, Volume 53, Issue 7, pp 1661–1672 | Cite as

Upper bound limit analysis of masonry retaining walls using PIV velocity fields

  • Benjamin Terrade
  • Anne-Sophie Colas
  • Denis Garnier
New Trends in Mechanics of Masonry


Masonry is the building of structures from individual units, with or without the use of mortar as a bonding component. Stone masonry structures are frequent in the regions where stones are ubiquitous. In Europe, it was massively used until the nineteenth century to build earth retaining walls. For instance, they represent 85% of the retaining walls in Great Britain and 60% in France. Most of these masonry walls are currently perfectly safe, showing an average durability of more than a century. The best economic interest is to maintain the stock in good order by identifying and repairing the structures at risk of collapse and to preserve the currently satisfactory structures at the lowest investment level. Unfortunately, there is not sufficient scientific knowledge to do so reliably. This work aims to develop a design method suitable for existing structures. The analytical model is based upon the yield design theory which provides a rigorous framework and has proven to be effective for this kind of structures. The strength domain of stone masonry is determined using the homogenization theory. The modelisation is carried out in 2D. An experimental campaign was carried out in order to verify the proposed model. The experimental setup is in 2D thanks to the use of Schneebeli rods and is considered to be a physical model and is not scaled. The theoretical failing load and the theoretical kinematics of the failure are compared with the experimental failing load and the actual kinematics of the failure. The discrepancies and differences between the two sets are then discussed.


Masonry Yield design Structural analysis 



The authors would like to warmly thank Patrick Boujard (IFSTTAR) and Chloé Richet (Ecole Nationale des Travaux Publics de l’Etat) for their assistance with the experimental programme, and Peter Vennemann for freely providing his software package for particle image velocimetry, JPIV.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Université Paris-Est, MAST, SDOA, IFSTTARMarne-la-ValléeFrance
  2. 2.Université Paris-Est, Laboratoire Navier (UMR 8205), ENPC, IFSTTAR, CNRSMarne-la-ValléeFrance

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