Computational Modeling of Multiphase Geomaterials 1st Edition by Fusao Oka, Sayuri Kimoto 1138430234 9781138430235
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Product details:
ISBN 10: 1138430234
ISBN 13: 9781138430235
Author: Fusao Oka, Sayuri Kimoto
Drawing on the authors’ well-regarded work in the field, this book provides readers with the knowledge and tools to tackle problems in geomechanics. It shows how numerical methods and constitutive modeling can help predict the behavior of geomaterials such as soil and rock. The authors describe the constitutive modeling of soils for rate-dependent behavior, strain localization, multiphase theory, and applications in the context of large deformations. They also emphasize viscoplasticity and water-soil coupling.
Table of contents:
1 Fundamentals in continuum mechanics
1.1 Motion
1.2 Strain and strain rate
1.2.1 Strain tensor
1.2.2 Compatibility relation of strain
1.2.3 Shear strain and deviatoric strain
1.2.4 Volumetric strain
1.3 Changes in area
1.4 Deformation rate tensor
1.5 Stress and stress rate
1.5.1 Stress tensor
1.5.2 Principal stresses and the invariants of the stress tensor
1.5.3 Stress rate tensor and objectivity
1.6 Conservation of mass
1.7 Balance of linear momentum
1.8 Balance of angular momentum and the symmetry of the stress tensor
1.9 Balance of energy
1.10 Entropy production and Clausius–Duhem inequality
1.11 Constitutive equation and objectivity
1.11.1 Principle of objectivity and constitutive model
1.11.2 Time shift
1.11.3 Translational motion
1.11.4 Rotational motion
References
2 Governing equations for multiphase geomaterials
2.1 Governing equations for fluid–solid two-phase materials
2.1.1 Introduction
2.1.2 General setting
2.1.3 Density of mixture
2.1.4 Definition of the effective and partial stresses of the fluid–solid mixture theory
2.1.5 Displacement-strain relation
2.1.6 Constitutive model
2.1.7 Conservation of mass
2.1.8 Balance of linear momentum
2.1.9 Balance equations for the mixture
2.1.10 Continuity equation
2.2 Governing equations for gas-watersolid three-phase materials
2.2.1 Introduction
2.2.2 General setting
2.2.3 Partial stresses
2.2.4 Conservation of mass
2.2.5 Balance of momentum
2.2.6 Balance of energy
2.3 Governing equations for unsaturated soil
2.3.1 Partial stresses for the mixture
2.3.2 Conservation of mass
2.3.3 Balance of linear momentum for the three phases
2.3.4 Continuity equations
References
3 Fundamental constitutive equations
3.1 Elastic Body
3.2 Newtonian viscous fluid
3.3 Bingham body and viscoplastic body
3.4 von Mises plastic body
3.5 Viscoelastic constitutive models
3.5.1 Maxwell viscoelastic model
3.5.2 Kelvin–Voigt model
3.5.3 Characteristic time
3.6 Elastoplastic Model
3.6.1 Yield conditions
3.6.2 Additivity of the strain
3.6.3 Loading conditions
3.6.4 Stability of elastoplastic material
3.6.5 Maximum work theorem
3.6.6 Flow rule and normality (evolutional equation of plastic strain)
3.6.7 Consistency conditions
3.7 Overstress type of elastoviscoplasticity
3.7.1 Perzyna’s model
3.7.2 Duvaut and Lions’ model
3.7.3 Phillips and Wu’s model
3.8 Elastoviscoplastic model based on stress history tensor
3.8.1 Stress history tensor and kernel function
3.8.2 Flow rule and yield function
3.9 Other viscoplastic and viscoelastic-plastic theories
3.10 Cyclic plasticity and viscoplasticity
3.11 Dissipation and the yield functions
References
4 Failure conditions and the Cam-clay model
4.1 Introduction
4.2 Failure criteria for soils
4.2.1 Failure criterion by Coulomb
4.2.2 Failure criterion by Tresca
4.2.3 Failure criterion by von Mises
4.2.4 Failure criterion by Mohr
4.2.5 Mohr–Coulomb failure criterion
4.2.6 Matsuoka–Nakai failure criterion
4.2.7 Lade failure criterion
4.2.8 Failure criterion on n plane
4.2.9 Lode angle and Mohr–Coulomb failure condition
4.3 Cam-clay model
4.3.1 Original Cam-clay model
4.3.2 Ohta’s theory
4.3.3 Modified Cam-clay model
4.3.4 Stress-dilatancy relations
References
5 Elastoviscoplastic modeling of soil
5.1 Rate-dependent and time-dependent behavior of soil
5.1.1 Strain rate-dependent behavior of clayey soil
5.1.2 Creep deformation and failure
5.1.3 Stress relaxation behavior
5.1.4 Strain rate-dependent compression
5.1.5 Isotaches
5.2 Viscoelastic constitutive models
5.3 Elastoviscoplastic constitutive models
5.3.1 Overstress models
5.3.2 Time-dependent model
5.3.3 Viscoplastic models based on the stress history tensor
5.4 Microrheology models for clay
5.5 Adachi and Oka’s viscoplastic model
5.5.1 Strain rate effect
5.5.2 Simulation by the Adachi and Oka’s model
5.5.2.1 Effect of secondary consolidation
5.5.2.2 Isotropic stress relaxation
5.5.3 Constitutive model for anisotropic consolidated clay
5.6 Extended viscoplastic model considering stress ratio-dependent softening
5.7 Elastoviscoplastic model for cohesive soil considering degradation
5.7.1 Elastoviscoplastic model considering degradation
5.7.2 Determination of the material parameters
5.7.3 Strain-dependent elastic shear modulus
5.8 Application to natural clay
5.8.1 Osaka Pleistocene clay
5.8.2 Osaka Holocene clay
5.8.3 Elastoviscoplastic model based on modified Cam-clay model
5.9 Cyclic elastoviscoplastic model
5.9.1 Cyclic elastoviscoplastic model based on nonlinear kinematical hardening rule
5.9.2 Cyclic elastoviscoplastic model considering structural degradation
5.9.2.1 Static yield function
5.9.2.2 Viscoplastic potential function
5.9.2.3 Kinematic hardening rules
5.9.2.4 Strain-dependent shear modulus
5.9.2.5 Viscoplastic flow rule
References
6 Virtual work theorem and finite element method
6.1 Virtual work theorem
6.1.1 Boundary value problem
6.1.2 Virtual work theorem
6.2 Finite element method
6.2.1 Discretization of equilibrium equation
6.2.2 Discretization of continuity equation
6.2.3 Interpolation function
6.2.4 Triangular element
6.2.5 Isoparametric elements
6.3 Dynamic Problem
6.3.1 Time discretization method
6.3.1.1 Linear acceleration method and Wilson θ method
6.3.1.2 Newmark β method
6.3.1.3 Central finite difference scheme
6.3.2 Mass matrix
6.4 Dynamic analysis of water-saturated soil
6.4.1 Equation of motion
6.4.2 Continuity equation
6.4.2.1 Galerkin method
6.4.2.2 Finite volume method
6.4.3 Time discretization
6.4.3.1 Equation of motion
6.4.3.2 Continuity equation
6.5 Finite deformation analysis for fluid–solid two-phase mixtures
6.5.1 Effective stress and fluid–solid mixture theory
6.5.2 Equilibrium equation
6.5.3 Continuity equation
6.5.4 Discretization of the weak forms for the equilibrium equation and the continuity equation
6.5.4.1 Discretization of the weak forms for the equilibrium equation
6.5.4.2 Discretization of the weak form for the continuity equation
References
7 Consolidation analysis
7.1 Consolidation behavior of clays
7.2 Consolidation analysis: small strain analysis
7.2.1 One-dimensional consolidation problem
7.2.2 Two-dimensional consolidation problem
7.2.3 Summary
7.3 Consolidation analysis with a model considering structural degradation
7.3.1 Effect of sample thickness
7.3.2 Simulation of Aboshi’s experimental results
7.3.2.1 Determination of material parameters
7.3.2.2 Elastic parameters
7.3.2.3 Viscoplastic parameters
7.3.2.4 Consolidation analysis
7.3.3 Effect of degradation
7.4 Consolidation analysis of clay foundation
7.4.1 Introduction
7.4.2 Consolidation analysis of soft clay beneath the embankment
7.4.2.1 Soil parameters
7.4.2.2 Soil response beneath embankment
7.5 Consolidation analysis considering construction of the embankment
7.5.1 Numerical example
References
8 Strain localization
8.1 Strain localization problems in geomechanics
8.1.1 Angle of shear band
8.2 Localization analysis
8.3 Instability of geomaterials
8.4 Noncoaxiality
8.5 Current stress-dependent characteristics and anisotropy
8.6 Regularization of Ill-posedness
8.6.1 Nonlocal formulation of constitutive models
8.6.2 fluid–solid two-phase formulation
8.6.3 Viscoplastic regularization
8.6.4 Dynamic formulation
8.6.5 Discrete model and finite element analysis with strong discontinuity
8.7 Instability and effects of the transport of pore water
8.7.1 Extended viscoplastic models for clay
8.7.2 Instability analysis of fluid-saturated viscoplastic models
8.7.2.1 Instability under locally undrained conditions
8.7.2.2 Instability analysis considering the pore water flow
8.8 Two-dimensional finite element analysis using elastoviscoplastic model
8.8.1 Effects of permeability
8.8.2 Strain localization analysis by the gradient-dependent elastoviscoplastic model
8.8.2.1 Finite element formulation of the gradient-dependent elastoviscoplastic model
8.8.2.2 Effect of the strain gradient parameter
8.8.2.3 Effect of the heterogeneity of the soil properties
8.8.2.4 Mesh-size dependency
8.9 Three-dimensional strain localization analysis of water-saturated clay
8.9.1 Undrained triaxial compression tests for clay using rectangular specimens
8.9.1.1 Clay samples and the testing program
8.9.1.2 Image analysis
8.9.2 Three-dimensional soil-water coupled finite element analysis method
8.9.3 Numerical simulation of triaxial tests for rectangular specimens
8.9.3.1 Determination of the material parameters
8.9.3.2 Boundary conditions
8.9.3.3 Comparison between experimental and simulation results
8.9.3.4 Three-dimensional shear bands
8.9.3.5 Effects of the strain rates
8.10 Application to bearing capacity and earth pressure problems
8.11 Summary
References
9 Liquefaction analysis of sandy ground
9.1 Introduction
9.2 Cyclic constitutive models
9.3 Cyclic elastoplastic model for sand with a generalized flow rule
9.3.1 Basic assumptions
9.3.2 Overconsolidation boundary surface
9.3.3 Fading memory of the initial anisotropy
9.3.4 Yield function
9.3.5 Plastic-strain dependence of the shear modulus
9.3.5.1 Method 1
9.3.5.2 Method 2
9.3.5.3 Method 3
9.3.5.4 Method 4
9.3.6 Plastic potential function
9.3.7 Stress-strain relation
9.4 Performance of the cyclic model
9.4.1 Determination of material parameters
9.5 Liquefaction analysis of a liquefiable ground
9.5.1 Vertical array records on Port Island
9.5.2 Numerical models
9.5.3 Common parameters
9.5.4 Parameters for elastoplasticity model
9.5.5 Parameters for elastoviscoplasticity model
9.5.6 Parameters for Ramberg-Osgood model
9.5.7 Finite element model and numerical parameters
9.5.8 Numerical results
9.6 Numerical analysis of the dynamic behavior of a pile foundation considering liquefaction
9.6.1 Simulation methods
9.6.2 Results and discussions
References
10 Recent advances in computational geomechanics
10.1 Thermo-hydro-mechanical coupled finite element method
10.1.1 Temperature-dependent viscoplastic parameter
10.1.2 Elastic and temperature-dependent stretching
10.1.3 Weak form of the equilibrium equation for water-soil mixture
10.1.4 Continuity equation
10.1.5 Balance of energy
10.1.6 Simulation of thermal consolidation
10.2 Seepage-deformation coupled analysis of unsaturated river embankment using multiphase elastoviscoplastic theory
10.2.1 Introduction
10.2.2 Governing equations and analysis method
10.2.3 Constitutive model for unsaturated soil
10.2.3.1 Overconsolidation boundary surface
10.2.3.2 Static yield function
10.2.3.3 Viscoplastic potential function
10.2.3.4 Viscoplastic flow rule
10.2.3.5 Constitutive model for pore water: soil-water characteristic curve
10.2.4 Simulation of the behavior of unsaturated soil by elastoviscoplastic model
10.2.5 Numerical analysis of seepagedeformation behavior of a levee
10.2.5.1 Analysis method
10.2.5.2 Deformation during the seepage flow
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