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shenghong c advanced computational methods geomechanics 2023

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Textbook in PDF format The aim of this book is intended, through parallel expounding, to help readers comprehensively grasp the intrinsic features of typical advanced computational methods. These methods are created in recent three decades for the understanding of the post-failure of geo-materials accompanied with discontinuous and finite deformation/dislocation, as well as the violent fluid-structure interaction accompanied with strong distortion of water surface. The strong points and weak points of the formalisms for governing equations, the discretization schemes, the nodal interpolation /approximation of field variables, and their connectivity (via support domains, covers, or enrichments), the basic algorithms, etc., are clarified. Being aware of that the differences in these methods are not so large as at the first glance, this book will help readers to select appropriate methods, to improve the methods for their specific purpose, and to evaluate the reliability/applicability of the outcomes in the hazard evaluation of geotechnical (hydraulic) structures beyond extreme work situation. This book may be looked at as an advanced continuation of “Computational Geomechanics and Hydraulic Structures” by the author (2018) (Springer-Verlag, ISBN 978-981-10-8134-7) which elaborates the fundamental computational methods in geomechanics for the routine design of geotechnical (hydraulic) engineering. Preface Introduction General History of the Computation From Ancient Calculation to Modern Computation Classification of Modern CMs State-of-the-Arts of Fundamental and Advanced CMs Mesh-Based Methods Mesh-Free Methods Particle-Based (Block-Type) Methods Further Reflections on Advanced CMs Formalisms in Continuum Mechanics Spatial Discretization Schemes Material Assumptions Concluding Remarks Motivations of This Book Layout of This Book Reminders and Suggestions References Preparative Knowledge of Material Properties General Structural Planes Particularizations of Structural Planes Measuring and Mapping of Rock Joint Attributes Geometrical Representation of Joint System Discrete Fracture Networks (DFNs) Concepts and State-of-the-Arts Generation of Stochastic DFNs by Monte-Carlo Method Application of DFNs Particle Assemblages Random Aggregate Techniques Hopper Discharge Techniques Basic Physical and Mechanical Properties of Water and Rock-Like Materials Mechanical Properties of Water Mechanical Properties of Concretes Mechanical Properties of Intact Rocks Mechanical Properties of Rock Joints Mechanical Properties of Jointed Rock Masses Concluding Remarks References Preparative Knowledge of Classical Mechanics General Classical Mechanics of Particles Kinematics of Continuum Two Ways to Observe the Motion of Continuum Observation of Motion Observation of Deformation Constitutive Relations Water Rock-Like Materials Dynamics of Continuum: Strong Forms Concepts Finite Volume and Infinitesimal Cell D’Alembert Principle for Continuum Well-Posed Problems for Fluids Well-Posed Problems for Solids Application of Strong Form in Elastic Fracture Mechanics Dynamics of Continuum: Weak Forms Concept Variational Principle Hamilton’s Principle Galerkin Weak Form Weighted Residual Method Specifications of Weak Form in Water Permeability Concluding Remarks Non-linear Constitutive Relations for the Dynamics of Continuum Non-linear Constitutive Relations for the Dynamics of Particle Cluster References Preparative Knowledge of Numerical Analysis General Definitions Significant Historical Events Paramount Issues Interpolation Overview Smooth Interpolation Segment (Patch) Interpolation Approximation Overview Least-Squares Approximation Inverse Distance Weighted Methods Radial Basis Functions Manifolds Numerical Integration (Quadrature) Concept General Formula Gauss–Legendre Integration Cubature Solution of Ordinary Differential Equations Finite Differences Finite Differential Methods Runge–Kutta Methods Stable Considerations Geometric Integration Higher-Order Differential Equations Solution of Partial Differential Equations Concept Pure Initial Value Problems Mixed Initial Boundary Value Problems Example—FLAC Solution for Weak Form Equations Ritz Method Finite Element Method Concluding Remarks Stiff Equation and Symplectic Method Error Analysis and Condition Number References General Finite Element Methods with Special Focus on XFEM General Fundamental Finite Element Method General Finite Element Method Crack-Surface Enrichment in XFEM Concept Displacement Interpolation Strain and Stress Governing Equation Set Crack-Tip Enrichment in XFEM Displacement Interpolation Strain and Stress Governing Equation Set Crack-Tip Enrichment Strategy Numerical Implementation Crack Growth Cracking Criteria Crack Growth Direction Implementation Validations and Applications Elastic and Discontinuous Problem of -D bar Cracking Growth in Concrete Arch Dam Concluding Remarks Implementation of XFEM Advances in XFEM References General Finite Element Methods with Special Focus on NMM General Covers and Manifold Elements Conceptual Illustration of One-Dimensional Problems Two-Dimensional Extension Kinematics Aspects Approximation of Displacement Field Specification of Weight Functions and Cover Functions Strain Stress Dynamics Aspects: Basic Formulation Concept Sub-matrices of Stiffness and Sub-vectors of Load Sub-vectors of Load Attributable to External Forces Dynamics Aspects: Crack Growth Problems Concept Displacement Enrichment Strain and Stress Governing Equation Set Crack Onset and Growth Criteria Integration Schemes Solution Procedure for Crack Growth Problems Validations One-Dimensional Bar Problem Computation of SIF Concluding Remarks Relation with Other Prevalent CMs Remarkable Developments and Applications Further Developments References Discrete Element Methods with Special Focus on DEM General Contact Detection Detection Schemes Contact Detection for Disc Elements Contact Detection for Polygonal Block Elements Formulation of DEM with Disc Elements Generation of Disc Element Assemblage Geometrical Parameters of Disc Elements Momentum Conservation Integration of Governing Equations Formulation of DEM with Polygonal Elements Generation of Block Element Assemblage Geometrical Parameters of Block Elements Momentum Conservation Integration of Equations Issues Related to Applications Stiffness Damping Critical Time-Marching Step Length Velocity-Weakening Friction Law Validations Single Block Vibration Triangular Block Slide Disc Compaction Test Cylinder Collapse Test Multi-block Landslide Multi-particle Landslide Concluding Remarks Relation with Other Prevalent CMs Remarkable Developments and Applications References Discrete Element Methods with Special Focus on DDA General Introduction to BEA Concept Formulation of BEA with Rigid Block Elements Formulation of BEA with Deformable Block Elements Key Algorithms Kinematics of DDA Deformation Patterns Types and Detection Techniques of Contact Dynamics of DDA Equilibrium Equation Sub-matrices of Stiffness and Sub-vectors of Strains/Stresses/Loads Sub-matrices of Stiffness and Sub-vectors of Displacement Constraints Compatibility Conditions at Block Contact Point Key Issues and Algorithms Time-Marching Step Length Damping Velocity-Weakening Friction Law Solution and Iteration of the System Equation Validations Cantilever Beam Bending Block Free Falling Block Sliding Engineering Applications Gravity Dam Stability: Baozhusi Project, China Landslide Accident Concluding Remarks Validations and Applications Improvements References Mesh-Free Methods with Special Focus on EFGM General Concept Kernel Functions MLS Approximation and Shape Functions Weight Functions Support Domain and Influence Domain Basic Formulation of EFGM Domain Discretization and Variable Approximation Governing Equations Implementation Dynamic Issues Governing Equations Solution Techniques Structural Plane Issues Concept Elastic Contact Contact with Frictional Shear Quadrature on Structural Plane and System Equation Solution Procedure Notes EFGM Near Crack-Tips and Nonconvex Boundaries Techniques for Crack Modeling Crack-Tip Enrichment Crack Growth Validations Contact Crack Within Plate Contact Block on Rigid Base Free Vibration Cantilever Simply Supported Beam Exerted by a Concentrated Impact Concluding Remarks Definition of MFMs Initiation and Early Developments Advances Since the s Applications Hybrid Methods References Mesh-Free Methods with Special Focus on SPH General Approximation in SPH Approximation of Field Functions Approximation of Function Derivatives Approximation of Function Gradients Construction of Smoothing Functions Basic Requirements Support and Influence Domains Specification of Smoothing Functions Formulation of Fundamental SPH for Weakly Compressible Fluids Continuity Equation Momentum Equation Energy Equation Solution Strategy Numerical Considerations Shock Wave and δ-SPH Artificial Viscosity Boundary Treatments Variable Smoothing Length Asymmetry of Particle Interaction Zero-Energy Mode Particle Interactions Time Integration Validations Dam Break Test Scott Russell’s Wave Generator Concluding Remarks Comments on MPMs Comments on SPH Improvements and Extensions Applications References Hybrid Methods with Special Focus on DEM-SPH General Concept Landslide and Surge Waves Interactions and Handshaking Algorithms for Solid Disc-Fluid Particle Systems Governing Equations of the Improved PFC for Solid Discs Governing Equations of the Improved SPH for Fluid Particles Solid–fluid Interactions Interactions and Hybrid Algorithms for Solid Polygon-Fluid Particle Systems Governing Equations of the Improved DEM for Solid Polygons Governing Equations of the Improved SPH for Fluid Particles Solid–fluid Interactions Validations and Applications Submarine Landslide-Tsunamis Subaerial Landslide-Tsunamis Application to Lituya Bay Landslide Concluding Remarks References

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shenghong c advanced computational methods geomechanics 2023