PSI - Issue 78

Valentina Picciano et al. / Procedia Structural Integrity 78 (2026) 1167–1174

1169

The PCI Design Handbook offers an alternative method based on extensive experimental data, identifying five main failure modes: vertical flexural cracking in the nib, direct shear failure at the nib-beam junction, diagonal tension cracking at the re-entrant corner, shear failure within the nib, and diagonal tension in the undapped region (Fig. 1a). However, this method does not incorporate inclined reinforcement and is limited to shear span-to-depth ratios below unity, making it less suitable for the assessment of existing bridge saddles. Additional models have been developed to address specific failure mechanisms. For example, kinematic approaches focus on assumed crack patterns and their associated energy dissipation mechanisms (Rajapakse et al. 2021). Numerical methods based on nonlinear fracture mechanics and finite element analysis offer a more refined understanding of saddle behaviour, especially when combined with degradation models that simulate long-term corrosion effects (Santarsiero et al. 2021). However, these methods are computationally intensive and less practical for rapid assessments across large bridge inventories. In order to support a broader understanding of Gerber saddles’ behaviour, an extensive review of experimental tests in the literature was conducted, leading to the creation of a dedicated database. The final database comprises 210 experimental tests sourced from 22 different research programs. For each test, key parameters were collected, including specimen geometry, reinforcement layout (vertical, horizontal, inclined), concrete strength, steel yield strength, loading configuration, and observed failure mode. In most cases, the failure mode was attributed according to the classification proposed in the PCI Design Handbook, allowing for consistent comparative analysis. Statistical analysis of the database revealed significant variability in specimen configurations. Approximately 60% of the specimens had a total depth exceeding 500 mm, and the majority exhibited a shear span-to-depth ratio ( a/h ) below 1.0, aligning with typical bridge applications. In terms of concrete strength, nearly half of the specimens were classified as high-strength ( f c > 40 MPa), while reinforcement grades varied, with over 50% using steel with yield strength below 320 MPa.

(a) (c) Fig. 1. a) Half-joint’s failure modes according to the PCI design Handbook; b) typical reinforcement layout with only horizontal and vertical rebars and c) also with inclined ones. Regarding reinforcement detailing, two main configurations were observed: a traditional layout with only vertical and horizontal rebars (Fig. 1b), and an enhanced layout including inclined reinforcement (Fig. 1c). Only 36 of the 210 specimens included inclined bars, yet their presence had a clear influence on failure behaviour. In tests with inclined reinforcement, combined failure modes (especially modes 3 and 4) were prevalent, while pure nib shear failure (mode 4) was significantly reduced. This suggests that inclined reinforcement not only increases load-bearing capacity but also contributes to controlling diagonal cracking and delaying brittle failure mechanisms (Santarsiero et al. 2025). 3. Machine learning for structural strength assessment To complement the statistical analysis mentioned above, the database was used to train supervised machine learning models to predict the ultimate load capacity of half-joints. This rich dataset enabled the application of regression techniques to model the relationship between the input parameters—such as geometry, material properties, and reinforcement layout—and the experimental load-bearing capacity, which served as the output variable. By learning (b)