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

Abstract

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.