Discontinuous deformation analysis in rock mechanics practice 1st Edition by Yossef H Hatzor, Guowei Ma, Gen hua Shi ISBN 1138027685 9781138027688

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Product details: 

ISBN 10: 1138027685

ISBN 13: 9781138027688

Author: Yossef H. Hatzor, Guowei Ma, Gen hua Shi

Table of contents: 

1. Introduction
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
1.7.1 Block system kinematics
1.7.2 Complete first order displacement approximation
1.7.3 Equilibrium, dynamics and energy consumption
1.7.4 Large Deformation
1.7.5 Efficiency
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
1.11.1 Coupling DDA with FEM
1.11.2 Coupling DDA with BEM
1.11.3 Coupling DDA with NMM
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
1.19.1 Historical overview
1.19.2 Modelling particulate media with DDA
1.20 Pore Pressure and Fluid Flow
1.20.1 Historical overview
1.20.2 Coupling DDA 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
2.1.1 Governing equations
2.1.2 Displacement approximation of a single block
2.2 Formulation of Matrices for Each Single Block
2.2.1 Sub-matrices of elastic strains
2.2.2 Sub-matrices of initial stress
2.2.3 Sub-matrices of point loading
2.2.4 Sub-matrices of line loading
2.2.5 Sub-matrices of body force
2.2.6 Sub-matrices of bolting connection
2.2.7 Sub-matrices of inertia force
2.2.8 Sub-matrices of displacement constraints at a point
2.2.9 Sub-matrices of displacement constraints in a direction
2.3 Interactions Between Blocks
2.3.1 Contact detection
2.3.2 Contact constraint enforcement
2.3.3 Open-close iterations
2.3.4 Formulation of contact matrices
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
3.1.1 Displacement weight function
3.1.2 Global equilibrium equation
3.2 Formulation of Matrices for Single Block
3.2.1 Sub-matrices of elastic strain
3.2.2 Sub-matrices of initial stress
3.2.3 Sub-matrices of point loading
3.2.4 Sub-matrices of line loading
3.2.5 Sub-matrices of surface loading
3.2.6 Sub-matrices of body force
3.2.7 Sub-matrices of bolting connection
3.2.8 Sub-matrices of inertia force
3.2.9 Sub-matrices of displacement constraints in a direction
3.2.10 Sub-matrices of fixed point
3.3 Interactions Among Blocks
3.3.1 Contact detection and types
3.3.2 Contact state and open-close iteration
3.3.3 Formulation of contact matrices
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
4.2.1 Number of joint sets
4.2.2 Types of joint sets
4.2.3 Joint set orientation
4.2.4 Joint set spacing and bias correction
4.2.5 Joint set dispersion
4.2.6 Joint length
4.2.7 Rock bridges and realistic mesh generation
4.3 Mechanical Input Parameters for Forward Modeling
4.3.1 Intact rock elements
4.3.2 Shear strength of the discontinuities
5. DDA verification
5.1 Introduction
5.2 Single Plane Sliding
5.2.1 2D-DDA
5.2.2 3D-DDA
5.3 Double Plane Sliding
5.4 Block Response to Cyclic Motion of Frictional Interface
5.4.1 2D-DDA
5.4.2 3D-DDA
5.5 Dynamic Rocking of Slender Blocks
5.6 Wave Propagation Phenomena
5.6.1 P wave propagation
5.6.2 Shear wave propagation
5.6.3 Concluding remarks regarding wave propagation accuracy
6. Underground excavations
6.1 Introduction
6.2 Shallow Underground Excavations
6.2.1 Block interactions
6.2.2 Joint spacing
6.2.3 Excavation depth
6.3 Deep Underground Excavations
6.3.1 Boundary conditions
6.3.2 Excavation damage zone
6.3.3 Rockbolting
6.3.4 Rockbursts
7. Rock slopes
7.1 Introduction
7.2 Rotational Failure Modes
7.2.1 Toppling
7.2.2 Block slumping
7.2.3 Overhanging slopes
7.3 Dynamic Rock Slope Stability Analysis
7.3.1 First introduction of time dependent accelerations to DDA
7.3.2 Loading methods
7.3.3 Consideration of local site effects
7.3.4 Application to single plane sliding
7.4 Rockbolt Reinforcement
8. Shi’s new contact theory
8.1 Introduction
8.2 Geometric Representations of Angles and Blocks
8.2.1 Discontinuous computations
8.2.2 Related mathematical symbols
8.2.3 Algebraic operations of blocks
8.2.4 Representation of solid angles
8.2.5 Inequality equations of angles
8.2.6 Representation of blocks
8.2.7 Structure of blocks
8.2.8 Inequality equations of blocks
8.3 Definition of the Entrance Block
8.3.1 Relations of two blocks
8.3.2 Definition of entrance block
8.3.3 Entrance block and parallel movement
8.3.4 Entrance block of a block and a point
8.3.5 The entrance block of a block and a ball
8.3.6 The entrance ball between two balls
8.3.7 Theorem of separation
8.3.8 Theorem of entrance
8.3.9 Theorem of distance
8.3.10 Theorem of lock
8.3.11 Examples of the entrance block
8.4 Basic Theorems of Entrance Block
8.4.1 Theorem of uniqueness
8.4.2 Theorem of finite covers of entrance blocks
8.4.3 Theorem of including
8.4.4 Theorem of union
8.4.5 Theorem of symmetry
8.4.6 Theorem of contact
8.4.7 Theorem of removability
8.4.8 Theorem of inner points
8.4.9 Theorem of convex blocks
8.5 Boundaries of the Entrance Solid Angles of 2D Solid Angles
8.5.1 Local entrance solid angle of 2D blocks
8.5.2 Existence of entrance solid angle boundary of 2D solid angles
8.5.3 Contact surface of 2D solid angles
8.5.4 Entrance of boundary vector to vector of 2D solid angles
8.5.5 Contact vectors of angle to angle contact
8.5.6 Finite covers of 2D parallel vector to vector entrance
8.5.7 Contact vectors of 2D entrance solid angle
8.6 Contact Vectors of 2D Solid Angles
8.6.1 Contact vectors of a 2D convex solid angle and a 2D concave solid angle
8.6.2 Contact vectors of 2D convex solid angles
8.6.3 Entrance solid angle of 2D round corner convex solid angle and concave solid angle
8.6.4 Entrance round corner solid angle of 2D round corner convex solid angles
8.7 Boundaries of an Entrance Block of 2D Blocks
8.7.1 Entrance of 2D block inner points
8.7.2 Entrance of 2D edge to edges
8.7.3 Contact edges of 2D block to block contact
8.7.4 Finite covers of 2D parallel edge to edge entrance
8.7.5 Contact edges of 2D entrance block
8.8 Contact Edges of 2D Blocks
8.8.1 Contact edges of 2D convex blocks
8.8.2 Contact edges of 2D general bocks
8.8.3 Applications of the theory of contact in 2D DDA
8.8.4 Applications of the new theory of contact in 2D NMM
8.9 Boundaries of Entrance Solid Angle of 3D Solid Angles
8.9.1 Local entrance angle of 3D angles
8.9.2 Existence of entrance solid angle boundary of 3D solid angles
8.9.3 Entrance of 3D solid angle inner points
8.9.4 Entrance of boundary solid angle to angle of 3D solid angles
8.9.5 Entrance of boundary angle to vector of 3D solid angles
8.9.6 Contact solid angle of 3D vertex to boundary angle contact
8.9.7 Contact solid angle of 3D boundary vector to vector contact
8.9.8 Finite covers of parallel boundary angle to vector entrance
8.9.9 Finite covers of parallel boundary angle entrance
8.9.10 Contact angles of 3D entrance solid angle
8.10 Contact Solid Angles of 3D Solid Angles
8.10.1 Contact plane of a 3D solid angle and half space
8.10.2 Contact plane of two 3D convex solid edges
8.10.3 Contact half-planes of a 3D concave solid edge and a 3D solid angle
8.10.4 Contact half-planes of a 3D convex solid edge and a 3D solid angle
8.10.5 Contact solid angles of two 3D convex solid angles
8.10.6 Contact solid angles of two 3D general solid angles
8.11 Boundaries of Entrance Block of 3D Blocks
8.11.1 Entrance of 3D block inner points
8.11.2 Entrance of boundary polygons of 3D blocks
8.11.3 Entrance of polygon to edge of 3D blocks
8.11.4 Contact polygon of 3D vertex to polygon contact
8.11.5 Contact polygon of 3D edge to edge contact
8.11.6 Finite covers of parallel polygon to edge entrance
8.11.7 Finite covers of parallel polygon entrance
8.11.8 Contact polygons of 3D entrance blocks
8.12 Contact Polygons of 3D Blocks
8.12.1 Contact polygons of two 3D convex blocks
8.12.2 Contact polygons of two general 3D blocks
8.12.3 Simple examples of the new contact theory in 3D DDA
8.13 Conclusions

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Yossef H Hatzor,Guowei Ma,Gen hua Shi,Discontinuous