78468 - Numerical Models for Geoengineering M

Course Unit Page

Academic Year 2019/2020

Course contents


Requirements/Prior knowledge

A prior knowledge and understanding of Continuum Mechanics, Hydraulics, Soil Mechanics and Rock Mechanics is required to attend with profit this course.

This knowledge is typically acquired during the following undergraduate courses: Structural Mechanics, Hydraulics, Geotechnics, Rock Engineering.

Fluent spoken and written Italian is a necessary pre-requisite: all lectures and tutorials, and all study material will be in Italian.


Constitutive modelling of soil and rock behaviour (5 hours). Elasticity. Perfect elasto-plasticity. Hardening elasto-plasticity. The Mohr-Coulomb model.

Finite Element theory (12 hours). Finite Element theory for linear materials. Finite Element theory for nonlinear materials. The code Plaxis.

Practical exercises with the finite element code Plaxis 2D (7 hours).


Requirements/Prior knowledge

A prior knowledge and understanding of basic statistics is required to benefit from this course. Moreover, the use of geographical information systems for the geoprocessing and visualization of spatial data is recommended.

Students are expected to have a general background on the most common topics related to Environmental Engineering, such as hydraulics and hydraulic protection of territory, geotechnics and rock mechanics, topography, georesources and mining engineering.

Fluent spoken and written Italian is a necessary pre-requisite: all lectures and tutorials, and the majority of the study material, will be in Italian.


Reminders in Probabilities and Statistics (4 hours).

Elementary statistics, frequency distributions, random variables, correlation, regression. Practical applications with Excel and VBA®.

Monovariate Stationary Geostatistics (14 hours).

Regionalized variables, Random functions and autocorrelation functions, experimental variograms and variogram modelling, regularization, dispersion, simple, ordinary and block kriging, co-kriging, mapping of estimated values and estimation precision. Practical applications with Excel and VBA®.

Introduction to multivariate and nonlinear geostatistics (2 hours).

Cross-variogram, co-kriging, drift, universal kriging. Hints.

Applications with dedicated open source software for regionalized data analysis and management (4 hours).



Lecture notes

Potts D.M., Zdravkovic L. (1999). Finite element analysis in geotechnical engineering. Theory and Application. Thomas Telford.

Plaxis manual: http://www.plaxis.nl/plaxis2d/manuals/



Bruno, R. and Raspa, G. (1994) - La pratica della geostatistica lineare: il trattamento dei dati spaziali - Edizioni Angelo Guerini ed Associati S.r.l., 170 pp.

Chiles, J.P. and Delfiner, P. (1999) - Geostatistics - Wiley Series in Probability and Statistics, - John Wiley and sons, Inc., 687 pp.

Remy N., Boucher A. and Wu J. (2009) – Applied Geostatistics with SGEMS. A User’s Guide - Cambridge University Press. 288 pp.

Lecture notes.

Teaching methods


Class lessons, exercises at the computer laboratory and at home



The module is taught mainly through face-to-face lectures. For a more effective understanding of the subject, class exercises on real data are provided to students.

Assessment methods


The exam consists in a:

- computer calculation with the Finite Element code Plaxis 2D

- oral question on the theoretical contents of the course

Higher grades will be awarded to students who demonstrate an organic understanding of the subject, a high ability for critical application, and a clear and concise presentation of the contents. To obtain a passing grade, students are required to at least demonstrate a knowledge of the key concepts of the subject, some ability for critical application, and a comprehensible use of technical language. A failing grade will be awarded if the student shows knowledge gaps in key-concepts of the subject, inappropriate use of language, and/or logic failures in the analysis of the subject.



The assessment and evaluation are based on a dissertation made by the student on a real case of spatial data processing. Students are required to present their work individually. The presentation of the work will be done within the examination periods.

The defense of the dissertation, through an oral test, will determine the mark. The scope of the oral test is to assess the critical and methodological skills acquired from the dissertation work.

Passing the exam is guaranteed to students who demonstrate well understanding of the subject and good operational capacity in the preparation of the dissertation. A higher score is awarded to students whose understanding of the issues is evaluated as highly positive. They should have achieved complete autonomy in the use of the methods and tools, even for applications different from those illustrated in the classroom. The mnemonic knowledge of the subject, the lack of critical analysis on their own work and a language, written and oral, inappropriate for a university course will lead to discrete assessments. Training gaps on the subject and a technically incorrect language will lead to an evaluation not exceeding the sufficiency. Unacceptable training gaps will lead to a negative evaluation.



The final grade will be calculated as an average between the grades obtained for Module 1 and Module 2.

Teaching tools


PowerPoint presentations

computer exercises with the code Plaxis 2D



The module combines a theoretical part (powerpoint presentations and lessons on the blackboard) and a practical part (computer exercises in the classroom, also related to the development and implementation of calculation procedures for the use of models introduced).

Office hours

See the website of Daniela Boldini

See the website of Roberto Bruno