PSI - Issue 78

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

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transverse elements—as long as proper assessment of existing reinforcement is conducted to avoid interference when drilling into the concrete. Experimental studies in the literature have quantified the average performance improvements provided by these techniques, both at service and ultimate limit states, including changes in failure mechanisms from the as-built to the strengthened condition. These outcomes have been deeply discussed in previous research by Santarsiero et al. (2025).

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Fig. 4. a) Different configuration of using external post-tensioning; b) steel jacketing intervention; c) externally bonded composites application.

5. Nonlinear FE analysis for the optimisation of post-tensioning interventions In this section, the structural behaviour of Gerber saddles reinforced with external post-tensioning was investigated through nonlinear finite element analysis. Two specimens from the experimental campaign by Rajapakse et al. (2022) were selected for detailed modelling, namely 1-OL1 and 2-OL3. These represented different reinforcement ratios and failure modes, allowing investigation into post-tensioning effectiveness across varying structural behaviours. The two Gerber saddles shared the same geometric configuration but differed significantly in vertical and horizontal reinforcement quantities, with 2-OL3 having approximately double the reinforcement of 1-OL1. Detailed information regarding specimens and modelling parameters can be found in Santarsiero and Picciano (2024). The numerical models were developed using the software ATENA (Cervenka Consulting 2021), including detailed 3D representations of the test setup with support and loading plates, reinforcement, and concrete volumes. The nonlinear material behaviour of concrete was modelled using equivalent uniaxial constitutive laws derived from biaxial failure criteria. The concrete model incorporated compression softening, tensile cracking, and fracture energy based crack propagation, ensuring an accurate representation of both pre- and post-peak behaviour ( Bažant and Oh 1983). Steel reinforcement was modelled using bilinear stress-strain laws, including strain hardening. Model calibration was based on material parameters derived from the experimental data, with particular emphasis on compressive strength ( f c = 56.8 MPa), rebars tensile resistance ( f y ranging from 509 to 599 MPa, and f u ranging from 634 to 703 MPa) and fracture energy of concrete ( G F = 101.2 N/m). The final models result in over 13,000 hexahedral elements and approximately 1,300 truss elements representing the reinforcement. Displacement-controlled analyses were carried out until complete failure was reached. The calibration phase demonstrated excellent agreement between numerical and experimental results for both modelled beams. Load-displacement curves from the simulations overlapped closely with the experimental ones, confirming the validity of the adopted constitutive models and modelling strategy. Furthermore, the numerical models were able to accurately replicate the observed cracking patterns at failure, including both the location and evolution of cracks, which is essential for assessing the effectiveness of post-tensioning interventions. These results confirm the ability of nonlinear finite element modelling to capture the complex behaviour of reinforced concrete saddles under load and to provide a reliable tool for evaluating and designing strengthening interventions using post-tensioning. The strengthening intervention consists of applying post-tensioning using two high-strength steel bars, one on each side of the saddle, anchored via steel plates to the concrete surfaces. The goal is to uniformly distribute compressive stresses to the concrete and enhance load-carrying capacity. The design method is based on a simplified equilibrium approach, similar to the kinematic limit analysis, in which a failure mechanism is assumed (inclined crack propagation