Course Title : Applied Elasticity for Rock Mechanics

Code 10F071
Course Year Master and Doctor Course
Term 2nd term
Class day & Period Fri 3rd
Location C1-172
Credits 2
Restriction No Restriction
Lecture Form(s) Lecture
Language Japanese
Instructor Sumihiko Murata, Assoc. Prof., Dept. of Urban Management

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 analysis of elasticity using the basic equations, constitutive equations, and the complex stress function are explained. In addition, poroelasticity is 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 homeworks (25% each) and semester final examination (50%).

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.
Poroelasticity 2 Basic equations and parameters of poroelasticity are explained. Futhrermore, the applications of poroelasticity are explained.
Summary and Achievement check 1 The contents of this class are summarized. In addition, the achievement of course goals is checked.


Handouts are delivered.


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


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

Independent Study Outside of Class

Review of the each class is required.

Web Sites

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

Additional Information

Office hour is set 10:30-12:00 and 14:30-1600 on the same day of the class.