The narthex of the Church of the Nativity in Bethlehem: A non-linear finite element approach to predict the structural damage

Abstract

Keywords:Masonry Church of the Nativity Narthex FE model Non-linear dynamic analysis Vault a b s t r a c tThe Church of the Nativity in Bethlehem has a narthex in the front that is as long as the façade of the Church and about six meters wide. Currently, the narthex is covered by five cross vaults, three of which in a dangerous state of decay, and it is internally divided by three walls perpendicular to the façade, which appears to be strongly rotated outwards with a maximum horizontal top displacement of about 40 cm. Inside the central cross vault, the narthex has been heavily damaged and propped since the thirties of the last century. Numerous attempts have been made over the time to identify the causes of such damage. Some archival researches, in-situ inspections of the subsoil and detailed laser scanner surveys, which were carried out during the recent restoration works in the Church and in the narthex, allowed for gaining a deeper insight into the construction features of the cross vaults and for putting forward some hypotheses about the possible causes of damage. This paper provides a scientific validation of these hypotheses by means of finite element numerical simulations, which try to reproduce the seismic response of the Church and the deformation process of a three-dimensional simplified model of the narthex from an assumed initial configuration up to an ultimate state of damage, comparable with the current one. Such models are discretized by means of tetrahedron elements obeying a damage plasticity law that exhibits a softening behavior in both tension and compression. The numerical simulations carried out provide some results that fit reasonably with the actual deformed configuration of the narthex and can be considered as a useful tool for further insights.

Stability analysis of leaning historic masonry structures

“…The adopted continuum plastic-damage model [61,49] is characterized by a yielding function with multiplehardening variables and two independent scalar damage variables, one for the tensile damage and the other for compressive damage . Being the model formulated in the context of nonassociated plasticity [61], the plastic potential is defined by the dilatancy angle , generally assumed equal to 10° for masonry [62], as well as by a smoothing parameter usually assumed equal to 0.1 [63]. In addition, the strength domain is specified by the ratio between the biaxial and uniaxial initial compressive strengths, typically assumed equal to 1.16 [64], and by the shape constant , normally assumed equal to 2/3 [63].…”

A 3D detailed micro-model for the in-plane and out-of-plane numerical analysis of masonry panels

“…It is obtained by a flow rule generated by a Drucker-Prager type plastic potential. In particular, it is defined by the dilatancy angle , typically assumed equal to 10° in agreement with experimental evidences [45] and previous numerical models [46,47], and a smoothing constant generally assumed equal to 0.1 [46].…”

“…Reference to [51] has been made to define the uniaxial inelastic stress-strain relationships. The evolution of the degradation damage scalar variables and has been kept substantially proportional to the decay of the uniaxial stresses, as successfully experienced is several numerical campaigns [46,13,52].…”

3D finite element coupled analysis model for geotechnical and complex structural problems of historic masonry structures: conservation of Abu Serga church, Cairo, Egypt

“…Subsoil behavior is studied in details. The masonry structure of the church was modeled using solid element module, the solid element properties taken as defined above in design criteria [23,24].…”