The concept of "State of Matter" is one establishment on which the particles theory, popular in the in physics/chemistry community, is based on. In that context, a distinction is made based on atomic particles interaction: matter in the solid state maintains a fixed volume and shape, matter in the liquid state maintains a fixed volume, but has a variable shape that adapts to fit its container, while matter in the gaseous state has both variable volume and shape. These definitions can be up-scaled, up to granular particles level, extending the concept of phase transition to granular materials. This aspect is central when studying granular materials mechanical behaviour, due to their twofold nature: either acting as a solid (landslide inception) or flowing like a fluid (landslide propagation). This thesis aims at interpreting these phase transition phenomena, initially considering dry conditions, in the light of strain hardening visco-elastoplasticity based on the critical state concept, interpreting this as a particular steady state under quasi static conditions, and kinetic theories of granular gases and demonstrating that crucial is the role of isotropic softening/hardening describing the size of the elastic domain, that is the capability of the solid skeleton of storing elastic energy according to permanent force chains. The main ingredients of the model are: (i) the additivity of quasi-static and collisional stresses, (ii) the energy balance equation governing the evolution of the granular temperature, interpreted this latter as an additional internal variable for the system for the collisional contribution, (iii) the mixed isotropic and kinematic hardening characterizing the quasi-static incremental constitutive relationship. The model has been both calibrated and validated on DEM triaxial numerical test results performed on dry assemblies of monodisperse spheres under true triaxial loading. When saturated conditions are concerned, the presence of water changes the dynamics of the grain-grain interaction, producing additional dissipations due to grain-water contacts and the classic Terzaghi's effective stress principle should be redefined. Following the same approach adopted in case of dry conditions, the extension of the constitutive model is tackled starting from an energetic point of view, analyzing new mechanisms arising in case of saturated media are concerned. In particular, the grain-grain interaction is damped by the presence of the liquid phase, thus the energy dissipation of the granular phase increases since the particle movements are bounded by the liquid. The dissertation is concluded by discussing the solutions of boundary value problems adopting the model previously conceived, implemented in a MPM numerical tool (ANURA3D), properly modified. These results, aimed at demonstrating the model applicability to real case problems, pave the way to the study of many geotechnical problems by means of a unique approach.
Il concetto di "Stato della Materia" consiste in una classificazione della forma che la materia può assumere. Sulla base dell’interazione fra le molecole è possibile distinguere: la materia allo stato solido, che mantiene un volume e una forma fissi, la materia allo stato liquido, che mantiene un volume fisso ma ha una forma variabile che si adatta al suo contenitore, e la materia allo stato gassoso, caratterizzata sia da volume che forma variabili. Queste definizioni possono essere rivisitate ad una diversa scala, quella dei grani, estendendo il concetto di transizione di fase ai materiali granulari. Questo aspetto è di primaria importanza nello studio del comportamento meccanico dei materiali granulari ogni qualvolta mostrano la loro duplice natura: possono presentarsi sotto forma di solido (come nella fase di innesco di una frana) o comportarsi come un fluido (propagazione della frana stessa). Lo scopo di questa tesi, ispirata dal fascino della natura cangiante del materiale, è quello di interpretare e riprodurre questi fenomeni di transizione di fase, dapprima in condizioni asciutte, attraverso un modello viscoelasto-plastico incrudente basato sul concetto di stato critico, interpretando quest’ultimo come un particolare stato stazionario in condizioni quasi statiche, e delle teorie cinetiche dei gas granulari, estensione ad una diversa scala di quelle dei gas perfetti. Il presente lavoro mette in luce, durante il cambiamento di fase, l’importanza dell’incrudimento isotropo, che descrive la dimensione del dominio elastico, ovvero la capacità dello scheletro solido di immagazzinare energia elastica attraverso una rete stabile di catene di forze. Il modello si caratterizza per: (i) l’additività dello sforzo quasi statico e collisionale, (ii) l’equazione di bilancio energetico che governa l’evoluzione della temperatura granulare, interpretata quest’ultima come una variabile interna aggiuntiva per il sistema, necessaria a definire il contributo collisionale, (iii) un incrudimento, sia isotropo che anisotropo, che governa il legame quasi-statico. Il modello è stato calibrato e validato sui risultati dei test numerici triassiali ("true-triaxial") DEM eseguiti su campioni ideali composti da sfere monodisperse. Nel caso di condizioni sature, la presenza dell’acqua entra in gioco e modifica la dinamica dell’interazione inter-granulare, dando luogo a meccanismi dissipativi aggiuntivi legati all’interazione tra parte liquida e grani. Seguendo un approccio analogo a quello adottato nel caso secco, l’estensione del modello è formulata sulla base di considerazioni energetiche e introducendo elementi di dissipazione aggiuntivi legati allo smorzamento dell’interazione tra i grani dovuta alla presenza dell’acqua. Nella seconda parte del lavoro, si discutono i risultati di simulazioni numeriche di problemi al contorno adottando il modello precedentemente concepito, implementato in un codice basato sul metodo MPM (ANURA3D), opportunamente modificato. Questi risultati, volti a dimostrare l’applicabilità del modello a problemi reali, incoraggiano l’utilizzo di questo strumento per lo studio di molti problemi geotecnici, caratterizzati da grandi spostamenti e cambiamenti del comportamento del materiale.
Phase transition in granular materials : theoretical and numerical analises
Marveggio, Pietro
2021/2022
Abstract
The concept of "State of Matter" is one establishment on which the particles theory, popular in the in physics/chemistry community, is based on. In that context, a distinction is made based on atomic particles interaction: matter in the solid state maintains a fixed volume and shape, matter in the liquid state maintains a fixed volume, but has a variable shape that adapts to fit its container, while matter in the gaseous state has both variable volume and shape. These definitions can be up-scaled, up to granular particles level, extending the concept of phase transition to granular materials. This aspect is central when studying granular materials mechanical behaviour, due to their twofold nature: either acting as a solid (landslide inception) or flowing like a fluid (landslide propagation). This thesis aims at interpreting these phase transition phenomena, initially considering dry conditions, in the light of strain hardening visco-elastoplasticity based on the critical state concept, interpreting this as a particular steady state under quasi static conditions, and kinetic theories of granular gases and demonstrating that crucial is the role of isotropic softening/hardening describing the size of the elastic domain, that is the capability of the solid skeleton of storing elastic energy according to permanent force chains. The main ingredients of the model are: (i) the additivity of quasi-static and collisional stresses, (ii) the energy balance equation governing the evolution of the granular temperature, interpreted this latter as an additional internal variable for the system for the collisional contribution, (iii) the mixed isotropic and kinematic hardening characterizing the quasi-static incremental constitutive relationship. The model has been both calibrated and validated on DEM triaxial numerical test results performed on dry assemblies of monodisperse spheres under true triaxial loading. When saturated conditions are concerned, the presence of water changes the dynamics of the grain-grain interaction, producing additional dissipations due to grain-water contacts and the classic Terzaghi's effective stress principle should be redefined. Following the same approach adopted in case of dry conditions, the extension of the constitutive model is tackled starting from an energetic point of view, analyzing new mechanisms arising in case of saturated media are concerned. In particular, the grain-grain interaction is damped by the presence of the liquid phase, thus the energy dissipation of the granular phase increases since the particle movements are bounded by the liquid. The dissertation is concluded by discussing the solutions of boundary value problems adopting the model previously conceived, implemented in a MPM numerical tool (ANURA3D), properly modified. These results, aimed at demonstrating the model applicability to real case problems, pave the way to the study of many geotechnical problems by means of a unique approach.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/183289