PSI - Issue 80

Riccardo Giacometti et al. / Procedia Structural Integrity 80 (2026) 219–231 R. Giacometti, N. Grillanda, V. Mallardo / Structural Integrity Procedia 00 (2023) 000–000

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S - S _

S _

Fig. 4: Masonry wall / pier on the soil. ¯ S is the masonry-soil contact surface.

3. Soil-structure interaction

Soil-structure interaction is an active field of research, especially in dynamic analysis, as reported in the Menglin et al. (2011). A review on the influence of the soil on the natural frequencies of the structure is investigated in Shayah (2025). Most of the contributions apply the Finite Element Method (FEM) and the BEM but refer mainly to bending resistant structures that are simpler to be modelled and analysed even in the presence of non-linearities. The FEM is used for modeling the structure whereas BEM results to be more suitable for describing the underneath soil. For instance in Qin et al. (2025) a new coupling technique is implemented in order to couple the FEM and the Time Domain BEM. In Romero et al. (2013) FEM and BEM are applied to analyse the propagation of waves in an elastic beam foundation. To this goal, a MatLab toolbox is also provided in Galv´ın and Romero (2014). Masonry structures are mainly dealt with experimental tests. In Alessandri et al. (2020) the e ff ects of the tra ffi c is experimentally measured on some historical masonry structures. Shaking-table tests are carried out on ancient masonry pagodas in Wu et al. (2025). In the static context special attention is devoted to the e ff ect of tunneling and excavation on the overhead structure. In the most recent contribution Yu et al. (2025) FEM is applied to compute the tunnelling-induced masonry-wall dam age: elastoplastic constitutive models are used for the masonry, rather unrealistic on historic masonry buildings, and the soil is discretised by FEM, hence, neglecting its infinite size. Previous publications contain strong simplification mainly in the soil (modelled as boundary condition on the structure) Giardina et al. (2013), Burd et al. (2022). A recent approach Mallardo and Iannuzzo (2025) performs the static analysis of a masonry building on an elastic soil by including both the infinite size of the soil and the no-tension behavior of the masonry and the unilateral contact with finite friction at the soil-masonry interface. The analysis is limited to 2D. The present contribution is an initial extension to 3D.

3.1. The interface model

The main idea of the present contribution stems from the typical foundation that usually occurs in historical ma sonry buildings, that is, the wall / pier is layered directly on the soil without reinforced concrete beams in beween. This entices the contact surface to be modelled as unilateral in compression with finite friction capacity. The mechanical problem to be solved has to compute the response of the masonry structure under static actions in unilateral contact (with finite friction) with the underneath soil modelled as elastic half-space (see Fig. 4). The problem is solved iteratively as follows.

1. Compute base reactions r m

0 of the loaded masonry model with fixed foundation

0 on the elastic half space as t s 0

2. Relocate r m

3. Compute displacements u s

1 on ¯ S of the elastic half-space under t s 0