224-0901/01 – Mathematical and Physical Modelling in Rock Engineering (MFMGI)
| Gurantor department | Department of Geotechnics and Underground Engineering | Credits | 5 |
| Subject guarantor | doc. RNDr. Eva Hrubešová, Ph.D. | Subject version guarantor | doc. RNDr. Eva Hrubešová, Ph.D. |
| Study level | postgraduate | Requirement | Optional |
| Year | | Semester | winter + summer |
| | Study language | Czech |
| Year of introduction | 2006/2007 | Year of cancellation | 2012/2013 |
| Intended for the faculties | HGF, FAST | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The aim of the course Mathematical and physical modeling in rock engineering is to acquaint students with the fundamentals of mathematical and physical modeling, basic methods, principles and application possibilities of different methods of modeling. Another objective is to understand the nature of the stochastic approach to model calculations and the use of methods of back analysis. By completing the course, students should be be able to analyze the problem in terms of the selection of appropriate methods of mathematical modeling to define the input data, apply the corresponding mathematical model and formulate and analyze the results.
Teaching methods
Individual consultations
Project work
Summary
The course is focused on mathematical and physical modeling, including basic principles of models, starting relationships and equations, principles of individual modeling methods (finite element method, boundary element method, finite difference method, discrete elements). Furthermore, the student acquainted with the principles of stochastic modeling (Monte Carlo simulation method, the method LHS) and back analysis methods and their application to input data objectification of mathematical models and increase their explanatory power.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Základy matematického a fyzikálního modelování, základní principy, typy metod.
2. Výchozí rovnice a vztahy matematických modelů
3. Základní konstitutivní modely chování zemin a hornin
4. Metoda konečných prvků a její aplikace při řešení úloh z oblasti horninového inženýrství
5. Charakteristika a možnosti aplikace metody hraničních prvků
6. Metoda konečných diferencí, principy, aplikace
7. Metoda oddělených elementů, podstata, aplikační možnosti
8. Stochastické modelování (simulační metoda Monte Carlo, metoda LHS)
9. Inverzní analýza a její využití pro spolehlivější stanovení charakteristik horninového prostředí
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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