PSI - Issue 78

Gregory Santilli Di Luia et al. / Procedia Structural Integrity 78 (2026) 1513–1520

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the need for analyses that consider its impact on the structure dynamic response. Therefore, degradation mechanisms were modelled considering the approaches and the scenarios described in the following Section. 4. Corrosion models and degradation scenarios Based on the on-site survey, concrete carbonation, along with the consequent cracking and corrosion of the reinforcement, was incorporated into the model to assess its impact on seismic vulnerability. For the steel bars cross sectional reduction, the approach developed by Tuutti (1982) was followed. This approach describes the corrosion process with two phases: ( i ) the initiation phase, involving the penetration of chlorides or carbonation to the depth of the reinforcement, and (ii) the propagation phase, during which, once passivation is lost, actual corrosion begins, leading to a reduction in the reinforcement bars. The calculation of the loss of the load-bearing cross-section of the reinforcement bars, namely the difference, ∆ ( ) , between initial value of the diameter and the reduced vale at time t , is carried out adopting the formulation proposed by Gotti et al. (2010): ∆ ( )= ∙ ∙[∅ 0 − ∙∅ ′ ( )] 2 4 > 0 (1) where Nₛ is the number of reinforcement bars, ∅ ₀ is their initial diameter, ∅ ′(t) is the corrosion penetration depth, t₀ is the corrosion initiation time, and the coefficient n accounts for the possibility of either one-sided or two-sided corrosion attack on the reinforcement. The corrosion penetration depth can be evaluated as follows: ∅ ′ ( ) = 0.0116 ∙ ∙ ( − 0 ) (2) where the constant 0.0116 is a conversion factor to switch from / 2 a / and is the corrosion rate, calculated according to (Vu and Stewart 2000): = 37.8∙(1− ) −1.64 (3) where c is the concrete cover depth and a/c is the water to cement ratio. Moreover, the degradation of concrete mechanical properties was considered using the formulation proposed by Coronelli and Gambrova (2004). The reduced concrete strength can be evaluated as follows: = 0 1+ 1 0 (4) where 0 is the undegraded concrete strength, K is a coefficient related to bar diameter and roughness (equal to 0.1 for medium-diameter ribbed bars), ε c0 is the strain at peak stress in compression, and ε 1 is an average value of the tensile strain in cracked concrete at right angles to the direction of the applied stress, which can be evaluated by means of the following relationship: 1 = − = (5) where b i is the width of the unaltered concrete cross-section and b f is the width after corrosion cracking, accounting for the number of steel bars, n bars , and the mean crack opening for each bar, w . Among the relationships proposed in literature to evaluate the crack opening w , the empirical model proposed by Vidal et al. (2004), which depends on the amount of steel damage necessary for cracking initiation, δ s0 , was assumed: = 0.0575( − 0 ) 0 (6) 0 =1−[1− 0 (7.53 + 9.32 0 0 )×10 −3 ] 2 (7)