The numerical methods are used for the geotechnical design of tunnels, slope stabilization and reinforcement, foundations and retaining structures. They represent the most complete method to tackle the soil/rock structure interaction and allow the designer to determine all the needed values to perform structural and geotechnical verifications. Developing good skills in planning, preparing, performing and interpreting the results from numerical models are key factors for the professional carrier in the civil engineering design and construction sectors. In line with the objectives of the Civil Engineering Master Course and the Geotechnical Engineering pathway, the NUMGE lectures are intended to introduce the students to the use of numerical methods in the geotechnical engineering practice. Fundamentals and theoretical aspects of numerical modeling methods will be described together with their application for the solution of geotechnical problems in relation to slope stability analyses, tunnel design, retaining structures and foundations design.

At the end of the classes, students will be able to: • Distinguish among the different numerical modeling techniques available to geotechnical engineers and choose the appropriate method to face a specific problem. • Understand which conditions, parameters, aspects need to be evaluated and determined together with their role in order to allow for reliable and useful results to be obtained. • Develop a numerical model. • Interpret, judge and validate the results obtained. • Stimulate criticisms and engineering judgment.

Students are required to have: • clear concept of stresses and strains and continuum mechanics, • knowledge on the investigation procedures for soils and rock masses, • knowledge on the geotechnical characterization procedures for soils and rocks, including laboratory and in situ tests, • basic skills on geotechnical design of foundations, diaphragm walls, tunnel liners and on slope stability analysis. The topics listed above are generally given by the Scienza delle costruzioni (Structural Mechanics), the Geotecnica (Geotechnics) and Meccanica delle Rocce (Rock Mechanics) classes.

Lectures will cover topics within: • the Finite Element Method (15 h) • constitutive modeling of geomaterials (8 h) • coupled problems (seepage, consolidation, thermo-hydro-mechanical) (10 h) • other numerical methods of interest in Geomechanics, e.g. BEM, DEM, FDEM (10 h) • case studies of engineering problems solved by different numerical methods, e.g. the design of tunnels in the urban environment, tunnels in squeezing and/or swelling conditions, slope stability problems, construction of retaining walls, energy geostructures and climate change issues, etc. (20 h)

The NUMGE class will include: • 57 hours of lectures in the classroom to develop knowledge on the different numerical methods, on their potential and limits, on proper modelling process and relevant applications (see programme). • 27 hours of exercise classes in the computer room (LAIB) with the use of dedicated software. During exercise classes, students will be asked to work on a real project and take advantage of the knowledge on numerical methods gained during lectures to solve the engineering problem proposed. Students will be asked to prepare a written report out of their work. This is intended to be done in small groups of two students.

Specific reading material together with the slides used will be made available to students during lectures and on the Portale della Didattica. Additional useful reading material (all available at the Politecnico di Torino libraries) are: • Finite element analysis in geotechnical engineering theory by David M Potts & Lidija Zdravkovic, Thomas Telford 1999 • Geotechnical modeling by David Muir Wood, Spon Press 2004 • The Finite Element Method: its basis and fundamentals (7th edition) by O. C. Zienkiewicz, R. L. Taylor, J.Z. Zhu Elsevier 2013 • Elementi di meccanica e ingegneria delle rocce by Marco Barla, Celid 2010 (in Italian)

Slides; Esercizi; Esercizi risolti;

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Elaborato progettuale in gruppo;

Exam: Written test; Compulsory oral exam; Group project;

... Scope of the exam is to ascertain that the student has assimilated all topics presented and is able to apply the theories and methods for the solution of practical geotechnical engineering problems. Votes are on a basis of thirty and is considered sufficient when the vote is at least 18/30. The exam consists in a written test, an oral examination and the writing up of a technical report. The technical report will be completed during the exercise classes and will describe the steps and outcomes of the project. Students can work in pairs during the exercise classes and prepare the report together. The report needs to be submitted at the latest during the written exam. Maximum vote will be: 30/30. The written exam consists of open queries and exercises to be solved with a pc available at the Laib. It will last between between 2 to 3 hours. Students will be allowed to use freely the notes distributed during lectures. Maximum vote will be: 30/30. The results will be published on the Portale della didattica, together with the dates for the oral examination and for consultation. The oral exam will consist of a discussion over the topics presented during lectures and exercise classes. Maximum vote will be: 30/30. The final mark will be obtained by combining the votes of the technical report (20%), the written exam (40%) and the oral exam (40%).

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.