PSI - Issue 78

Simone Reale et al. / Procedia Structural Integrity 78 (2026) 1657–1664

1660

Strategy 4 includes bond-slip and LCF. Bond-slip, included in the model through a zero length element, is described according to (Zhao and Sritharan, 2007). Corrosion is included by modifying the slip at yield stress s y c according to: ( ) = 2.54 (( 8(4 3 7 ) ) , √ ( ) ′ ( ) (2 + 1)) 1 +0.34 (14) where d b c is the residual diameter of a bar at time t and α s is a parameter taken as 0.4. The effects of corrosion on LCF are considered by modifying the α factor of Coffin-Manson fatigue model as per (Kashani et al., 2015): = [1 + 0.004 ] (15) Table 1. Overview of the corrosion damage modeling strategies applied for the long-term seismic performance assessment.

Modeling Strategy

Reinforcement Section Loss

Bond-Slip LCF

ε su

f c

f c

ε

f y

f u

'

cu

1 2 3 4

Yes Yes Yes Yes

No

No

No No

No

No

No No

No No No

No No No

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes

Yes Yes

Yes

Yes

3. Case Study The present investigation considers a prototype bridge designed according to modern design and durability standards. The structure is located in Reggio Calabria (Italy). The exposure conditions are assumed to be comparable to the XS3 Eurocode exposure class. The bridge consists of two 30 m simply supported spans supported by elastomeric devices. The deck is composed of six PC beams with a 0.25 m thick RC slab. The bridge bent includes three columns with 0.9x0.9 m section and a cap beam. The longitudinal reinforcement of the columns consists of 36 φ24 bars, w ith four legs φ10 stirrups with spacing 150 mm as transverse reinforcement. The concrete cover depth is 60 mm, according to Eurocode prescriptions. A water-to-cement ratio w/c of 0.45 has been assumed. 4. Long Term Seismic Performance Assessment 4.1. Corrosion Modeling Time dependent chloride concentration C(x,t) at a given depth x and time t is estimated through the error function solution of 1D Fick’s Second Law of Diffusion (Ferreira et al., 2015), as per Equation (1 6): ( , ) = 0 +( ,∆ − 0 ) ∙ [1 − ( −∆ 2∙√ ( )∙ )] (16) Where C 0 is the initial chloride content [wt.-%/c], C s,Δx is the chloride content resulting from environmental exposure at depth Δx , Δx is the depth of the convection zone [mm], erf is the Gaussian error function and D app (t) is the apparent chloride diffusion coefficient at time t [mm 2 /year]. Corrosion is assumed to start once that the critical concentration of free chloride ions C crit on the surface of steel bars is reached. Due to the inherent uncertainty of the process, the parameters of Equation (16) are modeled as Random Variables (RVs), as described in Table 2, and Monte Carlo simulation is performed to model chloride diffusion and corrosion propagation over time.