PSI - Issue 84

Siro Casolo et al. / Procedia Structural Integrity 84 (2026) 1214–1221

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1. Introduction The modelling of masonry arch bridges subject to in-plane dynamic actions is an open issue in scientific research, as it requires comprehensive, efficient and effective computational tools. Masonry is characterized by a complex mechanical behavior, both due to the mechanical characteristics of the single constituent materials and the phenomena related to the combined texture-bonding geometry. A further factor of complexity in the case of masonry arch bridges is related to the presence of a relevant infill consisting of loose granular geo-materials. In the analysis of such infrastructures, therefore, it is necessary to model the mechanical behavior of the masonry composite, the mechanical behavior of the geo-material used for the infill and the interaction between the latter and the masonry structural elements. Several strategies have been proposed for modelling masonry, geo-materials and their interaction (Cundall & Strack, 1979; Gambarotta & Lagomarsino, 1997; Luciano & Sacco, 1997; Azevedo et al. 2000; Casolo, 2004; De Bellis & Addessi, 2011; Rainone et al., 2023; 2024). Macro-scale strategies, based on the homogenization of the composite and on the use of equivalent continua, require a reduced computational effort but are unable to consider local and texture-bond effects (unless continua with enriched kinematics are used). Micro-scale strategies and discrete elements approaches, on the other hand, are partially able (Casolo et al., 2009; Lemos, J.V., 2019) to take these phenomena into account but require a modelling and computational effort that could be excessive for applications in professional contexts. A numerical strategy at the macro scale is here proposed for modelling masonry arch bridges subject to impacts with variable inclination in the plane. The strategy is based on the Rigid Body-Spring Model, RBSM, (Kawai, 1978) as proposed by Casolo (2004; 2009) for masonry, that can be also regarded as a specific implementation of the Heuristic Molecule approach (Casolo, 2021a). This numerical model allows the description of complex mechanical and texture-bond effects such as the stiffness and strength decay under cyclic loads, the orthotropy of the shear strength, interlocking and contact between masonry and infill. The dynamics of RBSM allows to analyse time histories of complex structural systems with a limited number of degrees of freedom (Casolo, 2021b). The manuscript is composed of five sections. Section 2 describes the proposed methodology for modelling the behavior of masonry arch bridges subjected to in-plane impacts. Section 3 presents the case study adopted: the San Marcello Pistoiese Bridge (Italy), whose data are available in the literature. Section 4 describes the numerical models implemented in the specific MatLAB code developed. Section 5 analyses the results obtained and, finally, Section 6 The several modelling strategies available in literature for masonry-like materials can be classified in micro-scale and macro-scale. Macro-scale strategies involve the smear out of masonry into a homogeneous solid continuum, generally based on a Cauchy orthotropic solid model. This approach is often cost-effective and provides good results for most collapse mechanisms (Gambarotta & Lagomarsino, 1997; Luciano & Sacco, 1997; Rainone et al., 2023; 2024). However, it may preclude the capturing of some important texture-bond effects that may be modelled by adopting continua with enriched kinematics (Uva & Salerno, 2006; Casolo, 2006; De Bellis & Addessi, 2011). Discrete models based on rigid elements and springs can significantly reduce the number of degrees of freedom of structural problems, while still allowing for bond-texture effects to be included. Based on an assemblage of rigid elements interconnected by springs, a RBSM allows to describe the elastic and post-elastic behavior of masonry panels subjected to boundary conditions in which the bond-texture effects are not negligible. The model has shown to be especially effective for dynamics, for example for modelling the seismic response of masonry towers (Casolo, 2021b), complex historical buildings (Casolo & Sanjust, 2009) and also the artillery bullet impact on ancient walls (Tateo & Casolo, 2021). It was also somehow prodromal for defining the concept of “Heuristic molecules” that have been recently applied for the design of an isotropic meta-material (Casolo, 2021, Da Silva et al. 2023). presents some concluding considerations and future directions for the research work. 2. How to evaluate the effects of impacts on existing structures and infrastructures 2.1. Mechanical modelling of masonry: state of the art and introduction to RBSM