General effective medium model for the complex permittivity extraction with an open-ended coaxial probe in presence of a multilayer material under test

The work presented in this thesis is focused on the open-ended coaxial-probe frequency-domain reflectometry technique for complex permittivity measurement at microwave frequencies of dispersive dielectric multilayer materials. An effective dielectric model is introduced and validated to extend the applicability of this technique to multilayer materials in on-line system context. In addition, the thesis presents: 1) a numerical study regarding the imperfectness of the contact at the probe-material interface, 2) a review of the available models and techniques, 3) a new classification of the extraction schemes with guidelines on how they can be used to improve the overall performance of the probe according to the problem requirements.

Applicazione ed integrazione di metodi di prospezione geofisica: studio idrogeofisico della Zona Insatura in condizioni idriche controllate

Il lavoro è incentrato sull’applicazione ed integrazione di differenti tecniche di indagine geofisica in campo ambientale e ingegneristico/archeologico. Alcuni esempi sono stati descritti al fine di dimostrare l’utilità delle metodologie geofisiche nella risoluzione di svariate problematiche. Nello specifico l’attenzione è stata rivolta all’utilizzo delle tecniche del Ground Penetrating Radar e del Time Domain Reflectometry in misure condotte su un corpo sabbioso simulante una Zona Insatura. L’esperimento è stato realizzato all’interno di un’area test costruita presso l’azienda agricola dell’Università La Tuscia di Viterbo. Hanno partecipato al progetto le Università di Roma Tre, Roma La Sapienza, La Tuscia, con il supporto tecnico della Sensore&Software. Nello studio è stato condotto un approccio definito idrogeofisico al fine di ottenere informazioni da misure dei parametri fisici relativi alla Zona Insatura simulata nell’area test. Il confronto e l’integrazione delle due differenti tecniche di indagine ha offerto la possibilità di estendere la profondità di indagine all’interno del corpo sabbioso e di verificare l’utilità della tecnica GPR nello studio degli effetti legati alle variazioni del contenuto d’acqua nel suolo, oltre a determinare la posizione della superficie piezometrica per i differenti scenari di saturazione. Uno specifico studio è stato realizzato sul segnale radar al fine di stabilire i fattori di influenza sulla sua propagazione all’interno del suolo. Il comportamento dei parametri dielettrici nelle condizioni di drenaggio e di imbibizione del corpo sabbioso è stato riprodotto attraverso una modellizzazione delle proprietà dielettriche ed idrologiche sulla base della dimensione, forma e distribuzione dei granuli di roccia e pori, nonché sulla base della storia relativa alla distribuzione dei fluidi di saturazione all’interno del mezzo. La modellizzazione è stata operata sulle basi concettuali del Differential Effective Medium Approximation.

Analytical methods for modeling elastic metasurfaces

This dissertation aims at developing advanced analytical tools able to model surface waves propagating in elastic metasurfaces. In particular, four different objectives are defined and pursued throughout this work to enrich the description of the metasurface dynamics. First, a theoretical framework is developed to describe the dispersion properties of a seismic metasurface composed of discrete resonators placed on a porous medium considering part of it fully saturated. Such a model combines classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. Second, an exact formulation based on the multiple scattering theory is developed to extend the two-dimensional classical Lamb’s problem to the case of an elastic half-space coupled to an arbitrary number of discrete surface resonators. To this purpose, the incident wavefield generated by a harmonic source and the scattered field generated by each resonator are calculated. The substrate wavefield is then obtained as solutions of the coupled problem due to the interference of the incident field and the multiple scattered fields of the oscillators. Third, the above discussed formulation is extended to three-dimensional contexts. The purpose here is to investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces. Finally, the multiple scattering formulation is extended to model flexural metasurfaces, i.e., an array of thin plates. To this end, the resonant plates are modeled by means of their equivalent impedance, derived by exploiting the Kirchhoff plate theory. The proposed formulation permits the treatment of a general flexural metasurface, with no limitation on the number of plates and the configuration taken into account. Overall, the proposed analytical tools could pave the way for a better understanding of metasurface dynamics and their implementation in engineered devices.

Flow of Complex Fluids in Geological Fractures

In this study, the lubrication theory is used to model flow in geological fractures and analyse the compound effect of medium heterogeneity and complex fluid rheology. Such studies are warranted as the Newtonian rheology is adopted in most numerical models because of its ease of use, despite non-Newtonian fluids being ubiquitous in subsurface applications. Past studies on Newtonian and non-Newtonian flow in single rock fractures are summarized in Chapter 1. Chapter 2 presents analytical and semi-analytical conceptual models for flow of a shear-thinning fluid in rock fractures having a simplified geometry, providing a first insight on their permeability. in Chapter 3, a lubrication-based 2-D numerical model is first implemented to solve flow of an Ellis fluid in rough fractures; the finite-volumes model developed is more computationally effective than conducting full 3-D simulations, and introduces an acceptable approximation as long as the flow is laminar and the fracture walls relatively smooth. The compound effect of shear-thinning fluid nature and fracture heterogeneity promotes flow localization, which in turn affects the performance of industrial activities and remediation techniques. In Chapter 4, a Monte Carlo framework is adopted to produce multiple realizations of synthetic fractures, and analyze their ensemble statistics pertaining flow for a variety of real non-Newtonian fluids; the Newtonian case is used as a benchmark. In Chapter 5 and Chapter 6, a conceptual model of the hydro-mechanical aspects of backflow occurring in the last phase of hydraulic fracturing is proposed and experimentally validated, quantifying the effects of the relaxation induced by the flow.