PSI - Issue 81

Denys Rudavskyi et al. / Procedia Structural Integrity 81 (2026) 151–155

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A strong correlation and good agreement were observed between the two methods across various ratios of the elastic properties between the injection material and the base material. The relative error of the numerical calculation compared to the analytical formula was consistently less than 5% (see Fig. 7) in the range E 2 / E 1 <0.05, which corresponds to injection repairing cracked concrete with a polyurethane filler.

Fig. 7. SIF K II comparison at the injection-repaired crack vicinity: circles – FEM calculation, solid line – analytical formula (3).

This consistency suggests that the derived analytical formulas (1) – (4), despite their simplified nature, can be effectively and efficiently used as a viable alternative to complex and time-consuming numerical calculations. The practical implication is that this formula provides a powerful tool for rapid, preliminary assessments of the strengthening effectiveness in concrete arch bridges, optimising the design and maintenance processes. 3. Results and Conclusions The results showed that the SIF KII for the polyurethane-filled crack is reduced by a factor of 4 compared to an identical empty crack. This significant reduction is achieved despite the low stiffness ratio of the filler material E 2 / E 1 =0.03, confirming the effectiveness of the injection technology in stress redistribution. The performed analysis demonstrated that the injection technology helps redistribute stresses along the surface crack front, preventing further crack propagation and improving the brid ge’s load -carrying capacity. These results confirm that the combined use of numerical modelling and analytical validation provides a robust framework for assessing and optimising strengthening methods for historical concrete bridges. It now enables the reliable assessment of the effectiveness of injection technologies for arbitrarily oriented cracks – a capability that standard analytical methods cannot provide. Furthermore, the developed FEM framework offers a robust foundation for automating the optimal selection of injection material properties for arbitrarily oriented surface cracks in concrete arch bridges, thereby maximising repair efficacy and cost effectiveness. Acknowledgements The research was carried out within the framework of a grant from the National Research Foundation of Ukraine, No. 2023.04/0132. References Gdoutos, E. E., 2020. Fracture Mechanics: An Introduction. Springer Int. Publ., Cham, 496 p. Panasyuk, V., Marukha, V., Sylovanyuk, V., 2014. Injection Technologies for the Repair of Damaged Concrete Structures. Springer, Dordrecht – Heidelberg – New York – London. Smith, B. J., 1992. Epoxy injection of bridge deck delamination. transportation research record. J. of the Transportation Research Board 1335, 10 – 18. Trout, J., 1997. Epoxy Injection in Construction. Hanley-Wood, Inc., 80 p.