PSI - Issue 84

Lorenzo Sangiuliano et al. / Procedia Structural Integrity 84 (2026) 1326–1333

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The increase in operational train speeds results in significant dynamic effects, mainly related to resonance phenomena, which tend to occur beyond 200 km/h, Savin (2001). These aspects play a crucial role not only in the design of new structures but also in the structural assessment of existing ones. The performance enhancement of trainsets, especially in terms of axle loads, makes resonant phenomena even more significant. This scenario requires the development and application of advanced numerical models capable of accurately representing the complex dynamic behavior of railway structures subjected to high speeds, Frýba (1996). To analyze the issue of dynamic amplifications caused by passing trains, numerous estimation methods have been developed and widely applied both in academic research and engineering practice, Goicolea et al. (2002). Among these, methods based on dynamic signature represent an established approach for identifying the critical speeds of trainsets. These methods, extensively addressed in the European ERRI D214 project and incorporated into both Eurocode EN1991-2 and the Spanish IAPF regulation, are based on analyzing the dynamic response of a simply supported deck subjected to periodic moving loads, modeled as a sequence of axles with regular spacing. In addition to the dynamic signature approach, other classical methods include the analytical solution for a moving load on a simply supported beam, which allows for the determination of the impact factor as a function of load speed. This method is included in the UIC 776-1R regulation and has historically underpinned earlier standards prior to the advent of high-speed rail. This closed-form model assumes a straight, linearly elastic beam with simplified boundary conditions and is therefore only applicable to straight, simply supported decks. While very useful during preliminary design stages, this approach is now recognized as insufficient when resonance effects are present—especially relevant in the case of high-speed trainsets. All these approaches share a fundamental limitation, which is the inability to be extended to more complex cases, such as bridges with curved geometries, continuous or hyperstatic girders, composite decks, or unconventional supports. As a result, the need for more versatile tools has led to the development of methodologies based on generalized numerical models and parametric modeling, capable of overcoming the constraints of classical methods. Starting from this limitation, the present article proposes an innovative workflow based on free parametric modeling of structures, which imposes no restrictions on bridge geometry, thus overcoming the limitations of traditional models. Parametric modeling involves not only geometric aspects but also includes mechanical parameters characterizing materials and sections, as well as parameters specific to dynamic analyses. This workflow also allows for the use of any load train, provided the axle spacings and weights of each axle are known. Once the problem is defined, the dynamic analysis can be carried out using an external software capable of carrying out Finite Element Analyses (FEA), then enabling the export of results such as the history of displacements and accelerations at a control point of the structure. The strength of this approach lies in the parametrization of the numerical model, the flexibility in selecting the traveling vehicle, and the ability to rapidly perform a series of analyses in a simple and efficient manner. 2. 2. Methodology: Proposed workflow The workflow for the evaluation of the dynamic response of railway bridges is made of five consecutive steps. Before outlining the steps of the workflow, it is necessary to define the results that can be achieved using the proposed method. In this study, the possible outputs consist of the time histories of accelerations and displacements at selected control points of the structure, which can be arbitrarily defined. In addition, the workflow provides the time histories of the stresses at the investigated locations. These quantities represent the fundamental results for evaluating the dynamic response of the bridge and for supporting subsequent structural assessments. The first one consists in defining the geometry of the bridge using parametric modeling software such as Rhinoceros 8 in combination with Grasshopper. This platform enables the generation of complex geometries with extreme flexibility, based on a set of user-defined parameters. The parametric logic allows for rapid exploration of a wide range of configurations by controlling geometric variables such as span lengths, curvature radii, inclinations, spacing between main girders, the number of beams and spans, deck length, pier height, and many others.