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Fractals in Geomechanics

Study program:
Mining Engineering (II semester -PhD)
Name of subject: Fractals in Geomechanics
Instructors:
Prof. Nebojša Vasović, Prof. Nebojša Gojković
Status: Optional
ECTS: 10
Prerequisites: -
Course Objectives:
An introduction to the basic concepts of fractal theory and application of fractal theory to related geotechnical engineering.
Learning Outcomes:
Fractal concepts will be applied to related geotechnical engineering problems’ research.
Content:

Theory teaching
Fractal definition. 2. Fragmentation.3. Fractal clustering. 4. Self-affine fractals. 5. Renormalization procedure. 6. Numerical estimation of fractal dimensions. 7. Fractals in geotectonics. 8. Fractals and coefficient of crack roughness (JRC). 9. Application of fractals for the classification of terrain according to Bieniawski (RMR). 10. Application of fractals in the study of cracking patherns and fragmentation in rock masses.

Practical teaching
Analysis and interpretation of articles published in international journals.

Suggested Reading List:
  1. Turcotte, D. 1997. Fractals and chaos in geology and geophysics. Cambridge University Press.
  2. Vijay, D. 2005. Fractals behavior of the earth system. Springer.
  3. Moon, F. 1992. Chaotic and fractal dynamics – an introduction for applied scientists and engineers. Wiley-VCH, Verlag.
  4. Heping, X., Zhida, C. 1988. Fractal geometry and fracture of rock. Acta mechanica sinica, Vol.4, No.3.
  5. Sezer, A., Altun, S., Erdogan, D., Goktepe, A.B. 2008. Correlation between CBR strength and fractal dimensions of sands. Proceedings of 12th International Conference of International Association for computer methods and advances in geomechanics (IACMAG),
  6. Perfect, E. 1997. Fractal models for the fragmentation of rocks and soils: a review. Engineering geology 48, 185-198
  7. Pal, S.K., Chakravarty, D. 2003. Rock mass characterization using fractals. National Conference on nonlinear systems and dynamics, India, 217-220.
  8. Belem, T., Homand-Etienne, F., Souley, M. 1997. Fractal analysis of shear joint roughness.International Journal of Rock mechanics and mining sciences. Vo.34, 1-11.
  9. Kolymbas, D. 2003. Fractals in geotechnical engineering. Exploratory Workshop, Innsbruck, 1-147
  10. Badge, M.N., Raina, A.K., Chakraborty, A.K., Jethwa, J.L. 2002. Rock mass characterization by fractal dimension. Engineering geology 63, 141-155.
Conduct of the Course:
Presentations, consultations
Fund hours:
Lectures Exercises Other forms of teaching Study research
4 0 0 0
Assessment:
Final Exam ECTS
Oral Exam60

Classwork Assessment ECTS
Seminars40
Additional Assessment Criteria: -


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