A multi-scale model for masonry domes: sensitivity to microstructure. The case of San Saturnino.

In this paper a multi-scale analysis, under service loads, is proposed to evaluate the sensitivity of masonry domes structural behaviour both to micro-geometry (masonry pattern) and to macro- geometry (dome shape). For masonry domes reference is made to membrane theory. Here the study is focused on the San Saturnino’s dome. The geometry of San Saturnino dome is obtained from a rigorous laser scanner survey. Hence, the effective geometry is taken into account for FEM modelling: both at micro-level (pattern) and macro-level (dome shape). As well known, the stresses diffusion in masonry domes, under membrane theory assumption, depends only on the macro-geometry, and the stresses distribution along meridians and parallels is only a problem of equilibrium [1], [2]. Strains distribution, on the contrary, depends both on micro-geometry of masonry and macro-geometry of dome; therefore the strains distribution envisages a problem about the constitutive function. Masonry stiffness has an influence on strains, both along parallels and meridians, thus it is relevant for the structural behaviour of domes and for their structural safety [3]. Here, a homogenisation procedure has been used to determine the constitutive function of masonry, in order to take into account the micro-geometry. The effective masonry pattern is considered: running bond pattern with concentric geometry. The analysis of the masonry dome behaviour is performed through a FEM procedure. The idea is to evaluate the effective texture - type of pattern - for strains distribution in parallels and meridians by reference to actual San Saturnino dome shape.