Plain Concrete under Freeze–Thaw Cycling

The key parameters of Mander model of plain concrete mainly include the peak stress, peak strain, and shape parameters. The peak stress and peak strain as given in Equations (1) and (2) were obtained as introduced in Section 2.2. In addition, by combining Equations (1)–(3), we can obtain the shape parameter by

$$r\left(N\right)=\frac{-22.38·N+2.651\times {10}^4}{-22.38·N+2.651\times {10}^4-\left(-0.0368\cdot N+30.52\right)/\left(0.000011\cdot N+0.00192\right)}$$

(10)

By substituting Equations (1), (2) and (10) into Equation (4), the time-varying Mander model of plain concrete could be obtained.

2.3.2. Constitutive Model of the Confined Concrete

(1)

Time-varying formula for the peak stress

Based on Equation (1) and the reinforcement information of the components, the peak stress of the confined concrete can be obtained by,

$$f_{{}_{\mathrm{cc}}}\left(N\right)=\left(-0.0368·N+30.52\right)·\left(-1.254+2.254\sqrt{1+\frac{7.94f_l}{-0.0368·N+30.52}}-2·\frac{f_l}{-0.0368·N+30.52}\right)$$

(11)

(2)

Time-varying formula for the peak strain

Based on Equations (1), (2) and (11), the peak strain of the confined concrete can be obtained by,

$${\epsilon }_{cc}\left(N\right)=\left(0.000011·N+0.00192\right)·\left(1+5·\left(k_2-1\right)\right)$$

(12)

where k₂ is the ratio of the peak stress of the confined concrete to that of plain concrete.

(3)

Time-varying equation for the shape parameter

Based on Equations (3), (6) and (7), the shape parameter of the confined concrete can be expressed as,

$$r\left(N\right)=\frac{E_c}{E_c-E_{sec}}=\frac{-22.38·N+2.651\times {10}^4}{\left(-22.38·N+2.651\times {10}^4\right)-f_{cc}/{\epsilon }_{cc}}$$

(13)

By substituting Equations (11)–(13) into Equation (4), the time-varying Mander model of the confined concrete could be obtained. Based on the proposed time-varying constitutive models of the plain and confined concrete, the deterioration model of RC columns could be obtained, which lays the foundation for the seismic fragility analysis of RC columns in the following subsections.

3. Seismic Fragility Theory

Many scholars have studied the seismic fragility of the as-built RC structures [20,34,35,36,37,38]. Seismic fragility function can be generally represented by,

$$\mathrm{Seismic} \mathrm{fragility}=P_f\left[D\ge C|IM\right]=P_f\left[C-D\le 0.0|IM\right]$$

(14)

where D is the seismic demand, C is the seismic capacity, and IM is the seismic intensity measure (IM). Likewise, the time-dependent seismic fragility function, considering the freeze–thaw damage, could be expressed as,

$$\mathrm{Seismic} \mathrm{fragility}=P_f\left[D\left(N\right)\ge C\left(N\right)|IM\right]=P_f\left[C\left(N\right)-D\left(N\right)\le 0.0|IM\right]$$

(15)

Many studies [39,40,41,42,43,44] have shown that, D and C could be assumed to follow the lognormal distributions when analyzing their seismic fragility. Therefore, freeze–thaw cycles could be introduced as a variable to build a new seismic fragility function, as shown in Equation (16).

$$P_f\left(N\right)=\varphi \left(\frac{\ln \left(M_{D|IM}\left(N\right)\right)-\ln \left(M_C\left(N\right)\right)}{\sqrt{{\beta }_{{}_{D|IM}}^2\left(N\right)+{\beta }_{{}_C}^2\left(N\right)}}\right)$$

(16)

where $M_{D|IM}\left(N\right)$ and $M_C\left(N\right)$ represent the mean values of D and C, respectively; ${\beta }_{D|IM}\left(N\right)$ and ${\beta }_C\left(N\right)$ represent the logarithmic standard deviations of D and C under different freeze–thaw circles, respectively. Equation (16) connects the seismic intensity with D and C, as well as the damage states through the probability theory. To simplify the calculation, this paper assumes that D and C are independent from each other [45]. According to [46], the probabilistic seismic demand model (PSDM) of a given column is expressed as,

$$\ln \left({\mu }_{\phi }\right)=\mathrm{a}+\mathrm{b}\cdot \ln \left(\mathrm{PGA}\right)$$

(17)

where a and b are the regression coefficients; and ${\mu }_{\phi }$ is the curvature ductility of the column.

4. Case-Study Analysis

4.1. Bridge Description and FE Modeling

During the service period of RC structures, the mechanical properties of concrete would be deteriorated due to freeze–thaw damage, which may seriously impair their seismic performance [17,26,27]. In order to study the deterioration effects caused by free-thaw damage on C30 concrete, a deterioration model of RC columns was constructed. A typical three-span continuous girder bridge was selected as the example. Figure 4 displays the layout and configuration of the bridge. In this case, C30 concrete was used for RC columns of the bridge.

OpenSEES [38,39,40,42,43] is an efficient nonlinear seismic analysis software, which has the advanced modeling capabilities and contains many material models, elements and algorithms for the seismic assessments of RC structures. Therefore, OpenSEES was utilized to construct the nonlinear FE model of the bridge. The superstructure was simulated by the elastic beam-column elements [38,39,42,43]. RC columns were modeled using the nonlinear beam-column elements [38,39,42,43]. Material model Concrete 04 was employed to simulate the cover and confined concrete, while Steel 02 was used to simulate steel bars. The bearings were all simulated by using the elastomeric bearing (plasticity) elements. Additionally, to simplify the modeling, the pile foundation system was modeled through linear elastic beam-column elements. Moreover, the transverse concrete stoppers were modeled using the hysteretic material and elastic-perfectly plastic gap elements [38,39,42,43]. The behavior of the abutments was simulated by considering the contributions made by the filled soils and piles, according to the method recommended by Caltrans [42,46].

For those bridges in the northern coastal areas of China, deterioration of RC columns is the primary reason causing the significant degradation in their structural resistance [15,17]. Therefore, this paper mainly studied the deterioration impacts caused by freeze–thaw cycling on the columns. To consider the uncertainties, a total of 17 random variables were considered, which are summarized in

Table 2. Statistical data of the considered random variables.

Parameter	Units	Distribution	Mean	Variation Coefficient	Reference
Yield strength of steel	MPa	Lognormal	335	0.07	[46,47]
Ultimate strain of steel	—	Lognormal	0.0017	0.2	[46,47]
Elastic modulus of steel	MPa	Normal	2 × 105	0.2	[48]
Elastic modulus of concrete	MPa	Normal	Equation (3)	0.12	[23,29]
Compressive strength of plain concrete	MPa	Lognormal	Equation (1)	0.15	[49]
Peak strain of plain concrete	—	Lognormal	Equation (2)	0.2	[49]
Compressive strength of confined concrete	MPa	Lognormal	Equation (11)	0.2	[33,49]
Peak strain of confined concrete	—	Lognormal	Equation (12)	0.2	[33,49]
Damping ratio	—	Normal	0.045	0.278	[34]
Deck mass ratios	—	Uniform	1.0	0.058	[34]
Concrete cover depth	mm	Normal	50	0.15	[48]
Bearing shear modulus	MPa	Uniform	1.365	0.3	[34]
Bearing coefficient of friction	MPa	Lognormal	0.36	0.1	[34]
Passive stiffness of abutment	kN/m	Uniform	3.2 × 105	0.25	[49]
Active stiffness of abutment	kN/m	Uniform	7.0 × 104	0.286	[34]
Translational stiffness of foundation	kN/m	Uniform	6.2 × 105	0.29	[49]
Rotational stiffness of foundation	kN·m/rad	Uniform	1.8 × 107	0.289	[49]

.

4.2. Selection of the Seismic Records

Based on the site conditions of the bridge, this paper selected 50 natural seismic records from the PEER Ground Motion Database [50]. Figure 5a displays the response spectra of the selected seismic records. As seen from Figure 5a, the mean value of acceleration spectra of the seismic records was consistent well with the target design response spectra according to [51]. Moreover, selection of the appropriate seismic IM is also critical. Based on several previous studies [52,53], the peak ground acceleration (PGA) is demonstrated to be a sufficient and practical IM. Thus, this study employed PGA as the seismic IM. Figure 5b shows the PGA distributions. As shown in Figure 5b, the selected seismic records covered a wide range of PGA. The moment magnitudes of the records were between 5.7 and 7.2 and their source distances were between 15 and 100 km, respectively.

4.3. Application of the Proposed Deterioration Model

4.3.1. Variation in the Constitutive Parameters

The proposed deterioration model was further applied to the seismic fragility analysis of RC columns of the bridge. Since the FE modeling of RC columns was simulated by using the distributed plasticity fiber-element model, seismic analysis of RC columns required the constitutive parameters of the concrete and steel bars. This paper mainly considered the deterioration effect of freeze–thaw damage on concrete. Figure 6 shows the variations of the peak strain and peak stress of RC columns under different freeze–thaw cycles. As seen from Figure 6, the peak stress and peak strain exhibited different trends as the increased of freeze–thaw cycles. For example, the peak stress decreased, whereas the peak strain increased with the increase of freeze–thaw cycles. Compared to the as-built columns, when freeze–thaw cycles was 150, the peak strain of plain concrete increased by 82.5%, while that of the confined concrete increased by 86.6%. Similarly, the peak stress of plain concrete reduced by 18.2%, whereas the peak stress of the confined concrete reduced by 16.64%. These observations suggested that the variations in the constitutive parameters of concrete due to the freeze–thaw damage should be carefully considered.

4.3.2. Seismic Fragility Analysis Considering the Freeze–Thaw Damage

In this case, 50 FE models of the bridge were generated by employing the uniform design method [38,39,42,46]. For simplicity, this paper only studied the longitudinal curvature ductility demand of the columns, which can be defined as the ratio of the maximum curvature to the curvature at which the outermost tensile bars first reaching the yield strength [33,34,40,42,45,49]. Linear regression analysis was performed by using Equation (17) to obtain the relevant PSDMs of the columns. The results are given in

Table 3. PSDMs of the columns.

Number of the Freeze–Thaw Cycles	PSDM	R2	${\mathit{\beta }}_{\mathit{D}|\mathbf{PGA}}$
0	$\ln \left({\mu }_{\phi }\right)=1.222+0.523·\ln \left(\mathrm{PGA}\right)$	0.797	0.411
50	$\ln \left({\mu }_{\phi }\right)=1.269+0.521·\ln \left(\mathrm{PGA}\right)$	0.782	0.414
100	$\ln \left({\mu }_{\phi }\right)=1.332+0.520·\ln \left(\mathrm{PGA}\right)$	0.773	0.425
150	$\ln \left({\mu }_{\phi }\right)=1.401+0.525·\ln \left(\mathrm{PGA}\right)$	0.769	0.438

. As seen from Table 3, the logarithmic standard deviation of D increased with the freeze–thaw cycles. It increased by 6.57% after 150 freeze–thaw cycles. This means that the deterioration of RC structures due to the freeze–thaw damage may result in a greater uncertainty to the predictive results of the seismic response of the columns, which should be carefully addressed.

Four damage states are defined based on the possible ductility levels of the columns [49], including (i) slight, (ii) moderate, (iii) extensive, and (iv) complete damage states. In specific, (1) the slight damage state is usually defined when steel bars reach the yielding strength; (2) the moderate damage state is defined following the concrete cracking; (3) the extensive damage state is defined when the concrete spalling is observed; and (4) the complete damage state is defined when steel bars are buckled, respectively [49]. The curvature ductility was employed as the damage index (DI). According to the available definitions of the damage states of RC columns in [45,49], the median values of the curvature ductility of the columns with the slight, moderate, extensive, and complete damage states are 1.29, 2.10, 3.52, and 5.24, respectively. In addition, the corresponding dispersion coefficients for these four damage states were assumed to be 0.59, 0.51, 0.64, and 0.65, respectively [45,49].

Figure 7 shows the generated fragility curves of the columns. As seen from Figure 7, the damage probability of the columns exceeded their ductility limit with the increase of freeze–thaw cycles, indicating the significance in considering the freeze–thaw damage on the deterioration of the concrete constitutive properties. In the first 100 freeze–thaw cycles, the growth of failure probability of the columns was relatively slow. Nevertheless, after 100 cycles, the growth of failure probability was relatively significant. For example, as shown in Figure 7c, for the pristine columns, the probability of extensive damage to the columns without freeze–thaw damage under a PGA of 0.6 g was 32.6%. However, after 150 freeze–thaw cycles, the probability of extensive damage exceeded 50%. Likewise, as shown in Figure 7d, compared to the as-built columns, the failure probability increased by 25.4% and 48.7% after 100 and 150 freeze–thaw cycles under a PGA of 1.5 g, respectively.

5. Conclusions

In this paper, the test results available in the literature regarding the freeze–thaw damage to C30 concrete were summarized. Variations in the constitutive parameters of C30 concrete subjected to freeze–thaw cycles were analyzed. The deterioration model of RC columns with respect to freeze–thaw factors was proposed. This deterioration model could be used to study the seismic performance of RC columns in the northern frozen coastal areas of China. By taking a continuous girder bridge as the example, the seismic fragilities of RC columns considering the deterioration effects caused by freeze–thaw damage on the constitutive properties of concrete were performed. The probabilistic seismic demand, seismic capacity, and seismic fragilities of RC columns of the bridge were comprehensively investigated by considering the uncertainties involved in the deterioration of the material properties, geometric dimensions, structural modeling, and ground motions. The results indicate that freeze–thaw damage has significant effects on the constitutive properties of concrete and it should be carefully considered in dealing with the probabilistic seismic demand and capacity, as well as fragility assessment of RC columns. In addition, the seismic fragilities of RC columns tend to exhibit a nonlinear increase trend with the severity of the damage state and the number of freeze–thaw cycles.

Moreover, this study provides new insights into the deterioration effects on the constitutive parameters of concrete caused by freeze–thaw damage, and it also investigates such deterioration effects on the seismic response and vulnerabilities of RC columns comprehensively for the first time. This paper mainly studies the seismic performance of RC columns affected by the freeze–thaw damage, which is significant in the investigations on the seismic performance of RC structures under the influences of multiple factors, such as the composite actions of freeze–thaw cycling and chloride-induced corrosion. Furthermore, in this paper, RC columns are mainly subjected to bending failure, and the shear failure belongs to the brittle failure. This paper does not specifically analyze the influence of shear failure, and it should be further studied in future. The established deterioration model is based on the material tests. The constitutive model of plain concrete has been verified, but relevant experimental studies should be further carried out to fully verify the validation of the constitutive model of the confined concrete in future.