The corrosion of reinforced concrete frames contributes to the decline in the performance of existing structures. The latter is due to the diffusion of aggressive agents in the concrete, such as carbon dioxide or chloride ions. This diffusion produces a reaction that gives corrosion products. The development of corrosion products leads to three main effects: the reduction of the steel section, the development of a specific cracking from the frame to the outside of the structure and the modification of the adhesion properties to the steel/concrete interface depending on the degree of corrosion [1, 2].

This study aims to elucidate the impact of diminished cross-sectional area in corroded steel reinforcement within reinforced concrete portal columns. This impact is assessed in the context of two distinct soil types and their influence on the seismic vulnerability of the reinforced concrete structure. Various approaches exist for appraising the seismic performance of a structure. In this research, a pushover analysis, capable of characterizing the nonlinear structural response during seismic events, is employed to pinpoint the performance points of portal frame structures along the capacity curve. The seismic performance of the corroded reinforced concrete (RC) frame structure was evaluated through numerical simulation, employing the pushover analysis method. This method was selected due to its widespread utilization and practicality in assessing the seismic performance of RC frame structures within the middle-low structural vulnerability category [3, 4]. Seismic loads are determined in adherence to the regulatory provisions outlined in the Moroccan Earthquake-Resistant Building Regulation RPS2011 [5], which defines equivalent static charges of triangular shape. Nonlinear behaviour is defined at the base of the plastic hinges. The plastic development state of the structure is effectively represented by the plastic development state of its plastic hinges. This correlation underscores the importance of the plastic development degree of the plastic hinges as a reflection of the overall plastic development degree of the structure. The outcomes of this analysis are graphically depicted by a curve that establishes a relationship between the base shear force and the top displacement of the structure.

Therefore, this study aims to determine the performance point of an RC portal frame in two different soil types by performing the pushover analysis on the SAP2000 software [6] while reducing the steel section at 25, 50, 75 and 100 years. On the other hand, the ductility of reinforced concrete structures corroded in different soil types is analyzed. Moreover, the interstorey displacement is determined according to the age of the building and the type of soil. Finally, the results will be discussed and interpreted.

The aim of this article is the determination of the performance point on the pushover curve in the case of a corroded reinforced concrete portal frame and tree-floor RC structure. This corrosion, due to the ingress of chloride ions, is of a generalized type in the reinforcement of the supporting elements: the ground floor columns. The calculation of the seismic forces is carried out in two site cases: site S1, representing rocky soil, and site S4, representing loose soil, defined according to the Moroccan standard: Earthquake resistant buildings regulation RPS2011.

The methodology used in this article is as follows:

• Modeling of the portal frame structure using SAP2000 software (materials and loads).
• Determination of the corrosion initiation time Tini.
• Estimation of the diameter of the reinforcement in the load-bearing elements on the ground floor at different ages of the portal frame (0, 25, 50, 75 and 100 years).
• Software modeling of the corroded structure and determination of plastic hinges.
• Application of pushover analysis.
• Comparison between the pushover curves obtained, the global displacement results and the inter-storey displacements in the two soil cases treated.

The building model has three stories with a story height of 3.5 m on the ground floor and 3.20m on the other floors (Fig. 1).

Table 1 details the characteristics of the structural elements.

Tables 2 and 3 [5] presents the seismic forces in the two cases of soil S1 (rocky soil) and S4 (loose soil).

With: T: fundamental period of vibration of a building (s); ν: Zone speed coefficient; S: soil factor. D: Dynamic amplification factor. I: priority coefficient. K: behaviour factor; W: weight of the structure. V: the base shear force.

Fig. (1). The characteristics of the portal frame studied, the size and location of the columns (PO 1-2) and beams (PT 1-2).

Table 2. Summary of the base shear force calculation.

Case	T (s)	v	S	D	I	K	W (KN)
Soil S1	0.516	0.17	1.8	1.864	1.2	3.5	1247.8	244.058
Soil S4	0.516	0.17	1	1.864	1.2	3.5	1247.8	135.587

The total lateral seismic force F (= the base shear force V) must be distributed over the height of the structure as follows: Part Ft of the force F is allocated to the top of the building, the rest(F-F_t) must be distributed over all levels including the top floor according to the following equation:

(1)

With: F_t=0 if T ≤ 0.7 s

F_t=0.07 T F if T > 0.7s

F: total lateral seismic force; F_n: horizontal design force applied at level n; W_n:total load at level n; h_n:height of the floor considered from the ground; T:fundamental period of the structure; F_t: additive force at the top storey.

In the case stated, the distribution of the horizontal seismic forces in KN at the different storeys F_n is in Table 3.

The Fn is presented in the Fig. (2).

According to DuraCrete [7] and Choe et al. [8, 9], the corrosion initiation time by penetration of chlorides is:

(2)

(3)

Where: a is the reinforcement cover depth, k_e is an environmental factor, k_t represents the influence of test methods to determine the empirical diffusion coefficient D₀, k_c is a parameter that accounts for the influence of curing, t₀ is the reference period for D₀, n is the age factor, X_i is a model uncertainty coefficient to account for the idealization implied by Fick’s second law, Cs is the chloride concentration on the surface, w/c is the water-to binder ratio, A_cs and ε_cs are model parameters, C_cr is the critical chloride concentration, and erf is the error function.

The calculation of the initiation time of corrosion by equations (2) and (3) is presented in Table 4 [7, 10, 11].

The diameter D(t) of the reinforcements at the end of (t-T_ini) is equal to [9, 12, 13]:

(4)

Where: D_i: initial diameter of the reinforcements; t: time (years) and T_f is the time when D_i=0.

Using equation (4), the bar diameters of the ground floor columns are calculated at 25, 50, 75 and 100 years, as shown in Table 5.

Table 6 gives the main values of concrete and steel. The degradation of the mechanical properties of steel is not considered because of their low weights, which has been demonstrated in the literature [14].

Also, the seismic coefficients used according to the soil are [15]:

• For soil S1: c_a = c_v = 0.18.
• For soil S4: c_a = 0.34 ; c_v = 0.528.

These results are obtained by combining the codes ATC40 [16] and RPS 2011 [5]. The plastic hinges will be introduced according to ASCE 41-31 [17] defined by default in the SAP2000 V20 software.

Fig. (2). Vertical distribution of seismic force.

Fig. (3). Capacity curves in the case of two soils.

In conclusion, this paper presents the variation of the seismic response of a reinforced concrete portal frame in two cases of soil (rocky and loose soil) and different ages of corrosion (at 25, 50, 75, and 100 years). The case treated is the moderate corrosion of the reinforcement of the ground floor columns according to the corrosion model by penetration of chlorides. This model allows the calculation of the corrosion initiation time and the variation of the section of the reinforcements. The seismic analysis is based on the static non-linear Pushover method. The seismic loads were computed in accordance with the guidelines stipulated in the Moroccan earthquake-resistant building regulations RPS 2011.

The pushover curves show that the corroded frame's seismic bearing capacity decreased significantly due to the corrosion of its rebars. Furthermore, it is observed that as the rate of rebar corrosion increases, there is a corresponding escalation in the gradual degradation of the structural bearing capacity. The corrosion of the reinforcement of the ground floor columns of the structure causes a loss of its ability to resist seismic loads with time. On the one hand, the top displacement increases over time. Indeed, on loose soil, it is noteworthy that the base shear force and the maximum displacement at the performance point assume a more critical significance. On the other hand, the ductility of the structure, which does not depend on the type of ground, increases with the corrosion time of the construction.

Likewise, the findings suggest that as the corrosion rate increases, the inter-storey displacement experiences a reduction. It is evident that there is a decrease in inter-storey displacement as the corrosion rate of the structure increases. The values of the inter-storey drift are essential in the case of loose soil S4 compared to rock soil S1.