Course detail

# Mathematical Modeling of Geotechnical Constructions

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

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

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

POTTS, M., D., ZDRAVKOVIĆ, L.: Finite Element Analysis in Geotechnical Engineering – Theory, 1999, Thomas Thelford Publishing, ISBN 0-7277-2753-2 (EN)
POTTS, M., D., ZDRAVKOVIĆ, L.: Finite Element Analysis in Geotechnical Engineering: Volume Two – Application, Thomas Thelford Publishing, 2001, ISBN 0-72-772783-4 (EN)
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)
NAKAI, Teruo. Constitutive Modeling of Geomaterials: Principles and Applications. CRC Press, 2012. 978-0415557269 (EN)
DESAI, Chandrakant S. Elementary Finite Element Method. Prentice Hall, 1978. 9780132566360 (EN)

Šejnoha, M., Pruška, J., Janda, T., Brouček, M.: Metoda konečných prvků v geomechanice :teoretické základy a inženýrské aplikace, ČVUT, 2015, 978-80-01-05743-8 (CS)
Herle, I.: Základy matematického modelování v geomechanice, UK Praha, Karolinum, 802460745X (CS)

Classification of course in study plans

• Programme N-P-C-SI Master's

branch S , 2 year of study, winter semester, compulsory-optional

• Programme N-K-C-SI Master's

branch S , 2 year of study, winter semester, compulsory-optional

#### Type of course unit

Lecture

26 hod., optionally

Teacher / Lecturer

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. 3. Introduction to the finite element method. 4. Review of soil constitutive models. Linear, non-linear elasticity. 5. Introduction to the plastic behavior of geomaterials. 6. Ideally plastic constitutive models. 7. Elastic – plastic constitutive models with hardening. 8. Theory and modeling of earth retaining structures I (gravity walls, cantilever embedded walls). 9. Theory and modeling of earth retaining structures II (propped, anchored walls, reinforced earth walls). 10. Undrained versus drained analysis, consolidation analysis.

Exercise

26 hod., compulsory

Teacher / Lecturer

Syllabus

1. Introduction to software Plaxis. 2. Introduction to software Plaxis - continued. 3. Structural and interfaces elements. 4. Numerical analysis of shallow foundation. 5. Numerical analysis of deep foundation. 6. Simulation of laboratory tests. 7. Numerical analysis retaining structure. 8. Numerical analysis retaining structure including ground water flow. 9. Solution of individual example. 10. Presentation of individual example