1st Edition

Discontinuous Deformation Analysis in Rock Mechanics Practice

ISBN 9781032096650
Published June 30, 2021 by CRC Press
410 Pages

USD $69.95

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Book Description

The numerical, discrete element, Discontinuous Deformation Analysis (DDA) method was developed by Dr. Gen-hua Shi while he was working at the University of California, Berkeley, under the supervision of Prof. Richard E. Goodman in the late 1980s. Two-dimensional DDA was published in 1993 and three-dimensional DDA in 2001. Since its publication DDA has been verified, validated and applied in numerous studies worldwide and is now considered a powerful and robust method to address both static and dynamic engineering problems in discontinuous rock masses.
In this book Yossef H. Hatzor and Guowei Ma, co-chairs of the International Society for Rock Mechanics (ISRM) Commission on DDA, join Dr. Shi in authoring a monograph that presents the state of the art in DDA research. A comprehensive discussion of DDA development since its publication is provided in Chapter 1, followed by concise reviews of 2D and 3D DDA in chapters 2 and 3. Procedures to select geological and numerical input parameters for DDA are discussed in Chapter 4, and DDA validation and verification is presented in Chapter 5. Applications of DDA in underground and rock slope engineering projects are discussed in chapters 6 and 7. In Chapter 8 the novel contact theory recently developed by Dr. Shi is published in its complete form, for the first time.
This book is published within the framework of the ISRM Book Series and is the contribution of the ISRM DDA Commission to the international rock mechanics community.

Table of Contents

1.1 Who should read this book?
1.2 How to use this book?
1.3 Continuous vs. discontinuous deformation
1.4 DDA history
1.5 Three decades of DDA research and development
1.6 DDA vs. FEM and DEM
1.7 Main features of DDA
1.8 Some limitations of the original DDA
1.9 Block discretization
1.10 Higher order displacement function
1.11 Coupling DDA with other numerical methods
1.12 Improved contact algorithms
1.13 Incorporation of viscous damping
1.14 Improved friction law for discontinuities
1.15 Gravity turn on and sequential excavation
1.16 Dynamic wave propagation and blasting
1.17 Masonry structures
1.18 Improved rockbolt element
1.19 Granular materials
1.20 Pore pressure and fluid flow
1.21 Current development of 3-D DDA

2 Theory of the discontinuous deformation analysis (DDA)
2.1 Governing equations and displacement approximation
2.2 Formulation of matrices for each single block
2.3 Interactions between blocks
2.4 Time integration scheme and governing equations for blocky systems
2.5 Simplex integration for 2-D DDA
2.6 Summary

3 Theory of the discontinuous deformation analysis in three dimensions
3.1 Block displacement approximation and global equilibrium equation
3.2 Formulation of matrices for single block
3.3 Interactions among blocks
3.4 Simplex integration for 3D DDA
3.5 Summary

4 Geological input parameters for realistic DDA modeling
4.1 Introduction
4.2 Realistic representation of rock mass structure
4.3 Mechanical input parameters for forward modeling

5 DDA verification
5.1 Introduction
5.2 Single plane sliding
5.3 Double plane sliding
5.4 Block response to cyclic motion of frictional interface
5.5 Dynamic rocking of slender blocks
5.6 Wave propagation phenomena

6 Underground excavations
6.1 Introduction
6.2 Shallow underground excavations
6.3 Deep underground excavations

7 Rock slopes
7.1 Introduction
7.2 Rotational failure modes
7.3 Dynamic rock slope stability analysis
7.4 Rockbolt reinforcement

8 Shi’s new contact theory
8.1 Introduction
8.2 Geometric representations of angles and blocks
8.3 Definition of the entrance block
8.4 Basic theorems of entrance block
8.5 Boundaries of the entrance solid angles of 2D solid angles
8.6 Contact vectors of 2D solid angles
8.7 Boundaries of an entrance block of 2D blocks
8.8 Contact edges of 2D blocks
8.9 Boundaries of entrance solid angle of 3D solid angles
8.10 Contact solid angles of 3D solid angles
8.11 Boundaries of entrance block of 3D blocks
8.12 Contact polygons of 3D blocks
8.13 Conclusions

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"This book brings the extraordinary power of DDA (Discontinuous Deformation Analysis) to the tool-baskets of engineers who are responsible for excavations and foundations in jointed and faulted rock masses. The mathematical basis for DDA originated in the brilliant PhD Dissertation and subsequent publications of Gen-hua Shi, and has been furthered by many applications in recent years. These include Professor Hatzor’s resourceful analyses of works needed to protect ancient surficial and underground structures in Israel. Important developments have been published in the proceedings of the International Assoc. for Computer Methods and Advances in Geomechanics, and in other recent engineering literature. With this book, the potential applications of DDA will be further recognized and applied for the benefit of the entire engineering community."

Professor Richard E. Goodman, Professor Emeritus at the department of Civil and Environmental Engineering, University of California, Berkeley.