Bulletin of Earthquake Engineering

, Volume 18, Issue 2, pp 673–724 | Cite as

Seismic capacity and multi-mechanism analysis for dry-stack masonry arches subjected to hinge control

  • Gabriel L. StockdaleEmail author
  • Vasilis Sarhosis
  • Gabriele Milani
S.I. : 10th IMC conference


Masonry arches are vulnerable to seismic actions. Over the last few years, extensive research has been carried out to develop strategies and methods for their seismic assessment and strengthening. The application of constant horizontal accelerations to masonry arches is a well-known quasi-static method, which approximates dynamic loading effects and quantifies their stability, while tilting plane testing is a cheap and effective strategy for experimentation of arches made of dry-stack masonry. Also, the common strengthening techniques for masonry arches are mainly focusing on achieving full strength of the system rather than stability. Through experimentation of a dry-stack masonry arch it has been shown that the capacity of an arch can be increased, and the failure controlled by defining hinge positions through reinforcement. This paper utilizes experimentally obtained results to introduce: (1) static friction and resulting mechanisms; and (2) the post-minimum mechanism reinforcement requirements into the two-dimensional limit analysis-based kinematic collapse load calculator (KCLC) software designed for the static seismic analysis of dry-stack masonry arches. Computational results are validated against a series of experimental observations based on tilt plane tests and good agreement is obtained. Discrete element models to represent the masonry arch with different hinge configurations are also developed to establish a validation trifecta. The limiting mechanism to activate collapse of arches subjected to hinge control is investigated and insights into the optimal reinforcement to be installed in the arch are derived. It is envisaged that the current modelling approach can be used by engineers to understand stability under horizontal loads and develop strengthening criteria for masonry arches of their care.


Masonry arch Tilt test KCLC DEM Admissible mechanism Seismic capacity 



This research was partially supported by the Global Challenge Research Fund provided by British Academy (CI170241). We also thank our colleagues from Newcastle University who provided insight and expertise in the area of experimental testing.


  1. Alexakis H, Makris N (2014) Limit equilibrium analysis and the minimum thickness of circular masonry arches to withstand lateral inertial loading. Arch Appl Mech 8(5):757–772CrossRefGoogle Scholar
  2. Alexandros L, Kouris S, Triantafillou TC (2018) State-of-the-art on strengthening of masonry structures with textile reinforced mortar (TRM). Constr Build Mater 188:1221–1233. CrossRefGoogle Scholar
  3. Anania L, D’Agata G (2017) Limit Analysis of vaulted structures strengthened by an innovative technology in applying CFRP. Constr Build Mater 145:336–346. CrossRefGoogle Scholar
  4. Angelillo M (ed) (2014) Mechanics of masonry structures. Springer, LondonGoogle Scholar
  5. Bertolesi E, Milani G, Carozzi FG, Poggi C (2018) Ancient masonry arches and vaults strengthened with TRM, SRG and FRP composites: numerical analyses. Compos Struct 187:385–402CrossRefGoogle Scholar
  6. Bhattacharya S, Nayak S, Dutta SC (2014) A critical review of retrofitting methods for unreinforced masonry structures. Int J Disaster Risk Reduct 7:51–67CrossRefGoogle Scholar
  7. Borri A, Castori G, Corradi M (2011) Intrados strengthening of brick masonry arches with composite materials. Compos Part B 42:1164–1172CrossRefGoogle Scholar
  8. Bui TT, Limam A, Sarhosis V, Hjiaj M (2017) Discrete element modelling of the in-plane and out-of-plane behaviour of dry-joint masonry wall constructions. Eng Struct 136:277–294CrossRefGoogle Scholar
  9. Calderini C, Lagomarsino S (2014) Seismic response of masonry arches reinforced by tie-rods: static tests on a scale model. J Struct Eng 141(5):1. CrossRefGoogle Scholar
  10. Cancelliere I, Imbimbo M, Sacco E (2010) Experimental tests and numerical modelling of reinforced masonry arches. Eng Struct 32:776–792CrossRefGoogle Scholar
  11. Carozzi FG, Poggi C, Bertolesi E, Milani G (2018) Ancient masonry arches and vaults strengthened with TRM, SRG and FRP composites: experimental evaluation. Compos Struct 187:466–480CrossRefGoogle Scholar
  12. Ceroni F, Salzano P (2018) Design provisions for FRCM systems bonded to concrete and masonry elements. Compos B Eng 143:230–242CrossRefGoogle Scholar
  13. Clemente P (1998) Introduction to dynamics of stone arches. Earthq Eng Struct Dyn 27(5):513–522CrossRefGoogle Scholar
  14. Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of the Symposium of the International Society for Rock Mechanics, Nancy, France, vol 1, pp 11–18Google Scholar
  15. De Lorenzis L, DeJong M, Ochsendorf J (2007) Failure of masonry arches under impulse base motion. Earthq Eng Struct Dyn 36(14):2119–2136CrossRefGoogle Scholar
  16. De Luca A, Giordano A, Mele E (2004) A simplified procedure for assessing the seismic capacity of masonry arches. Eng Struct 26(13):1915–1929CrossRefGoogle Scholar
  17. DeJong M (2009) Seismic assessment strategies for masonry structures. Ph.D. Dissertation, Massachusetts Institute of Technology, MassachusettsGoogle Scholar
  18. DeJong MJ, De Lorenzis L, Adams S, Ochsendorf JA (2008) Rocking stability of masonry arches in seismic regions. Earthq Spectra 24(4):847–865CrossRefGoogle Scholar
  19. De Santis S, de Felice G (2014) Overview of railway masonry bridges with a safety factor estimate. Int J Archit Herit 8(3):452–474CrossRefGoogle Scholar
  20. De Santis S, Hadad HA, De Caso y Basalo F, de Felice G, Nanni A (2018a) Acceptance criteria for tensile characterization of fabric-reinforces cementitious matrix systems for concrete and masonry repair. J Compos Constr 22(6):04018048. CrossRefGoogle Scholar
  21. De Santis S, Roscini F, de Felice G (2018b) Full-scale tests on masonry vaults strengthened with Steel Reinforced Grout. Compos B 141:20–36CrossRefGoogle Scholar
  22. Dimitri R, Tornabene F (2015) A parametric investigation of the seismic capacity for masonry arches and portals of different shapes. Eng Fail Anal 52:1–34CrossRefGoogle Scholar
  23. Fanning PJ, Sobczak L, Boothby TE, Salomoni V (2005) Load testing and model simulations for a stone arch bridge. Bridge Struct 1(4):367–378CrossRefGoogle Scholar
  24. Forgács T, Sarhosis V, Bagi K (2017) Minimum thickness of semi-circular skewed masonry arches. Eng Struct 140(1):317–336CrossRefGoogle Scholar
  25. Formisano A, Marzo A (2017) Simplified and refined methods for seismic vulnerability assessment and retrofitting of an Italian cultural heritage masonry building. Comput Struct 180:13–26. CrossRefGoogle Scholar
  26. Gaetani A, Lourenço PB, Monti G, Moroni M (2016) Shaking table tests and numerical analysis on a scaled dry-joint arch undergoing windowed sign pulses. Bull Earthq Eng 1:2. CrossRefGoogle Scholar
  27. Gattesco N, Boem I, Adretta V (2018) Experimental behavior of non-structural masonry vaults reinforced through fibre-reinforced mortar coating and sujected to cyclic horizontal loads. Eng Struct 172:419–431CrossRefGoogle Scholar
  28. Giamundo V, Sarhosis V, Lignola GP, Sheng Y, Manfredi G (2014) Evaluation of different computational strategies for modelling low strength masonry. Eng Struct 73:160–169CrossRefGoogle Scholar
  29. Gilbert M, Melbourne C (1994) Rigid-block analysis of masonry structures. Struct Eng 72(21):356–361Google Scholar
  30. Group, I.C. (2015) 3DEC version 5.00 distinct-element modeling of jointed and blocky material in 3D. MinneapolisGoogle Scholar
  31. Hendry AW (1998) Structural masonry. Palgrave Macmillan, MacmillanCrossRefGoogle Scholar
  32. Heydariha JZ, Ghaednia H, Nayak S, Das S, Bhattacharya S, Dutta SC (2019) Experimental and field performance of pp band-rertrofitted masonry: evaluation of seismic behaviour. J Perform Constr Facil 33(1):04018086. CrossRefGoogle Scholar
  33. Heyman J (1966) The stone skeleton. Int J Solids Struct 2(2):249–279CrossRefGoogle Scholar
  34. Heyman J (1969) The safety of masonry arches. Int J Mech Sci 11(4):363–385CrossRefGoogle Scholar
  35. Huerta S (2005) The use of simple models in the teaching of the essentials of masonry arch behavior.  In: Theory and practice of constructions: knowledge, means and models. Didactis and research experiences. Fondazione Flaminia, Ravenna, Italia, pp 747–761. ISBN 888990003 2Google Scholar
  36. Krstevska L, Tashkov L, Naumovski N, Florio G, Formisano A, Fornaro A, Landolfo R (2010) In-situ experimental testing of four historical buildings damaged during the 2009 L’Aquila earthquake. In: COST ACTION C26: Urban Habitat Constructions under Catastrophic Events—Proceedings of the Final Conference, pp 427–432Google Scholar
  37. Modena C, Tecchio G, Pellegrino C, da Porto F, Donà M, Zampieri P, Zanini MA (2015) Reinforced concrete and masonry arch bridges in seismic areas: typical deficiencies and retrofitting strategies. Struct Infrastruct Eng 11(4):415–442. CrossRefGoogle Scholar
  38. Ochsendorf JA (2002) Collapse of masonry structures. University of Cambridge, CambridgeGoogle Scholar
  39. Oliveira DV, Basilio I, Lourenço PB (2010) Experimental behavior of FRP strengthened masonry arches. J Compos Constr 14(3):312–322CrossRefGoogle Scholar
  40. Oppenheim IJ (1992) The masonry arch as a four-link mechanism under base motion. Earthq Eng Struct Dyn 21(11):1005–1017CrossRefGoogle Scholar
  41. Pelà L, Aprile A, Benedetti A (2009) Seismic assessment of masonry arch bridges. Eng Struct 31(8):1777–1788CrossRefGoogle Scholar
  42. Pelà L, Aprile A, Benedetti A (2013) Comparison of seismic assessment procedures for masonry arch bridges. Constr Build Mater 38:381–394CrossRefGoogle Scholar
  43. Sarhosis V, Sheng Y (2014) Identification of material parameters for low bond strength masonry. Eng Struct 60:100–110CrossRefGoogle Scholar
  44. Sarhosis V, Bagi K, Lemos JV, Milani G (2016a) Computational modeling of masonry structures using the discrete element method. IGI Global, HersheyCrossRefGoogle Scholar
  45. Sarhosis V, De Santis S, di Felice G (2016b) A review of experimental investigations and assessment methods for masonry arch bridges. Struct Infrastruct Eng 12(11):1439–1464Google Scholar
  46. Sarhosis V, Asteris P, Wang T, Hu W, Han Y (2016c) On the stability of colonnade structural systems under static and dynamic loading conditions. Bull Earthq Eng 14(4):1131–1152CrossRefGoogle Scholar
  47. Stockdale G (2016) Reinforced stability-based design: a theoretical introduction through a mechanically reinforced masonry arch. Int J Masonry Res and Innov 1(2):101–142CrossRefGoogle Scholar
  48. Stockdale G, Milani M (2018a) Diagram based assessment strategy for first-order analysis of masonry arches. J Build Eng 22:122–129CrossRefGoogle Scholar
  49. Stockdale G, Milani M (2018b) Interactive MATLAB-CAD limit analysis of horizontally loaded masonry arches. In: 10th IMC Conference Proceedings. International Masonry Society, pp 208–306Google Scholar
  50. Stockdale G, Sarhosis V, Milani G (2018a) Increase in seismic resistance for a dry joint masonry arch subjected to hinge control. In: 10th IMC Conference Proceedings. International Masonry Society, pp 968–981Google Scholar
  51. Stockdale G, Tiberti S, Camilletti D, Papa G, Habieb A, Bertolesi E, Milani G, Casolo S (2018b) Kinematic collapse load calculator: circular arches. SoftwareX 7:174–179CrossRefGoogle Scholar
  52. Tralli A, Alassandri C, Milani G (2014) Computational methods for masonry vaults: a review of recent results. Open J Civ Eng 8(1):272–287CrossRefGoogle Scholar
  53. Zampieri P, Zanini MA, Modena C (2015) Simplified seismic assessment of multi-span masonry arch bridges. Bull Earthq Eng 13(9):2629–2646CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Architecture, Built Environment and Construction EngineeringPolitecnico di MilanoMilanItaly
  2. 2.School of EngineeringNewcastle UniversityNewcastle upon TyneUK

Personalised recommendations