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Continuum and Computational Mechanics for Geomechanical Engineers [Hardback]

(University of the Ryukyus, Nishihara, Japan)
  • Format: Hardback, 326 pages, height x width: 246x174 mm, weight: 970 g, 25 Tables, black and white; 14 Line drawings, color; 167 Line drawings, black and white; 48 Halftones, black and white; 14 Illustrations, color; 215 Illustrations, black and white
  • Series: ISRM Book Series
  • Pub. Date: 21-Apr-2021
  • Publisher: CRC Press
  • ISBN-10: 036768053X
  • ISBN-13: 9780367680534
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  • Format: Hardback, 326 pages, height x width: 246x174 mm, weight: 970 g, 25 Tables, black and white; 14 Line drawings, color; 167 Line drawings, black and white; 48 Halftones, black and white; 14 Illustrations, color; 215 Illustrations, black and white
  • Series: ISRM Book Series
  • Pub. Date: 21-Apr-2021
  • Publisher: CRC Press
  • ISBN-10: 036768053X
  • ISBN-13: 9780367680534
Other books in subject:

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.

About the author xi
Acknowledgments xiii
Preface xv
1 Fundamental operations
1(10)
1.1 Scalar
1(1)
1.2 Vector
1(1)
1.3 Vector operations
1(3)
1.3.1 Addition and subtraction
1(1)
1.3.2 Dot product
2(1)
1.3.3 Cross product
2(1)
1.3.4 Unit vector
2(1)
1.3.5 Coordinate systems and base vectors
3(1)
1.3.6 Vector operations on a Cartesian coordinate system
3(1)
1.4 Tensors of rank n
4(3)
1.4.1 Definition of tensors of rank n
4(2)
1.4.2 Tensor operations
6(1)
1.5 Matrix representation of tensors
7(1)
1.5.1 Matrix representation of vectors
7(1)
1.5.2 Matrix representation of tensors
7(1)
1.6 Coordinate transformation
8(1)
1.7 Derivation of tensorial quantities
9(2)
1.7.1 Derivative of a scalar function
9(1)
1.7.2 Divergence
9(1)
1.7.3 Rotation
9(1)
1.7.4 Gradient of a vector: second-order tensor
9(1)
1.7.5 Divergence of a tensor (second-order tensor)
10(1)
References
10(1)
2 Stress analysis
11(7)
2.1 Definition of a stress vector
11(1)
2.2 Stress tensor
11(1)
2.3 Relationship between a stress vector and a stress tensor: Cauchy's law
12(2)
2.4 Stress transformation
14(1)
2.5 Principal stresses and stress invariants
15(1)
2.6 Geometrical representation of stress tensor on the Mohr circle for the 2D condition
15(3)
References
17(1)
3 Deformation and strain
18(8)
3.1 Preliminaries
18(1)
3.2 Derivation of a strain tensor using the Lagrangian description
19(2)
3.3 Derivation of a train tensor using the Eulerian description
21(2)
3.4 Relationship between the small strain theory and the finite strain theory
23(1)
3.5 Geometrical interpretations of a strain tensor
23(3)
3.5.1 Uniaxial deformation
23(1)
3.5.2 Simple shear deformation
24(1)
References
25(1)
4 Fundamental conservation laws
26(17)
4.1 Fundamental conservation laws for one-dimensional cases
26(9)
4.1.1 Mass conservation law
26(1)
4.1.2 Momentum conservation law
27(1)
4.1.3 Energy conservation laws
28(2)
4.1.4 Fundamental governing equations for coupled hydro-mechanical phenomena
30(5)
4.2 Multi-dimensional conservation laws
35(1)
4.2.1 Mass conservation laws for seepage and diffusion phenomena
35(1)
4.2.2 Momentum conservation law
36(1)
4.2.3 Angular momentum conservation law
36(1)
4.2.4 Energy conservation law
36(1)
4.3 Derivation of governing equations in the integral form
36(7)
4.3.1 Mass conservation law
36(2)
4.3.2 Momentum conservation law
38(1)
4.3.3 Angular momentum conservation law
39(1)
4.3.4 Energy conservation law
40(1)
References
41(2)
5 Constitutive laws
43(37)
5.1 One dimensional (1D) constitutive laws
43(14)
5.1.1 1D linear constitutive laws
43(6)
5.1.2 1D non-linear constitutive laws for solids
49(8)
5.2 Multi-dimensional constitutive laws
57(2)
5.2.1 Fourier's law
57(1)
5.2.2 Fick's law
57(1)
5.2.3 Darcy's law
57(1)
5.2.4 Hooke's law
58(1)
5.2.5 Newton's law
58(1)
5.2.6 Kelvin--Voigt's law
58(1)
5.2.7 Navier-Stokes law
58(1)
5.3 Non-linear behavior (elasto-plasticity and elasto-visco-plasticity) for solids
59(11)
5.3.1 Elasto-plastic law
59(3)
5.3.2 Elasto-visco-plasticity
62(3)
5.3.3 Yield/failure criteria
65(5)
5.4 Equivalent models for discontinua
70(10)
5.4.1 Equivalent elastic compliance model (Singh's model)
71(2)
5.4.2 Crack tensor model (CTM)
73(1)
5.4.3 Damage model
73(1)
5.4.4 Microstructure models
74(2)
5.4.5 Homogenization technique
76(1)
References
77(3)
6 Laboratory tests
80(41)
6.1 Laboratory tests on mechanical properties
80(21)
6.1.1 Uniaxial compression tests
81(1)
6.1.2 Direct and indirect tensile strength tests (Brazilian tests)
82(3)
6.1.3 Triaxial compression tests
85(1)
6.1.4 Post-failure behavior in uniaxial and triaxial compression tests
85(4)
6.1.5 Direct shear tests
89(4)
6.1.6 Tilting tests
93(4)
6.1.7 Experimental techniques for creep tests
97(4)
6.2 Thermal properties of rocks and their measurements
101(6)
6.3 Tests far seepage parameters
107(7)
6.3.1 Falling head tests
108(1)
6.3.2 Transient pulse test method
109(5)
6.4 Tests far diffusion parameters
114(7)
References
118(3)
7 Methods for exact (closed-form) solutions
121(71)
7.1 Basic approaches
121(1)
7.1.1 Intuitive function methods
121(1)
7.1.2 Solution by separating variables
121(1)
7.1.3 Complex variable method
122(1)
7.2 Closed-form solutions for solids
122(40)
7.2.1 Visco-elastic rock sample subjected to uniaxial loading
122(5)
7.2.2 Visco-elastic layer on an incline
127(5)
7.2.3 One-dimensional bar embedded in rock
132(2)
7.2.4 Circular cavity in the elastic rock under a far-field hydrostatic stress
134(3)
7.2.5 Unified analytical solutions for circular/spherical cavity in an elasto-plastic rock
137(16)
7.2.6 Foundations-bearing capacity
153(2)
7.2.7 Two-dimensional closed-form solution methods
155(6)
7.2.8 Three-dimensional closed-form solutions
161(1)
7.3 Closed-form solutions for fluid flow through porous rocks
162(15)
7.3.1 Some considerations on the Darcy law for rocks and discontinuities
162(5)
7.3.2 Permeability tests based on a steady-state flow
167(2)
7.3.3 Permeability tests based on a non-steady-state flow (transient flow tests)
169(8)
7.4 Temperature distribution in the vicinity of geological active faults
177(3)
7.5 Closed-form solutions for diffusion problems
180(6)
7.5.1 Drying testing procedure
180(5)
7.5.2 Saturation testing technique
185(1)
7.6 Evaluation of creep-like deformation of semi-infinite soft rock layer
186(6)
References
188(4)
8 Methods for approximate solutions
192(58)
8.1 Comparison of exact and approximate solutions
192(6)
8.1.1 Exact (closed-form) solution
193(1)
8.1.2 Finite difference method
193(1)
8.1.3 Finite element method
194(3)
8.1.4 Comparisons
197(1)
8.2 ID hyperbolic problem: equation of motion
198(5)
8.2.1 Weak form formulation
199(1)
8.2.2 Discretization
199(3)
8.2.3 Specific example
202(1)
8.2.4 ID parabolic problem: creep problem
202(1)
8.2.5 ID elliptic problem: static problem
202(1)
8.2.6 Computational examples
203(1)
8.3 Parabolic problems: heat flow, seepage and diffusion
203(6)
8.3.1 Introduction
203(1)
8.3.2 Governing equation
204(1)
8.3.3 Weak form formulation
205(1)
8.3.4 Discretization
205(2)
8.3.5 Steady-state problem
207(1)
8.3.6 Specific example
208(1)
8.3.7 Example 1: simulation of a solid body with heat generation
208(1)
8.3.8 Example 2: simulation of a diffusion problem
208(1)
8.4 FEM for ID pseudo-coupled parabolic problems: heat flow and thermal stress; swelling and swelling pressure
209(9)
8.4.1 Introduction
209(1)
8.4.2 Governing equations
210(1)
8.4.3 Coupling of heat and stress fields
211(1)
8.4.4 Weak form formulation
212(1)
8.4.5 Discretization
213(3)
8.4.6 Specific example
216(1)
8.4.7 Example: simulation of heat generation and associated thermal stress
216(2)
8.5 Hydro-mechanical coupling: seepage and effective stress problem
218(8)
8.5.1 Introduction
218(1)
8.5.2 Governing equations
218(1)
8.5.3 Weak form formulation
219(1)
8.5.4 Discretization
220(4)
8.5.5 Specific example
224(1)
8.5.6 Example: simulation of settlement under sudden loading
225(1)
8.6 Biot problem: coupled dynamic response of porous media
226(7)
8.6.1 Introduction
226(1)
8.6.2 Governing equations
226(1)
8.6.3 Weak form formulation
227(1)
8.6.4 Discretization
228(4)
8.6.5 Specific example
232(1)
8.6.6 Example: simulation of dynamic response of saturated porous media
233(1)
8.7 Introduction of boundary conditions in a simultaneous equation system
233(3)
8.7.1 Formulation
233(2)
8.7.2 Actual implementation and solution of Eq. (8.216b)
235(1)
8.8 Rayleigh damping and its implementation
236(1)
8.9 Non-linear problems
236(1)
8.10 Multi-dimensional situations
236(6)
8.10.1 Shape functions
237(4)
8.10.2 Numerical integration
241(1)
8.11 Special numerical methods for media having discontinuities
242(8)
8.11.1 No-tension finite element method
242(1)
8.11.2 Pseudo discontinuum finite element method
243(1)
8.11.3 Smeared crack element
243(1)
8.11.4 Finite element method with joint or interface element (FEM-J)
244(1)
8.11.5 Discrete finite element method (DFEM)
245(1)
8.11.6 Displacement discontinuity method (DDM)
246(1)
8.11.7 Discrete element method (DEM)
246(2)
8.11.8 Discontinuous deformation analysis method (DDA)
248(1)
References
248(2)
9 Applications of approximate methods in geo-engineering problems
250(53)
9.1 Applications in continuum
250(29)
9.1.1 The stress state of earth and earth's crust
250(2)
9.1.2 Evaluation of the tunnel face effect
252(2)
9.1.3 Three-dimensional simulation of the excavation of a railway tunnel supported with forepoles, rockbolts, shotcrete and steel ribs
254(3)
9.1.4 Effect of bolting pattern in underground excavations
257(1)
9.1.5 Numerical studies on the indentation (impression) experiment
257(4)
9.1.6 The evaluation of the long-term response of an underground cavern
261(1)
9.1.7 Long-term stability of the Derinkuyu underground city, Cappadocia, Turkey
262(3)
9.1.8 Stability analyses of Tomb of Pharaoh Amenophis III, Luxor, Egypt
265(1)
9.1.9 Dynamic response of a large underground cavern
265(1)
9.1.10 Response and stability of abandoned room and pillar mine under static and earthquake loading
266(5)
9.1.11 Modal analyses of shafts at the Horonobe Underground Laboratory
271(1)
9.1.12 Temperature and stress distributions around an underground opening
272(1)
9.1.13 Water-head variations in rock mass around an underground cavern
273(1)
9.1.14 Breakout formation in boreholes in sedimentary rocks due to moisture loss
274(5)
9.2 Applications in discontinuum
279(24)
9.2.1 Earthquake fault rupture simulation
279(3)
9.2.2 Pseudo-dynamic analyses on the interaction of structures and earthquake faults
282(1)
9.2.3 Dynamic stability conditions of a single rock block
282(2)
9.2.4 Stability of a slope against planar sliding
284(1)
9.2.5 Stability of rock slope against columnar toppling
285(1)
9.2.6 Stability of rock slope against flexural toppling and its stabilization
286(2)
9.2.7 Retrofitting of unlined tunnels
288(2)
9.2.8 Analysis of backfilling of abandoned mines
290(4)
9.2.9 Simulation of creep-like deformation of the Babadag landslide by DFEM
294(2)
9.2.10 Simulation of creep-like deformation of a rock block at the Nakagusuku Castle
296(3)
References
299(4)
Appendix 1 Gauss divergence theorem 303(2)
Appendix 2 Geometrical interpretation of the Taylor expansion 305(1)
Appendix 3 Reynolds transport theorem 306(1)
Appendix 4 The Gauss elimination method and its implementation 307(3)
Appendix 5 Constitutive modeling of discontinuities and interfaces 310(4)
Appendix 6 Thin band element for modeling discontinuities and interfaces in numerical analyses 314(7)
Index 321
Dr. Ömer Aydan was born in 1955, and studied Mining Engineering at the stanbul Technical University, Turkey (B.Sc., 1979), Rock Mechanics and Excavation Engineering at the University of Newcastle upon Tyne, UK (M.Sc., 1982), and finally received his Ph.D. in Geotechnical Engineering from Nagoya University, Japan in 1989. He worked at Nagoya University as a research associate (1987-1991), and at the Department of Marine Civil Engineering at Tokai University, first as Assistant Professor (1991-1993), then as Associate Professor (1993-2001), and finally as Professor (2001-2010). He then became Professor of the Institute of Oceanic Research and Development at Tokai University, and he moved to Department of Civil Engineering, the University of Ryukyus (Nishihara, Okinawa, Japan) the professor of Material Science and he retired at the March of 2020 as Emeritus Professor. He has been an adjunct staff of the University of the Ryukyus Disaster Prevention Research Center for Island Regions since 2014 and served as the director of the Center until he retired. He established the natural disaster simulation facility. Dr. Ömer Aydan has played an active role on numerous ISRM, JSCE, JGS, SRI and Rock Mech. National Group of Japan committees, and has organized several national and international symposia and conferences. He organized 2019 Rock Dynamics Summit in Okinawa in May 7-11, 2019 as the world top level conference in Rock Dynamics. He was also made Honorary Professor in Earth Science by Pamukkale University in 2008. He is currently the Vice President at Large of the International Society for Rock Mechanics and Rock Engineering. He was appointed as the associate editor of the Journal Rock Mechanics and Rock Engineering in April, 2020. He is the author and/or one of the authors of more than 600 scientific papers and the author of five international books on rock mechanics and co-authored five more international books.