Chen Shenghong. Advanced Computational Methods and Geomechanics

Singapore: Springer, 2023. — 782 p.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