Investigation of the Structural Response of Masonry Structures

  • Georgios A. Drosopoulos
  • Jan Phakwago
  • Maria E. Stavroulaki
  • Georgios E. StavroulakisEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 962)


Methods used for the structural evaluation of masonry structures and monuments are presented in this article. Limit analysis is initially presented as a tool for the study of the collapse mechanism and limit load of masonry structures. Unilateral contact-friction laws are introduced between the stones, to describe damage due to opening-sliding. Related applications to masonry arch bridges as well as comparison with experimental investigations, are presented. Νon-linear finite element analysis, using similar concepts taken from non-smooth mechanics, is also presented. Eventually, numerical homogenization methods are adopted for the evaluation of masonry walls. A microscopic sample (Representative Volume Element) consisting of masonry and mortar joints is chosen and average stress and stiffness are derived numerically. Then, they are used within a macroscopic homogeneous model, for the representation of the structural response. Applications of the mentioned approaches to masonry bridges and walls offer a further insight on the response of these structures.


Unilateral contact Limit analysis Masonry arches-homogenization 


  1. 1.
    Drosopoulos, G.A., Stavroulakis, G.E., Massalas, C.V.: Limit analysis of a single span masonry bridge with unilateral frictional contact interfaces. Eng. Struct. 28, 1864–1873 (2006)CrossRefGoogle Scholar
  2. 2.
    Leftheris, B.P., Stavroulaki, M.E., Sapounaki, A.C., Stavroulakis, G.E.: Computational mechanics for heritage structures. WIT Press, Southampton (2006)Google Scholar
  3. 3.
    Betti, M., Drosopoulos, G.A., Stavroulakis, G.E.: Two non-linear finite element models developed for the assessment of failure of masonry arches. Comptes Rendus Mecanique 336(1–2), 42–53 (2008)CrossRefGoogle Scholar
  4. 4.
    Drosopoulos, G.A., Giannis, K., Stavroulaki, M.E., Stavroulakis, G.E.: Metamodelling-assisted numerical homogenization for masonry and cracked structures. J. Eng. Mech. (ASCE) 144, 04018072 (2018)CrossRefGoogle Scholar
  5. 5.
    Stavroulaki, M.E., Riveiro, B., Drosopoulos, G.A., Solla, M., Koutsianitis, P., Stavroulakis, G.E.: Modelling and strength evaluation of masonry bridges using terrestrial photogrammetry and finite elements. Adv. Eng. Softw. 101, 136–148 (2016)CrossRefGoogle Scholar
  6. 6.
    Ferris, M.C., Tin-Loi, F.: Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int. J. Mech. Sci. 43, 209–224 (2001)CrossRefGoogle Scholar
  7. 7.
    Stavroulakis, G.E., Panagiotopoulos, P.D., Al-Fahed, A.M.: On the rigid body displacements and rotations in unilateral contact problems and applications. Comput. Struct. 40, 599–614 (1991)CrossRefGoogle Scholar
  8. 8.
    Zohdi, T.,I., Wriggers, P.: An Introduction to Computational Micromechanics. Springer, The Netherlands (2008).
  9. 9.
    Nguyen, V.P., Stroeven, M., Sluys, L.J.: Multiscale continuous and discontinuous modeling of heterogeneous materials: a Review on recent developments. J. Multiscale Model. 3, 1–42 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Smit, R.J.M., Brekelmans, W.A.M., Meijer, H.E.H.: Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Eng. 155, 181–192 (1998)CrossRefGoogle Scholar
  11. 11.
    Kouznetsova, V.G.: Computational homogenization for the multi-scale analysis of multi-phase materials. PhD thesis, Technical University Eindhoven, The Netherlands (2002)Google Scholar
  12. 12.
    Drosopoulos, G.A., Wriggers, P., Stavroulakis, G.E.: A Multi-scale computational method including contact for the analysis of damage in composite materials. Comput. Mater. Sci. 95, 522–535 (2014)CrossRefGoogle Scholar
  13. 13.
    Miehe, C., Koch, A.: Computational micro-to-macro transitions of discretized microstructures undergoing small strains. Arch. Appl. Mech. 72, 300–317 (2002)CrossRefGoogle Scholar
  14. 14.
    Page, J.: Masonry arch bridges. TRL State of Art Review. Her Majesty’s Stationary Office, London (1993)Google Scholar
  15. 15.
    Page, J.: Load test to collapse on masonry arch bridges. Transport Research Laboratory. In: Melbourne, C. (Ed.) Arch Bridges, pp. 289–298. Thomas Telford Ltd., Bolton (1995)Google Scholar
  16. 16.
    Drosopoulos, G.A., Stavroulakis, G.E., Massalas, C.V.: FRP reinforcement of stone arch bridges: unilateral contact models and limit analysis. Compos. B 38(2), 144–151 (2006)CrossRefGoogle Scholar
  17. 17.
    Drosopoulos, G.A., Stavroulakis, G.E., Massalas, C.V.: Influence of the geometry and the abutments movement on the collapse of stone arch bridges. Constr. Build. Mater. 22(3), 200–210 (2008)CrossRefGoogle Scholar
  18. 18.
    Drosopoulos, G.A.: Non-linear analysis of stone arch bridges with the usage of a unilateral contact-friction model. PhD Thesis, Department of Material Science and Technology, University of Ioannina, Ioannina, Greece (2006)Google Scholar
  19. 19.
    Gilbert, M. (Ed.): Ring theory and modelling guide. University of Sheffield. LimitState Ltd., Sheffield (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Georgios A. Drosopoulos
    • 1
  • Jan Phakwago
    • 1
  • Maria E. Stavroulaki
    • 2
  • Georgios E. Stavroulakis
    • 3
    Email author
  1. 1.Discipline of Civil Engineering, Structural Engineering and Computational Mechanics Group (SECM)University of KwaZulu-NatalDurbanSouth Africa
  2. 2.School of Architecture, Applied Mechanics LaboratoryTechnical University of CreteChaniaGreece
  3. 3.School of Production Engineering and ManagementInstitute of Computational Mechanics and Optimization, Technical University of CreteChaniaGreece

Personalised recommendations