# Climate Change Impact on Corrosion of Reinforced Concrete Bridges and Their Seismic Performance
## 3 Structural Modelling and Analysis Method  
To assess the seismic vulnerability of existing RC viaducts in the presence of corrosion of the steel reinforcement due to carbonation, the structural modelling approach described in [56] is used. This method starts with the realization of simplified 3D FEMs (finite element models) by means of the MIDAS Civil 2023 commercial software [57], using only Timoshenko beam elements to implement the main structural elements, such as the deck, the pier caps, and the piers, in order to optimize the computational effort, while the elastomeric bearings are modelled using elastic links characterized by rotational and translational stiffnesses, evaluated as reported in [58]. The connection between the previously mentioned elastic links and the beam elements of the deck and the pier caps is realized by means of rigid links (Figure 7). In order to obtain the correct dynamic behavior of this type of structure, a reduction in the piers' bending stiffness is introduced by means of appropriate scale factors, considering the main points which define the moment-curvature (M-x) diagram of the piers' gross-sections, applied to the concrete cross-section elastic stiffness, which characterizes the piers of the viaduct, using the relation reported in [59]. The stiffness which characterizes the deck, instead, is not reduced, as this remains within the elastic range when the viaduct is subjected to a seismic event [60; 61]. The pier foundations and the abutment are not implemented in the FEM but are modelled as perfect restraints, applied at the node located at the bottom end of the pier and at the nodes representing the base of the elastomeric bearings present in the abutment-deck interface, respectively. The presence of the deck pavement and guard rails (non-structural elements) is introduced in the FEM by means of uniform distributed loads applied, in correspondence with the beam elements representing the deck. Also, the presence of the deck cross beams is added through the application of nodal loads to the beam elements representing the deck, in correspondence with their position along the deck's longitudinal axis. The traffic load is not considered in this work, according to the method reported in [16]. For each pier, two collapse mechanisms are evaluated: (i) the ductile and (ii) the brittle collapse mechanism. In particular, the first failure mechanism is governed by the trend of the M-x diagram, which characterizes the pier gross-section and presents a large strain-hardening plastic behavior, which follows an initial elastic branch; the second failure mechanism is defined by a load-displacement diagram having a linear behavior, until the ultimate shear strength of the monitored structural element is reached. It is important to highlight that the first failure mechanism is governed by the rotational capacity of the monitored plastic hinge. The development of the second failure mechanism depends on the pier shear strength. To introduce the non-linear behavior of the materials, two different constitutive laws are adopted: the Kent and Park model [62] and Park strain hardening [63] model, for concrete and steel reinforcement, respectively. Figure 6: Evaluation of \(i_{corr}\) variations over time for low, moderate, and high corrosion scenarios (\(i_{corr,20}=0.1\), \(1\), and \(5\)\(\mu\)A/cm\({}^{2}\)). Considering the first ductile failure mechanism, the verification criteria adopted is the achievement of 3% of the ultimate rotation, \(\theta_{\mathrm{u}}\), while the brittle collapse mechanism is the overcoming of the shear strength of the considered pier, evaluated using the cyclic shear resistance method proposed by [64]. The corrosion effects are implemented in the FEM using an analytical model that describes the evolution of the reduction of the steel reinforcement diameter.