Impact of Corrosion on the Behaviour of Reinforced Concrete Buildings

Abstract

Corrosion significantly contributes to the deterioration of reinforced concrete (RC) structures. This work investigates its impact on the seismic behaviour of RC buildings. A simplified numerical simulation strategy was developed and validated, analysing two columns with corrosion rates of 0% and 20%, based on existing experimental research found in the literature. Subsequently, five distinct scenarios were developed, incorporating various corrosion rates of 0%, 10%, and 20%, applied to a structure designed in accordance with the Eurocode 8. Nonlinear pushover analyses were conducted to derive capacity curves and bilinear curves, focusing on key parameters such as maximum strength and corresponding drift, initial stiffness, secant stiffness, yield force and drift. Displacement and drift profiles per floor were analysed at the significant damage performance point (SD). The results indicate a clear negative impact of corrosion on structural performance, evidenced by reduced capacity to withstand deformations and lateral forces, alongside an increased likelihood of damage to non-structural elements.

1. Introduction

The recent seismic event in Turkey [1] tragically highlighted the vulnerability of reinforced concrete (RC) structures in high-seismicity regions. With about 87% of the affected buildings made of RC, corrosion was one of the factors that contributed to their poor performance and collapse, worsening the effects of seismic actions. Also, other research works focused on the seismic vulnerability of existing industrial and residential RC structures (not considering the corrosion effect) [2,3,4]. Understanding the impact of corrosion on the seismic behaviour of RC structures is essential for ensuring safety and durability. Corrosion in RC structures has four main consequences: (a) cracking and delamination of the cover, exposing reinforcement; (b) reduction in the cross-sectional area of reinforcement; (c) degradation of the bond between steel and concrete; and (d) deterioration of the mechanical properties of steel, particularly its deformation capacity [5,6,7]. Numerous studies, including those by Aminulai et al. [8], Guo et al. [9], Meda et al. [10], Yang et al. [11], and Yao et al. [12], have shown that corrosion significantly affects damage states, failure mechanisms, flexural capacity, and energy dissipation. While Berto et al. [13] and Dizaj et al. [14] have replicated corrosion effects in numerical simulations, predicting the seismic behaviour of corroded structures remains challenging due to limited research. Still, there is a very reduced number of works on the effect of corrosion on the structural response of RC structures when subjected to lateral loadings. Based on this motivation, this research work aims to perform a preliminary study of the seismic behaviour of RC structures with corrosion. The detailed analysis and understanding of the effect of corrosion on various response parameters of an RC building subjected to seismic action was the focus of this study. In this regard, it was necessary to propose and validate a simplified numerical simulation, which would allow predicting the seismic behaviour of RC structures with corrosion. The validation of the proposed numerical simulation strategy was carried out by simulating two experimental tests conducted by Meda et al. [10] on columns with and without corrosion. The columns were subjected to combined bending with cyclic loading. The validation was carried out by comparing the experimental and numerical force–displacement responses, evaluating the accuracy of the numerical predictions with respect to key response parameters such as initial stiffness, peak strength, and overall behaviour.

After this validation, the main objective was to study the seismic behaviour of a building under different corrosion scenarios, considering the possible environments in which it might be exposed. In this context, four scenarios with different corrosion configurations were considered. The first scenario represents an extreme situation in which all façade elements are subjected to corrosion, allowing for a comprehensive analysis of the total effect of deterioration. The second scenario restricts corrosion to specific elements of certain façades, reflecting a more directional exposure and enabling the evaluation of the influence of corrosion location on structural behaviour. In the third scenario, a more realistic configuration is considered, where the outer rebars of the same element are corroded while the inner rebars remain intact, applicable to all façades. Finally, the fourth scenario addresses variable corrosion along the different floors of the structure, highlighting the impact of soil conditions on structural integrity.

For each of these scenarios, nonlinear pushover analyses were performed to assess the effect of corrosion, identifying the most critical scenarios that increase the seismic vulnerability of the structure. The capacity curves, performance points, initial stiffness, yield point, maximum resistance, and inter-storey drift profile are discussed and compared.

2. Numerical Modelling of Reinforced Concrete Elements with Corrosion

Numerical simulation plays a crucial role in understanding and analysing structures. Its main objective is to reproduce and predict, as realistically as possible, the behaviour of simulated structures under various types of actions, allowing for the identification of potential structural vulnerabilities. For the development and analysis of this study, it was first necessary to define a numerical modelling strategy to simulate the behaviour of RC elements with corrosion. To ensure that the simulation effectively predicted real behaviour, the numerical modelling was validated through the simulation of two experimental tests conducted by Meda et al. [10] on RC columns with (20% corrosion rate) and without corrosion (0% corrosion rate). The validation of the numerical strategy will be assessed by comparing the experimental and numerical force–displacement curves.

2.1. Numerical Modelling Strategy

The numerical simulation was carried out using the SeismoStruct software [15]. The modelling strategy adopted herein for simulating the RC elements (i.e., beams and columns) involved the use of the inelastic force-based frame elements with seven integration sections per element, in which each section was discretized into 204 fibers, with each fiber assigned a uniaxial constitutive model (i.e., steel reinforcement, confined concrete, or unconfined concrete). Further details regarding the implementation of the algorithm can be found in the software manual [15].

To characterize the behaviour of steel and concrete under both conditions (corroded and non-corroded), the uniaxial constitutive model proposed by Monti-Nuti [16] was adopted for steel, and the model proposed by Mander et al. [17] was adopted for concrete. Figure 1 provides an overview of the numerical modelling strategy assumed. The uniaxial constitutive model proposed by Monti-Nuti [16] is capable of capturing the post-elastic buckling behaviour of reinforcing bars under compression. It combines the stress–strain relationship proposed by Menegotto and Pinto [18] with the isotropic hardening rules proposed by Filippou et al. [19], and incorporates buckling degradation rules introduced by Monti and Nuti [20]. Additionally, a memory rule proposed by Fragiadakis et al. [21] is included to enhance numerical stability and accuracy under transient seismic loading. The use of this model is recommended for simulating RC elements where reinforcement buckling is expected, such as columns subjected to severe cyclic loading or, for example, elements with corroded rebars. The uniaxial material model proposed by Mander et al. [17] follows the constitutive law proposed by Mander et al. [17], combined with the cyclic loading rules developed by Martinez-Rueda and Elnashai [22]. The confining effects provided by lateral transverse reinforcement are incorporated using the formulation by Mander et al. [17], which assumes a constant confining pressure throughout the entire stress–strain response.

To simulate the effects of corrosion on the RC elements, two fundamental strategies were implemented. The first involved reducing the effective area of the longitudinal and transverse reinforcement in a corroded RC element, simulating the loss of cross-section resulting from the corrosion process. It is important to note that in this software, when modelling stirrups, only the selection of bars with standard diameters is allowed, making it impossible to introduce intermediate ones. To address this limitation, the adopted solution was to adjust the spacing between the stirrups in order to achieve the desired equivalent cross-sectional area.

The second strategy involved modifying the mechanical properties of the steel, specifically reducing the yield strength and ultimate strain, achieved through calibration.

2.2. Calibration of the Numerical Modelling Strategy

2.2.1. Description of the Experimental Campaign

In the context of this work, the study conducted by Meda et al. [10] was selected as a reference, where their objective was to evaluate the structural behaviour of RC columns subjected to uniaxial lateral cyclic loading after artificial corrosion had been induced. Each column had a square cross-section measuring $0.3\times 0.3$ square meters and was reinforced longitudinally with four steel bars of 16 mm in diameter. The transverse reinforcement consisted of steel stirrups with a diameter of 8 mm, spaced at intervals of 300 mm. The total height of the columns was 1.8 m.

The foundation block supporting the columns measured $1.3\times 0.6\times 0.5$ cubic meters and was reinforced with a combination of different steel bars. The top and bottom longitudinal reinforcements consisted of steel bars with a diameter of 20 mm, while the midsection longitudinal reinforcement was composed of bars with a diameter of 12 mm. Additionally, vertical distribution reinforcement was incorporated using steel bars with a 12 mm diameter, spaced at intervals of 150 mm, ensuring structural integrity and load distribution.

The mean mechanical properties of the materials used in the experimental campaign are presented in

Table 1. Mechanical properties (mean values) of steel and concrete according to Meda et al. [10].

Concrete		Steel
$f_c$ (MPa)	20	$f_y$ (MPa)	520
$f_t$ (MPa)	2.2	${\epsilon }_{ult,s}$ (%)	13.72
$E_c$ (GPa)	30	$E_s$ (GPa)	210

, where for concrete, $f_t$ denotes the tensile strength, $f_c$ the compressive strength, and $E_c$ the modulus of elasticity, while for steel, $f_y$ represents the yield strength, ${\epsilon }_{ult,s}$ the ultimate strain, and $E_s$ the modulus of elasticity.

Each test involved the application of a uniaxial lateral cyclic load at a height of 1.5 m. The top of the column was constrained, allowing it to rotate and translate within the plane of load application, while displacements and rotations out of this plane were restricted. The bases/foundations of the column were fixed, with all degrees of freedom constrained.

Additionally, a compressive axial load of 400 kN was applied at the top of the column, corresponding to a reduced axial load ratio of 0.22. The displacement history applied to the top of the column is presented in Figure 2 and consisted of repeating three cycles for each of the following target displacements: 2.5 mm, 3 mm, 4 mm, 4.5 mm, 6 mm, 7.5 mm, 11.5 mm, 15 mm, 19 mm, 22.5 mm, 30 mm, 37.5 mm, 52.5 mm, and 75 mm.

2.2.2. Considerations on the Numerical Simulation

The selection of the appropriate uniaxial constitutive model for steel and concrete was achieved through an iterative calibration process, comparing numerical results with experimental data for both uncorroded and corroded conditions.

For the simulation of the cyclic loading, a static time–history analysis was employed. This analysis involves applying a displacement history at the top of the column based on the horizontal displacement history curve used in the experimental test, which was represented in Figure 2.

Table 2. Numerical parameters used to simulate the steel uniaxial material curve.

Corrosion Level	0%	20%	Ratio
$E_s$ (GPa)	210	210	1.00
$f_y$ (MPa)	520	312	0.60
$\mu$	0.015	0.015	1.00
$R_0$	20	18.9	0.95
$a_1$	19.6	18.6	0.95
$a_2$	0.15	0.15	1.00
P	0.6	0.6	1.00
r (%)	2.5	5.00	2.00
${\epsilon }_{ult,s}$	0.1372	0.0410	0.30
$\gamma$ (kN/m3)	78.00	78.00	1.00

presents a comparison of the parameters adopted for each scenario, highlighting the modifications made to simulate the effects of corrosion on the mechanical properties of steel. The parameters considered include the strain hardening parameter ($\mu$), the initial transition curve parameter ($R_0$), the transition curve calibration coefficients ($a_1$ and $a_2$), the kinematic/isotropic weighting coefficient (P), the unloading correction parameter (r), and the specific weight ($\gamma$). Throughout the iterations, it was observed that the parameters defining the stress–strain curve for the concrete model remained constant for both conditions.

Table 3. Numerical parameters used to simulate the concrete uniaxial material curve.

Concrete
$f_c$ (MPa)	$f_t$ (MPa)	$E_c$ (GPa)	${\epsilon }_{ult,c}$	$\gamma$ (kN/m3)
20	2.2	30	0.02	24

lists the parameters used to simulate concrete behaviour.

2.2.3. Uncorroded Column

Figure 3 presents a comparison between the numerical (Numeric_Sit0%) and experimental (Test_Sit0%) responses of the uncorroded column. A positive correlation was observed between the two responses until the drift reached 2%, after which a slight deviation from the experimental response occurred concerning the load capacities and the degradation of resistance.

A slight difference was observed in the initial stiffness, where the numerical response was overestimated by approximately 13% for positive cycles and 2% for negative cycles. Specifically, the numerical simulation demonstrated satisfactory accuracy in capturing the maximum force, with discrepancies of only 3% and 7% compared to the experimental values for positive and negative cycles, respectively. It is also important to note that the maximum force occurred at different drift levels; the numerical model reached the maximum force at a drift of 3.49%, which was approximately 2.13 times and 2.28 times greater than that observed in the experimental response for the positive and negative directions, respectively.

2.2.4. Corroded Column

Upon analysing the force–drift curves related to the corroded column, as presented in Figure 4, it is evident that the numerical model (Numeric_Sit20%) also demonstrated a good prediction of the experimental response (Test_Sit20%), except for the post-peak stage.

A slight difference was noted regarding the initial stiffness, with the numerical response overestimating by approximately 9.52% for positive cycles and 5.74% for negative cycles. For the maximum force, the model exhibited excellent accuracy in its prediction, as it occurred at nearly identical levels (overestimating by 0.6% and underestimating by 1% for the positive and negative directions, respectively). The numerical model reached the maximum force in the positive direction at a drift of 1.26%, while the experimental response yielded a value of 1.21%. In the negative direction, the numerical model achieved a drift value of 1.27%, compared to the experimental value of 1.24%. Similarly to the uncorroded column, the experimental response exhibited a progressive degradation of resistance with the increase in lateral displacements, attributed to the buckling of the reinforcement bars, which, in the presence of corrosion, escalated the level of degradation for the same target displacement.

2.2.5. Global Comparison

The comparison between the numerical and experimental results demonstrated a good correlation, validating the model. In Figure 5, it is observed that the model was able to replicate, with precision, both the initial stiffness and the maximum strength of the two tested columns. It is evident that, with the increase in lateral displacements, the reference column exhibited a progressive degradation of resistance. However, this phenomenon was not captured by the numerical model.

Table 4. Key parameters of experimental and numerical response.

Corrosion Level	Cycles	Model	Initial Stiffness (kN/m)	Maximum Strength (kN)	Drift (Maximum Strength) (%)
0%	Positive	Experimental	9068	63.53	1.63
	Positive	Numerical	10,215	65.74	3.49
	Negative	Experimental	6900	60.11	1.53
	Negative	Numerical	7004	64.48	3.49
20%	Positive	Experimental	10,857	44.21	1.21
	Positive	Numerical	11,891	44.48	1.26
	Negative	Experimental	7022	44.81	1.24
	Negative	Numerical	7426	44.36	1.27

and

Table 5. Ratios of key parameters.

Corrosion Level	Cycles	Initial Stiffness (kN/m)	Maximum Strength (kN)	Drift (Maximum Strength) (%)
0%	Positive	1.13	1.03	2.13
	Negative	1.02	1.07	2.28
20%	Positive	1.10	1.01	1.04
	Negative	1.06	0.99	1.02

present the key parameters of the force–drift curves. Table 5 shows the initial stiffness, maximum strength, and displacement values at maximum strength for columns without corrosion and with 20% corrosion. Also, it illustrates the ratios between the numerical and experimental values of these parameters.

3. Study Case

In this section, the case study of this research work will be presented, along with a detailed description of the methodology adopted to assess the effect of corrosion on the seismic behaviour. The building selected for the case study was designed by Maranhão et al. [23] as part of a research project that combined the design of buildings according to the enhanced ductility requirements of Eurocode 8 [24] with the optimization of structural design.

Initially, an overview of the case study will be provided, including a detailed characterization of its geometry, structural system, cross-sections, reinforcement detailing, constituent materials, and the applied loads considered in the analysis.

Since the primary objective of this work is to study the impact of corrosion on the seismic behaviour of the RC building structure, different scenarios will be defined, corresponding to different intensities and locations of corrosion in the structural elements.

Finally, the methodology adopted for studying the seismic behaviour of the buildings will be described in detail, with an emphasis on the chosen type of analysis, and the structural response parameters obtained from these analyses will be presented.

3.1. General Description

In the investigation conducted by Maranhão et al. [23], the frame system features a square layout of 18 m per side, totalling 324 m², with 6 m × 6 m modules (Figure 6a). The building has five floors, with a height of 4 m for the ground floor and 3 m for the upper floors, resulting in a total height of 16 m (Figure 6b). The columns are fully fixed at ground level.

A 15 cm thick solid slab is specified for all floors. The building is regular in both plan and elevation, with no torsional flexibility and a variable height configuration. It is symmetrical along both longitudinal and transverse axes, and Maranhão et al. [23] designated it as intended for office use.

3.2. Materials and Actions

Maranhão et al. [23] specified the structure to be made of C30/37 concrete, with properties defined per Eurocode 2 [25] and EN 206-1:2007 [26]. The reinforcement steel is classified as B500, with mechanical properties in accordance with EN 10080:2005 [27]. The vertical loads for the structural design correspond to characteristic loads for office buildings, detailed in

Table 6. Vertical loads considered for the case study.

Load Type	Floor	Load	Value
Structure self-weight (Gk,1)	All floors	Primary seismic members (columns and beams) Slabs: solid RC 15 cm thick	$\gamma =25{\mathrm{kN}/\mathrm{m}}^3$
Other permanent loads (Gk,2)	1st to	External walls and partitions with $3.0\mathrm{kN}/\mathrm{m}$ (per unit of wall length)	$12{\mathrm{kN}/\mathrm{m}}^2$
		Finishings	$1.3{\mathrm{kN}/\mathrm{m}}^2$
	(n)th (roof)	Finishings	$1.0{\mathrm{kN}/\mathrm{m}}^2$
Live loads (Qk)	1st to	Building for use as civil dwellings, falling into usage category A	$2.0{\mathrm{kN}/\mathrm{m}}^2$
	(n)th (roof)	Roof category H—Roofs not accessible except for normal maintenance and repair	$1.0{\mathrm{kN}/\mathrm{m}}^2$

.

Due to the nature of the study conducted by Maranhão et al. [23], the structure was designed with the aim of maximizing the optimization of sections and quantities of reinforcement used while maintaining the ductility level DCM required by Eurocode 8 [24]. It is important to mention that, besides the fact that the probability of developing corrosion in structures designed with past codes (prior to Eurocodes), this work aims to assess the impact of corrosion in well-designed RC structures.

3.3. Corrosion Scenarios

Four corrosion propagation scenarios have been defined for the RC elements, accounting for different environmental conditions and exposure levels during their service life. Each scenario analysed three corrosion levels: 0% (no corrosion—considered as the reference, REF), 10% (CL10%), and 20% (CL20%).

Scenario 1: This environmental exposure scenario, characterized by high aggressiveness, considers corrosive processes in all RC elements in direct contact with the external environment (shown in red in Figure 7a). It represents the most severe degradation condition, assuming all exposed structural elements experience corrosion simultaneously.

Scenario 2: A differential exposure to corrosion was considered, focusing on specific facades of the structure to simulate directional exposure to corrosive agents influenced by factors like wind direction, solar orientation, and precipitation. This scenario was divided into two situations: Situation A, where corrosion occurs on the lateral facades (where forces are applied), and Situation B, where corrosion is observed on the frontal facades (perpendicular to the applied forces). In both situations, all RC structural elements in direct contact with the affected facades were subject to corrosion processes (shown in red in Figure 7b), with uniform corrosion considered at the cross-sectional level.

Scenario 3: A more realistic corrosion configuration was established, focusing on the steel bars in the peripheral zone of the RC structural elements in direct contact with the external environment (shown in red in Figure 7c). This scenario assumes that while the outer bars of the elements are subject to corrosion, the inner reinforcements remain relatively protected by the concrete. Implementing this scenario in the SeismoStruct program [15] revealed limitations: the software does not permit distinct material properties for individual bars within the same element, complicating the simulation of localized corrosion. Consequently, the modelling approach was adapted to apply uniform modifications to the material properties for all bars in the corroded elements, reducing the area only for the outer bars while keeping the inner bars’ dimensions unchanged. Additionally, differential area reduction for stirrups was not possible, leading to the assumption of uniform corrosion along their entire length, representing the most unfavourable scenario.

Scenario 4: A non-uniform vertical distribution of corrosion was simulated to reflect the differential exposure of structural elements due to corrosive soils at lower levels. The scenario included three corrosion zones: the first zone (red), from the ground to the first floor, with a corrosion level of 20%; the second zone (yellow), from the first to the third floor, with a level of 10%; and the third zone above the third floor, with a corrosion level of 0%. This configuration is illustrated in Figure 7d.

The decision to model corrosion uniformly across the cross section in Scenarios 1 and 2 was based on the need to simulate the overall loss of structural capacity under aggressive environmental conditions, assuming the simultaneous exposure of the full reinforcement cage. Although uniform corrosion does not represent the most localized effects observed in practice, it provides a conservative approximation suitable for global performance assessments in the absence of more detailed data. In Scenario 3, a more realistic representation of corrosion was attempted by applying degradation only to the outer reinforcement layers, as these are typically the most exposed to environmental agents such as chlorides and carbonation. This modelling choice reflects the initial stages of corrosion propagation, where the outer bars begin to deteriorate while the inner reinforcement remains relatively protected by the concrete cover. However, the numerical implementation of this scenario was constrained by the modelling capabilities of the software, which do not allow assigning distinct material properties to individual bars within the same cross-section. To approximate this effect, the model reduced the area only for the outer bars, while the geometry of the inner bars was preserved. For stirrups, a uniform reduction was applied along their entire length, as localized degradation could not be specified. This simplification represents a conservative approach and may lead to a slight overestimation of the damage in some regions. These limitations are acknowledged and indicate an area for refinement in future studies using more advanced modelling tools.

3.4. Analysis Methodology

Non-linear pushover adaptive analyses were conducted by incrementally applying lateral loads until collapse or a predefined deformation level was reached. These analyses produced capacity curves, yielding values for initial stiffness, maximum strength, corresponding global drift, and secant stiffness. Idealized bilinear curves were also derived, providing yield parameters such as yield force and displacement, along with profiles of inter-storey displacements and drifts. The analysis focused on structural deformation parameters at the performance point corresponding to the significant damage (SD) limit state.

The performance points for the Damage Limitation (DL) and Imminent Collapse (NC) limit states were also marked on the capacity curves. The seismic characteristics of the structure’s location, as defined by Maranhão et al. [23], were as follows:

• Seismic Type 1: Higher magnitudes, distant epicenters, and longer durations, with lower frequencies that may resonate with building natural frequencies.
• Soil Type A: Rock or other geological formations classified as rocky.
• Importance Class II: Ordinary buildings that do not fall into other categories.
• Damping Coefficient: 5% (a typical value for RC structures).
• Seismic Zone 1.3: Corresponds to the Lisbon area.

It is important to note that the seismic performance assessment presented in this study is based on adaptive pushover analysis, which is a nonlinear static method. As such, no direct seismic input (e.g., accelerograms, PGA, frequency content, or duration) is applied. Instead, lateral loads are incrementally applied following adaptive patterns that reflect the evolving modal properties of the structure throughout the analysis. This method allows for an efficient and insightful evaluation of the global and local capacity of the structure under increasing seismic demand, without the need for specific time–history records.

4. Discussion of Results

The analysis of the scenarios enhanced the understanding of corrosion’s impact on structural elements and overall lateral response, forming a basis for assessing the structure’s seismic vulnerability. Capacity curves and their idealized bilinear counterparts will be presented for various corrosion rates, with extracted parameters discussed for comparison analyses. Finally, the structure’s displacement and drift profiles will be shown to complement the assessment of corrosion’s effects on seismic behaviour.

4.1. Scenario 1

A comparison of the capacity curves (CC) and the corresponding idealized bilinear curves (BL) obtained for the analysed corrosion rate levels is presented in Figure 8. Bilinear curves were computed according to the Eurocode 8 [28] proposal.

Table 7. Scenario 1: extracted response parameters for each corrosion level.

Response Parameters	Ref	CL 10%	CL 20%
Initial Stiffness (kN/m)	18,422	18,211	18,108
Maximum Strength (kN)	2542	2371	2141
Drift (Maximum Strength) (%)	1.32	1.31	1.22
Secant Stiffness (kN/m)	12,003	11,293	10,981
Yield Force (kN)	1017	949	857
Yield Drift (%)	0.35	0.33	0.30

summarizes the extracted parameter values from the capacity curves and idealized bilinear curves for the various corrosion rates analysed.

The performance points (DL, SD, and NC) showed similar variations across corrosion rates, with 0% and 10% rates at the same drift level, while 20% shifted to higher drift levels.

Table 8. Scenario 1: Corresponding base shear and drift for each of the performance points.

Corrosion Level		0%	10%	20%
Damage Limitation	Base shear (kN)	1773	1725	1810
	Drift (%)	0.68	0.68	0.78
Significant Damage	Base shear (kN)	2119	2048	2052
	Drift (%)	0.87	0.87	1.00
Near Collapse	Base shear (kN)	2456	2297	1813
	Drift (%)	1.51	1.51	1.73

lists the baseline cut values and corresponding drift for each performance point.

An overview of the changes in the main structural parameters is presented in Figure 9 for corrosion rates of 10% (CL_10%) and 20% (CL_20%), compared to the initial state (0% corrosion).

The initial stiffness of the structure was the least affected compared to other parameters. At a 10% corrosion rate (ratio of 0.99), the structure maintained its original stiffness, indicating no loss of concrete section or change in the modulus of elasticity. At 20% corrosion, the ratio was 0.98, still showing a minimal impact on initial stiffness.

The maximum strength ratio was 0.93 for 10% corrosion, suggesting preserved structural integrity, but it dropped by 16%, reaching 0.84 at 20% corrosion, indicating a significant loss in capacity to resist lateral actions. Drift ratios for maximum strength were 0.99 at 10% and 0.92 at 20%, with differences becoming noticeable only at 20%. Secant stiffness ratios were 0.94 for 10% and 0.91 for 20%, reflecting slight post-elastic degradation. Yield strength ratios were 0.93 for 10% and 0.86 for 20%, showing decreased capacity to withstand lateral actions. Yield displacement ratios also indicated reduced deformation capacity, at 0.94 for 10% and 0.86 for 20%. In addition to the analysis of the capacity curve and bilinear representation, the absolute inter-storey displacements for each floor have been extracted (Figure 10a), along with the corresponding inter-storey drifts (Figure 10b) related to the damage limit state of SD.

The displacement profile analysis showed that, at 0% and 10% corrosion rates, floor displacements were nearly identical (ranging from 0.037 to 0.14), indicating minimal impact on flexibility and primarily affecting resistance. The capacity curve indicated that the damage state SD for both scenarios occurred at similar inter-storey drift levels, suggesting that corrosion up to 10% did not significantly affect deformation capacity. However, at a 20% corrosion rate, inter-storey displacements increased by 12.75% to 16.87%, indicating greater flexibility. The damage state SD point for 20% corrosion occurred at a higher displacement level, which was unexpected. At 10% corrosion, the inter-storey drifts remained largely unchanged, suggesting minimal compromise in deformation capacity. In contrast, at 20% corrosion, the inter-storey drifts increased by 10% to 16.33%, indicating a significant effect on structural performance under lateral loads. Notably, the drift between the ground and first floors exceeded the 1% limit for all corrosion rates, indicating a significant risk of damage to non-structural elements, according to Eurocode 8 [24], especially for rates above 10%.

4.2. Scenario 2.A

The capacity curves (Figure 11) indicate that the structural behaviour at a 20% corrosion rate (CL20%_CC) is distinct from the uncorroded state (REF_CC), while the curve for a 10% corrosion rate (CL10%_CC) shows no significant variation.

Table 9. Scenario 2.A: extracted response parameters for each corrosion level.

Response Parameters	Ref	CL 10%	CL 20%
Initial Stiffness (kN/m)	18,422	18,380	18,399
Maximum Strength (kN)	2542	2487	2306
Drift (Maximum Strength) (%)	1.32	1.31	1.22
Secant Stiffness (kN/m)	12,003	11,843	11,824
Yield Force (kN)	1017	995	922
Yield Drift (%)	0.35	0.34	0.31

summarizes the parameter values extracted from the capacity curves and the idealized bilinear curves for this scenario, corresponding to the various corrosion rates analysed.

The capacity curve analysis showed that performance points varied similarly for each corrosion rate, with the 10% and 20% rates located at the same drift level, while the initial state was at lower drift levels.

Table 10. Scenario 2.A: corresponding base shear and drift of performance points.

Corrosion Level		0%	10%	20%
Damage Limitation	Base shear (kN)	1773	1946	1899
	Drift (%)	0.68	0.78	0.78
Significant Damage	Base shear (kN)	2119	2276	2184
	Drift (%)	0.87	1.00	1.00
Near Collapse	Base shear (kN)	2456	2273	1943
	Drift (%)	1.51	1.73	1.73

lists the base shear values and corresponding drifts for each performance point. Figure 12 provides an overview of changes in key structural parameters for 10% (CL_10%) and 20% (CL_20%) corrosion rates compared to the initial state (0% corrosion).

The initial stiffness ratios remained constant at 1.0 for both corrosion levels, indicating no degradation in response parameters. The maximum strength ratio was 0.98 for 10% corrosion, suggesting negligible impact, while it decreased to 0.91 for 20%, indicating a 9% reduction in structural capacity. Drift associated with maximum strength also decreased with corrosion; for 10%, the ratio was 0.99, maintaining deformation levels, while it dropped to 0.92 for 20%, indicating reduced deformation capacity and increased fragility. Secant stiffness ratios were 0.99 for both corrosion rates, showing no change. Yield values mirrored maximum strength behaviour: 0.98 for 10% corrosion, indicating almost the same capacity as the initial state, and 0.91 for 20%, highlighting a reduced ability to withstand deformations before nonlinear behaviour. The yield drift for 10% corrosion was 0.99, similar to the uncorroded structure, but decreased to 0.92 for 20%, indicating yielding with less deformation. In addition to the capacity curve and bilinear representation analysis, absolute inter-storey displacements (Figure 13a) and the corresponding inter-storey drifts (Figure 13b) were extracted for the damage limit state SD.

The displacement profile between 0% and 10% corrosion showed a significant increase in displacement from 12.90% to 15.60%, indicating enhanced flexibility. For both 10% and 20% corrosion, displacements at each floor were similar, ranging from 0% to 4%, likely due to the SD point’s location on the capacity curve, where both rates were at similar inter-storey drift levels, contrary to expectations that increased corrosion would lead to smaller displacements.

The inter-storey drift profile analysis revealed a clear decrease in values with building height, regardless of corrosion level. For 10% corrosion, the inter-storey drifts increased compared to the initial condition, ranging from 10% to 15.56%, indicating a significant compromise in lateral resistance. However, at 20% corrosion, no increase in inter-storey drifts was observed. Notably, the drift between the ground and first floors exceeded 1% for all corrosion rates, highlighting a substantial risk of damage to non-structural elements, especially under seismic actions as corrosion increases.

4.3. Scenario 2.B

The capacity curves in Figure 14 show a similar degradation trend as in scenario 2.A, with slight increases.

Table 11. Scenario 2.B: extracted response parameters for each corrosion level.

Response Parameters	Ref	CL 10%	CL 20%
Initial Stiffness (kN/m)	18,422	18,249	18,108
Maximum Strength (kN)	2542	2420	2215
Drift (Maximum Strength) (%)	1.32	1.31	1.22
Secant Stiffness (kN/m)	12.003	11,524	11,357
Yield Force (kN)	1017	968	922
Yield Drift (%)	0.35	0.33	0.31

summarizes the parameter values extracted from the capacity curves and the idealized bilinear curves for this scenario, corresponding to the various corrosion rates analysed.

The capacity curve analysis revealed similar variations in performance points for each corrosion rate, as seen in scenario 2.A.

Table 12. Scenario 2.B: corresponding base shear and drift of performance points.

Corrosion Level		0%	10%	20%
Damage Limitation	Base shear (kN)	1773	1907	1833
	Drift (%)	0.68	0.78	0.78
Significant Damage	Base shear (kN)	2119	2226	2104
	Drift (%)	0.87	0.99	1.00
Near Collapse	Base shear (kN)	2456	2180	1824
	Drift (%)	1.51	1.72	1.73

lists the base shear values and corresponding drift for each performance point.

An overview of the changes in the main structural parameters is presented in Figure 15 for corrosion rates of 10% (CL_10%) and 20% (CL_20%) compared to the initial state (0% corrosion).

In scenario 2.B, the initial stiffness remained unchanged from the non-corroded condition, with ratios of 0.99 for 10% corrosion and 0.98 for 20%. Maximum strength ratios showed a progressive loss with corrosion: 0.95 at 10% (5% reduction) and 0.87 at 20% (13% loss). Drift ratios also decreased, with values of 0.99 for 10% and 0.92 for 20%, indicating increased fragility with higher corrosion. Secant stiffness ratios were more affected than in scenario 2.A, at 0.96 for 10% and 0.95 for 20%, reflecting deterioration in post-elastic behaviour. Yield force ratios were 0.95 for 10% and 0.91 for 20%, while yield displacement ratios were 0.96 for 10% and 0.89 for 20%.

The primary variable affecting differences between scenarios 2.A and 2.B is the location of applied lateral forces, with front facades experiencing more stress. Consequently, scenario 2.A shows less impact compared to scenario 2.B, which exhibits moderate reductions with increasing corrosion.

In addition to the capacity curve analysis, absolute inter-storey displacements (Figure 16a) and the corresponding inter-storey drifts (Figure 16b) were obtained for the damage limit state SD.

The displacement profile showed an increase from 12.92% to 15.51% between 0% and 10% corrosion, indicating greater flexibility in the structure. Inter-storey displacements remained nearly constant at corrosion rates of 10% and 20%, linked to the position of the damage limit state (SD) on the capacity curve, which was the same for both rates but lower at 0% corrosion. The inter-storey drift profile revealed a continuous reduction with increasing floor height, regardless of corrosion levels. At 10% corrosion, inter-storey drifts exceeded those at 0% corrosion, highlighting a significant impact on performance and susceptibility to deformation. However, at 20% corrosion, drifts remained stable across floors, indicating no further increase in flexibility. Drifts between the ground and first floors exceeded the 1% limit under all corrosion conditions, raising the risk of failures in non-structural elements. This suggests that even low corrosion levels can lead to significant issues, which may worsen with further deterioration.

4.4. Scenario 3

A comparison of the capacity curves (CCs) and their corresponding idealized bilinear curves (BLs) for the analysed corrosion rate is presented in Figure 17.

Table 13. Scenario 3: extracted response parameters for each corrosion level.

Response Parameters	Ref	CL 10%	CL 20%
Initial Stiffness (kN/m)	18,422	18,348	18,392
Maximum Strength (kN)	2542	2413	2211
Drift (Maximum Strength) (%)	1.32	1.31	1.25
Secant Stiffness (kN/m)	12,003	11,491	11,057
Yield Force (kN)	1017	965	885
Yield Drift (%)	0.35	0.33	0.30

summarizes the parameter values from the capacity curves and idealized bilinear curves for the analysed corrosion rates. The performance points showed similar variations for each corrosion rate, as seen in scenarios 2.A and 2.B.

Table 14. Scenario 3: corresponding base shear and drift of performance points.

Corrosion Level		0%	10%	20%
Damage Limitation	Base shear (kN)	1773	1922	1866
	Drift (%)	0.68	0.77	0.78
Significant Damage	Base shear (kN)	2119	2239	2121
	Drift (%)	0.87	0.99	1.00
Near Collapse	Base shear (kN)	2456	2167	1930
	Drift (%)	1.51	1.72	1.73

lists the base shear values and corresponding drifts for each performance point.

An overview of the changes in the main structural parameters is presented in Figure 18 for corrosion rates of 10% (CL_10%) and 20% (CL_20%), compared to the initial state (0% corrosion).

The initial stiffness ratio of 1.0 in both scenarios indicates no change, suggesting that corroded external bars did not affect elastic stiffness at loading onset. Maximum resistance decreased by 5% at 10% corrosion and 13% at 20%, indicating that corrosion impacted the load-bearing capacity. The corresponding drift at maximum resistance decreased only at 20% corrosion, with ratios of 0.99 for 10% and 0.94 for 20%, showing reduced deformation absorption ability at higher corrosion rates. Secant stiffness also slightly decreased with increased corrosion, affecting post-elastic performance: the ratio was 0.96 for 10% and 0.92 for 20%. A decrease in yield strength and drift was noted, with ratios of 0.95 for 10% and 0.87 for 20%, indicating that the structure yields with smaller deformations when external bars are corroded. The analysis of the capacity curves and bilinear models enabled the extraction of the absolute inter-storey displacements (Figure 19a) and inter-storey drifts for each floor (Figure 19b) corresponding to the performance state point SD. Between corrosion rates of 0% and 10%, the displacement profile increased from 12.07% to 14.51%. However, between 10% and 20% corrosion, displacements remained similar across floors, varying by up to 3%. The performance state point SD on the capacity curve indicated that significant damage occurred at 10% and 20% corrosion at the same displacement level, while for 0% corrosion, this point appeared at a lower displacement.

Inter-storey drift distribution along the building height showed a clear reduction with increasing height, regardless of corrosion levels. Similar to previous scenarios, a 10% corrosion rate led to increased floor drift, ranging from 7.7% to 14.69%, making the structure more vulnerable to larger deformations. In contrast, at 20% corrosion, inter-storey drifts showed minimal variation (up to 3.4%). Drifts between the ground and first floors exceeded the 1% limit in all cases, with the risk of non-structural damage increasing with higher corrosion rates.

4.5. Scenario 4

Figure 20 shows the capacity curves and idealized bilinear curves for both the uncorroded condition (REF) and the corroded condition (WC), which, as previously mentioned in Section 3.3, consists of two simultaneously corroded zones: 20% from the ground floor to the first floor and 10% from the first to the third floor.

The parameter values from the capacity curves and idealized bilinear curves for the analysed corrosion rates are summarized in

Table 15. Scenario 4: extracted response parameters for each corrosion level.

Response Parameters	Ref	WC
Initial Stiffness (kN/m)	18,422	18,243
Maximum Strength (kN)	2542	2349
Drift (Maximum Strength) (%)	1.32	1.22
Secant Stiffness (kN/m)	12,003	12,048
Yield Force (kN)	1017	940
Yield Drift (%)	0.35	0.32

. The performance points (DL, SD, and NC) on the capacity curves showed a similar pattern to scenarios 2 and 3.

Table 16. Scenario 4: corresponding base shear and drift of performance points.

Corrosion Level		Ref	WC
Damage Limitation	Base shear (kN)	1773	1896
	Drift (%)	0.68	0.78
Significant Damage	Base shear (kN)	2119	2213
	Drift (%)	0.87	1.00
Near Collapse	Base shear (kN)	2456	1969
	Drift (%)	1.51	1.73

presents the base shear values and corresponding drift for each performance point. Figure 21 shows the changes in primary structural parameters due to corrosion (WC) compared to the initial uncorroded state.

The initial stiffness ratio was 0.99, indicating a minimal impact of corrosion on this parameter, while the secant stiffness ratio was 1. This is due to the upper uncorroded floors still significantly contributing to the structure’s behaviour. The maximum strength ratio from the capacity curve was 0.92, reflecting an 8% reduction in resistance capacity, primarily due to corrosion affecting the lower facade elements where stress concentration is higher. The drift at maximum strength also showed a ratio of 0.92, indicating an 8% reduction in deformation capacity. The yield strength ratio was 0.92, highlighting an 8% reduction in elastic capacity due to corrosion in the lower floors. Lastly, the drift corresponding to yield strength had a ratio of 0.93, suggesting that corrosion advanced the yield point with less deformation, indicating increased fragility.

The analysis of the capacity curves and bilinear models enabled the extraction of the absolute inter-storey displacements (Figure 22a) and inter-storey drifts for each floor (Figure 22b) corresponding to the performance state point SD.

The displacement profile reveals increased fragility in the structure, with displacements rising from 12.52% to 18.15% in the corroded state. The inter-storey drift profile showed a consistent decrease with building height, with higher inter-storey drift values per floor in the corroded scenario, indicating reduced lateral resistance and increased susceptibility to deformations. Notably, the drift between the ground and first floors exceeded the 1% limit in both states.

4.6. Global Comparison

Figure 23 provides a comparative overview of all analysed scenarios with key parameters presented in a normalized format.

Figure 23a shows the normalized initial stiffness for each scenario, indicating negligible variation across different corrosion rates, remaining close to 1, which suggests that structural stiffness is largely unaffected by corrosion levels (10% and 20%). Figure 23b illustrates the normalized maximum strength values, showing a consistent decrease with increasing corrosion rates. For 10% corrosion, values range from 0.93 (Scenario 1, greatest loss) to 0.98 (Scenario 2.A, least affected), with Scenarios 2.B and 3 at 0.95. At 20% corrosion, Scenario 1 drops to 0.84, while Scenario 2.A remains stable at 0.91; Scenarios 2.B and 3 are around 0.87. Scenario 4, with varying corrosion, shows a normalized maximum strength of 0.92, indicating a moderate impact. The normalized drift at yield values in Figure 23c decreases with increasing corrosion rates. For 10% corrosion, values range from 0.94 (Scenario 1, greatest reduction) to 0.98 (Scenario 2.A, least impact), with Scenarios 2.B and 3 at 0.96 and 0.95, respectively. At 20% corrosion, Scenario 1 drops to 0.86, while Scenario 2.A remains at 0.91. Scenarios 2.B and 3 show values of 0.89 and 0.87, and Scenario 4 presents a drift of 0.93, similar to the 10% corrosion scenarios. Figure 23d shows the secant stiffness for each scenario, revealing minor differences of up to 3% between corrosion rates. Scenario 1 experienced the greatest reductions, with 6% and 9% losses at 10% and 20% corrosion, respectively. In contrast, Scenario 2.A had only a 1% reduction for both rates. Scenario 2.B showed intermediate reductions of 4% and 5%, while Scenario 3 had reductions of 4% and 8%. Corrosion did not affect Scenario 4. Figure 24 illustrates the degradation of maximum strength and initial stiffness with increasing corrosion across different scenarios. Overall, the results indicate minimal variation in the seismic response of the structure due to corrosion, in contrast to more concerning findings in the existing literature. This discrepancy may be attributed to the predominant influence of the central columns, which remain unaffected by corrosion, thereby limiting its impact on the overall structural behaviour. Furthermore, since initial stiffness is primarily governed by the concrete, the reduction in the reinforcement bar cross-section does not significantly alter the initial response. Additionally, the case study developed by Maranhão et al. [23] was optimized, and during nonlinear pushover analyses, the effects of corrosion may not have been adequately detected or assessed.

Finally, it is important to clarify that the type of damage observed in the structures subjected to the four corrosion scenarios was largely similar, and was characterised by a shear failure, primarily due to the reduction in transverse reinforcement area caused by corrosion. No consistent pattern was identified regarding which specific element reached the shear failure first. However, in all cases, the first failure occurred in a column located on the ground floor of the building.

5. Conclusions and Future Works

RC structures are widely used in modern construction; however, over their service life, they are subject to degradation processes such as corrosion. Understanding how corrosion affects the seismic behaviour of these structures is therefore essential. Nevertheless, predicting this behaviour remains a significant challenge in numerical modelling. Additionally, the literature presents a scarcity of studies on modelling strategies that incorporate the effects of corrosion in reinforced concrete structures, making this field even more complex and underexplored.

This research work set out two main objectives: first, to contribute to scientific advancements in the numerical simulation of the seismic behaviour of RC structures subjected to corrosion, and second, to investigate the impact of corrosion on the seismic performance of these structures.

To achieve these goals, simplified simulation strategies were proposed and validated to represent the effects of corrosion on reinforcement bars within reinforced concrete structures. Following the validation process, an analysis of five distinct scenarios was conducted using the nonlinear pushover analysis method, allowing for a detailed characterization of the structural capacity and deformability under different levels of corrosion-induced degradation. The following conclusions were drawn from the development and validation of numerical simulation strategies:

• The model accurately reproduced experimental results by properly defining material properties and simulation strategies, validating its application for assessing corrosion effects on structures under lateral loads;
• Initial stiffness and maximum strength were captured well, with errors not exceeding 13% for positive cycles and 6% for negative cycles in initial stiffness and 3% and 7% for maximum strength;
• A significant challenge was simulating bond conditions between concrete and steel; neglecting this led to models that failed to show resistance degradation with increasing displacements.

The following conclusions were drawn from the study of the seismic behaviour of different scenarios:

• Initial stiffness showed minimal degradation with increasing corrosion, while maximum strength and corresponding displacements significantly decreased. A 10% corrosion rate reduced maximum strength by 2–7%, and a 20% rate reduced it by 9–16%. Displacements associated with maximum strength decreased by 1–5% and 8–13% for 10% and 20% corrosion rates, respectively;
• Yield force and yield displacement indicated that corrosion degraded the structure’s elastic behaviour, increasing vulnerability to seismic actions. Yield force decreased by 2–7% for 10% corrosion and 9–16% for 20%, while yield displacement decreased by 1–6% and 6–14%, respectively;
• High corrosion levels significantly altered the dynamic behaviour, particularly affecting lower floors, which experienced drifts exceeding 1%. This raises concerns about potential damage to non-structural elements (e.g., infill walls), highlighting the need to consider corrosion’s impact on overall building safety and post-seismic repair costs.

One of the main limitations of this study lies in the simplifications adopted in corrosion modelling, particularly the assumption of uniform degradation in certain scenarios and the inability to assign different material properties to individual reinforcement bars. While these assumptions allowed for a consistent and comparative analysis, they may not fully capture the localized effects of corrosion observed in real structures. More refined simulations need to be carried out, focusing on real corroded structures, and comparison with the results obtained herein may be validated.

Also, given the large number of parameters involved in the corrosion scenarios and structural configurations, a more comprehensive statistical or sensitivity-based approach could offer further insight into the influence of each variable.