Computational Methods for Masonry Vaults: A Review of Recent Results

Abstract

The paper concisely reviews the available numerical methods to analyze masonry vaults up to collapse, putting in evidence pros and limitations of each approach. To be reliable, any procedure adopted should take into account the distinctive aspects of masonry mechanical behavior, namely the scarce (or zero) tensile strength, the good compressive resistance and the observed formation of failure mechanisms constituted by rigid macro-blocks in mutual roto-translation. Classic no-tension material models disregard the little but not null tensile strength and make the hypothesis of (1) infinitely elastic behavior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (especially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal also with anisotropy induced by texture, little tensile strength and softening in tension, as well as finite strength in compression. Traditionally, limit analysis has proven to be the most effective for a fast and reliable evaluation of the load carrying capacity of vaulted masonry structures. Classic lower and upper bound theorems recall respectively the concepts of equilibrium and formation of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorem, whereas FE limit analysis approaches with rigid elements take inspiration from the upper bound point of view. An alternative to limit analysis is represented by traditional FEM combined with either elasto-plastic or damaging models with softening, usually adapted to masonry from other materials, which are capable of providing a large set of output numerical information but that still remain very demanding

The effects of in-plane shear displacements at the springings of Gothic cross vaults

“…The mortar is a mix of one part lime and three parts sand, plus water and PVA glue, which creates a sufficient yet weak bond to allow failure to occur along the joints rather than the blocks [28]. Earlier work showed that the weight of the material does not affect the static response of the vault to support spread so there was no need to increase dead load by adding lead weight to simulate self-weight of stone [5], [23], [28].…”

Seismic capacity and multi-mechanism analysis for dry-stack masonry arches subjected to hinge control

“…There does exist a significant amount of analysis tools, techniques, and experimental investigations aimed at the assessment of arches and existing structures (Sarhosis et al 2016b;Tralli et al 2014;Hendry 1998). For earthquake loading, the commonly used techniques are divided into limit analysis (LA) and numerical analyses approaches.…”

Thrust Network Analysis of Masonry Vaults Subject to Vertical and Horizontal Loads

“…This estimate of r is used in (11) to obtain a new value of reference thrusts that, in turn, is used again in (8) to obtain a new estimate of r. The procedure is iterated until the convergence condition (9) is fulfilled. Finally, at convergence, formula (10) is applied to evaluate actual values of thrust in each branch of the network.…”

“…It was recently contributed by O'Dwyer [10] and fully developed by Block and coworkers in recent times [2,3]. Alternative approaches can be found in [1,4,11].…”