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El. knyga: Discontinuous Deformation Analysis in Rock Mechanics Practice

(School of Civil and Resource Engineering, The University of Western Australia, Crawley, WA, Australia), , (Ben-Gurion University of the Negev, Beer-Sheva, Israel)
  • Formatas: 410 pages
  • Serija: ISRM Book Series
  • Išleidimo metai: 20-Jul-2017
  • Leidėjas: CRC Press
  • ISBN-13: 9781317416937
Kitos knygos pagal šią temą:
  • Formatas: 410 pages
  • Serija: ISRM Book Series
  • Išleidimo metai: 20-Jul-2017
  • Leidėjas: CRC Press
  • ISBN-13: 9781317416937
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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.

Recenzijos

"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 Hatzors 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.

About the authors xiii
Acknowledgments xvii
Foreword xix
1 Introduction
1(40)
1.1 Who should read this book?
1(1)
1.2 How to use this book?
1(1)
1.3 Continuous vs. discontinuous deformation
2(6)
1.4 DDA history
8(1)
1.5 Three decades of DDA research and development
9(1)
1.6 DDA vs. FEM and DEM
9(1)
1.7 Main features of DDA
10(2)
1.7.1 Block system kinematics
10(1)
1.7.2 Complete first order displacement approximation
11(1)
1.7.3 Equilibrium, dynamics and energy consumption
11(1)
1.7.4 Large Deformation
11(1)
1.7.5 Efficiency
12(1)
1.8 Some limitations of the original DDA
12(3)
1.9 Block discretization
15(2)
1.10 Higher order displacement function
17(2)
1.11 Coupling DDA with other numerical methods
19(4)
1.11.1 Coupling DDA with FEM
19(2)
1.11.2 Coupling DDA with BEM
21(1)
1.11.3 Coupling DDA with NMM
22(1)
1.12 Improved contact algorithms
23(3)
1.13 Incorporation of viscous damping
26(1)
1.14 Improved friction law for discontinuities
27(2)
1.15 Gravity turn on and sequential excavation
29(1)
1.16 Dynamic wave propagation and blasting
30(3)
1.17 Masonry structures
33(1)
1.18 Improved rockbolt element
33(1)
1.19 Granular materials
34(3)
1.19.1 Historical overview
34(1)
1.19.2 Modelling particulate media with DDA
35(2)
1.20 Pore pressure and fluid flow
37(3)
1.20.1 Historical overview
37(2)
1.20.2 Coupling DDA and fluid flow
39(1)
1.21 Current development of 3-D DDA
40(1)
2 Theory of the discontinuous deformation analysis (DDA)
41(32)
2.1 Governing equations and displacement approximation
41(4)
2.1.1 Governing equations
41(1)
2.1.2 Displacement approximation of a single block
42(3)
2.2 Formulation of matrices for each single block
45(9)
2.2.1 Sub-matrices of elastic strains
45(1)
2.2.2 Sub-matrices of initial stress
46(1)
2.2.3 Sub-matrices of point loading
47(1)
2.2.4 Sub-matrices of line loading
47(1)
2.2.5 Sub-matrices of body force
48(1)
2.2.6 Sub-matrices of bolting connection
49(2)
2.2.7 Sub-matrices of inertia force
51(1)
2.2.8 Sub-matrices of displacement constraints at a point
52(1)
2.2.9 Sub-matrices of displacement constraints in a direction
53(1)
2.3 Interactions between blocks
54(14)
2.3.1 Contact detection
55(2)
2.3.2 Contact constraint enforcement
57(1)
2.3.3 Open-close iterations
58(2)
2.3.4 Formulation of contact matrices
60(8)
2.4 Time integration scheme and governing equations for blocky systems
68(2)
2.5 Simplex integration for 2-D DDA
70(1)
2.6 Summary
71(2)
3 Theory of the discontinuous deformation analysis in three dimensions
73(30)
3.1 Block displacement approximation and global equilibrium equation
73(4)
3.1.1 Displacement weight function
73(3)
3.1.2 Global equilibrium equation
76(1)
3.2 Formulation of matrices for single block
77(11)
3.2.1 Sub-matrices of elastic strain
77(1)
3.2.2 Sub-matrices of initial stress
78(1)
3.2.3 Sub-matrices of point loading
79(1)
3.2.4 Sub-matrices of line loading
79(1)
3.2.5 Sub-matrices of surface loading
80(1)
3.2.6 Sub-matrices of body force
81(1)
3.2.7 Sub-matrices of bolting connection
82(2)
3.2.8 Sub-matrices of inertia force
84(1)
3.2.9 Sub-matrices of displacement constraints in a direction
85(1)
3.2.10 Sub-matrices of fixed point
86(2)
3.3 Interactions among blocks
88(10)
3.3.1 Contact detection and types
88(1)
3.3.2 Contact state and open-close iteration
88(3)
3.3.3 Formulation of contact matrices
91(7)
3.4 Simplex integration for 3D DDA
98(3)
3.5 Summary
101(2)
4 Geological input parameters for realistic DDA modeling
103(28)
4.1 Introduction
103(1)
4.2 Realistic representation of rock mass structure
103(25)
4.2.1 Number of joint sets
107(2)
4.2.2 Types of joint sets
109(4)
4.2.3 Joint set orientation
113(6)
4.2.4 Joint set spacing and bias correction
119(2)
4.2.5 Joint set dispersion
121(2)
4.2.6 Joint length
123(1)
4.2.7 Rock bridges and realistic mesh generation
124(4)
4.3 Mechanical input parameters for forward modeling
128(3)
4.3.1 Intact rock elements
128(1)
4.3.2 Shear strength of the discontinuities
129(2)
5 DDA verification
131(36)
5.1 Introduction
131(1)
5.2 Single plane sliding
132(11)
5.2.1 2D-DDA
133(4)
5.2.2 3D-DDA
137(6)
5.3 Double plane sliding
143(3)
5.4 Block response to cyclic motion of frictional interface
146(8)
5.4.1 2D-DDA
147(1)
5.4.2 3D-DDA
148(6)
5.5 Dynamic rocking of slender blocks
154(3)
5.6 Wave propagation phenomena
157(10)
5.6.1 P wave propagation
157(4)
5.6.2 Shear wave propagation
161(4)
5.6.3 Concluding remarks regarding wave propagation accuracy
165(2)
6 Underground excavations
167(32)
6.1 Introduction
167(1)
6.2 Shallow underground excavations
167(15)
6.2.1 Block interactions
168(3)
6.2.2 Joint spacing
171(6)
6.2.3 Excavation depth
177(5)
6.3 Deep underground excavations
182(17)
6.3.1 Boundary conditions
182(2)
6.3.2 Excavation damage zone
184(3)
6.3.3 Rock bolting
187(3)
6.3.4 Rock bursts
190(9)
7 Rock slopes
199(34)
7.1 Introduction
199(2)
7.2 Rotational failure modes
201(12)
7.2.1 Toppling
201(6)
7.2.2 Block slumping
207(3)
7.2.3 Overhanging slopes
210(3)
7.3 Dynamic rock slope stability analysis
213(12)
7.3.1 First introduction of time dependent accelerations to DDA
213(1)
7.3.2 Loading methods
214(2)
7.3.3 Consideration of local site effects
216(5)
7.3.4 Application to single plane sliding
221(4)
7.4 Rock bolt reinforcement
225(8)
8 Shi's new contact theory
233(128)
8.1 Introduction
233(2)
8.2 Geometric representations of angles and blocks
235(11)
8.2.1 Discontinuous computations
235(1)
8.2.2 Related mathematical symbols
235(2)
8.2.3 Algebraic operations of blocks
237(1)
8.2.4 Representation of solid angles
237(3)
8.2.5 Inequality equations of angles
240(2)
8.2.6 Representation of blocks
242(2)
8.2.7 Structure of blocks
244(1)
8.2.8 Inequality equations of blocks
245(1)
8.3 Definition of the entrance block
246(12)
8.3.1 Relations of two blocks
246(3)
8.3.2 Definition of entrance block
249(1)
8.3.3 Entrance block and parallel movement
249(1)
8.3.4 Entrance block of a block and a point
249(1)
8.3.5 The entrance block of a block and a ball
249(2)
8.3.6 The entrance ball between two balls
251(2)
8.3.7 Theorem of separation
253(1)
8.3.8 Theorem of entrance
253(1)
8.3.9 Theorem of distance
253(1)
8.3.10 Theorem of lock
254(3)
8.3.11 Examples of the entrance block
257(1)
8.4 Basic theorems of entrance block
258(5)
8.4.1 Theorem of uniqueness
258(1)
8.4.2 Theorem of finite covers of entrance blocks
258(1)
8.4.3 Theorem of including
259(1)
8.4.4 Theorem of union
260(1)
8.4.5 Theorem of symmetry
260(1)
8.4.6 Theorem of contact
261(1)
8.4.7 Theorem of removability
262(1)
8.4.8 Theorem of inner points
262(1)
8.4.9 Theorem of convex blocks
262(1)
8.5 Boundaries of the entrance solid angles of 2D solid angles
263(10)
8.5.1 Local entrance solid angle of 2D blocks
264(1)
8.5.2 Existence of entrance solid angle boundary of 2D solid angles
264(2)
8.5.3 Contact surface of 2D solid angles
266(1)
8.5.4 Entrance of boundary vector to vector of 2D solid angles
266(1)
8.5.5 Contact vectors of angle to angle contact
267(2)
8.5.6 Finite covers of 2D parallel vector to vector entrance
269(3)
8.5.7 Contact vectors of 2D entrance solid angle
272(1)
8.6 Contact vectors of 2D solid angles
273(14)
8.6.1 Contact vectors of a 2D convex solid angle and a 2D concave solid angle
273(2)
8.6.2 Contact vectors of 2D convex solid angles
275(5)
8.6.3 Entrance solid angle of 2D round corner convex solid angle and concave solid angle
280(4)
8.6.4 Entrance round corner solid angle of 2D round corner convex solid angles
284(3)
8.7 Boundaries of an entrance block of 2D blocks
287(7)
8.7.1 Entrance of 2D block inner points
287(1)
8.7.2 Entrance of 2D edge to edges
287(2)
8.7.3 Contact edges of 2D block to block contact
289(2)
8.7.4 Finite covers of 2D parallel edge to edge entrance
291(2)
8.7.5 Contact edges of 2D entrance block
293(1)
8.8 Contact edges of 2D blocks
294(12)
8.8.1 Contact edges of 2D convex blocks
294(4)
8.8.2 Contact edges of 2D general blocks
298(1)
8.8.3 Applications of the theory of contact in 2D DDA
299(4)
8.8.4 Applications of the new theory of contact in 2D NMM
303(3)
8.9 Boundaries of entrance solid angle of 3D solid angles
306(22)
8.9.1 Local entrance angle of 3D angles
307(1)
8.9.2 Existence of entrance solid angle boundary of 3D solid angles
307(2)
8.9.3 Entrance of 3D solid angle inner points
309(1)
8.9.4 Entrance of boundary solid angle to angle of 3D solid angles
309(1)
8.9.5 Entrance of boundary angle to vector of 3D solid angles
310(3)
8.9.6 Contact solid angle of 3D vertex to boundary angle contact
313(2)
8.9.7 Contact solid angle of 3D boundary vector to vector contact
315(2)
8.9.8 Finite covers of parallel boundary angle to vector entrance
317(6)
8.9.9 Finite covers of parallel boundary angle entrance
323(1)
8.9.10 Contact angles of 3D entrance solid angle
324(4)
8.10 Contact solid angles of 3D solid angles
328(12)
8.10.1 Contact plane of a 3D solid angle and half space
328(1)
8.10.2 Contact plane of two 3D convex solid edges
328(2)
8.10.3 Contact half-planes of a 3D concave solid edge and a 3D solid angle
330(2)
8.10.4 Contact half-planes of a 3D convex solid edge and a 3D solid angle
332(2)
8.10.5 Contact solid angles of two 3D convex solid angles
334(3)
8.10.6 Contact solid angles of two 3D general solid angles
337(3)
8.11 Boundaries of entrance block of 3D blocks
340(13)
8.11.1 Entrance of 3D block inner points
340(1)
8.11.2 Entrance of boundary polygons of 3D blocks
340(2)
8.11.3 Entrance of polygon to edge of 3D blocks
342(1)
8.11.4 Contact polygon of 3D vertex to polygon contact
343(2)
8.11.5 Contact polygon of 3D edge to edge contact
345(2)
8.11.6 Finite covers of parallel polygon to edge entrance
347(2)
8.11.7 Finite covers of parallel polygon entrance
349(3)
8.11.8 Contact polygons of 3D entrance blocks
352(1)
8.12 Contact polygons of 3D blocks
353(6)
8.12.1 Contact polygons of two 3D convex blocks
353(4)
8.12.2 Contact polygons of two general 3D blocks
357(2)
8.12.3 Simple examples of the new contact theory in 3D DDA
359(1)
8.13 Conclusions
359(2)
References 361(20)
Subject Index 381
Professor Yossef H. Hatzor is currently Lemkin Chair Professor of Rock Mechanics, Department of Geological and Environmental Sciences, the director of the engineering geology program and of the rock mechanics laboratory at Ben-Gurion University of the Negev, Israel. His research focuses on the development, verification, validation, and application of Block Theory, the numerical Discontinuous Deformation Analysis, and the Numerical Manifold Method, by developing analytical solutions that can be used as a basis for code verification, conducting laboratory experiments that can be used for code validation, and monitoring rock mass deformation in the field for addressing key rock mechanics issues. Professor Hatzor is involved in major geotechnical engineering projects in Israel, including dynamic stability analysis and reinforcement design of the Masada world heritage site. Yossef is the founding president of Israel Rock Mechanics Association, an ISRM national group, and served as IRMA president between 2003 and 2014. In 2007 he was appointed as Chair Professor in Rock Mechanics by BGU Senate. In 2011 he won the competitive visiting professorship appointment for senior international scientists by the Chinese Academy of Sciences and he holds this position at the Rock and Soil Mechanics Institute of the CAS in Wuhan, where he collaborates with colleagues from the National Key Laboratory of Geomechanics and Geotechnical Engineering on projects involving deep tunnels in various geological conditions in China. Yossef is co-chair of the ISRM DDA Commission. He is the recipient of several national and international research awards and is a member of the editorial boards of both the International Journal of Rock Mechanics and Mining Sciences, and Rock Mechanics and Rock Engineering.



Prof Guowei Ma obtained his BSc from Beijing University in 1989, MEng from Xian Jiaotong University in 1992, PhD from Nanyang Technological University, Singapore in 2000. He worked subsequently in Xian Jiaotong University/China, Iwate University/Japan, University of Delaware/USA, Nanyang Technological University (NTU)/Singapore and the University of Western Australia (UWA)/Australia. He had been the Secretary General of the Society of Rock Mechanics & Engineering Geology (Singapore) and the Secretary General of the Association of Computational Mechanics (Singapore). He is currently the President of the Western Australia Chinese Scientists Association (WACSA). Guoweis research interests include rock dynamics, analysis of discontinuous deformation, dynamic constitutive models of materials and protective structures. He is also the Associate Editor of International Journal of Protective Structures, and an Editorial Board Member of 6 other international journals. He co-authored 2 books published by Springer, edited 2 conference proceedings and 3 special issues of international journals. He authored over 300 peer reviewed international journal and conference papers.



Dr. Genhua Shi, acknowledged as a professional consultant in rock and structural engineering, is the chairman of the DDA Company in California, USA, and the chief scientist of the Discontinuous Deformation Analysis Laboratory, Yangtze River Scientific Research Institute. He obtained his BSc and MEng from Beijing University, China respectively in 1963 and 1968, and his PhD from University of California at Berkeley, USA in 1988. He has put forward the Key Block theory and Discontinuous Deformation Analysis method, now widely studied and applied in rock mechanics and rock engineering fields worldwide. He is also the inventor of the Numerical Manifold Method, which is a novel method for the analysis of both continuous and discontinuous material behaviors. He has been actively involved in many worldly famous projects related to rock mechanics in-situ tests, nuclear waste storage, blasting design of rock engineering, stability analysis of rock slopes and rock foundations, underground excavation support design and construction, and dam design and dam foundation analysis. His papers have appeared in profound journals, and in significant conferences such as the series of North American Rock Mechanics Symposiums, and the series of Conferences on Analysis of Discontinuous Deformation. Genhua is the recipient of the China Natural Science Award and other international awards. He resides in Belmont, California, USA.