A response surface approach for uncertainty propagation in unreinforced masonry walls with interval mechanical properties

The accurate definition of the mechanical properties of masonry is quite challenging due to various sources of uncertainty, even in regularly constructed assemblies. Factors such as workmanship techniques, block geometry and texture, properties of individual components (mortar and bricks/stones), environmental conditions, and existing damage or degradation all contribute to variations in the mechanical properties of masonry. Available experimental data on masonry are often insufficient for a reliable probabilistic characterization of the uncertain properties. To address this issue, the present paper proposes a novel non-probabilistic framework for the analysis of masonry structures with uncertain mechanical properties. By applying the so-called Improved Interval Analysis via Extra Unitary Interval , the uncertain parameters are described as interval variables with assigned lower bound and upper bound. Then, focusing on unreinforced masonry walls, the interval mechanical properties are incorporated into a finite element model based on a simplified micro-modelling approach. Uncertainty propagation is efficiently performed by adopting a ratio-of-polynomials Response Surface, which requires only a few deterministic analyses. The entire procedure is implemented in the ABAQUS environment using Python scripts to perform multiple deterministic analyses. Numerical results concerning a benchmark wall demonstrate the accuracy and efficiency of the proposed approach in predicting resistance bounds and associated failure modes under in-plane and out-of-plane loading conditions, considering various uncertainty scenarios.