Modeling and computing is becoming an essential part of the analysis and design of an engineered system. This is also true of geotechnical systems , such as soil foundations, earth dams and other soil-structure systems. The general goal of modeling and computing is to predict and understand the behaviour of the system subjected to a variety of possible conditions/scenarios (with respect to both external stimuli and system parameters), which provides the basis for a rational design of the system. The essence of this is to predict the response of the system to a set of external forces. The modelling and computing essentially involve the following three phases: (a) Idealization of the actual physical problem, (b) Formulation of a mathematical model represented by a set of equations governing the response of the system, and (c) Solution of the governing equations (often requiring numerical methods) and graphical representation of the numerical results. This book will introduce these phases.
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Preface Introduction BASIC MECHANICS Stresses and Strains Introduction Reference Coordinate System: Notations Strains Stresses Mohr's Circle Physical Laws and Governing Equations Introduction Idealizations Total and Effective Stresses in Soils Law of Conservation of Momentum: Equilibrium Equations Law of Conservation of Mass ELEMENTAL RESPONSE: CONSTITUTIVE MODELS I. Introduction II. Soil Behavior: From Experimental Results III. Modeling of Soil Behavior Elasticity Elastic Constitutive Law Plasticity Theory: Nonlinear Deformation of Soils Introduction Nonlinear Deformation of Soils Elements of Plasticity Yielding Criteria Post-Yield Behavior Perfect Plasticity Hardening Plasticity Loading/Unloading Criterion Exercise Problems Viscoelasticity and Viscoplasticity Introduction Viscoelastic Behavior: Fundamental Rheological Models Viscoelastic Behavior: Composite Rheological Models Formulation Methods in Viscoelasticity 1-D Viscoelastic Analysis of Soil Layers under Vertical Circular Loading Viscoplasticity Exercise Problems SYSTEM RESPONSE: METHODS OF ANALYSES Analytical Methods Introduction 1-D Flow through a Land Mass: Island Recharge Problem Regional Groundwater Flow: Steady State Seepage 1-D Deformation of a Soil Column 1-D Consolidation of a Soil Column: Decoupled Flow and Deformation Contaminant Transport 1-D Coupled Flow and Deformation 2-D Coupled Flow and Deformation Exercise Problems Semi-Analytical Methods Introduction Stress Analysis Quasi-Static Analysis of Multi-Layer Porous Media under Waves Exercise Problems Finite Difference Method Introduction Finite Difference Approximation of Derivatives FDM for Consolidation (Parabolic) Equation FDM for Seepage (Laplace) Equation: 2-D Steady State Flow FDM for Groundwater Flow: Aquifer Simulation FDM for Consolidation of a Layered System FDM for Laterally Loaded Piles: Soil-Structure Interaction Error, Convergence and Stability Exercise Problems Finite Element Method Introduction Direct Stiffness Method Galerkin Method of Weighted Residual FEM: 1-D Problems FEM: 2-D Problems Basic Element Formulations The Principle of Minimum Potential Energy Isoparametric Element Formulation Exercise Problems Appendices A.1 Fourier Series and Fourier Transform A.2 Laplace Transform A.3 MATLAB Commands: FFT, IFFT, FFTSHIFT A.4 Solution Flow Chart for the Analysis of a Viscoelastic Material A.5 Analytical Solution of Wave-Induced Porous Soil Layer Response A.5 Semi-Analytical Solution of Wave-Induced Multi-Layer Porous Soil Response References Index
M. S. Rahman is a Professor of Civil Engineering at North Carolina State University. M. B. Can UElker is an Associate Professor of Civil Engineering at Istanbul Technical University in Turkey.