Homogenization approach for the evaluation of crack patterns induced by foundation settlement on an old masonry building

A numerical FE homogenization approach for the interpretation of existing crack patterns induced by founda-tion settlement on old masonry buildings is discussed. The approach is quite general and may be applied to any case study. It relies on a 3D FE discretization of the entire structure by means of rigid infinitely resistant six-noded wedge ele-ments and non-linear interfaces, exhibiting deterioration of the mechanical properties. Soil is modeled by means of elastic translational springs, with values derived from at hand simplified approaches. The case study analyzed is the so called “Siloteca” [1] building in Milan, Italy, which belongs to a more complex built ag-gregate, originally conceived by the French Napoleonic army as riding stable during the Cisalpina Republic. At present, the building is utilized as an archive within the Science and Technology Museum. The aggregate may be regarded as be-ing subdivided into two separate blocks, with each one further sub-divided into eight isolated buildings. Nowadays, only six stables of one of the blocks are still present. Two of the six structures now serve as a Museum deposit and are the ob-jects of the present study, whereas the other four are in worst condition, partially roofed and collapsed and in a general de-cayed state. Siloteca exhibits meaningful crack patterns and an active overturning mechanism of the main façade. The masonry face texture is relatively regular and well organized; its section is constituted of three leaves of header bricks, one leaf being alternatively constituted by one-half brick. A quite large sub-vertical crack is present in the central long wall, at a distance of about 10 meters from the main façade, which is progressively rocking. The reason of the façade movements at the base is probably due to differential settlements of the foundation, as a consequence of a large excavation realized some decades ago to install large gas oil tanks for the museum. In this paper, for a direct mechanical interpretation of the reasons at the base of the formation of the crack pattern, a sim-ple but effective fully equilibrated model is discussed, facilitating in the accurate prediction of the position of the cracks. The model is also utilized to estimate soil elastic vertical stiffness –within a Winker approximation- to be used in a second phase with the fully non-linear FE code. Once the soil constants are at disposal from such a procedure, a homogenized non-linear FE code recently proposed by the second author [2, 3] is utilized to have an insight into the state of mechanical degradation of the structure. A hypothesis on foundation settlement is provided to justify the crack maps exhibited by the structure.