PSI - Issue 62

Simone Celati et al. / Procedia Structural Integrity 62 (2024) 361–368

366

6

Simone Celati et alii/ Structural Integrity Procedia 00 (2019) 000 – 000

( , ) =

( ) −

(12) The assessment of the time-dependent bending capacity follows the methodology detailed in both Section 2 and Section 3.1. Specifically, the corrosion model, described in Sections 2.1 and 2.2 for corrosion initiation and propagation, is utilized to determine the remaining area of each tendon. Subsequently, Section 3.1 outlines the models for the residual strength of corroded cables and the bending resistance. Permanent and traffic loads are considered, and their distributions are outlined in Section 3.2. The bending demand is calculated, accounting for the Courbon redistribution of loads as explained in Section 3.2. The environmental variables and the mechanical variables considered in the vector are outlined in Table 1. Table 1. Input variables and associated distributions and parameters Variable Distribution Mean Standard Deviation aa Variable Distribution Mean Standard Deviation c [mm] D 35 - K E +++ LN 1 0.1 Ccr + B 0.6 0.15 K C ++++ LN 1 0.05 Cs + LN 2 0.9 M G [kNm] ** N 11248 562 A0 [mm 2 ] D 38.48 - M Q [kNm] NS 8136 234 V ,corr,a [mm/year] ++ W 0.03 0.02 EC D 2 - fy [MPa] +++ N 1414 353.5 RH [%] +++++ W [0;100] 75 15 fc [MPa] * LN 44.1 8.82 [CO 2 ] [%] ++++++ D 0.04 - K R +++ LN 1.2 0.18 Cl [kg/m 3 ] D 300 - N: Normal; D: Deterministic; B: Beta; LN: Log-normal; W: Weibull; NS: Non-standard form. *Evaluated considering 30 MPa as the 5% characteristic value, with a coefficient of variation equal to 0.20. ** Evaluated considering a coefficient of variation equal to 0.05. + (International Federation for Structural Concrete, 2015); ++ (DuraCrete, 2000); +++ (JCSS, 2001); ++++ (Straub et al., 2009); +++++ (Lay et al., 2003); ++++++ (Stewart and Peng, 2008) 3.4. Reliability evaluation The probability of failure and the reliability index are computed annually based on the established probabilistic model. Calculations are executed by performing a Monte Carlo Simulation with 10 7 samples. Because the time dependent variables are evaluated each year and the load are modelled as the maximum annual load, the resulting failure probability represents annual failure probability. Fig. 2 depicts the annual failure probability and reliability index when either the proposed degradation model or the conventional model for chloride-induced corrosion is considered. The provided figures indicate that the proposed model (solid line) has a longer time to active corrosion and a slower corrosion rate. As a result, the probability of failure over time increases and becomes unacceptable for broader time frames compared to when only chlorides-induced corrosion (dashed line) is taken into account.

a)

b)

Fig. 2. a) Girder’s annual failure probability; b) Girder’s annual reliability index