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

Department

Institute of Geotechnics (GTN)

Learning outcomes of the course unit

Aim of subject:
• To gain a basic theoretical knowledge of the principle and methods of mathematical modeling,
• To gain an overview of basic constitutive models of geomaterials and their proper choice with respect to a soil type, construction to be analyzed and type of analysis,
• To understand a process of creating a mathematical model and limitations of mathematical modeling in geotechnical engineering,
• Learning to use the software Plaxis 2D (Brinkgreve et al., 2012) for the purpose of solving standard boundary value problems in plane strain conditions.

The outcome of the course is to provide basic knowledge of mathematical modeling in geotechnical engineering. Students get an overview of the frequently used soil constitutive models and learn about the construction of mathematical model both theoretically and practically. Students will learn to use the program Plaxis 2D for solutions of standard boundary value problems in geotechnical engineering.

Prerequisites

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

Co-requisites

Not required.

Recommended optional programme components

Optionally, students can attend lectures, field trips and workshops that are offered to them during the semester.

Not applicable.

Planned learning activities and teaching methods

Practice takes the form of individual work on the PC. Student deals with the selected examples of geotechnical structures (a common theme). At the end of the semester the student demonstrates knowledge and skills on an individual example, that at the end of orally presented.
Generally - teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for credit:
- Participation in education,
- Solve the separate tasks (joint award)
- Solving a separate task completed his oral presentations.

Requirements for passing the exam - test the theoretical knowledge of the subject matter in the form of a written examination followed by an oral part.

Language of instruction

Czech

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.
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. Undrained versus drained analysis, consolidation analysis.
9. Theory and modeling of earth retaining structures I (gravity walls, cantilever embedded walls).
10. Theory and modeling of earth retaining structures II (propped, anchored walls, reinforced earth walls).
11. Theory and modeling of embankments and cuts.

Aims

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 B-P-C-SI (N) Bachelor's

branch K , 4. year of study, summer semester, 4 credits, compulsory-optional

• Programme B-P-E-SI (N) Bachelor's

branch K , 4. year of study, summer semester, 4 credits, compulsory-optional

• Programme B-K-C-SI (N) Bachelor's

branch K , 4. year of study, summer semester, 4 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, 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. Undrained versus drained analysis, consolidation analysis.
9. Theory and modeling of earth retaining structures I (gravity walls, cantilever embedded walls).
10. Theory and modeling of earth retaining structures II (propped, anchored walls, reinforced earth walls).
11. Theory and modeling of embankments and cuts.

seminars

26 hours, 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. Numerical analysis of embankment.
10. Solution of individual example.
11. Presentation of individual example.