Elastic-plastic-softening evolutionary analysis of masonry arches: The application of the cohesive/overlapping crack model

The structural behaviour of masonry arches has been deeply investigated over the centuries, starting with the first theoretical approach by Hook in 1675. Later, with the introduction of the Theory of Elasticity, the graphical procedure illustrated by Méry (1840) gained high recognition in the field of arch design. More recently, following the formulation by Heyman (1966), which is based on Plastic Theory concepts, the modern Limit Analysis was introduced. Nevertheless, all these models are not able to describe the behaviour of arch structures in a comprehensive way, since they are not capable to predict the damage evolutionary process that affects the load bearing capacity of masonry arches. Recent studies have provided a model to analyse masonry arches based on Linear Elastic Fracture Mechanics, leading to the definition of the fracturing benefit, which, analogously to the plastic benefit for Limit Analysis, describes how the arch thrust line is affected by crack formation and the maximum admissible load evaluated by means of Fracture Mechanics is larger than the load predicted by Theory of Elasticity. In this framework, the Cohesive/Overlapping Crack Model is able to simulate the transition between cracking or crushing failure in the arch cross-section, highlighting a strong correlation between the structural behaviour of the arch and its size. In the present Master Thesis, the Cohesive/Overlapping Crack Model is extended to the study of masonry or plain concrete arch structures, which are subjected to off-center compression. Multi-cracking and multi-crushing damage phenomena are simulated by means of the Crack Length Control Scheme, in order to obtain a complete load history of the arch structure. This Nonlinear Fracture Mechanics model reveals a high capability in predicting the elastic-plastic-softening behaviour of the arch as well as the local mechanical instabilities, such as snap-back and snap-through, occurring during the post-cracking regime. In the first part of this Thesis, the main models proposed in the scientific literature for arch analysis are briefly summarized. Then, the principles of Nonlinear Fracture Mechanics are introduced, with particular focus on the Cohesive/Overlapping Crack Model. In the third part of the Thesis, the new model for arch analysis is introduced and a description of the adopted numerical procedures is provided. In the last part, some parametric analyses about scale effects in masonry arches are reported together with the results obtained for the Mosca Bridge case-study. Finally, some future developments and applications of the model are presented.