Continuum and Computational Mechanics for Geomechanical Engineers
The field of rock mechanics and rock engineering utilizes the basic laws of continuum mechanics and the techniques developed in computational mechanics. This book describes the basic concepts behind these fundamental laws and their utilization in practice irrespective of whether rock/rock mass contains discontinuities.
This book consists of nine chapters and six appendices. The first four chapters are concerned with continuum mechanics aspects, which include the basic operations, definition of stress and strain tensors, and derivation of four fundamental conservation laws in the simplest yet precise manner. The next two chapters are the preparation for computational mechanics, which require constitutive laws of geomaterials relevant to each conservation law and the procedures for how to determine required parameters of the constitutive laws.
Computational mechanics solves the resulting ordinary and partial differential equations. In Chapter 7, the methods of exact (closed-form) solutions are explained and they are applied to ordinary/partial differential equations with solvable boundary and initial conditions. In Chapter 8, the fundamentals of approximate solution methods are explained for one dimension first and then how to extend them to multi-dimensional problems. The readers are expected to learn and clearly understand how they are derived and applied to various problems in geomechanics.
The final chapter involves the applications of the approximate methods to the actual problems in practice for geomechanical engineers, which cover the continuum to discontinuum, including the stress state of the earth as well as the ground motions induced by earthquakes. Six appendices are provided to have a clear understanding of continuum mechanics operations and procedures for how to deal with discontinuities/interfaces often encountered in rock mechanics and rock engineering.
1. Fundamental operations 2. Stress analysis 3. Deformation and strain 4. Fundamental conservation laws 5. Constitutive laws 6. Laboratory tests 7. Methods for exact (closed-form) solutions 8. Methods for approximate solutions 9. Applications of approximate methods in geo-engineering problems Appendix 1: Gauss divergence theorem Appendix 2: Geometrical interpretation of the Taylor expansion Appendix 3: Reynolds transport theorem Appendix 4: The Gauss elimination method and its implementation Appendix 5: Constitutive modeling of discontinuities and interfaces Appendix 6: Thin band element for modeling discontinuities and interfaces in numerical analyses