Experimental and numerical evaluation of geometrical imperfection effects on the load bearing capacity of small-scaled voussoir arches

The study of the behaviour of masonry arches represents a complex problem, which involves different aspects that can significantly affect the load bearing capacity of such structures. In this regard, geometrical imperfections, such as the irregular shape of the arch blocks, the initial position of the first and last voussoirs (boundary conditions), the alignment between the adjoining blocks and the rounded corners of each block, play an important role. An experimental campaign was conducted on a toy arch made by eleven irregular blocks, with the aim of evaluating the effect of such irregularities. A numerical model was developed basing on lower bound (LB) and upper bound (UB) limit analysis approaches (referred to as the static and the kinematic theorem, respectively). A linear programming (LP) solving algorithm was implemented in the software MATLAB and used to solve the minimization/maximization problems. The probability distribution of each considered nonlinearity was estimated, the results of the numerical analysis were correlated with the experimental outcomes and a Montecarlo simulation was carried out to validate the hypothesised probability distributions.