Course detail

Mathematical Modeling of Geotechnical Constructions

FAST-BFB008Acad. year: 2025/2026

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.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Ing. Juraj Chalmovský, Ph.D.

Department

Institute of Geotechnics (GTN)

Entry knowledge

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

Rules for evaluation and completion of the course

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

Aims

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

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DAVIS, Robert Olin; SELVADURAI, Antony PS. Elasticty and geomechanics. Cambridge university press, 1996. 9780521498272 (EN)
DAVIS, Robert Olin; SELVADURAI, Antony PS. Plasticity and geomechanics. Cambridge university press, 2005. 9781139436526 (EN)
DESAI, Chandrakant S. Elementary Finite Element Method. Prentice Hall, 1978. 9780132566360 (EN)
HERLE, Ivo. Základy matematického modelování v geomechanice. Praha: Karolinum, Učební texty Univerzity Karlovy v Praze, 2003. 802460745X (CS)
NAKAI, Teruo. Constitutive Modeling of Geomaterials: Principles and Applications. CRC Press, 2012. 978-0415557269  (EN)
POTTS, David M., et al. Finite element analysis in geotechnical engineering: application. London: Thomas Telford, 2001. ISBN 0-72-772783-4  (EN)
POTTS, David M., et al. Finite element analysis in geotechnical engineering: theory. London: Thomas Telford, 1999. ISBN 0-7277-2753-2  (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BPC-SI Bachelor's

    specialization K , 4 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Juraj Chalmovský, Ph.D.

Syllabus

  • 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.
  • 11. Theory and modeling of underground structures.

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Juraj Chalmovský, Ph.D.

Syllabus

  • 1. Introduction to the used software.
  • 2. Structural and interface elements.
  • 3. Numerical analysis of shallow foundations.
  • 4. Numerical analysis of deep foundations.
  • 5. Simulation of laboratory tests.
  • 6. Numerical analysis of propped retaining structures.
  • 7. Numerical analysis of anchored retaining structures.
  • 8. Numerical analysis of embankments.
  • 9. Solution of an individual task.
  • 10. Solution of an individual task.
  • 11. Presentation of an individual task.