Limit Analysis of Masonry Structures Accounting for Uncertainties in Constituent Materials Mechanical Properties

Denis Benasciutti 1, Gabriele Milani *, 2
1 DIEGM, Dipartimento di Ingegneria Elettrica Gestionale Meccanica, via delle Scienze 208, 33100 Udine (Italy) and
2 IBK-ETHZ, Institut f. Baustatik und Konstruktion, Swiss Federal Institute of Technology, Wolfgang-Pauli-Str. 15, 8093 Zürich, Switzerland

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Creative Commons License
© 2008 Benasciutti and Milani.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Institut f. Baustatik und Konstruktion, Swiss Federal Institute of Technology (ETH), Wolfgang-Pauli-Str. 15, 8093 Zürich, Switzerland (Formerly: ENDIF, Engineering Department in Ferrara, University of Ferrara, via Saragat 1, 44100 Ferrara, Italy); E-mails:, milani@ibk.baug.ethz.c


The uncertainty often observed in experimental strengths of masonry constituent materials makes critical the selection of the appropriate inputs in the finite elements limit analysis of complex masonry buildings, as well as requires modeling the building ultimate load as a random variable. The most direct approach to solve limit analysis problems in presence of random input parameters is the use of extensive Monte Carlo (MC) simulations. Nevertheless, when MC methods are used to estimate the collapse load cumulative distribution of a masonry structure, large scale linear programming problems must be numerically tackled several times, so precluding the practical utilization of large scale MC simulations. To reduce the computational cost of a traditional MC approach, in the present paper direct computer calculations are replaced with inexpensive Response Surface (RS) models. In particular, RS models are utilized for the limit analysis of a masonry structure in- and out-of-plane loaded, assuming input mechanical properties as random parameters. Two different RS models are analyzed, derived respectively from small scale (20 replicates) MC and Latin Hypercube (LH) simulations. The accuracy of the estimated RS models, as well as the good estimations of the collapse load cumulative distributions obtained via polynomial RS models in comparison with large scale MC simulations, show how the proposed approach could be a useful tool in problems of technical interest.

Keywords: Masonry, Limit analysis, Monte carlo simulations, Latin Hypercube.