Comparison between analytical and numerical methods for the assessment of masonry arch bridges: Case study of Clemente Bridge on Savio river

This research has focused on the study of the behavior and of the collapse of masonry arch bridges. The latest decades have seen an increasing interest in this structural type, that is still present and in use, despite the passage of time and the variation of the transport means. Several strategies have been developed during the time to simulate the response of this type of structures, although even today there is no generally accepted standard one for assessment of masonry arch bridges. The aim of this thesis is to compare the principal analytical and numerical methods existing in literature on case studies, trying to highlight values and weaknesses. The methods taken in exam are mainly three: i) the Thrust Line Analysis Method; ii) the Mechanism Method; iii) the Finite Element Methods. The Thrust Line Analysis Method and the Mechanism Method are analytical methods and derived from two of the fundamental theorems of the Plastic Analysis, while the Finite Element Method is a numerical method, that uses different strategies of discretization to analyze the structure. Every method is applied to the case study through computer-based representations, that allow a friendly-use application of the principles explained. A particular closed-form approach based on an elasto-plastic material model and developed by some Belgian researchers is also studied. To compare the three methods, two different case study have been analyzed: i) a generic masonry arch bridge with a single span; ii) a real masonry arch bridge, the Clemente Bridge, built on Savio River in Cesena. In the analyses performed, all the models are two-dimensional in order to have results comparable between the different methods taken in exam. The different methods have been compared with each other in terms of collapse load and of hinge positions.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Elastic Propagation in random media: applications to the imaging of volcano structures

High-frequency seismograms contain features that reflect the random inhomogeneities of the earth. In this work I use an imaging method to locate the high contrast small- scale heterogeneity respect to the background earth medium. This method was first introduced by Nishigami (1991) and than applied to different volcanic and tectonically active areas (Nishigami, 1997, Nishigami, 2000, Nishigami, 2006). The scattering imaging method is applied to two volcanic areas: Campi Flegrei and Mt. Vesuvius. Volcanic and seismological active areas are often characterized by complex velocity structures, due to the presence of rocks with different elastic properties. I introduce some modifications to the original method in order to make it suitable for small and highly complex media. In particular, for very complex media the single scattering approximation assumed by Nishigami (1991) is not applicable as the mean free path becomes short. The multiple scattering or diffusive approximation become closer to the reality. In this thesis, differently from the ordinary Nishigami’s method (Nishigami, 1991), I use the mean of the recorded coda envelope as reference curve and calculate the variations from this average envelope. In this way I implicitly do not assume any particular scattering regime for the "average" scattered radiation, whereas I consider the variations as due to waves that are singularly scattered from the strongest heterogeneities. The imaging method is applied to a relatively small area (20 x 20 km), this choice being justified by the small length of the analyzed codas of the low magnitude earthquakes. I apply the unmodified Nishigami’s method to the volcanic area of Campi Flegrei and compare the results with the other tomographies done in the same area. The scattering images, obtained with frequency waves around 18 Hz, show the presence of high scatterers in correspondence with the submerged caldera rim in the southern part of the Pozzuoli bay. Strong scattering is also found below the Solfatara crater, characterized by the presence of densely fractured, fluid-filled rocks and by a strong thermal anomaly. The modified Nishigami’s technique is applied to the Mt. Vesuvius area. Results show a low scattering area just below the central cone and a high scattering area around it. The high scattering zone seems to be due to the contrast between the high rigidity body located beneath the crater and the low rigidity materials located around it. The central low scattering area overlaps the hydrothermal reservoirs located below the central cone. An interpretation of the results in terms of geological properties of the medium is also supplied, aiming to find a correspondence of the scattering properties and the geological nature of the material. A complementary result reported in this thesis is that the strong heterogeneity of the volcanic medium create a phenomenon called "coda localization". It has been verified that the shape of the seismograms recorded from the stations located at the top of the volcanic edifice of Mt. Vesuvius is different from the shape of the seismograms recorded at the bottom. This behavior is justified by the consideration that the coda energy is not uniformly distributed within a region surrounding the source for great lapse time.