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)

Lecture slides; Exercises; Exercise with solutions ;

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%).

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.