Structural Evaluation of Typical Historical Masonry Vaults of Cagliari: Sensitivity to Bricks Arrangements

Masonry vaults have a great diffusion in the historical architectural heritage: in this work, their structural behavior is investigated. Attention is focused on lowered sail vaults composed by several brick arrangements, a typical nineteenth-century masonry vault which have great diffusion in Cagliari (Sardinia). The target is evaluating the role played by bricks arrangement in their mechanical behavior. A series of rigorous laser scanner surveys have been performed in order to obtain the effective geometry both at macro-level – the vault shape – and at micro-level – brick patterns. A NURBS (Non-Uniform Rational B Spline) representation of the geometry is adopted and adaptive upper bound limit analyses are performed. NURBS entities, which are common in commercial CAD packages, have the great advantage to describe complex geometries such as curved elements, with very few elements. An upper bound limit analysis formulation is adopted, in which the NURBS elements forming the mesh are idealized as rigid bodies with dissipation allowed only along interfaces. The mesh constituted by few NURBS elements is progressively adjusted through a genetic algorithm in order to minimize the live load multiplier. Limit analysis is performed initially to determine the collapse multiplier of vertical loads, to assess the load bearing capacity of the vault, then attention is focused on differential settlements, that may be a serious hazard for this structural typology

Fast Seismic Vulnerability Evaluation of Historical Masonry Aggregates through Local Analyses: an Adaptive NURBS-based Limit Analysis Approach

An efficient computational tool for the local failures analysis in historical masonry aggregates is proposed. A NURBS (Non-Uniform Rational B-Spline) representation of geometry is adopted. NURBS entities, which are common in commercial CAD packages, have the great advantage to describe complex geometries (such as curved elements and walls with a high number of holes) with very few elements. An upper bound limit analysis formulation is implemented, in which the adopted NURBS elements are idealized as rigid bodies with dissipation allowed only along interfaces. The mesh of NURBS elements is progressively adjusted through a genetic algorithm in order to minimize the live load multiplier. This procedure is applied in the evaluation of the horizontal load multiplier associated with the activation of local mechanisms during a seismic event. Some case studies, referring to masonry aggregates located in the historical centers of Arsita (Abruzzo region, Italy) and Sora (Lazio region, Italy), are here presented. A quick evaluation of the seismic vulnerability is performed through the presented NURBS-based computational tool, showing the high importance of the local response in the study of the seismic behavior of masonry aggregates

UB-ALMANAC: An adaptive limit analysis NURBS-based program for the automatic assessment of partial failure mechanisms in masonry churches

As well known, masonry churches fail upon formation of partial failure mechanisms, usually activating at very low levels of horizontal accelerations, which are responsible for the collapse of specific macro-blocks, typically the façade, the apse, lateral naves long walls, etc. Such collapses are a sort of fingerprint for a church and are dependent on the peculiar geometric features of each structure. In order to cope with such unique behavior, the Italian Guidelines on Cultural Heritage for the safety assessment of historical masonry churches require the separate analysis of 28 pre-assigned failure mechanisms by means of the application of the upper bound theorem of limit analysis in presence of a no-tension material. The utilization of an arbitrary subset of mechanisms, whilst fully justified by past earthquakes experience, could in principle lead to an overestimation of the load carrying capacity and force practitioners to calculations that are still not fully automated. In this context, we present here an efficient and straightforward automatic Upper Bound Adaptive LiMit ANAlysis program for masonry Churches: UB-ALMANAC. The code proposed in this paper relies into a rough finite element discretization constituted by few NURBS rigid elements joined by elasto-plastic interfaces. The mesh is directly prepared within a CAD environment based on the 3D model of the whole church, thus being immediately conceived at architectural level. Limit analysis is then performed automatically under the desired horizontal loads distribution, using the kinematic theorem of limit analysis with dissipation allowed only along interfaces and progressive adaptation of the mesh through a Genetic Algorithm, leading to a quick estimation of the first activating failure mechanism and the most vulnerable macro-block. Three small-medium size churches damaged by the recent Emilia Romagna (2012) and Monti Sibillini (2016) seismic sequences are analyzed and results are compared with both alternative numerical approaches and the actual damages observed. Very good match is systematically found, meaning that the proposed tool could represent a breakthrough toward the full automation of the limit analysis assessment of partial failure mechanisms for churches

Adaptive limit analysis of historical masonry structures modeled as NURBS solids

In this work, we propose an adaptive upper bound limit analysis based on the representation of geometry through NURBS-solids. A NURBS-solid is a closed volume identified by boundary NURBS surfaces (Non-Uniform Rational Bezier Spline). Differently from using NURBS surfaces representing masonry shell-elements, NURBS-solids allow an accurate representation of masonry three-dimensional macro-blocks, such as vaults or walls with variable thickness. The initial model is subdivided into very few macro-elements, each one is still a NURBS solid and is considered as a rigid block. Since dissipation occurs only along interfaces, NURBS boundary surfaces represent possible fracture zones. An upper bound limit analysis is applied. The minimum kinematic multiplier is found by modifying the initial subdivision of solids until the real collapse mechanism is reproduced. This automatic research is performed through a Genetic Algorithm. A simple numerical example is finally reported

Seismic vulnerability of masonry historical structures: A simple adaptive nurbs FE approach for the limit and the subsequent non-linear static analysis with few dofs

The present contribution deals with an innovative evaluation of the vulnerability and static seismic behavior of existing masonry structures and monumental buildings. For a given masonry construction, a discretization through few NURBS surfaces is realized. NURBS surfaces are converted into shell elements which are assumed rigid and infinitely resistant. The non-linearities typical of the masonry material (almost no tensile strength, frictional behavior in shear, and relatively larger resistance in compression) are imposed at interfaces between adjacent elements, which represent in this way possible fracture lines. Once defined a horizontal load configuration, an adaptive upper bound limit analysis is applied. As final result, the collapse mechanism and the collapse load multiplier are found. Then, to provide the complete non-linear structural response, a FE model composed of elastic elements representing macro-blocks and non-linear contact-based interfaces or plastic damaging strips corresponding to the cracks is derived. On such model, static non-linear analyses can be performed easily at a fraction of the computational burden needed by standard approaches. Several examples including masonry churches, vaults, and buildings are presented. Finally, a novel limit analysis computational technique based on a discretization through NURBS solid elements is introduced and future perspectives of the research are drawn

Advanced Structural Investigation Through Structural Health Monitoring and Adaptive Limit Analysis: the Case of a Damaged Masonry Arch Bridge in India

In the following work, a Structural Health Monitoring (SHM) procedure combined with adaptive limit analysis is presented with reference to a damaged masonry arch bridge located near Mumbai (India). SHM is performed by monitoring the crack growth under different load conditions. Vibrating wire displacement transducers have been used for this purpose. Then, an adaptive upper bound limit analysis based on a Non-Uniform Rational B-Spline (NURBS) geometrical model, capable of taking into account the existing cracks, has been followed to investigate the residual load-bearing capacity. The obtained results show that the damaged masonry bridge still presents a margin of safety under traffic loads

Fast Adaptive Limit Analysis of Masonry Arch Bridges in Presence of Differential Settlements of Bridge Piles

In this work, we present a fast and reliable NURBS-based kinematic approach for the evaluation of the settlements-response of masonry arch bridges. This method is based on a discretization of the arch through NURBS rigid blocks. Here, the use of NURBS (Non-Uniform Rational B-Spline) approximating functions allows composing mesh through very few elements maintaining the exact representation of the three-dimensional curved shape. The main non-linear properties of masonry (almost null tensile strength, high crushing resistance, and frictional behavior in shear) are assigned at interfaces, which represent possible hinges between the curved macro-blocks. Starting from a known displacement applied at the external boundaries, a simple linear programming problem can be written to determine the discontinuous displacement field. Then, a meta-heuristic mesh-adaptation procedure is applied to exclude mesh dependency effects. The initial mesh is adjusted by modifying the shape of macro-blocks until interfaces coincide with the correct position of cracks. The settlement-response is so obtained