


Politecnico di Torino  
Academic Year 2017/18  
04FDENG Mechanics of Porous Media 

Master of sciencelevel of the Bologna process in Mathematical Engineering  Torino 





Subject fundamentals
The course aims at describing some mathematical models of use in civil and environmental engineering.
The microstructural description of porous media and multiphase systems is briefly introduced, justifying the upscaling at a macroscopic scale. Balance equations and constitutive relationships at the macroscopic scale are then discussed, with emphasis on the formulation of elasto hardening plastic constitutive laws. Mathematical models aimed at the description of physical processes will be successively developed on basis of the balance equations and of the constitutive laws. These models find application in the fields of earth sciences, geotechnics and biomechanics.. 
Expected learning outcomes
The students are expected to learn the fundamental aspects of mechanics of porous media and multiphase systems, together with some models for specific applications.

Prerequisites / Assumed knowledge
Continuum Mechanics

Contents
Part 1: Fundamentals of mechanics of porous materials
1. Structure of porous media and definition of the Representative Elementary Volume; 2. Phases and interaction between phases; 3. Macroscopic description of porous media; 4. Eulerian and Lagrangian description of the balance equations. Part 2.: Constitutive laws 1. Introduction to constitutive laws; 2. Elastic models; 3. Elastoplastic hardening models. Part 3: Models and modeling issues: 1. SaffmanTaylor instability; 2. Sedimentation, consolidation and subsidence; 3. Dynamics of fluids with variable density under thermal and concentration gradients; 4. Dynamics of fluid with variable density in fractured porous media; 5. Hydrochemomechanical behavior of active clays; 6. 2 D flow with averaging along the vertical direction; 7. Some aspects of dynamics of fluids in porous media; 8. Biomechanics; 
Texts, readings, handouts and other learning resources
R. Lancellotta (2004). Geotecnica. Zanichelli, 3° edizione (capitoli 2, 3, 4, 7).
R. Lancellotta (2009). Geotechnical Engineering. Taylor & Francis, London. A. Romano, R. Lancellotta, A. Marasco (2004). Continuum Mechanics using Matematica: Fundamentals, Applications and Scientific Computing with Matematica. Birkhauser. For the part on the applications Lectures Notes are available on the "portale della didattica" 
Assessment and grading criteria
The evaluation will be equally based on:
The discussion of the results of a project that the students will carry out in groups. Each project will be on a theme agreed between the members of each group and the professors. Each group will be formed by a maximum number of students to be determined when the project will be assigned; An oral exam aimed at verifying the knowledge of the fundamentals of the mechanics of porous media. The oral exam will last approximately 20 minutes, with at least one question for each of the parts of the program of the course. The student will have to show that he/she acquired the language skills and the logical synthesis required to use the fundamentals of the Mechanics of Porous Media, the constitutive models and the mathematical issues, for the formulation of models aimed at reproducing phenomena such as those discussed in the third part of the course. 
