Study on Seismic Collapse Fragility of Corroded Platform Canopies with Different Fortification Intensities in China

Abstract

Twelve reinforced concrete (RC) railway platform canopies were designed for zones with different seismic fortification intensities (SFIs) in accordance with the Code for Seismic Design of Buildings (2024 Edition) GB/T 50011-2010. Numerical models were created in OpenSees for each structure under three conditions: no corrosion, 5% corrosion loss of reinforcement, and 15% corrosion loss of reinforcement, using the Modified Ibarra–Medina–Krawinkler (ModIMK) hysteretic model. Through IDA, seismic collapse fragility was assessed in accordance with the requirements of the Standard for Anti-collapse Design of Building Structures T/CECS 392-2021. The results are: (1) Double-column canopies strongly resist deterioration from reinforcement corrosion. Each structure with different SFIs meets the code’s collapse probability limit under all three corrosion levels when subjected to the maximum considered earthquake (MCE) and the extreme considered earthquake (ECE, an earthquake larger than MCE). (2) When subjected to MCE, Single-column canopies with different SFIs also meet the code’s collapse probability limit under the three corrosion levels. (3) When subjected to ECE, the collapse probability of single-column canopies with 5% corrosion increases compared to uncorroded structures at SFIs ranging from 6 to 8; for SFIs 8.5 and 9, the collapse probability decreases. The structure with SFI 8.5 has the highest risk and does not comply with the code. (4) When subjected to ECE, the collapse probability of the single-column canopy with 15% corrosion increases significantly compared to uncorroded structures at all SFIs. Structures with SFIs ranging from 7.5 to 9 fail to meet code requirements. This paper systematically investigates the collapse fragility of platform canopies with different seismic fortification intensities in China, examining three corrosion states: no corrosion, 5% corrosion, and 15% corrosion. It provides important guidance for the rational design of platform canopies and for analyzing the impact of corrosion levels on their collapse behavior.

1. Introduction

Railway platform canopies are a critical component of the railway system, with their structural safety directly affecting the normal operation of the railway network and passenger safety. Reinforced concrete (RC) railway platform canopies, compared to steel structures, are less prone to vibration and have lower maintenance costs, making them widely used in many small and medium-sized stations. These structures often feature large cantilevered beams and slabs, necessitating simultaneous consideration of horizontal and vertical seismic forces. Under significant seismic loads, they are prone to collapse. As open-air structures, platform canopies are susceptible to corrosion over time, which significantly degrades structural performance. Consequently, investigating the seismic collapse resistance of corroded railway platform canopies holds substantial practical significance.

In recent years, some scholars have investigated the seismic performance of individual reinforced concrete canopy structures through numerical simulations or experiments [1,2,3,4,5]. Others have conducted anti-seismic collapse studies on single reinforced concrete canopy structures [6,7]. However, these structures used for studies were designed according to seismic codes prior to 2024 and did not analyze their performance when structural corrosion occurs. Furthermore, they focused solely on specific canopy structures and seismic fortification intensities (SFIs), neglecting to evaluate seismic collapse resistance in accordance with current collapse codes. There remains a lack of generalized research addressing different canopy types and varying SFIs. Additionally, their numerical models predominantly employ fiber elements and solid elements, making it challenging to accurately simulate the complex damage states that occur during structural collapse.

Numerical models used in structural collapse research must be capable of simulating conditions under severe damage. The Ibarra-Medina-Krawinkler (IMK) model proposed by Ibarra et al. [8] effectively captures the degradation of structural strength and stiffness. Compared to fiber elements and solid elements, it more accurately accounts for phenomena such as reinforcement buckling, reinforcement slippage, stirrup failure, and localized concrete crushing. Consequently, it has been widely applied in earthquake collapse studies. Lignos [9,10] further refined this model, yielding the modified IMK (ModIMK) model. Early research on the IMK model primarily focused on reinforced concrete square columns [11,12]. Recently, Dai [13] and Liu [14,15] extended its application to RC circular columns, enabling the ModIMK model to be used in the collapse analysis of structures incorporating them. Dai [16] also established a ModIMK model for corroded square columns, while Liu [17] created a ModIMK model for corroded circular columns. This enables the use of ModIMK models for performance studies of corroded structures.

Accordingly, this paper aims to investigate the seismic collapse fragility of corroded circular column platform canopy structures in China. To achieve this, six typical single-column and six double-column canopies with SFIs ranging from 6 to 9 degrees were designed according to the Building Seismic Design Code (2024 Edition) GB/T 50011-2010 [18]. Three corrosion scenarios of reinforcing bars—uncorroded, 5% corrosion, and 15% corrosion—were considered. Numerical OpenSees (3.3.0) models based on the ModIMK model were established, and Incremental Dynamic Analysis (IDA) was performed in accordance with the Code for Seismic Collapse-Resistant Design of Building Structures T/CECS 392-2021 [19]. The seismic collapse fragility curves for the corroded platform canopies were ultimately derived, and the collapse probabilities for each structure were analyzed.

2. Platform Canopy Structural Design

Select typical structural forms and dimensions for single-column and double-column canopies using PKPM software (2025R2.3). Next, through iterative optimization, the designs closely approach code minimum requirements. Key control factors are the column axial compression ratio, elastic inter-story drift angle, and member shear compression ratio. Detailed information is provided in

Table 1. Detailed information of the platform canopies designed by PKPM.

Structure Number	Canopy Type	Seismic Fortification Intensity	Column Section	Cantilever Beam Section	Section of Transverse Frame Beam	Concrete Grade
PC-1-6	Single-column canopies	6	450	300 × 600	\	C30
PC-1-7	Single-column canopies	7	500	300 × 600	\	C30
PC-1-7.5	Single-column canopies	7.5	550	300 × 600	\	C30
PC-1-8	Single-column canopies	8	600	300 × 650	\	C35
PC-1-8.5	Single-column canopies	8.5	700	300 × 650	\	C35
PC-1-9	Single-column canopies	9	800	300 × 700	\	C35
PC-2-6	Double-column canopy	6	300	250 × 550	250 × 450	C30
PC-2-7	Double-column canopy	7	350	250 × 550	250 × 450	C30
PC-2-7.5	Double-column canopy	7.5	400	250 × 600	250 × 450	C30
PC-2-8	Double-column canopy	8	450	250 × 600	250 × 500	C35
PC-2-8.5	Double-column canopy	8.5	550	250 × 650	250 × 600	C35
PC-2-9	Double-column canopy	9	650	250 × 650	250 × 600	C40

. The naming format is PC-Canopy Type-SFI: PC is platform canopy, types 1 and 2 are single- and double-column, respectively. For example, PC-2-7 is a double-column canopy with SFI 7.

2.1. Single-Column Canopies

Six single-column canopy designs, based on Weinan West Station on the Ningxi Railway, were developed to investigate seismic collapse fragility. Site classification is Category II, seismic group II, and building category C. SFIs (PGA) include: 6 degrees (0.05 g), 7 degrees (0.10 g), 7.5 degrees (0.15 g), 8 degrees (0.20 g), 8.5 degrees (0.30 g), 9 degrees (0.40 g). Columns are 6 m tall with 4 m cantilevered beams. The canopy slab live load is 0.5 kN/m²; dead load depends on slab thickness. HRB400 is used as longitudinal reinforcement, and HPB300 as transverse reinforcement. Figure 1 shows the structure diagram; Table 1 provides details.

2.2. Double-Column Canopy

The double-column canopy design references Ankang West Station and also features six structural variants. The site classification is Category II, seismic group II, and building category C. The canopy columns with all SFIs are 6 m tall, with transverse frame beams spanning 5.4 m and cantilever beams projecting 3.25 m. The canopy live load is set at 0.5 kN/m², while the dead load is determined based on the canopy slab thickness. HRB400 is used as longitudinal reinforcement, while HPB300 is used as transverse reinforcement. Refer to Figure 2 for the specific structural layout and Table 1 for detailed design information.

3. Numerical Model

A central transverse bay of the circular-column frame canopy was selected for analysis. The lower ends of the columns are rigidly connected to the foundation, and the connections between beams and columns are also rigid. The structure is a cast-in-place reinforced concrete structure. OpenSees was used to create separate analysis programs for each of the 12 canopy structures. In the models, zero-length elements were placed at both ends of the columns and frame beams, and cantilever beams had zero-length elements near their column ends. The peak-oriented modified IMK material model was used for these zero-length elements. The middle sections of the columns and frame beams, as well as the cantilevered beam portions, were modeled as elastic beam-column elements.

Based on the actual reinforcement configuration of the beams and columns, model parameters for each plastic hinge were calculated using estimation formulas from references [13,14,15]. Next, following the methods of Ibarra [20] and Zareian [21], the rotational stiffness of plastic hinges and the elastic member stiffness were adjusted. Other ModIMK parameters and structural damping were then sequentially adjusted. Finally, due to the “strong column-weak beam” design, beam-column joints have high shear resistance, so their shear deformation is disregarded, and they are assumed rigid.

To consider corrosion’s impact on structural performance, we adjusted ModIMK parameters for the uncorroded structure, as described in [16,17].

Given the canopy structure’s large-span cantilever beams and slabs, which are significantly affected by vertical seismic forces, both the PKPM design and the OpenSees numerical model analysis incorporated vertical seismic actions.

4. Structural Seismic Collapse Fragility Analysis Process

Structural collapse fragility analysis involves issues such as selecting seismic records and seismic intensity indicators, defining structural collapse criteria, and establishing the fragility curve method.

4.1. Seismic Records and Seismic Intensity Indicators

This study uses the IDA method to analyze how structures resist seismic collapse as earthquake intensity is gradually increased. Since earthquakes are random, one IDA result may not be reliable. To reduce the risk of calculation errors, many seismic records are required [22]. This study uses 22 far-field records (epicentral distances > 10 km) recommended by the American ATC-63 program [23] as seismic inputs. Through in-depth research, Tang [24] and Yang [25] found that these records are suitable for analyzing the structural vulnerability of buildings with different seismic fortification intensities in China.

The platform canopy structure features a large cantilever beam; therefore, both horizontal and vertical seismic forces must be considered in the seismic analysis. Since some of the 22 records lacked vertical records, we applied the same seismic records to both the horizontal and vertical directions, using the intensity ratio of 1:0.65 for horizontal and vertical records as specified in Chinese standards.

The selection of seismic intensity indicators significantly impacts IDA results. The most commonly used indicators are PGA and structural first-period spectral acceleration $S_a\left(T_1\right)$ [22]. Following ATC-63 recommendations, using $S_a\left(T_1\right)$ as the intensity indicator instead of PGA can substantially reduce the variability of analysis results. This paper adopts $S_a\left(T_1\right)$ as the seismic intensity indicator. The calculation of $S_a\left(T_1\right)$ is based on the response spectrum curves provided by the Chinese seismic code GB/T 50011 and T/CECS 392.

4.2. Canopy Collapse Criteria

Platform canopies often have large-span cantilever beams and slabs, making them susceptible to vertical seismic effects. Therefore, this study considers both horizontal and vertical seismic forces. Collapse criteria are referenced in T/CECS 392 and FEMA 350 [26]. Collapse occurs if: (1) Structural tangent stiffness from the IDA curve drops to 20% of its initial value; or (2) Column displacement angle reaches 0.045; or (3) Cantilever beam displacement angle reaches 0.045.

4.3. Seismic Collapse Fragility Analysis Process

Structural collapse fragility analysis followed the approach in [27]. Numerical models of both uncorroded and corroded canopy structures were built in OpenSees. Using IDA, we obtained the collapse probability for structures with different SFIs. Assume that the collapsed probability follows the log-normal distribution, collapse fragility curves were then fitted using the maximum likelihood method for each canopy structure. Finally, we calculated the collapse probability under the maximum considered earthquake (MCE) and the extreme considered earthquake (ECE, an earthquake larger than MCE).

5. Collapse Fragility Analysis Results for Platform Canopies

5.1. Collapse Fragility Curves

The analysis of structural fragility involves numerous uncertainties that influence the results. These factors fall into two primary categories: uncertainties in seismic ground motion and uncertainties in structural modeling [27].

Structural modeling uncertainties are relatively complex; this paper focuses solely on seismic motion uncertainties. The fitted collapse fragility curves for uncorroded single-column and double-column canopies at various SFIs are shown in Figure 3 and Figure 4. To analyze the impact of corrosion levels on structural collapse performance, the seismic collapse fragility of structures with varying degrees of corrosion was compared, as shown in Figure 5 and Figure 6.

The structural collapse fragility curve is obtained by fitting a log-normal distribution to the collapse points on each IDA curve; the formulation for the fragility curve is as follows:

$$P\left(\mathrm{collapse}∣S_a\left(T_1\right)\right)=\mathsf{\Phi }\left({\displaystyle \frac{\mathrm{l}\mathrm{n}{S}_a\left(T_1\right)-\mathrm{l}\mathrm{n}\theta }{{\beta }_{\mathrm{R}\mathrm{T}\mathrm{R}}}}\right)$$

(1)

Here, θ is the median value of Sa(T₁) at a 50% probability of structural collapse; β_RTR is the logarithmic standard deviation resulting from uncertainties in the seismic record; and c is the cumulative distribution function of the standard normal distribution.

The values of θ and β_RTR for each fragility curve, obtained through maximum likelihood estimation, are shown in

Table 2. Maximum likelihood estimation results of fragility function parameters.

Canopy Type	Corrosion Condition	θ/g and βRTR	6-Degree	7-Degree	7.5-Degree	8-Degree	8.5-Degree	9-Degree
Single-column canopy	Uncorroded	θ/g	0.27	0.46	0.73	0.99	1.49	2.34
		βRTR	0.2	0.23	0.25	0.16	0.14	0.13
	5% corrosion	θ/g	0.27	0.43	0.71	0.98	1.44	2.33
		βRTR	0.20	0.21	0.27	0.19	0.16	0.15
	15% corrosion	θ/g	0.19	0.31	0.49	0.76	1.20	1.82
		βRTR	0.29	0.15	0.19	0.19	0.16	0.17
Double-column canopy	Uncorroded	θ/g	0.83	1.38	2.10	2.88	3.87	5.22
		βRTR	0.25	0.24	0.29	0.34	0.15	0.16
	5% corrosion	θ/g	0.82	1.31	1.88	2.68	3.42	5.20
		βRTR	0.28	0.27	0.25	0.30	0.30	0.16
	15% corrosion	θ/g	0.76	1.09	1.67	2.37	2.60	4.65
		βRTR	0.24	0.36	0.25	0.34	0.14	0.15

. Table 2 reveals the following: (1) Under identical corrosion conditions, the value of θ increases as the seismic fortification intensity increases, indicating that canopies designed for higher seismic intensities possess greater resistance to seismic collapse. As the corrosion rate increases, the value of θ decreases, indicating that structural corrosion reduces the structure’s resistance to seismic collapse. Under identical conditions, the value of θ for double-column canopies is greater than that for single-column canopies, indicating that double-column canopies possess stronger resistance to seismic collapse than single-column canopies. (2) As seismic design intensity and corrosion levels increase, the value of β_RTR does not exhibit a clear pattern. Under identical conditions, the value of β_RTR for double-column canopies is greater than that for single-column canopies, indicating that the fragility curve of double-column canopies exhibits greater dispersion.

Our analysis shows that for single-column canopies, the primary failure locations are at the base of the column, while for double-column canopies, they are primarily at the base of the cantilever beam.

5.2. Collapse Probability Analysis of Canopy Structures

Due to the complexity of earthquakes, many regions have experienced seismic events exceeding the maximum considered earthquake (MCE) intensity specified in the seismic code GB/T 50011. Therefore, the collapse resistance code T/CECS 392 stipulates seismic intensities greater than MCE, referred to as the extreme considered earthquake (ECE). This code requires verification of the structures’ collapse resistance under both MCE and ECE. Their corresponding PGA values are listed in

Table 3. PGA values for earthquakes of two collapse-prevention levels.

Seismic Fortification Intensity (PGA)	6 (0.05 g)	7 (0.10 g)	7.5 (0.15 g)	8 (0.20 g)	8.5 (0.30 g)	9 (0.40 g)
Fortification intensity (cm/s2)	50	100	150	200	300	400
Maximum considered earthquake (MCE) (cm/s2)	125	220	310	400	510	620
Extreme considered earthquake (ECE) (cm/s2)	160	320	460	600	840	1080

.

5.2.1. Collapse Probability of Uncorroded Canopy Structures

Based on the fitted fragility curve equations, the collapse probabilities for structures at different SFIs under both MCE and ECE were calculated and summarized in

Table 4. Probability of collapse for platform canopies with different corrosion rates.

Canopy Type	Corrosion Condition	Earthquake Intensity	6-Degree	7-Degree	7.5-Degree	8-Degree	8.5-Degree	9-Degree
Single-column canopy	Uncorroded	MCE	0	0	0.02	0	0	0
		ECE	0	1.35	3.03	1.97	20.03	11
	5% corrosion	MCE	0	0	0.05	0.001	0	0
		ECE	0.0024	1.89	4.68	6.76	35.0	17.28
	15% corrosion	MCE	0.08	0	0.09	0.05	0.015	0.008
		ECE	2.52	8.5	18.95	23.77	55.34	49.96
Double-column canopy	Uncorroded	MCE	0	0	0	0	0	0
		ECE	0	0	0	0.07	0	0
	5% corrosion	MCE	0	0	0	0	0.03	0
		ECE	0	0	0	0	0.2	0
	15% corrosion	MCE	0	0	0	0	0	0
		ECE	0	0.04	0	0.022	0.01	0.001

.

As shown in Table 4, the double-column platform canopy structures designed according to the Chinese code can meet the requirements of Code T/CECS 392 when subjected to MCE and ECE, without accounting for structural modeling uncertainties. The collapse probability limit for structures under MCE is 5%, and for ECE, it is 10%. This demonstrates that double-column platform canopies designed in accordance with Chinese seismic codes exhibit strong resistance to collapse during earthquakes.

Single-column platform canopies exhibit markedly different behavior. When subjected to MCE, the collapse probability of all structures with different SFIs is 0%, except for structures with the SFI of 7.5, which have a collapse probability of 0.02%—still well below the code’s 5% limit. This confirms that single-column structures designed in accordance with Chinese seismic codes exhibit sufficient seismic collapse resistance under MCE. However, when subjected to ECE, the collapse probabilities for structures with SFIs of 6 to 9 degrees are: 0%, 1.35%, 3.03%, 1.97%, 20.03%, and 11.0%, respectively. Notably, structures with SFI 8.5 and 9 degrees exceed the code’s collapse probability limit. This indicates that single-column canopy structures with SFIs 8.5 and 9 face significant collapse risks under ECE.

Analysis of collapse probabilities reveals that double-column structures designed in accordance with Chinese codes exhibit superior seismic collapse resistance and are suitable for all SFIs regions. In regions with SFIs of 8.5 and 9, single-column platform canopies should be avoided whenever possible. Alternatively, measures such as controlling canopy cantilever length and column height can be implemented to mitigate the risk of collapse.

5.2.2. Collapse Probability of Corroded Canopy Structures

(1) For Single-Column Canopies

Table 4 shows the collapse probability of single-column platform canopy structures with different levels of corrosion. The summary is as follows:

(a) With minor corrosion (5% corrosion rate): Collapse probability remains negligible under MCE, meeting the requirements of T/CECS 392. Under ECE, the collapse probability for single-column canopies with SFI 8.5 reaches 35%, exceeding the code’s 10% limit; structures with SFI 9 show a collapse probability of 17.28%, also exceeding the code’s limit. All other cases meet code requirements.

(b) When the structure is severely corroded (corrosion rate of 15%): When subjected to MCE, the collapse probability is very low, and all structures meet the requirements of T/CECS 392. Under ECE, collapse probabilities exceed the 10% threshold from SFI 7.5 to 9. Particularly at SFIs 8.5 and 9, collapse probabilities reach 55.34% and 49.96%, posing significant collapse risks. Even at an SFI of 7 degrees, the collapse probability reaches 8.5%, indicating a notable collapse risk.

(c) Compared to uncorroded single-column canopy structures: When subjected to MCE, collapse probabilities remain extremely low for both uncorroded intact structures, structures with 5% corrosion, and structures with 15% corrosion. When subjected to ECE, structures with 15% corrosion generally exhibit the highest collapse probability, followed by those with 5% corrosion, while uncorroded structures have the lowest collapse probability.

(2) For double-column canopy structures

As shown in Table 4, for double-column platform canopy structures with 5% and 15% corrosion, the collapse probability remains low under both MCE and ECE, meeting the requirements of T/CECS 392. This demonstrates that double-column canopies exhibit strong resistance to corrosion-related deterioration.

6. Conclusions

This paper designs 12 railway platform canopies with varying seismic fortification intensities (SFIs) in accordance with the Seismic Design Code for Buildings (2024 Edition). Using the IDA method, we analyze the seismic collapse fragility of structures under three conditions: no corrosion; 5% corrosion mass—loss of reinforcement; and 15% corrosion mass—loss of reinforcement. The main conclusions are as follows:

(1) Uncorroded canopy structures: (a) For double-column canopies, the collapse probability of all structures with different SFIs under MCE and ECE remains significantly below the threshold requirements of the Code for Seismic Collapse-Resistant Design of Building Structures T/CECS 392-2021; (b) for single-column canopies, structures of all SFIs meet code requirements when subjected to MCE. However, collapse probabilities for structures with SFIs of 8.5 and 9 exceed code limits when subjected to ECE, reaching 20.03% and 11%, respectively.

(2) Corroded double-column canopies: Under 5% and 15% corrosion, the collapse probability remains low under both MCE and ECE. This shows strong resistance to corrosion degradation.

(3) Corroded single-column canopy: (a) When subjected to MCE, the collapse probability of structures with 5% and 15% corrosion is very low, far below code-specified limits; (b) When subjected to ECE, the collapse probability of the structure with 5% corrosion exceeds that of uncorroded structures at all SFIs. The collapse probabilities for the structures with SFI 8.5 and SFI 9 fail to meet code requirements; (c) when subjected to ECE, the structure with 15% corrosion exhibits significant performance degradation, with collapse probabilities far exceeding that of the uncorroded structure. Structures with SFIs from 7.5 to 9 all fail to meet the code’s collapse probability limits. For structures designed for SFIs 8.5 and 9, their collapse probabilities reach 55.34% and 49.96%, respectively, indicating substantial collapse risk.

This study provides important reference values for improving the seismic design of platform canopies and for investigating the impact of corrosion on their collapse resistance.