Issue 51

G. Cocchetti et alii, Frattura ed Integrità Strutturale, 51 (2020) 356-375; DOI: 10.3221/IGF-ESIS.51.26 356 Focussed on Fracture and Damage Detection in Masonry Structures Analytical and numerical analysis on the collapse modes of least- thickness circular masonry arches at decreasing friction Giuseppe Cocchetti Politecnico di Milano, Dipartimento di Ingegneria Civile e Ambientale, piazza L. da Vinci 32, I-20133 Milano, Italy giuseppe.cocchetti@polimi.it , http://orcid.org/0000-0002-9695-2967 Egidio Rizzi* Università degli studi di Bergamo, Dipartimento di Ingegneria e Scienze Applicate, viale G. Marconi 5, I-24044 Dalmine (BG), Italy egidio.rizzi@unibg.it , http://orcid.org/0000-0002-6734-1382 A BSTRACT . Departing from pioneering Heyman modern rational investigations on the purely-rotational collapse mode of least-thickness circular masonry arches, the hypothesis that joint friction shall be high enough to prevent inter-block sliding is here released. The influence of a reducing Coulomb friction coefficient on the collapse modes of the arch is explicitly inspected, both analytically and numerically, by tracing the appearance of purely-rotational, mixed sliding-rotational and purely-sliding modes. A classical doubly built-in, symmetric, complete semi-circular arch, with radial joints, under self-weight is specifically considered, for a main illustration. The characteristic values of the friction coefficient limiting the ranges associated to each collapse mode are first analytically derived and then numerically identified, by an independent self-implementation, with consistent outcomes. Explicit analytical representations are provided to estimate the geometric parameters defining the limit equilibrium states of the arch, specifically the minimum thickness to radius ratio, at reducing friction. These formulas, starting from the analysis of classical Heymanian instance of purely-rotational collapse, make new explicit reference to the mixed sliding- rotational collapse mode, arising within a narrow range of limited friction coefficients (or friction angles). The obtained results are consistently compared to existing numerical ones from the competent literature. 1 K EYWORDS . Circular masonry arches; Couplet-Heyman problem; Reducing friction; Purely-rotational mode; Mixed sliding-rotational mode; Purely-sliding mode. Citation: Cocchetti, G., Rizzi, E., Analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction, Frattura ed Integrità Strutturale, 51 (2020) 356-375. Received: 30.06.2019 Accepted: 05.11.2019 Published: 01.01.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 1 An earlier version of the present work with preliminary developments was presented at the SAHC12 conference in Wroclaw, Poland, October 15-17, 2012 [7].