Modeling and Mechanics of Granular and Porous Materials

Soils are complex materials: they have a particulate structure and fluids can seep through pores, mechanically interacting with the solid skeleton. Moreover, at a microscopic level, the behaviour of the solid skeleton is highly unstable. External loadings are in fact taken by grain chains which are continuously destroyed and rebuilt. Many issues of modeling, even of the physical details of the phenomena, remain open, even obscure; de Gennes listed them not long ago in a critical review. However, despite physical complexities, soil mechanics has developed on the assumption that a soil can be seen as a continuum, or better yet as a medium obtained by the superposition of two and sometimes three con and the other fluids, which occupy the same portion of tinua, one solid space. Furthermore, relatively simple and robust constitutive laws were adopted to describe the stress-strain behaviour and the interaction between the solid and the fluid continua. The contrast between the intrinsic nature of soil and the simplistic engi neering approach is self-evident. When trying to describe more and more sophisticated phenomena (static liquefaction, strain localisation, cyclic mo bility, effects of diagenesis and weathering, ..... ), the nalve description of soil must be abandoned or, at least, improved. Higher order continua, incrementally non-linear laws, micromechanical considerations must be taken into account. A new world was opened, where basic mathematical questions (such as the choice of the best tools to model phenomena and the proof of the well-posedness of the consequent problems) could be addressed.

The modeling of granular and porous materials affects a variety of problems that arise from the need to describe the behavior of materials that exist naturally in our surroundings. This work covers all major topics in modeling soil behavior, including transport phenomena: namely, mechanics of porous and granular media, flow and transport phenomena in particulate materials, and numerical simulation methods. It may serve as a reference or seminar text for graduate students, researchers and scientists in applied mathematics, continuum mechanics, finite element methods, solid mechanics, and hydraulics engineering.

I Mechanics of Porous Media.- 1 Constitutive Equations and Instabilities of Granular Materials.- 2 Micromechanical Modeling of Granular Materials.- 3 Thermodynamic Modeling of Granular Continua Exhibiting Quasi-Static Frictional Behaviour with Abrasion.- 4 Modeling of Soil Behaviour: from Micro-Mechanical Analysis to Macroscopic Description.- 5 Dynamic Thermo-Poro-Mechanical Stability Analysis of Simple Shear on Frictional Materials.- II Flow and Transport Phenomena in Particulate Materials.- 6 Mathematical Models for Soil Consolidation Problems: a State of the Art Report.- 7 Flow of Water in Rigid and Non-Rigid, Saturated and Unsaturated Soils.- 8 Mass Exchange, Diffusion and Large Deformations of Poroelastic Materials.- III Numerical Simulations.- 9 Continuum and Numerical Simulation of Porous Materials in Science and Technology.- 10 A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media.- 11 Numerical Modeling of Initiation and Propagation Phases of Landslides.