Course detail

Mathematical Modeling of Geotechnical Constructions

FAST-NFB014Acad. year: 2020/2021

The course is mainly focused on geotechnical constructions analyses using the finite element method. In the first part of the course, basics of continuum mechanics will be repeated. The major emphasis is placed on a description of soil constitutive models, starting with the simplest elastic models, continuing with more complicated models involving plastic (irreversible) component of strain. In the following part of the course, students will become familiar with the process of creating a mathematical model both from a theoretical and practical point of view. Acquired knowledge will be applied in order to solve various types of geotechnical constructions (shallow foundations, deep foundations, earth retaining structures, embankments, cuts, underground structures) using Plaxis 2D software. In the last part of the course, students will prepare and present their individual projects.


Institute of Geotechnics (GTN)

Learning outcomes of the course unit

Main output is acquiring knowledge build-up of mathematical model selected geotechnical problems (slope stability, reinforcement soil, retaining wall and tunnel). It means definition the boundary conditions, selection constitutional models etc. The selected themes are educated on the concrete examples using software on the Department of Geotechnics.


Soil mechanics, Foundation Engineering, Underground structures, Elasticity and plasticity.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Introduction, basic aspects and reasons of applying numerical methods in geotechnics, examples of practical applications.
2. Continuum mechanics – summarization, review of numerical methods. Review of soil constitutive models.
3. Introduction to the finite element method. Linear, non-linear elasticity.
4. Introduction to the plastic behavior of geomaterials.
5. Perfectly plastic constitutive models.
6. Elastic – plastic constitutive models with hardening.
7. Undrained versus drained analysis, consolidation analysis.
8. Theory and modeling of foundations.
9. Theory and modeling of earth retaining structures, excavations.
10. Theory and modeling of earth constructions. Stability analysis.


To obtain theoretical basics of the mathematical modelling of geotechnical problems.
To learn to utilise selected software for design of geotechnics structures.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Classification of course in study plans

  • Programme NPC-SIS Master's, 2. year of study, winter semester, 5 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer


26 hours, compulsory

Teacher / Lecturer