PSI - Issue 80

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ScienceDirect

Procedia Structural Integrity 80 (2026) 219–231 Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000

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Fracture, Damage and Structural Health Monitoring Crack pattern scenarios in masonry structures Riccardo Giacometti a , Nicola Grillanda a , Vincenzo Mallardo a, ∗ a Department of Architecture, University of Ferrara, Via Quartieri 8, 44121 Ferrara, Italy b Seconda ffi liation, Address, City and Postcode, Country Fracture, Damage and Structural Health Monitoring Crack pattern scenarios in masonry structures Riccardo Giacometti a , Nicola Grillanda a , Vincenzo Mallardo a, ∗ a Department of Architecture, University of Ferrara, Via Quartieri 8, 44121 Ferrara, Italy b Seconda ffi liation, Address, City and Postcode, Country

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi Abstract Historical masonry structures constitute a vast array of the historical cultural heritage worldwide. The interest in their preservation has been pushing researchers to develop theoretical and numerical methodologies for the structural assessment of such construc tions. Two are the main sources of damage in masonry structures: dynamic actions and di ff erential settlements. The former are mainly related to the seismic events and to the tra ffi c-induced vibrations, the former can be caused by di ff erent phenomena such as tunnelling operations, subway construction, underground car park insertions, soil weakening due to pipe breakage, scouring, etc. Both problems pose modelling issues. The masonry cannot be modelled as an elastic or elastic-plastic material as it is an assembly of rigid or quasi-rigid bricks in mostly unilateral contact with finite friction. The lack of tension is particularly realistic for historic masonry structures where the mortar layers have strongly deteriorated. The foundation is frequently a simple contact between ma sonry and soil with no bending-resistant beam between them. Based on some experiences of the authors Alessandri et al. (2014), Tiberti et al. (2020), Mallardo and Iannuzzo (2025), Grillanda and Mallardo (2025), the present contribution intends to present some recent results on the modelling of the masonry structure and on the influence of the soil on the masonry behaviour. With ref erence to seismic action, the masonry is described by an upper bound limit analysis numerical approach currently under study. The masonry continuous model is discretized with planar elements whose kinematics is composed of a rigid body motion and a plastic deformation. An homogenization procedure is applied. The homogenized plastic strain rates provide a reliable representation of the cracks on the masonry. The problem can be written as a linear programming problem. Optimization of the compatible plastic strain rate distribution and minimization of the load factor can be achieved through a simple iterative local mesh refinement. Fur thermore, a novel approach is presented to investigate the e ff ects of di ff erential settlements on two and three dimensional masonry structures by explicitly coupling the soil with the masonry structure while still considered as composed of no-tension material. The soil behaviour is included through a boundary integral approach, which avoids mesh discretisation issues. Some recent results will be presented to show the e ffi ciency of both the approaches. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Homogenization; No-tension material; Limit Analysis; Half-space fundamental solution; Di ff erential settlements. Abstract Historical masonry structures constitute a vast array of the historical cultural heritage worldwide. The interest in their preservation has been pushing researchers to develop theoretical and numerical methodologies for the structural assessment of such construc tions. Two are the main sources of damage in masonry structures: dynamic actions and di ff erential settlements. The former are mainly related to the seismic events and to the tra ffi c-induced vibrations, the former can be caused by di ff erent phenomena such as tunnelling operations, subway construction, underground car park insertions, soil weakening due to pipe breakage, scouring, etc. Both problems pose modelling issues. The masonry cannot be modelled as an elastic or elastic-plastic material as it is an assembly of rigid or quasi-rigid bricks in mostly unilateral contact with finite friction. The lack of tension is particularly realistic for historic masonry structures where the mortar layers have strongly deteriorated. The foundation is frequently a simple contact between ma sonry and soil with no bending-resistant beam between them. Based on some experiences of the authors Alessandri et al. (2014), Tiberti et al. (2020), Mallardo and Iannuzzo (2025), Grillanda and Mallardo (2025), the present contribution intends to present some recent results on the modelling of the masonry structure and on the influence of the soil on the masonry behaviour. With ref erence to seismic action, the masonry is described by an upper bound limit analysis numerical approach currently under study. The masonry continuous model is discretized with planar elements whose kinematics is composed of a rigid body motion and a plastic deformation. An homogenization procedure is applied. The homogenized plastic strain rates provide a reliable representation of the cracks on the masonry. The problem can be written as a linear programming problem. Optimization of the compatible plastic strain rate distribution and minimization of the load factor can be achieved through a simple iterative local mesh refinement. Fur thermore, a novel approach is presented to investigate the e ff ects of di ff erential settlements on two and three dimensional masonry structures by explicitly coupling the soil with the masonry structure while still considered as composed of no-tension material. The soil behaviour is included through a boundary integral approach, which avoids mesh discretisation issues. Some recent results will be presented to show the e ffi ciency of both the approaches. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Homogenization; No-tension material; Limit Analysis; Half-space fundamental solution; Di ff erential settlements.

∗ Corresponding author. Tel.: + 39-339-382-0473 ; fax: + 39-0532-293621. E-mail address: mlv@unife.it ∗ Corresponding author. Tel.: + 39-339-382-0473 ; fax: + 39-0532-293621. E-mail address: mlv@unife.it

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi 10.1016/j.prostr.2026.02.022 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi.