Numerical Methods and Implementation in Geotechnical Engineering - Part 2

Table of Contents

Chapter 1 Distinct Element Method and Other Numerical Methods
1.1. Introduction to Distinct Element Method
1.2. General Formulation of Dem
1.2.1. The Force-Displacement Law
1.2.2. Law of Motion
1.2.3. Measuring Logic for Particle Formulation
1.2.4. Contact Constitutive Models
1.2.5. Model Generation
1.2.6. Modelling of Joints/Contacts
1.3. Distinct Element Particle Analysis of 3D Slope
1.3.1. Dem Analysis of 3D Slope with Curvature
1.3.2. Laboratory and 3D Dem Analysis of Failure Mechanism of Slope Under External Surcharge
1.4. Discontinuous Deformation Analysis
1.4.1. Refined Dda Formulation by the Authors
1.4.2. Discussion on Dda
1.5. The Developments of Nmm
1.5.1. Two Dimensional Manifold Methods Based on Finite Element Covers And Comparisons with Other Methods
1.5.2. A Brief Review of 2D Covers in Manifold Method
1.5.2.1. Finite Covers Formed by Mathematical Mesh and Physical Mesh
1.5.2.2. Finite Covers Formed by Finite Element Nodes and Physical Boundaries
1.5.2.3. Cover Functions and Weight Functions Based on Finite Element Mesh
1.5.2.4. Equilibrium Equations
1.5.3. A Supplement About Generation of Manifold Element
1.5.4. Comparison with Other Numerical Methods
1.5.5. Applications to Some Examples
1.5.5.1. Tunnel Excavation
1.5.5.2. Coal Extraction-Compared with Coupling Method of Dda and Fem
1.5.6. Wilson Non-Conforming Element in Numerical Manifold Method
1.5.6.1. Stiffness Matrix
1.5.6.2. Inertial Force Matrix
1.5.6.3. Fixed Point Matrix
1.5.6.4. Initial Stress Matrix
1.5.6.5. Point Loading Matrix
1.5.6.6. Body Loading Matrix
1.5.7. Three-Dimensional Finite Element Covers of Manifold Method
1.5.8. Brief Review of Previous Methods for Contact Detecting and Representation
1.5.8.1. Direct Test for Contacts
1.5.8.2. Common-Plane Test for Contacts
1.5.9. Penetration Edges Method for Detecting and Representing Contacts Between 3-D Blocks
1.5.9.1. Description and Classification of Contacts Between 3-D Blocks
1.5.9.2. Definition of Penetration Edge
1.5.9.3. Obtaining Penetration Edges
1.5.9.4. Testing and Distinguishing Contacts by Information of Penetration Edges
1.5.10. Discussion of Contact Type
1.5.11. Three Dimensional Manifold Method Based on Tetrahedron Element
1.5.12. Displacement Functions and Weight Functions of a Tetrahedron Element
1.6. Equilibrium Equations for 3D Nmm Based on Tetrahedron Element
1.6.1. Stiffness Matrix
1.6.2. Initial Stress Matrix
1.6.3. Point Loading Matrix
1.6.4. Body Force Matrix
1.6.5. Inertia Force Matrix
1.6.6. Fixed Point Matrix
1.7. 3D Contact Detection
1.7.1. Normal Contact Matrix
1.7.2. Shear Contact Matrix
1.7.3. Friction Force Matrix
1.7.4. Three Dimensional Manifold Method Based on Hexahedron Element
1.7.5. Displacement Functions and Weight Functions of a Hexahedron Element
1.7.6. Mapping Between Isoparametric Coordinates and Global Coordinates
1.7.7. Equilibrium Equations for 3D Nmm Based on Hexahedron Element
1.7.8. Stiffness Matrix
1.7.9. Initial Stress Matrix
1.7.10. Point Loading Matrix
1.7.11. Body Loading Matrix
1.7.12. Inertia Force Matrix
1.7.13. Fixed Point Matrix
1.8. 3D Contact Detection
1.8.1. Normal Contact Matrix
1.8.2. Shear Contact Matrix
1.8.3. Friction Force Matrix
1.9. Spectral Element Method (Sem)
1.9.1. Comparisons of Sem with Fem
1.10. Introduction to Meshless Method
1.10.1. Smoothed Particle Hydrodynamics Method (Sph)
1.10.2. Materials Point Method (Mpm)
Appendix 1-1 Program Dda Using Lahey Fortran and Interacter Graphics Library

Chapter 2 Optimization Analysis in Geotechnical Engineering Problems
2.1. Introduction
2.2. Optimization Analysis in Slope Stability Problems
2.2.1. Fundamental Problem
2.2.2. Formulation of Extremum Principle-Lower Bound Approach
2.2.3. Location of Critical Failure Surface - Upper Bound Approach
2.2.4. Limit Analysis of Slope Stability Problem
2.2.5. Powell Method
2.2.6. Dfp Method
2.3. Bearing Capacity Determination
2.4. Large Strain Pile Driving Wave Equation Back Analysis
2.4.1. Reflection
2.4.2. Expansion
2.4.3. Contraction
2.4.4. Reducing the Side Length
2.5. Parameter Estimation for Distinct Element Analysis
2.6. Lateral Earth Pressure Determination
2.7. Comparisons with Variational Principle
2.8. Heuristic Optimization Methods
2.8.1. Simulated Annealing Algorithm (Sa)
2.8.2. Genetic Algorithms (Ga)
2.8.3. Particle Swarm Optimization Algorithm (Pso)
2.8.4. Tabu Search Algorithm
2.8.5. Ant Colony Algorithm
2.8.6. Complex Method
2.9. Presence of Soft Band in Slope Stability Problem
2.10. Hybrid Heuristic Optimization Methods
2.10.1. Particle Swarm Optimization Coupled with Harmony Search (Hmpso)
2.10.2. Tabu Simulated Annealing Complex Method (Tsac)
2.11. Discussion
Appendix 2-1 GRG Program for Convex Optimization, Using Finite Difference Method to Form the Gradient for the Objective Function for a Pile Driving Problem

Chapter 3 Reliability Analysis in Geotechnical Engineering
3.1. Introduction
3.1.1. Case 1: Kaolin in Saprolite in Hong Kong (Parry, 1999)
3.1.2. Case 2: Kwun Lung Lau Landslide in Hong Kong (Morgenstern, 1994; Wong And Ho, 1997)
3.2. An Introduction to the Probability Theory
3.3. Spatial Variability
3.4. Review of Fundamental Probabilistic Methods
3.4.1. First-Order Reliability Method
3.4.2. Second-Order Reliability Method
3.4.3. Finite Element Reliability Method
3.4.3.1. Random Finite-Element Method
3.4.3.2. Stochastic Finite-Element Method
3.5. Simplified Approach for Locating the Critical Probabilistic Slip Surface in Limit Equilibrium Analysis
3.5.1. System Reliability Index with Floating Surfaces
3.5.2. Reliability Index for Specific Slip Surfaces
3.5.3. Search for the Critical Probabilistic Slip Surface
3.5.4. Procedure for the Mcsm
3.5.5. Observations on the Mcsm for Two Cases
3.5.5.1. Example 1
3.5.5.2. Example 2
3.5.6. Proposal for Rapid Analysis
3.5.6.1. Illustration of the Results from Rapid Analysis Using Previous Examples 1 & 2
3.5.7. Observation and Discussion on the Fast Method
3.6. Efficient System Reliability Analysis of Soil Slopes Using Multivariate Adaptive Regression Splines-Based Monte Carlo Simulation
3.6.1. Introduction
3.6.2. Review of Qrsm and Srsm
3.6.3. Mars-Based RSM
3.6.4. Mars-Based Mcs for System Reliability Analysis of Slopes
3.6.4.1. Define the Parameters
3.6.4.2. Establish a Deterministic Stability Analysis Model
3.6.4.3. Generate Training Samples
3.6.4.4. Prepare the Training Data Sets for Mars-Based RSM
3.6.4.5. Calibrate the Mars-Based RSM
3.6.4.6. Validate the Mars-Based RSM
3.6.4.7. Mcs for Computing Pf
3.6.4.8. Check the Accuracy of the Msc Estimation
3.6.5. Illustrative Examples
3.6.5.1. Example #1: a Three-Layered Cohesive Slope with GFP
3.6.5.2. Example #2: a Two-Layered Cohesive Slope with Smp
3.7. Genetic Algorithm Optimized Taylor Kriging Surrogate Model For System Reliability Analysis of Soil Slopes
3.7.1. Introduction
3.7.2. Kriging Method
3.7.2.1. Classical Kriging Theory
3.7.2.2. Theory of Tk
3.7.3. Gatk Surrogate Model
3.7.3.1. Genetic Algorithm
3.7.3.2. Gatk Model
3.7.4. Validation of Gatk
3.7.4.1. Analytical Validation of Gatk−Example #1
3.7.4.2. Analytical Validation of Gatk−Example #2
3.7.4.3. System Reliability Analysis Using Gatk Surrogate Model
3.7.5. Illustrative Examples for Gatk Surrogate Model
3.7.5.1. A Homogeneous C-ϕ Slope
3.7.5.2. A Heterogeneous Two-Layered Soil Slope
3.8. Conditional Random Field Reliability Analysis of a Cohesionfrictional Slope
3.8.1. Introduction
3.8.2. Simulation of Conditional Random Field
3.8.3. Probabilistic Analysis of a Slope Based on Subset Simulation
3.8.4. Implementation Procedure of Conditional Probabilistic Analysis
3.8.5. Illustrative Example
3.8.5.1. Basic Model for Illustration
3.8.5.2. Reliability Results Based on Unconditional Random Fields
3.8.5.3. Reliability Results Based on Conditional Random Fields
3.8.5.5. Effects of Conditional Random Fields on the Fs
3.8.6. Effects of Conditional Random Fields on the Spatial Variation of the Critical Slip Surface
3.8.7. Effects of Conditional Random Fields on the Probability of Failure

Samples

Author

• J. H. Wang
• Li Liang
• W. H. Fung Ivan
• Y.M. Cheng