PSI - Issue 84

Alessandro Nettis et al. / Procedia Structural Integrity 84 (2026) 653–660

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3. Methodology In this Section, the new proposed geometric model is detailed and the adopted methodology to calibrate it is presented. As stated in Section 2.2, the model is based on a parabolic shape to geometrically model the corrosion pit on a single wire. The basic concept of the proposed model is to compute the area loss of a prestressing steel wire by intercepting the uncorroded wire circle with a specific parabola, whose vertical axis runs through the circumference centre. An example of a corrosion pit obtained following such model is represented in Figure 2.

Figure 2. An example of corrosion pit according to the proposed geometric model: is the parabola opening parameter, is the maximum pit depth and is the radius of the external wire of a strand. Analytically, by adopting a proper Cartesian coordinate system , the generic steel wire with radius can be modelled through a circular shape, adopting Equation (6). The coordinate system’s origin can be conveniently placed at the centre-top of the wire circle. In such configuration, the corrosion pit can be modelled by a parabola whose intercept represents the maximum depth of the pit (assuming in this case a negative value, see Figure 1). As a consequence, the parameter , hereafter referred to as , can range between the two extreme situations of uncorroded wire ( =0 ) and fully corroded wire ( =2 ). For a given , an infinite number of possible values of area loss can be theoretically defined given by the parabolas bundle described by Equation (7). ( ): 2 + ( + ) 2 = 2 (6) ( , ): = 2 − (7) This parabolas bundle has a single parameter , representing the parabola opening. The intersection of such bundle with the wire circumference, considering the domain, always exists and is represented by two distinct points. For this reason, an area resulting from the intersection between the parabolas bundle and the wire circumference can always be computed and represent exactly the corrosion pit area. Such model can be adopted for simulating values of area loss for prestressing strands in probabilistic structural analysis, through appropriate statistical distributions for the two parameters. Herein, a statistical distribution describing the parameter is proposed. Such distribution is fitted on the experimental results obtained by Vecchi et al. (Vecchi et al., 2021) on naturally corroded prestressing strands, adopting the following methodology. An example of the data available in the database is reported in Table 1.

Table 1. Corrosion data of a corroded strand extracted from the database provided by Vecchi et al. (Vecchi et al., 2021).

[mm] 1.198

[mm] , [mm 2 ] 1.98 3.87

[mm] 20.29

Identifying Code PB9-L(12-82)

Wire

W1 W2

1.336 3.98 First, the maximum pit depth and the area loss are retrieved from the database for each single wire. The wire circumference ( ) is analytically modelled in the most appropriate coordinate system. Then, the parabolas bundle ( , ) is defined following Equation (7), where coincides with . Solving the corresponding equation system (Equation (8)), two intersection points 1 =( 1 ( ), 1 ( )) and 2 =( 2 ( ), 2 ( )) can be computed . 27.03 2.36