PSI - Issue 78

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

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where c 0 is the concrete cover. The crack opening increases with the expansion of corrosion products up to a critical width, conventionally sets to 1 mm. The spalling of concrete cover is assumed to occur when this threshold is reached. Figure 3 illustrates the temporal evolution of two critical parameters influencing the durability of reinforced concrete structures: the reduction of cross-sectional area of the rebar and the reduction of concrete compressive strength, caused by the rebar corrosion-induced cracking. In the investigated case study, it has been assumed that the rebar corrosion begins in the twelfth year when the carbonation depth exceeds the concrete cover thickness, that corrosion progresses linearly, as a uniform corrosion rate has been assumed once initiated and that Compressive strength reduces over time, after the corrosion initiation. The evolution is therefore characterised by an initial slight decrease up to about 40 years, after which the strength drastically declines as corrosion reaches an advanced state. In the following Sections, the analyses are conducted by considering the undegraded structure first, and then a degraded state after 10, 20, 50, and 100 years. This timescale encompasses the bridge current age, which is over 50 years old, and the nominal lifespan of such structures, which is usually 100 years.

(a) (b) Fig.3. (a) Evolution of corrosion over time; (b) Degradation of compressive strength over time due to cracking

5. Impact of corrosion on the structural response 5.1. Influence of degradation on vibration modes

According to what is described in section 4, several eigenvalue analyses were carried out by varying the mechanical parameters of the materials at each step, to account for a progressive increase of degradation, from the intact structure (t 0 ) to the degraded structure at 100 years (t 100 ). Figure 4 presents the mode shapes for the three lowest modes of vibration at time 0, whereas Figure 5 illustrates the evolution of the corresponding periods over time (expressed in years), reflecting the progressive degradation of the material properties. It is worth noting that the elastic modulus of concrete was determined as a function of the varying compressive strength, in accordance with the Italian standard (NTC, 2018).

(a)

(b)

(c)

Fig.4. Bridge mode shapes:(a) first mode; (b) second mode; (c) third mode.

While the analysis demonstrates that mode shapes and participating masses are poorly affected by corrosion, likely