Advanced computational methods and geomechanics / / Shenghong Chen

• Autore: Chen Shenghong
• Pubblicazione: Singapore : , : Springer, , [2023]; ©2023
• Descrizione fisica: 1 online resource (782 pages)
• Disciplina: 624.1510151
• Soggetto topico: Engineering geology - Mathematics; Engineering geology
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General -- 1.2 History of the Computation -- 1.2.1 From Ancient Calculation to Modern Computation -- 1.2.2 Classification of Modern CMs -- 1.3 State-of-the-Arts of Fundamental and Advanced CMs -- 1.3.1 Mesh-Based Methods -- 1.3.2 Mesh-Free Methods -- 1.3.3 Particle-Based (Block-Type) Methods -- 1.4 Further Reflections on Advanced CMs -- 1.4.1 Formalisms in Continuum Mechanics -- 1.4.2 Spatial Discretization Schemes -- 1.4.3 Material Assumptions -- 1.5 Concluding Remarks -- 1.5.1 Motivations of This Book -- 1.5.2 Layout of This Book -- 1.5.3 Reminders and Suggestions -- References -- 2 Preparative Knowledge of Material Properties -- 2.1 General -- 2.2 Structural Planes -- 2.2.1 Particularizations of Structural Planes -- 2.2.2 Measuring and Mapping of Rock Joint Attributes -- 2.2.3 Geometrical Representation of Joint System -- 2.3 Discrete Fracture Networks (DFNs) -- 2.3.1 Concepts and State-of-the-Arts -- 2.3.2 Generation of Stochastic DFNs by Monte-Carlo Method -- 2.3.3 Application of DFNs -- 2.4 Particle Assemblages -- 2.4.1 Random Aggregate Techniques -- 2.4.2 Hopper Discharge Techniques -- 2.5 Basic Physical and Mechanical Properties of Water and Rock-Like Materials -- 2.5.1 Mechanical Properties of Water -- 2.5.2 Mechanical Properties of Concretes -- 2.5.3 Mechanical Properties of Intact Rocks -- 2.5.4 Mechanical Properties of Rock Joints -- 2.5.5 Mechanical Properties of Jointed Rock Masses -- 2.6 Concluding Remarks -- References -- 3 Preparative Knowledge of Classical Mechanics -- 3.1 General -- 3.2 Classical Mechanics of Particles -- 3.3 Kinematics of Continuum -- 3.3.1 Two Ways to Observe the Motion of Continuum -- 3.3.2 Observation of Motion -- 3.3.3 Observation of Deformation -- 3.4 Constitutive Relations -- 3.4.1 Water -- 3.4.2 Rock-Like Materials. ; 3.5 Dynamics of Continuum: Strong Forms -- 3.5.1 Concepts -- 3.5.2 Finite Volume and Infinitesimal Cell -- 3.5.3 D'Alembert Principle for Continuum -- 3.5.4 Well-Posed Problems for Fluids -- 3.5.5 Well-Posed Problems for Solids -- 3.5.6 Application of Strong Form in Elastic Fracture Mechanics -- 3.6 Dynamics of Continuum: Weak Forms -- 3.6.1 Concept -- 3.6.2 Variational Principle -- 3.6.3 Hamilton's Principle -- 3.6.4 Galerkin Weak Form -- 3.6.5 Weighted Residual Method -- 3.6.6 Specifications of Weak Form in Water Permeability -- 3.7 Concluding Remarks -- 3.7.1 Non-linear Constitutive Relations for the Dynamics of Continuum -- 3.7.2 Non-linear Constitutive Relations for the Dynamics of Particle Cluster -- References -- 4 Preparative Knowledge of Numerical Analysis -- 4.1 General -- 4.1.1 Definitions -- 4.1.2 Significant Historical Events -- 4.1.3 Paramount Issues -- 4.2 Interpolation -- 4.2.1 Overview -- 4.2.2 Smooth Interpolation -- 4.2.3 Segment (Patch) Interpolation -- 4.3 Approximation -- 4.3.1 Overview -- 4.3.2 Least-Squares Approximation -- 4.3.3 Inverse Distance Weighted Methods -- 4.3.4 Radial Basis Functions -- 4.3.5 Manifolds -- 4.4 Numerical Integration (Quadrature) -- 4.4.1 Concept -- 4.4.2 General Formula -- 4.4.3 Gauss-Legendre Integration -- 4.4.4 Cubature -- 4.5 Solution of Ordinary Differential Equations -- 4.5.1 Finite Differences -- 4.5.2 Finite Differential Methods -- 4.5.3 Runge-Kutta Methods -- 4.5.4 Stable Considerations -- 4.5.5 Geometric Integration -- 4.5.6 Higher-Order Differential Equations -- 4.6 Solution of Partial Differential Equations -- 4.6.1 Concept -- 4.6.2 Pure Initial Value Problems -- 4.6.3 Mixed Initial Boundary Value Problems -- 4.6.4 Example-FLAC -- 4.7 Solution for Weak Form Equations -- 4.7.1 Ritz Method -- 4.7.2 Finite Element Method -- 4.8 Concluding Remarks -- 4.8.1 Stiff Equation and Symplectic Method. ; 4.8.2 Error Analysis and Condition Number -- References -- 5 General Finite Element Methods with Special Focus on XFEM -- 5.1 General -- 5.1.1 Fundamental Finite Element Method -- 5.1.2 General Finite Element Method -- 5.2 Crack-Surface Enrichment in XFEM -- 5.2.1 Concept -- 5.2.2 Displacement Interpolation -- 5.2.3 Strain and Stress -- 5.2.4 Governing Equation Set -- 5.3 Crack-Tip Enrichment in XFEM -- 5.3.1 Displacement Interpolation -- 5.3.2 Strain and Stress -- 5.3.3 Governing Equation Set -- 5.3.4 Crack-Tip Enrichment Strategy -- 5.3.5 Numerical Implementation -- 5.4 Crack Growth -- 5.4.1 Cracking Criteria -- 5.4.2 Crack Growth Direction -- 5.4.3 Implementation -- 5.5 Validations and Applications -- 5.5.1 Elastic and Discontinuous Problem of 1-D bar -- 5.5.2 Cracking Growth in Concrete Arch Dam -- 5.6 Concluding Remarks -- 5.6.1 Implementation of XFEM -- 5.6.2 Advances in XFEM -- References -- 6 General Finite Element Methods with Special Focus on NMM -- 6.1 General -- 6.2 Covers and Manifold Elements -- 6.2.1 Conceptual Illustration of One-Dimensional Problems -- 6.2.2 Two-Dimensional Extension -- 6.3 Kinematics Aspects -- 6.3.1 Approximation of Displacement Field -- 6.3.2 Specification of Weight Functions and Cover Functions -- 6.3.3 Strain -- 6.3.4 Stress -- 6.4 Dynamics Aspects: Basic Formulation -- 6.4.1 Concept -- 6.4.2 Sub-matrices of Stiffness and Sub-vectors of Load -- 6.4.3 Sub-vectors of Load Attributable to External Forces -- 6.5 Dynamics Aspects: Crack Growth Problems -- 6.5.1 Concept -- 6.5.2 Displacement Enrichment -- 6.5.3 Strain and Stress -- 6.5.4 Governing Equation Set -- 6.5.5 Crack Onset and Growth Criteria -- 6.5.6 Integration Schemes -- 6.5.7 Solution Procedure for Crack Growth Problems -- 6.6 Validations -- 6.6.1 One-Dimensional Bar Problem -- 6.6.2 Computation of SIF -- 6.7 Concluding Remarks. ; 6.7.1 Relation with Other Prevalent CMs -- 6.7.2 Remarkable Developments and Applications -- 6.7.3 Further Developments -- References -- 7 Discrete Element Methods with Special Focus on DEM -- 7.1 General -- 7.2 Contact Detection -- 7.2.1 Detection Schemes -- 7.2.2 Contact Detection for Disc Elements -- 7.2.3 Contact Detection for Polygonal Block Elements -- 7.3 Formulation of DEM with Disc Elements -- 7.3.1 Generation of Disc Element Assemblage -- 7.3.2 Geometrical Parameters of Disc Elements -- 7.3.3 Momentum Conservation -- 7.3.4 Integration of Governing Equations -- 7.4 Formulation of DEM with Polygonal Elements -- 7.4.1 Generation of Block Element Assemblage -- 7.4.2 Geometrical Parameters of Block Elements -- 7.4.3 Momentum Conservation -- 7.4.4 Integration of Equations -- 7.5 Issues Related to Applications -- 7.5.1 Stiffness -- 7.5.2 Damping -- 7.5.3 Critical Time-Marching Step Length -- 7.5.4 Velocity-Weakening Friction Law -- 7.6 Validations -- 7.6.1 Single Block Vibration -- 7.6.2 Triangular Block Slide -- 7.6.3 Disc Compaction Test -- 7.6.4 Cylinder Collapse Test -- 7.6.5 Multi-block Landslide -- 7.6.6 Multi-particle Landslide -- 7.7 Concluding Remarks -- 7.7.1 Relation with Other Prevalent CMs -- 7.7.2 Remarkable Developments and Applications -- References -- 8 Discrete Element Methods with Special Focus on DDA -- 8.1 General -- 8.2 Introduction to BEA -- 8.2.1 Concept -- 8.2.2 Formulation of BEA with Rigid Block Elements -- 8.2.3 Formulation of BEA with Deformable Block Elements -- 8.2.4 Key Algorithms -- 8.3 Kinematics of DDA -- 8.3.1 Deformation Patterns -- 8.3.2 Types and Detection Techniques of Contact -- 8.4 Dynamics of DDA -- 8.4.1 Equilibrium Equation -- 8.4.2 Sub-matrices of Stiffness and Sub-vectors of Strains/Stresses/Loads -- 8.4.3 Sub-matrices of Stiffness and Sub-vectors of Displacement Constraints. ; 8.4.4 Compatibility Conditions at Block Contact Point -- 8.5 Key Issues and Algorithms -- 8.5.1 Time-Marching Step Length -- 8.5.2 Damping -- 8.5.3 Velocity-Weakening Friction Law -- 8.5.4 Solution and Iteration of the System Equation -- 8.6 Validations -- 8.6.1 Cantilever Beam Bending -- 8.6.2 Block Free Falling -- 8.6.3 Block Sliding -- 8.7 Engineering Applications -- 8.7.1 Gravity Dam Stability: Baozhusi Project, China -- 8.7.2 Landslide Accident -- 8.8 Concluding Remarks -- 8.8.1 Validations and Applications -- 8.8.2 Improvements -- References -- 9 Mesh-Free Methods with Special Focus on EFGM -- 9.1 General -- 9.2 Concept -- 9.2.1 Kernel Functions -- 9.2.2 MLS Approximation and Shape Functions -- 9.2.3 Weight Functions -- 9.2.4 Support Domain and Influence Domain -- 9.3 Basic Formulation of EFGM -- 9.3.1 Domain Discretization and Variable Approximation -- 9.3.2 Governing Equations -- 9.3.3 Implementation -- 9.4 Dynamic Issues -- 9.4.1 Governing Equations -- 9.4.2 Solution Techniques -- 9.5 Structural Plane Issues -- 9.5.1 Concept -- 9.5.2 Elastic Contact -- 9.5.3 Contact with Frictional Shear -- 9.5.4 Quadrature on Structural Plane and System Equation -- 9.5.5 Solution Procedure -- 9.5.6 Notes -- 9.6 EFGM Near Crack-Tips and Nonconvex Boundaries -- 9.6.1 Techniques for Crack Modeling -- 9.6.2 Crack-Tip Enrichment -- 9.6.3 Crack Growth -- 9.7 Validations -- 9.7.1 Contact Crack Within Plate -- 9.7.2 Contact Block on Rigid Base -- 9.7.3 Free Vibration Cantilever -- 9.7.4 Simply Supported Beam Exerted by a Concentrated Impact -- 9.8 Concluding Remarks -- 9.8.1 Definition of MFMs -- 9.8.2 Initiation and Early Developments -- 9.8.3 Advances Since the 2000s -- 9.8.4 Applications -- 9.8.5 Hybrid Methods -- References -- 10 Mesh-Free Methods with Special Focus on SPH -- 10.1 General -- 10.2 Approximation in SPH -- 10.2.1 Approximation of Field Functions. ; 10.2.2 Approximation of Function Derivatives.
• Titolo autorizzato: Advanced Computational Methods and Geomechanics
• ISBN: 9789811974274; 9789811974267
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910639883103321
• Lo trovi qui: Univ. Federico II
• Serie: Springer tracts in civil engineering.