224-0901/02 – Mathematical and Physical Modelling in Rock Engineering (MFMGI)

Gurantor departmentDepartment of Geotechnics and Underground EngineeringCredits10
Subject guarantordoc. RNDr. Eva Hrubešová, Ph.D.Subject version guarantordoc. RNDr. Eva Hrubešová, Ph.D.
Study levelpostgraduateRequirementOptional
YearSemesterwinter + summer
Study languageCzech
Year of introduction2011/2012Year of cancellation2013/2014
Intended for the facultiesFAST, HGFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
HRU30 doc. RNDr. Eva Hrubešová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 2+0
Part-time Examination 16+0

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


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:

Potts, D. Zdravkovic, L. Finite element analysis in geotechnical engineering. Telford, 1999. ISBN 0 72772753 2. Gioda, Z.: Modeling in Geomechanics. Wiley 2000. Baecher, G.B., Christian, J.T. Reliability and Statistics in Geotechnical Engineering. Wiley, 2003. ISBN 0-471-49833-5.

Recommended literature:

Bull, J.W. Numerical Analysis and Modeling in Geomechanics. Spon Press. 2003. ISBN 0-415-24328-9.

Way of continuous check of knowledge in the course of semester


Other requirements

There are no other special requirements


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1.The fundamentals of mathematical and physical modeling, basic principles, types of methods. 2.Basic equations and the relationship of the mathematical models. 3.Basic constitutive models of the behavior of soils and rocks. 4.Finite element method and its application in solving problems in the field of rock engineering 5.Characteristics and capabilities of the boundary element method 6.Finite difference method, principles, applications 7.Distinct element method, principles, application options 8.Stochastic modeling methods (Monte Carlo simulation method, LHS method) 9.Back analysis and its use for the reliable determination of the characteristics of the geological environment

Conditions for subject completion

Part-time form (validity from: 2011/2012 Winter semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2013/2014 (P3655) Civil Engineering (3607V035) Geotechnics P Czech Ostrava Optional study plan
2013/2014 (P3655) Civil Engineering (3607V035) Geotechnics K Czech Ostrava Optional study plan
2012/2013 (P3607) Civil Engineering (3607V035) Geotechnics K Czech Ostrava Optional study plan
2012/2013 (P3607) Civil Engineering (3607V035) Geotechnics P Czech Ostrava Optional study plan
2012/2013 (P3655) Civil Engineering (3607V035) Geotechnics K Czech Ostrava Optional study plan
2012/2013 (P3655) Civil Engineering (3607V035) Geotechnics P Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner