Performance-based damage assessment of masonry structures subjected to settlement using rigid block models

The issue of built Cultural Heritage (CH) exposed to natural hazards is a challenging topic in both research and engineering practice. In the last decades, many efforts were addressed to the protection of CH against seismic hazard, which is the main threat for the integrity and stability of structures. On the other hand, settlements induced by hydrogeological phenomena such as subsidence and landslides also represent a severe risk for existing buildings. Nevertheless, the investigation of damage induced by settlements on structures is a still open challenge. Empirical approaches were proposed, commonly based on the assessment of damage in terms of local parameters, e.g. crack widths. However, the severity of crack width can be affected by different factors such as structural configuration, masonry texture and material properties. Thus, models for the quantitative assessment of damage in terms of global safety levels of structures subjected to foundation movements are demanded. In this framework, this dissertation thesis aims at the development and application of a numerical approach based on rigid block modelling for the performance-based damage assessment of masonry structures subjected to settlement. Two in-house numerical models are proposed, namely a rigid block model with rigid contacts for the linear kinematic analysis and a rigid block model with no-tension elastic contacts for the non-linear kinematic analysis. The first tool aims at the prediction of the failure shape for settled structures as well as the value of the base reaction at the onset of mechanism. It is worth noting that masonry buildings usually exhibit a resilient safety behaviour with respect to settlements. Conversely, appropriate considerations of serviceability limit state are demanded to control damage on the structure and preserve the aesthetics. To this end, the non-linear kinematic model aims to predict the response of masonry structures under settlements also in the early damage states. The output is mainly represented by specific capacity curves, named "push-down curves", where the loss of base reaction is plotted as a function of the displacement of a control point at the settling support. Thus, the numerical formulation allows the damage propagation monitoring, from crack opening until incipient collapse. The dissertation thesis explores the possibility to use such a capacity curve to propose criteria for the displacement-based damage assessment and quantification. A comparison of the proposed approach with empirical damage classification methods is performed

The prediction of collapse mechanisms for masonry structures affected by ground movements using Rigid Block Limit Analysis

Abstract Masonry structures belonged to the Cultural Heritage suffered severe damages in the last decays due to the action of the settlement-induced ground movements. The researchers have been developing numerical tools for the vulnerability analysis and assessment of masonry structures subjected to settlements. Continuous, discrete and rigid block models were proposed in literature. The analysis of both local or global failure modes due to settlement is a still debated topic, involving several questions related to the modelling techniques and to the investigation of the parameters which affect the masonry behaviour against foundation movements. In this framework, the paper focuses on a numerical approach for the settlement analysis based on the rigid block limit analysis. The Italian Code (NTC 2018) also suggests linear kinematic approach for the seismic-induced collapse mechanisms analysis. In such a formulation, the structure is modelled as a collection of polyhedral rigid blocks assuming frictional contact interfaces with infinite compressive strength and zero tensile strength and neglecting the mortar contribution. Originally formulated for the in-plane and out-of-plane mechanisms analysis, the numerical formulation was recently improved in order to analyze blocky-structures subjected to uniform settlement. Numerical case study of a monumental masonry church facade subjected to uniform settlement at the base was presented in this paper aiming at testing the numerical procedure. The results were discussed to evaluate the software capability and accuracy in the settlement-induced collapse mechanisms prediction

Rigid block and finite element analysis of settlement-induced failure mechanisms in historic masonry wall panels

The paper is related to the assessment of collapse mechanisms of historic masonry structures suffering settlements induced by ground movements. Two numerical strategies are adopted in order to study the influence of the settled zone on the cracking of masonry buildings: a discrete rigid block model and a continuous homogenized model. The first approach provides an estimate of the collapse load and failure pattern of masonry based on the lower bound theorem of limit analysis. The second approach is formulated in the framework of multi-surface plasticity and implemented in a FE code for the path-following non-linear analysis of masonry wall described as continuous anisotropic plate. Several settlement configurations, of masonry walls under moving ground support are investigated and the corresponding failure patterns resulting from the analysis are obtained resulting in local or global failure modes. The results of the two modeling formulations are compared and discussed in order to highlight the features of the two different approaches in the prediction of settlement-induced damage

Shake‑table testing of a stone masonry building aggregate: overview of blind prediction study

City centres of Europe are often composed of unreinforced masonry structural aggregates, whose seismic response is challenging to predict. To advance the state of the art on the seismic response of these aggregates, the Adjacent Interacting Masonry Structures (AIMS) subproject from Horizon 2020 project Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA) provides shake-table test data of a two-unit, double-leaf stone masonry aggregate subjected to two horizontal components of dynamic excitation. A blind prediction was organized with participants from academia and industry to test modelling approaches and assumptions and to learn about the extent of uncertainty in modelling for such masonry aggregates. The participants were provided with the full set of material and geometrical data, construction details and original seismic input and asked to predict prior to the test the expected seismic response in terms of damage mechanisms, base-shear forces, and roof displacements. The modelling approaches used differ significantly in the level of detail and the modelling assumptions. This paper provides an overview of the adopted modelling approaches and their subsequent predictions. It further discusses the range of assumptions made when modelling masonry walls, floors and connections, and aims at discovering how the common solutions regarding modelling masonry in general, and masonry aggregates in particular, affect the results. The results are evaluated both in terms of damage mechanisms, base shear forces, displacements and interface openings in both directions, and then compared with the experimental results. The modelling approaches featuring Discrete Element Method (DEM) led to the best predictions in terms of displacements, while a submission using rigid block limit analysis led to the best prediction in terms of damage mechanisms. Large coefficients of variation of predicted displacements and general underestimation of displacements in comparison with experimental results, except for DEM models, highlight the need for further consensus building on suitable modelling assumptions for such masonry aggregates

Rigid block modelling approach for the prediction of seismic performance of adjacent interacting masonry structures

The current paper discusses the contents of the work completed for the project “SERA AIMS – BLIND PREDICTION COMPETITION”. The competition was focused on the prediction of the response of a masonry building composed of two adjacent interacting structural units under earthquake excitation. This research investigates the response of the experimental mock-up by using a numerical model based on the rigid block limit analysis and mathematical programming. The results of the analysis, namely, the failure modes and the corresponding collapse load multipliers, are related to base shear and peak ground accelerations observed for the damage and ultimate limit states using code provisions for the assessment of failure mechanisms in existing masonry structures. Finally, a preliminary comparison of numerical and experiemental results is presented

LiABlock_3D: A Software Tool for Collapse Mechanism Analysis of Historic Masonry Structures

A rigid block model is proposed for collapse mechanism analysis of three-dimensional historic masonry structures subjected to point live loads, seismic-induced lateral loads and settlements. The model is made of polyhedral rigid blocks interacting at no-tension, frictional contact interfaces and can be used to represent complex assemblages and bond patterns. The formulation and the solution procedure of the underlying limit equilibrium analysis problem were implemented in LiABlock_3D, a MATLAB based tool with Graphical User Interface (GUI). The software was designed to import the geometric model from commercial Computer Aided Design (CAD) tools, thus allowing high flexibility of structural configurations and masonry patterns. The graphical interface is also used to define material properties as well as boundary and loading conditions. Numerical and experimental case studies from the literature were analyzed to show the ability of the model developed in predicting the collapse behavior of a variety of structural typologies. Those include arches, vaults, and domes under vertical and horizontal live loads and spreading supports. A two-story masonry building with a barrel vault at first level is also analyzed under variable lateral loads and support movement. Potentialities and limitations of the proposed formulation and tool are discussed on the basis of the results obtained and also in terms of computational efficiency

Collapse mechanism analysis of historic masonry structures subjected to lateral loads: A comparison between continuous and discrete models

The aim of this paper is to show to what extent a simple constitutive model can adequately describe the collapse mechanisms of historic masonry structures under horizontal seismic loads. Referring to block masonry, the paper presents the formulation and the numerical implementation of a constitutive relationship for modeling masonry structures regarded at a macroscopic scale as homogenized anisotropic continuum. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in a FE code by means of a minimization algorithm directly derived from the Haar-Karman principle. A sensitivity analysis to mechanical and geometrical parameters was carried out to show the influence on the predicted response of small-scale wall components from the literature. The model is then used for the analysis of a numerical case study which is representative of a masonry church subjected to horizontal seismic action. The result of the model will be compared with those obtained by a rigid block model (RBM) of the same small-scale masonry prototypes and of the church building. In the paper, the results of the two models are discussed and analyzed in the way to highlight the weakness and the potentiality of the two different approaches

Fractures around Trochanteric Nails: The “Vergilius Classification System”

Introduction. The fractures that occurred around trochanteric nails (perinail fractures, PNFs) are becoming a huge challenge for the orthopaedic surgeon. Although presenting some specific critical issues (i.e., patients’ outcomes and treatment strategies), these fractures are commonly described within peri-implant ones and their treatment was based on periprosthetic fracture recommendations. The knowledge gap about PNFs leads us to convene a research group with the aim to propose a specific classification system to guide the orthopaedic surgeon in the management of these fractures. Materials and Methods. A steering committee, identified by two Italian associations of orthopaedic surgeons, conducted a comprehensive literature review on PNFs to identify the unmet needs about this topic. Subsequently, a panel of experts was involved in a consensus meeting proposing a specific classification system and formulated treatment statements for PNFs. Results and Discussion. The research group considered four PNF main characteristics for the classification proposal: (1) fracture localization, (2) fracture morphology, (3) fracture fragmentation, and (3) healing status of the previous fracture. An alphanumeric code was included to identify each characteristic, allowing to describe up to 54 categories of PNFs, using a 3- to 4-digit code. The proposal of the consensus-based classification reporting the most relevant aspects for PNF treatment might be a useful tool to guide the orthopaedic surgeon in the appropriate management of these fractures