Mechanics of Non-Homogeneous and Anisotropic Foundations

Although realistic soil and rock foundations reveal noticeable deviations in their properties from homogeneity and isotropy, the model of the homogeneous isotropie elastic half-space is widely used when studying static and dynamie interactions between a defonnable foundation and structures. This is explained by significant mathematieal difficulties inherent in problems conceming mechanies of anisotropie and heterogeneous elastic bodies. Solving the basic static and dynamie problems for heterogeneous and anisotropic half-spaces, such as different contact problems and problems of constructing Green's functions, has become possible in the last few decades due to the development of computer engineering techniques and numerical methods. This book contains the results of investigations in the area of statics and dynamies of heterogeneous and anisotropic foundations, carried out by the author in the last five years while working in the Faculty of Civil Engineering at Technion - Israel Institute of Technology. The book is directed at engineers and scientists in the areas of soil mechanics, soil-structures interaction, seismology and geophysics. Some characteristic features of the book are: i) Constructing (Chap.l) solutions in a general fonn for the heterogeneous (in the depth direction) transversely isotropic elastic half-space subjected to different loadings, hannonic in time. Characteristics of the given half-space have an influence on functions (of depth z and parameter k of Hankel's transfonns), which are detennined from a system of ordinary differential equations.

Table of Contents:
1. General Solutions of Harmonic Vibrations in Heterogeneous Transversely Isotropic Half-Space.- 1.1 Basic Relationships of Theory of Elasticity for Transversely Isotropic Body.- 1.2 Particular Solutions for Transversely Isotropic Heterogeneous Elastic Medium.- 1.3 Statement of Boundary Conditions for Planes z = const.- 1.4 General Solution for Harmonic Vibration of Half-Space Subjected to Surface Loads.- 1.5 General Solution for Harmonic Vibrations of Half-Space Subjected to Loads Applied below its Surface.- 1.6 Application of Functions Related to Dilatation and Rotation of Displacement Field.- 1.7 Application of Superposition Principle to Loadings of Rectangular and Circular Domains.- 2. Static and Dynamic Problems for Homogeneous Transversely Isotropic Half-Space.- 2.1 Vibrations of Half-Space Subjected to Vertical Force Applied to Half-Space Surface.- 2.2 Model of Deformable Foundation as Limiting Case of Transversely Isotropic Half-Space.- 2.3 Vibrations of Half-Space Subjected to Action of Horizontal Force Applied to Half-Space Surface.- 2.4 Torsional Vibrations of Half-Space.- 2.5 Action of Force Applied in Infinite Space.- 2.6 Vibrations of Transversely Isotropic Half-Space under Action of Force Applied within Half-Space.- 2.7 Contact Problems for Transversely Isotropic Half-Space.- 2.8 Plane Problems for Transversely Isotropic Half-Space.- 3. Mechanics of Isotropic Half-Space with Shear Modulus Varying Linearly with Depth.- 3.1 Fundamental Solutions of System of Equations (1.130)–(1.133).- 3.2 Vibrations of Isotropic Linearly Heterogeneous Half-Space under Action of Vertical Force Applied to Half-Space Surface.- 3.3 Vibrations of Isotropic Linearly Heterogeneous Half-Space under Action of Horizontal Force Applied to Half-Space Surface.- 3.4 DeterminingProperties of Linearly Heterogeneous Half-Space Using Characteristics of Surface Waves.- 3.5 Some Static Problems for Linearly Heterogeneous Half-Space.- 3.6 Dynamic Stiffness of Circular Disk Resting on Linearly Heterogeneous Half-Space.- 3.7 Vibrations of Linearly Heterogeneous Half-Space Subjected to Force Applied within Half-Space.- 3.8 Plane Problems for Linearly Heterogeneous Half-space.- 4. Mechanics of Transversely Isotropic Half-Space with Stiffness Varying Exponentially with Depth.- 4.1 Vibrations of Transversely Isotropic Half-Space Having Elastic Coefficients Bounded at Infinite Depth.- 4.2 Vibrations of Transversely Isotropic Half-Space with Stiffness Increasing without Bounds.- 5. Application of Numerical—Analytical Methods to Static and Dynamic Problems for Heterogeneous Half-Space.- 5.1 Introduction.- 5.2 Heterogeneous Half-Space Subjected to Vertical Force Applied to Half-Space Surface.- 5.3 Heterogeneous Half-Space Subjected to Horizontal Force Applied to Half-Space Surface.- 5.4 Vibration Problems for Heterogeneous Half-Space Subjected to Force Applied within Half-Space.- 5.5 Static solutions.- 5.6 Contact Problems for Circular Disk Resting on Half-Space with Stiffness Increasing with Depth by Power Law.- References.