## Course Title : Applied Elasticity for Rock Mechanics

Code 10F071 Master and Doctor Course 2nd term Fri 3rd C1-172 2 No Restriction Lecture Japanese S. Murata

### Course Description

Theory of elasticity relating to the deformation and failure of rock and rock mass　and design of rock structures is explained. Specifically, two-dimensional and three-dimensional analysis of elasticity using the basic equations, constitutive equations, and the complex stress function are explained. Several applications of this analysis to rock mechanics, rock engineering, and fracture mechanics are also explained.

Evaluation is made by the score of two report problems or homework and semester final exam.

### 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.

### Course Topics

Theme Class number of times Description
Airy’s stress function and complex stress function 2 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.
Two-dimensional elastic analysis using the complex stress function 8 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.
Application of two-dimensional elastic analysis 2 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.
Three-dimensional theory of elasticity 2 Stress functions to solve the three-dimensional elastic problem are explained, and some examples of the three-dimensional elasticity solution are explained.
Summary and Achievement check 1 The contnts of this class are summarized. In addition, the achievement of course goals is checked.

### Textbook

Handouts are delivered.

### Textbook(supplemental)

J.C. Jaeger, N.G.W. Cook, and R.W. Zimmerman: Fundamentals of Rock Mechanics -4th ed., Blackwell Publishing, 2007, ISBN-13: 978-0-632-05759-7

### Prerequisite(s)

The knowledge and calculation skill of calculus, vector analysis and complex analysis are required.

### Web Sites

Web page of this lecture is not specifically provided. When preparing it by need, the information is shown in the class.