A Non-Linear Finite Element Approach to predict the Structural Damage of the Narthex of the Bethlehem Nativity Church

摘要

The Church of the Nativity in Bethlehem has a narthex at the front as long as the facade of the Church and about six meters wide. Currently the narthex is covered by five cross vaults in a dangerous state of decay and is internally divided by three walls perpendicular to the facade, which appears to be strongly rotated outwards with a maximum horizontal top displacement of about 40 cm. Inside the central cross vault is heavily damaged and propped since the 1930s. There have been numerous attempts over time to identify the causes of such a damage. Recent restoration works, still going on in the church and in the narthex, made it possible to have a more precise insight into the construction features of the cross vaults, as a result of: archival researches; in-situ inspections of the subsoil; and a detailed laser scanner survey. All collected data enabled some hypotheses, about the possible causes of the damage, to be advanced. This paper provides a scientific validation of these hypotheses through an advanced finite element numerical simulation which attempts to reproduce the evolution of the damage up to a deformed configuration quite close to the real one, starting from a three-dimensional simplified and undeformed model of the narthex. Such a model is then discretized by means of tetrahedron elements obeying a damage plasticity law which exhibit a softening behavior in both tension and compression. The numerical simulation provides some results that fit reasonably with the actual deformed configuration; therefore it can be considered as a useful tool for further insights.