京都大学 京都大学

Applied Elasticity for Rock Mechanics

Numbering Code G-ENG01 6F071 LJ77 Year/Term 2022 ・ Second semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Fri.3
Instructor name FUKUYAMA EIICHI (Graduate School of Engineering Professor)
MURATA SUMIHIKO (Graduate School of Engineering Associate Professor)
Outline and Purpose of the Course Theory of elasticity relating to the deformation and failure of rock and rock mass and design of rock structures is explained. Specifically, two-dimensional analyses of elasticity using the basic equations, the constitutive equations, and the complex stress function are explained. Several applications to rock mechanics, rock engineering, and fracture mechanics are also explained. Then, strain and stress field ahead of the propagating crack is theoretically investigated. And the stress change due to the crack propagation is explained.
Course Goals The goal of this class is to master the theory of elasticity so as to solve the elastic problem in rock mechanics, rock engineering, and fracture mechanics.
Schedule and Contents 1.-2. Airy's stress function and complex stress function (2 times)
Airy's stress function used to solve a two-dimensional elastic problem is first explained, and then the complex stress functions that are the representation of Airy's stress function by the complex variables are explained.

3.-6. Two-dimensional elastic analysis using the complex stress function (4 times)
Analytical solutions of two-dimensional elastic problems in fracture mechanics and rock engineering are derived by using the complex stress functions. The mechanical behavior of rock material is also explained based on the derived solutions.

7. Application of two-dimensional elastic analysis (1 time)
The theory of rock support, ground characteristic curve, theoretical equations used for the evaluation of rock stress, which are derived from the solution of two-dimensional elastic problem, are explained.

8.-10. Propagating two-dimensional mode 1 crack (3 times)
Suddenly appeared two-dimensional mode 1 stationary crack is investigated to theoretically obtain a stress and displacement field around the crack. The solution is extended to a mode 1 crack propagating at a constant velocity. Then the solution is further extended for the cases with non-uniform propagation velocity. Finally, the same procedure is applied to obtain the solutions for mode 2 and mode 3 cracks.

11.-12. Stress field at a crack tip and path-independent integrals (2 times)
Using the two-dimensional solution for cracks propagating with non-uniform velocity, how to evaluate the stress field at the crack tip is explained. And path independent integrals around the crack tip is introduced.

13.-14. Effects of viscoelasticity and high strain rate on the crack propagation (2 times)
When the crack surfaces behaves viscoelastically or high strain rate is applied at the crack tip, the effects to the crack propagation are investigated in comparisons to the cases with perfect linear elasticity.

Examination (1 time)

15. Feedback (1 time)
The contents of this class are summarized. In addition, the achievement of course goals is checked.
Evaluation Methods and Policy Evaluation is made by the score of two report problems or homeworks (25% each) and semester final examination (50%).
Course Requirements The knowledge and calculation skill of calculus, vector analysis and complex analysis are required.
Study outside of Class (preparation and review) Review of the each class is required.
Textbooks Textbooks/References Handouts are delivered.
References, etc. Jaeger, J. C., N. G. W. Cook, and R. W. Zimmerman: Fundamentals of Rock Mechanics -4th ed., Blackwell Publishing, 2007, ISBN-13: 978-0-632-05759-7

Freund, L. B.: Dynamic Fracture Mechanics, Cambridge University Press, 1990, ISBN: 0-521-30330-3
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