Geotechnics of Roads, 2-Volume Set

Cover
Volume 01
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Acknowledgments
List of mathematical symbols
Introduction
1 Distribution of stresses and strains in roads
1.1 Fundamental relationships and definitions
1.1.1 Stresses in particulate media
1.1.2 Representation of stresses in a continuum media
1.1.3 Geometric derivation of strains
1.2 Fundamental definitions of elasticity
1.2.1 Equilibrium equations
1.2.2 Relationships between stresses and strains for isotropic linear elasticity
1.2.3 Strain compatibility equations
1.3 Plane strain problems
1.3.1 Airy’s stress function
1.4 Some useful elastostatic solutions for stress distribution
1.4.1 Boussinesq’s solution
1.4.2 Cerrutti’s solution
1.4.3 Fröhlich solution
1.4.4 Stress components from triangular loads
1.5 Anisotropy
1.6 Generalities about the elastic limit
1.6.1 Physical meaning of a yield criterion
1.6.2 Representation of yield criteria in the plan of principal stresses
1.6.3 Some classical yield criteria of geomaterials
1.7 Contact problems in road engineering
1.7.1 Contact between two spheres
1.7.2 Contact between an ellipsoid and a flat surface
1.7.3 Contact between a cylindrical body and an elastic half space
1.7.4 Internal stresses in Hertzian contacts
1.7.5 Non Hertzian contacts
1.7.5.1 Contact between a rigid cone and an elastic half space
1.7.5.2 Contact between a rigid cylinder and an elastic half-space
1.8 Elastodynamic solutions
1.8.1 Lumped spring-dashpot model
1.8.2 Cone macro element model
1.8.3 Propagation of surface waves
1.9 Response of a multilayer linear elastic system
1.10 Generalities about tire-road interaction
1.10.1 Theoretical basis derived from the Hertz theory
1.10.2 Tire interaction on bare soils
1.10.3 Tire interaction on pavements
2 Unsaturated soil mechanics applied to road materials
2.1 Physical principles of unsaturated soils
2.1.1 Potential of water in a porous media
2.1.2 Surface tension
2.1.3 Contact angle
2.1.4 Capillarity and Laplace’s equation
2.1.5 Thermophysical properties of moist air
2.1.6 Psychrometric equation
2.1.7 Raoult’s Law
2.1.8 Relationship between suction and relative humidity: the Kelvin equation
2.1.9 Osmotic, capillary, and total suction
2.1.10 Dissolution of gas and tensile strength of water
2.1.11 Reduction of the freezing point of water
2.2 Water Retention Curve
2.2.1 Water retention curve for drainage
2.2.2 Water retention curve in wetting
2.2.3 Hysteresis of the water retention curve
2.2.4 Methods for measurement of suction
2.2.4.1 Suction plate
2.2.4.2 Pressure plate
2.2.4.3 Osmotic control
2.2.4.4 Vapor control
2.2.4.5 Tensiometers
2.2.4.6 Thermocouple psychrometers
2.2.4.7 Chilled mirror apparatus
2.2.4.8 Filter paper
2.2.4.9 Other methods
2.2.5 Models for adjusting the Water Retention Curve
2.2.5.1 Correlations for the Water Retention Curve proposed in the MEPDM
2.2.6 Evolution of suction during compaction and water retention model
2.3 Flow of water and air in unsaturated soils
2.3.1 Assessment of the functions of relative permeability
2.3.1.1 Steady State Methods
2.3.1.2 Unsteady State Methods
2.3.1.3 Indirect methods
2.3.2 Continuity equation for water flow in unsaturated soils
2.3.2.1 Continuity equation in terms of diffusivity
2.4 Heat transport and thermal properties of unsaturated soils
2.4.1 Thermal conductivity models
2.4.1.1 Johansen’s model
2.4.1.2 Côté and Konrad model
2.4.2 Heat capacity of soils
2.5 Mechanical properties of unsaturated soils
2.5.1 Shear strength of unsaturated materials
2.5.2 Compressibility of unsaturated materials
2.5.3 Stiffness of unsaturated materials
2.6 Modeling the behavior of unsaturated soils using the Barcelona Basic Model, BBM
3 Compaction
3.1 Mechanical framework of soil compaction
3.2 Stress distributions
3.2.1 Tire compactors
3.2.2 Cylinder compactors
3.2.3 Sheepsfoot and padsfoot compactors
3.2.4 Vibratory compactors
3.2.5 Polygonal drums and impact compactors
3.2.6 Theoretical analysis of vibratory rollers
3.3 Relationships between soil compaction and stress paths
3.3.1 Static compaction along an oedometric path
3.3.1.1 Fine-grained soils
3.3.1.2 Coarse grained soils
3.3.1.3 Effect of cyclic loading
3.3.2 Static compaction along a triaxial path
3.3.3 Static compaction along stress paths with inversion or rotation
3.3.4 Dynamic compaction
3.3.5 Effects of temperature
3.4 Relationships between laboratory and field compaction
3.5 Compaction interpreted in the framework of unsaturated soil mechanics
3.6 Compaction characteristics for fine grained soils
3.7 Compaction characteristics for granular soils
3.8 Compaction controlled by the degree of saturation
4 Embankments
4.1 Embankments on soft soils
4.1.1 Stability analysis
4.1.2 Shear strength parameters
4.1.2.1 Total Stress Analysis
4.1.2.2 Effective Stress Analysis
4.1.2.3 Analysis of the generalized bearing capacity failure
4.1.2.4 Analysis of rotational failure
4.1.2.5 Sources of inaccuracy of a computed safety factor
4.1.2.6 Numerical methods for limit state analysis
4.1.3 Analysis of settlements
4.1.3.1 Immediate settlements
4.1.3.2 Primary consolidation
4.1.3.3 Radial consolidation
4.1.3.4 Secondary compression
4.1.4 Constructive methods for embankments over soft soils
4.1.4.1 Methods without substitution of soft soil
4.1.4.2 Methods with partial or total substitution of the soft soil
4.1.5 Instrumentation and control
4.1.6 Use of geosynthetics in embankments
4.1.6.1 Geosynthetic reinforced embankments
4.1.6.2 Systems of geosynthetics and columns
4.2 Behavior of the fill of the embankment
4.2.1 Modeling behavior of compacted soils under wetting using the Barcelona Basic Model BBM
4.2.2 Microstructure and volumetric behavior
5 Mechanical behavior of road materials
5.1 From micromechanics to macromechanics
5.1.1 Micromechanical stiffness in the elastic domain
5.1.1.1 Behavior under compressive forces
5.1.1.2 Behavior under compressive and shear forces
5.1.2 Elastoplastic contact
5.1.3 Anisotropy
5.1.4 Effect of water
5.1.5 Particle Strength
5.2 Laboratory characterization of road materials
5.2.1 The CBR test
5.2.1.1 Theoretical analysis of the CBR test
5.2.2 Characterization of stiffness under small strains
5.2.3 Transition from small to large strains
5.2.4 Cyclic triaxial tests
5.2.5 Comparison between monotonic and cyclic behavior
5.2.6 Advanced mechanical characterization of road materials
5.3 Modeling the mechanical behavior of road materials
5.3.1 Models describing the resilient modulus
5.3.2 Models describing resilient modulus and Poisson’s ratio
5.3.3 Permanent strain under cyclic loading
5.4 Geomechanical approach to ranking of road materials
6 Climate effects
6.1 Heat flow over road structures
6.1.1 Irradiance at the surface of the earth
6.2 Flow of water in road structures
6.2.1 Infiltration of water
6.2.1.1 Uniform infiltration through layers of asphalt materials
6.2.1.2 Local infiltration through cracks in asphalt layers
6.2.1.3 Relationship between precipitation and infiltration
6.2.2 Evaporation
6.3 Thermo-Hydro-Mechanical modeling applied to pavement structures
6.3.1 Conservation equations
6.3.2 Phenomenological relationships
6.3.3 Derivation of equations for water and gas flow in non-isothermal conditions
6.3.4 Boundary conditions
6.4 Empirical method based on the Thornthwaite Moisture Index
6.5 Frost action
6.5.1 Mechanism of water migration affecting roads during freezing and thawing
6.5.1.1 Relationships between frozen and unsaturated soils
6.5.1.2 Mechanical properties of soils after freezing and thawing
6.5.2 Criteria for frost susceptibility
6.5.2.1 Criteria based on material properties
6.5.2.2 Criteria based on material characteristics in unsaturated states
6.5.2.3 Laboratory tests for evaluating frost susceptibility
6.6 Basic principles for road structure sub-drainage
6.6.1 Drainage materials
6.6.2 Flow of water trough a drainage layer
6.6.3 Effects of drainage layer capillarity
6.6.4 Design of drainage layers
7 Non destructive evaluation and inverse methods
7.1 Non destructive evaluation
7.1.1 Deflection based methods
7.1.2 Dynamic methods
7.1.2.1 Steady state methods
7.1.2.2 Transient methods
7.1.2.3 Seismic methods
7.1.2.4 Methods based on the dispersion of Rayleigh waves
7.2 Methods based on electromagnetic waves
7.2.1 Infrared thermography
7.2.2 Ground penetrating radar
7.3 Forward and inverse analysis of road structures
7.3.1 Forward analysis
7.3.1.1 Static analysis
7.3.1.2 Dynamic Methods
7.3.2 Inverse methods
7.4 Continuous Compaction Control and Intelligent Compaction CCC/IC
7.4.1 Compaction Meter Value (CMV)
7.4.2 Oscillometer Value (OMV)
7.4.3 Compaction Control Value (CCV)
7.4.4 Roller Integrated Stiffness, ks
7.4.5 Omega Value Ω
7.4.6 Vibratory Modulus, Evib
7.4.7 Machine Drive Power MDP
7.4.8 Relationship between modulus and CCC/CI values
7.4.9 Correlations between CCC measurements and geomechanical properties
7.4.10 Quality control based on CCC measurements
7.4.10.1 Option 1
7.4.10.2 Option 2
7.4.10.3 Option 3
References
Index
Volume 02
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Author Biography
Acknowledgments
List of mathematical symbols
Introduction
1 Distribution of stresses and strains in roads
1.1 Relevant equations
1.1.1 Boussinesq’s solution
1.1.2 Cerruti’s solution
1.1.3 Fröhlich solution
1.1.4 Tire–soil interaction
1.1.5 Road–vehicle interaction
1.1.5.1 Mathematical description of road profiles
1.1.6 Burmister’s method
1.2 Example 1: Calculation of the stress distribution produced by vertical loads using Boussinesq’s solution
1.2.1 Loaded area and uniform stress
1.2.2 Superposition of the stresses produced by each individual loaded area
1.2.3 Requirements of Cohesion corresponding to the Mohr–Coulomb criterion
1.2.4 Concluding remarks
1.3 Example 2: Use of Cerruti’s solution to calculate the stresses produced by horizontal loads
1.3.1 Stresses in the half-space
1.3.2 Requirements of cohesion for the Mohr–Coulomb criterion
1.3.3 Concluding remarks
1.4 Example 3: Tire–road interaction using the Hertz theory and the Fröhlich stress distribution
1.4.1 Elastic properties of the equivalent tire
1.4.2 Contact stress applied by the tire on the road
1.4.3 Stresses in the half-space using the Fröhlich solution for stress distribution
1.4.4 Concluding remarks
1.5 Example 4: Calculation of the vehicle–road interaction
1.5.1 Discretization in time of the differential equation
1.5.2 Vehicle interaction in a bumpy road
1.5.3 Vehicle interaction on actual roads
1.5.4 Concluding remarks
1.6 Examples 5: Computation of stresses in a three-layered road structure using Burmister’s method
1.6.1 Approximation of the load using Bessel functions
1.6.2 Calculation of the vertical and radial stresses using Burmister’s method
1.6.3 Concluding remarks
1.7 Example 6: Tridimensional distribution of stresses produced by moving wheel loads
1.7.1 Stresses produced by a circular load in a cylindrical coordinate system
1.7.2 Transformation of stresses from cylindrical into Cartesian coordinates
1.7.3 Principal stresses, rotation, and invariants p and q
1.7.4 Concluding remarks
2 Unsaturated soil mechanics applied to road materials
2.1 Relevant equations
2.1.1 Water retention curve
2.1.2 Assessment of the hydraulic conductivity based on the water retention curve
2.1.3 Flow of water in unsaturated materials
2.1.4 Thermal properties of unsaturated materials
2.1.5 Heat flow in unsaturated materials
2.2 Example 7: Assessment of the water retention curve using the empirical model proposed in the Mechanistic Empiric Pavement Design Guide (MEPDG)
2.3 Example 8: Method for calculating the unsaturated hydraulic conductivity based on the water retention curve
2.3.1 Limits of integration and sub-intervals
2.3.2 Volumetric water content and derivative with respect to suction
2.3.3 Denominator of Equation 2.13
2.3.4 Numerator of Equation 2.13
2.4 Example 9: Simplified calculation of water infiltration
2.5 Example 10: Numerical calculation of water flow in unsaturated materials, application to road structures
2.5.1 Part A. Numerical solution of the nonlinear partial differential equation describing the flow of water in unsaturated soils using the explicit finite difference method
2.5.1.1 Discretization in space
2.5.1.2 Discretization in time
2.5.1.3 Implementation of the explicit Finite Difference Method
2.5.1.4 Boundary conditions
2.5.1.5 Initial conditions
2.5.2 Part B. Numerical solution using the data of the example
2.5.2.1 Water retention curves
2.5.2.2 Discretization in space
2.5.2.3 Discretization in time
2.5.2.4 Boundary and initial conditions
2.5.2.5 Simulation
2.6 Example 11: Numerical solution of the heat flow in road structures
2.6.1 Part A. Numerical solution of the diffusion equation using the implicit finite difference method
2.6.1.1 Discretization in space
2.6.1.2 Discretization in time
2.6.1.3 Implementation of the FDM using the implicit solution
2.6.1.4 Boundary conditions
2.6.1.5 Initial conditions
2.6.2 Part B. Numerical solution using the data of the example
2.6.2.1 Thermal conductivity and heat capacity
2.6.2.2 Discretization in space
2.6.2.3 Discretization in time
2.6.2.4 Boundary and initial conditions
2.6.2.5 Simulation
3 Compaction
3.1 Relevant equations
3.1.1 Summary of the equations describing the BBM
3.1.2 Effect of cyclic loading
3.1.3 Evolution of the water retention curve during compaction
3.1.4 A linear packing model for establishing the relationship between grain size distribution and density
3.1.4.1 Virtual compacity of binary mixtures
3.1.5 Virtual compacity of binary mixtures without interaction
3.1.6 Virtual compacity of binary mixtures with total interaction
3.1.7 Virtual compacity of binary mixtures with partial interaction
3.1.7.1 Virtual compacity of polydisperse mixtures
3.1.7.2 Actual compacity of granular mixtures
3.1.7.3 Assessment of compacted densities using the linear packing model
3.2 Example 12: Simulation of field compaction using the BBM
3.2.1 Stress distribution produced by one tire on the surface of the soil
3.2.2 Stress distribution within the soil mass
3.2.3 Stress distribution produced by the whole compactor
3.2.4 Compaction profiles calculated using the BBM
3.2.5 Effect of the loading cycles
3.2.6 Effect of the water content
3.3 Example 13: Use of the linear packing model to compute the density of a compacted material based on its grain size distribution
3.3.1 Virtual compacity
3.3.2 Actual compacity
3.3.3 Dry density
3.3.4 Results of the model and comparison with the Proctor test
4 Embankments
4.1 Relevant equations
4.1.1 Stress components due to triangular loads
4.1.2 Immediate settlements
4.1.3 Primary consolidation
4.1.4 Radial consolidation
4.1.5 Increase of shear strength for staged construction
4.1.6 Generalized bearing capacity
4.1.7 The BBM including the effect of soil’s microstructure
4.2 Example 14: Embankments on soft soils
4.2.1 Stress distribution beneath the symmetry axis of the embankment
4.2.2 Immediate and consolidation settlements
4.2.3 Vertical stress distribution under the embankment for the final height of the fill.
4.2.4 Evaluation of the bearing capacity for the staged construction
4.2.5 Evaluation of the bidimensional consolidation
4.2.6 Evolution of the undrained shear strength considering the 2D consolidation
4.2.7 Evaluation of the safety factor before placing each stage
4.2.8 Analysis of the radial drainage
4.3 Example 15: Analysis of the collapse of embankments under soaking using the BBM
4.3.1 Simulation of the oedometric compaction
4.3.2 Post compaction
4.3.3 Reloading
4.3.3.1 Elastic domain
4.3.3.2 Elastoplastic domain
4.3.4 Soaking
4.3.5 Concluding remarks
4.4 Example 16: Effect of the soil’s microstructure in the collapse of embankments
4.4.1 Initial conditions
4.4.2 Oedometric compression
4.4.2.1 Elastic compression
4.4.2.2 Elastoplastic compression
4.4.3 Saturated oedometric compression
5 Mechanical behavior of road materials
5.1 Relevant equations
5.1.1 Models describing the resilient modulus
5.1.2 Models describing the resilient Young’s modulus and Poisson’s ratio
5.1.3 Effect of water in the resilient Young’s modulus
5.2 Example 17: Adjustment of the measured resilient Young’s modulus using different models
5.2.1 Fitting the experimental results using the k − θ model
5.2.2 Fitting the experimental results using the three parameters model
5.2.3 Fitting the experimental results using Boyce’s model
5.2.4 Fitting the experimental results using the linear model
5.2.5 Performance of the different models to predict resilient Young’s moduli and Poisson’s ratios
5.3 Example 18: Assessment of the effect of the water content of the granular layer on the fatigue life of a low-traffic road structure
5.3.1 Fitting the experimental measures of suction using the van Genuchten equation
5.3.2 Evaluation of the models that describe the effect of the water content on the resilient Young’s modulus
5.3.2.1 Models recommended in the MEPD
5.3.2.2 Model with two state variables: vertical total stress and suction
5.3.2.3 Model based on effective stress
5.3.2.4 Comparison of models’ performance
5.3.3 Fatigue lifespan of the bituminous layer depending on the water content of the granular layer
5.3.4 Concluding remarks
6 Climate effects
6.1 Relevant equations
6.1.1 Heat flow in road structures
6.1.2 Flow of water through a drainage layer
6.2 Example 19: Evolution of the temperature in a road structure depending on the environmental variables
6.2.1 Environmental variables
6.2.2 Heat flow due to solar radiation
6.2.3 Discretization in space
6.2.4 Discretization in time
6.2.5 Continuity equation between layers
6.2.6 Analysis of the boundary conditions
6.2.7 Analysis of the time step
6.2.8 Numerical solution
6.3 Example 20: Assessment of the local infiltration through cracks in the top layer of a road
6.3.1 Infiltration through single cracks
6.3.2 Infiltration through a squared net of cracks
6.4 Example 21: Drainage layers in road structures
7 Nondestructive evaluation and inverse methods
7.1 Relevant equations
7.1.1 Theoretical analysis of vibratory rollers
7.1.2 Contact between a cylindrical body and an elastic half-space
7.1.3 The cone macroelement model
7.1.4 Continuous compaction control (CCC)
7.2 Example 22: Soil–drum interaction assuming an elastic soil’s response
7.2.1 Discretization in time of the dynamic equation
7.2.2 Effect of Young’s modulus on the soil–drum interaction
7.2.3 Effect of the dynamic load
7.3 Example 23: Analysis of the soil–drum interaction considering the soil’s reaction into the elastoplastic domain of behavior
7.3.1 Contact soil–drum under monotonic loading and elastoplastic behavior
7.3.2 Cyclic loading with elastoplastic soil’s response
7.3.3 Dynamic soil–drum interaction considering the elastoplastic contact
Bibliography
Index