Masonry arches are a defining feature of historical infrastructure, commonly found in viaducts, aqueducts and monumental architecture. Built according to traditional techniques and empirical knowledge, these structures often show signs of deterioration due to age, limited maintenance and exposure to natural or anthropogenic actions such as seismic activity, soil settlement and material decay. These factors can compromise their structural integrity and complicate safety assessments. This study investigates the stability of masonry arches subjected to horizontal loading, which typically triggers a four-hinge collapse mechanism. A parametric analysis is carried out to explore the effect of localised damage, modelled as a reduction in thickness along the intrados, on the collapse behaviour of arches with varying geometries, ranging from elliptical to full-centred profiles. To reflect realistic construction conditions, the study incorporates arches with variable thickness. The collapse multiplier is calculated for both undamaged and damaged configurations, the latter involving different positions of the reduced-thickness zone. The results highlight the most critical damage locations and reveal how geometric parameters influence structural sensitivity. The proposed approach offers a streamlined yet informative method for assessing the vulnerability of historic masonry arches and can assist in prioritising conservation and strengthening strategies.
DhirPKLosannoDTubaldiE, et al. Performance and robustness assessment of roadway masonry arch bridges to scour-induced damage using multiple traffic load models. Eng Struct2025; 325: 119441.
2.
ZiziMChisariCDe MatteisG. Effects of pre-existing damage on vertical load-bearing capacity of masonry arch bridges. Eng Struct2024; 300: 117205.
3.
De La HireP. Traité de Mécanique, 1695.
4.
MascheroniL. Nuove Ricerche Sull’equilibrio Delle Volte. Bergamo: Milano per Giovanni Silvestri, 1785.
5.
MéryE.Sur l’equilibre Des Voûtes En Berceau; Annales des ponts et Chausséss XIX, Ed. Paris: Dunode éditeur, 1840.
6.
HeymanJ. The stone skeleton. Int J Solids Struct1966; 2: 249–279.
7.
HeymanJ. The Masonry Arch. Chichester: Ellis Horwood Limited, 1982.
8.
BenvenutoE. An introduction to the history of structural mechanics - part II: vaulted structures and elastic. New York, NY: Springer- Verlag New York Inc, Ed., 1991.
9.
MonacoMBergamascoIBettiM. A no-tension analysis for a brick masonry vault with Lunette. J Mech Mater Struct2018; 13: 703–714.
10.
ClementePSaittaFBuffariniG, et al. Masonry arch bridges with finite compression strength subject to horizontal longitudinal seismic actions. Appl Sci2023; 13: 7509.
11.
CastellanoAEliaIFraddosioA, et al. A new experimental approach for small-scale dynamic tests on masonry arches aimed at seismic assessment. Int J Masonry Res Innov2022; 7: 89–112.
12.
CusanoCMontaninoAOlivieriC, et al. Graphical and analytical quantitative comparison in the domes assessment: the case of San Francesco Di Paola. Appl Sci2021; 11: 3622.
13.
PellecchiaDMarmoFRosatiL. Accounting for material strength in the thrust line analyses of unstrengthened and strengthened arches. Compos Struct2025; 358: 118926.
14.
CennamoCDi GennaroLFrunzioG, et al. Modelling a double-shell dome interconnected with a wooden structure: San Gennaro Chapel in Naples. Int J Space Struct2025. Epub ahead of print. DOI:10.1177/09560599251333277.
15.
CennamoCDi GennaroLFrunzioG, et al. Structural assessment of the double-shell dome in San Gennaro Chapel, Naples (Italy). In: MazzolaniFMLandolfoRFaggianoB (eds) Lecture notes in civil engineering ((LNCE, volume 596)). Cham: Springer Nature, 2025, vol. 2, pp.253–261.
16.
GalvezFSorrentinoLDizhurD, et al. Seismic rocking simulation of unreinforced masonry parapets and façades using the discrete element method. Earthq Eng Struct Dyn2022; 51: 1840–1856.
17.
AlShawaOLiberatoreDSorrentinoL. The effect of the vertical component of ground motion on a Masonry cross vault model. In: EndoYHanazatoT (eds) Structural analysis of historical constructions. Cham: Springer, 2024, Vol. 47, pp.1181–1188.
18.
PenazzatoLOliveiraDVRapicavoliD, et al. Numerical investigation of a medieval masonry arch bridge based on a discrete macro-element modeling approach. In: Proceedings of the 1st conference of the European Association on quality control of bridges and structures (ed. PellegrinoCFaleschiniFZaniniMA, et al.), Padova (Italy), 29 August–1 September 2022, Vol. 200. Cham: Springer.
19.
KaralarMÇufalıG. Structural assessment of historical stone bridges with the finite element method under dynamic effects of arch shape: the Antik Iscehisar bridge. Appl Sci2023; 13: 10740.
20.
MajtanECunninghamLSRogersBD. Numerical study on the structural response of a masonry arch bridge subject to flood flow and debris impact. Structures2023; 48: 782–797.
21.
MalenaMAngelilloMFortunatoA, et al. Arch bridges subject to pier settlements: continuous vs. piecewise rigid displacement methods. Meccanica2021; 56: 2487–2505.
22.
MassaroLDi GennaroLGuadagnuoloM, et al. Strengthening of masonry arches: the “Santa Maria Delle Grazie.” In: COMPDYN proceedings, National Technical University Of Athens, Athens (Greece), 12–14 June 2023. Eccomas Proceedia.
23.
CusanoCAngjeliuGMontaninoA, et al. Considerations about the static response of masonry domes: a comparison between limit analysis and finite element method. Int J Mason Res Innov2021; 6: 502–528.
24.
OlivieriCCockingSFabbrocinoF, et al. Seismic capacity of purely compressed shells based on airy stress function. Contin Mech Thermodyn2025; 37: 21.
25.
RiosAJNelaBPingaroM, et al. Parametric analysis of masonry arches following a limit analysis approach: influence of joint friction, pier texture, and arch shallowness. Math Mech Solids2025; 30: 137–165.
26.
BuzzettiMPingaroNMilaniG. Automatic detection of local collapse mechanisms in historical masonry buildings: fast and robust FE upper bound limit analysis. Eng Fail Anal2025; 170: 109310.
27.
BrandonisioGAngelilloMDe LucaA. Seismic capacity of buttressed masonry arches. Eng Struct2020; 215: 110661.
28.
FunariMFMehrotraALourençoPB. A Tool for the rapid seismic assessment of historic masonry structures based on limit analysis optimisation and rocking dynamics. Appl Sci2021; 11: 942.
GalassiS. An alternative approach for limit analysis of masonry arches on moving supports in finite small displacements. Eng Fail Anal2023; 145: 107004.
31.
GrillandaNMallardoV. Compatible strain-based upper bound limit analysis model for masonry walls under in-plane loading. Comput Struct2025; 313: 107743.
32.
ZonaRFerlaPMinutoloV. Limit analysis of conical and parabolic domes based on semi-analytical solution. J Build Eng2021; 44: 103271.
33.
HuaYMilaniG. Simple modeling of reinforced masonry arches for associated and non-associated heterogeneous limit analysis. Comput Struct2023; 280: 106987.
34.
ComoM. Statics of historic masonry constructions. Cham: Springer, 2013.
35.
AngelilloM. The model of Heyman and the statical and kinematical problems for masonry structures. Int J Mason Res Innov2019; 4: 14–21.
36.
GaetaniAMontiGPaoloneA, et al. Seismic capacity of masonry groin vaults through upper bound limit analysis. In: Proceedings of the structural analysis of historical constructions: anamnesis, diagnosis, therapy, controls - proceedings of the 10th international conference on structural analysis of historical constructions, SAHC 2016; Leuven, Belgium, 13–15 September, 2016, pp.1505–1512. London: Taylor & Francis Group.
37.
FrunzioGDi GennaroL. The out of plane behaviour of masonry infilled frames. In J Phys Conf Ser2021; 2090: 012148.
38.
TecchioGDonàMSalerE, et al. Fragility of single-span masonry arch bridges accounting for deterioration and damage effects. Eur J Environ Civil Eng2023; 27: 2048–2069.
39.
Augusthus-NelsonLSwiftG. Experimental investigation of the residual behaviour of damaged masonry arch structures. Structures2020; 27: 2500–2512.
40.
Di GennaroLGuadagnuoloMMonacoM. Rocking analysis of towers subjected to horizontal forces. Buildings2023; 13: 762.
41.
Di GennaroLde CristofaroMLoretoG, et al. In-Situ load testing of an ancient masonry structure using fibre optics. Structures2024; 70: 107567.
42.
Di GennaroLDamianoEDe CristofaroM, et al. An innovative geotechnical and structural monitoring system based on the use of NSHT. Smart Mater Struct2022; 31: 065022.
43.
ZampieriPZaniniMAFaleschiniF.Influence of Damage on the Seismic Failure Analysis of Masonry Arches. Constr Build Mater2016; 119: 343–355.
44.
Di GennaroLZiziMChisariC, et al. Structural assessment of damaged masonry arch bridges: a parametric study based on limit analysis. In: Proceedings of the 18th world conference on earthquake engineering WCEE2024, Milano, 30 June–July 5 2024. Tokio: International Association for Earthquake Engineering.
45.
CrisfieldMAPackhamAJ. A Mechanism program for computing the strength of masonry arch bridges. Report, Transport and Road Research Laboratory, Washington, 1987.
46.
MascoloIGesualdoAOlivieriC, et al. On blocks detection in unilateral masonry-like structures: a rigid-elastic displacement approach. Int J Mason Res Innov2022; 7: 395–405.
47.
IannuzzoADe SerioFGesualdoA, et al. Crack patterns identification in masonry structures with a C° displacement energy method. Int J Mason Res Innov2018; 3: 295–323.
48.
IannuzzoADe LucaAFortunatoA, et al. Fractures Detection in masonry constructions under horizontal seismic forces | Rilevazione Di Fratture Nelle Costruzioni in Muratura Sotto Forze Sismiche Orizzontali. Ing Sismica2018; 35: 87–103.
BenedettiACollaCPignagnoliG, et al. Static and dynamic investigation of the Taro masonry bridge in Parma, Italy. In: AguilarRTorrealvaDMoreiraS, et al. (eds) Structural analysis of historical constructions, vol 18. Cham: Springer, 2019, pp.2264–2272.
51.
BreymannGA. Trattato Generale Di Costruzioni Civili, Con Cenni Speciali Intorno Alle Costruzioni Grandiose. Milano: Francesco Vallardi, 1881.
52.
GautierH. Traitè Des Ponts, Ou Il Est Parlè de Ceux Des Romains e de Ceux Des Modernes. Cailleau: Paris, 1716.
53.
ZerlengaO. La Forma Ovata in Architettura. Rappresentazione Geometrica. Napoli: CUEN, 1997.
54.
RosinPLPittewayMLV. The ellipse and the five-centred arch. Math Gazette2001; 85: 13–24.
55.
RosinPL. A family of constructions of approximate ellipses. Int J Shape Model2002; 8: 193–199.
56.
RosinPL. Survey and comparison of traditional piecewise circular approximations to the ellipse. Comput Aided Geom Des1999; 16: 269–286.
57.
PengY. Chebyshev approximating four pieces of circular arc to ellipse in machining and operating. Chin J Mech Eng2004; 40: 257–269.
58.
ContiGPaolettiRTrottaA. Ellipses and ovals: two curves so close and so far. Sci Philos2021; 2021: 133–159.
59.
OchsendorfJA. Collapse of masonry structures. Dissertation, Cambridge University Department of Engineering, UK, 2002.
60.
ClementePOcchiuzziARaithelA. Limit behavior of stone arch bridges. J Struct Eng1995; 121: 1045–1050.
61.
ComoM. Equilibrium and collapse analysis of masonry bodies. Meccanica1992; 27: 185–194.
62.
CrespinoEAdriaenssensSFraddosioA, et al. A multi-objective optimization approach for novel shell/frame systems under seismic load. Structures2024; 65: 106625.
63.
KamińskiTBieńJ. Application of kinematic method and FEM in analysis of ultimate load bearing capacity of damaged masonry arch bridges. Proc Procedia Eng2013; 57: 524–532.
