Mechanics of Non-Homogeneous and Anisotropic Foundations

ISBN-13: 9783642536021 / Angielski / Miękka / 2012 / 364 str.

B. Grigori Muravskii;B. Krasovitski

Opis

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.

Spis treści

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.- 1.5.1 Action of Vertical Force.- 1.5.2 Action of Horizontal Force.- 1.6 Application of Functions Related to Dilatation and Rotation of Displacement Field.- 1.6.1 Vertical Force Applied within Half-Space.- 1.6.2 Horizontal Force Applied within Half-Space.- 1.7 Application of Superposition Principle to Loadings of Rectangular and Circular Domains.- 1.7.1 Vertical Load Distributed Uniformly over Rectangular Domain.- 1.7.2 Horizontal Load Distributed Uniformly over Rectangular Domain.- 1.7.3 Vertical Load Distributed Uniformly over Circular Domain.- 1.7.4 Horizontal Load Distributed Uniformly over Circular Domain.- 1.7.5 Axisymmetric Radial Load Applied to Circular Domain.- 1.7.6 Antisymmetric Vertical Load Applied to Circular Domain.- 1.7.7 Horizontal Load Acting in Tangential Direction.- 1.7.8 Self-Balanced Horizontal Load.- 1.7.9 Loading of Infmite Strip.- 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.- 2.1.1 Static Action of Vertical Force.- 2.1.2 Free Vibrations of Half-Space.- 2.1.3 Forced Vibrations of Half-Space.- 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.- 2.3.1 Static Action of Horizontal Force.- 2.3.2 Analysis of Amplitudes of Vibrations.- 2.4 Torsional Vibrations of Half-Space.- 2.5 Action of Force Applied in Infinite Space.- 2.5.1 Action of Vertical Force.- 2.5.2 Action of Horizontal Force.- 2.6 Vibrations of Transversely Isotropic Half-Space under Action of Force Applied within Half-Space.- 2.6.1 Action of Vertical Force.- 2.6.2 Action of Horizontal Force.- 2.7 Contact Problems for Transversely Isotropic Half-Space.- 2.7.1 Static Stiffnesses for Circular Disk on Transversely Isotropic Half-Space.- 2.7.2 Dynamic Stiffnesses for Circular Disk on Transversely Isotropic Half-Space.- 2.8 Plane Problems for Transversely Isotropic Half-Space.- 2.8.1 Action of Vertical Load Distributed Uniformly along Infmite Line on Half-Space Surface.- 2.8.2 Action of Horizontal Load Distributed Uniformly along Infmite Line on Half-Space Surface.- 2.8.3. Contact Problems for Strip Stamp.- 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 Determining Properties of Linearly Heterogeneous Half-Space Using Characteristics of Surface Waves.- 3.4.1 Application of Solution Related to Vertical Vibrations of Half-Space Surface under Action of Vertical Force.- 3.4.2 Application of Solution Related to Horizontal Vibrations of Half-Space Surface under Action of Horizontal Force.- 3.5 Some Static Problems for Linearly Heterogeneous Half-Space.- 3.5.1 Displacements of Half-Space Surface under Action of Surface Concentrated Forces.- 3.5.2 Static Stiffnesses for Circular Disk Resting on Isotropic 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.- 3.7.1 Action of Vertical Force.- 3.7.2 Action of Horizontal Force.- 3.8 Plane Problems for Linearly Heterogeneous Half-space.- 3.8.1 Action of Vertical Load Distributed Uniformly over Infinite Straight Line on Half-Space Surface.- 3.8.2 Action of Horizontal Load Distributed Uniformly over Infmite Straight Line on Half-Space Surface.- 3.8.3 Static Surface Green’s Functions in 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.- 4.1.1 Variation of Elastic Parameters of Half-Space with Depth.- 4.1.2 Construction of Fundamental Solutions.- 4.1.3 Vibrations of Half-Space under Action of Vertical Force Applied to Half-Space Surface.- 4.1.4 Vibrations of Half-Space under Action of Horizontal Force Applied to Half-Space Surface.- 4.2 Vibrations of Transversely Isotropic Half-Space with Stiffness Increasing without Bounds.- 4.2.1 Varying of Elastic Parameters of Half-Space with Depth.- 4.2.2 Construction of Fundamental Solutions.- 4.2.3 Vibrations of Half-Space under Action of Vertical Force Applied to Half-Space Surface.- 4.2.4 Vibrations of Half-Space under Action of Horizontal Force Applied to Half-Space Surface.- 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.- 5.2.1 Application of Thin Layer Technique for Numerical Solution of Differential Equations.- 5.2.2 Application of Runge-Kutta Method for Numerical Solution of Differential Equations.- 5.2.3 Parameter Determination for Isotropic Half-Space with Shear Modulus Varying by Power Law (Action of Vertical Force).- 5.3 Heterogeneous Half-Space Subjected to Horizontal Force Applied to Half-Space Surface.- 5.3.1 Application of Thin Layer Technique for Numerical Solution of Differential Equations.- 5.3.2 Application of Runge-Kutta Method for Numerical Solution of Differential Equations.- 5.3.3 Parameter Determination for Isotropic Half-Space with Shear Modulus Varying by Power Law (Action of Horizontal Force).- 5.4 Vibration Problems for Heterogeneous Half-Space Subjected to Force Applied within Half-Space.- 5.4.1 Action of Vertical Force. Application of Thin Layer Technique for Numerical Solution of Differential Equations.- 5.4.2 Action of Vertical Force. Application of Runge—Kutta Method for Numerical Solution of Differential Equations.- 5.4.3 Action of Horizontal Force. Application of Thin Layer Technique for Numerical Solution of Differential Equations.- 5.4.4 Action of Horizontal Force. Application of Runge—Kutta Method for Numerical Solution of Differential Equations.- 5.5 Static solutions.- 5.6 Contact Problems for Circular Disk Resting on Half-Space with Stiffness Increasing with Depth by Power Law.- 5.6.1 Static Stiffnesses for Circular Disk.- 5.6.2 Dynamic Stiffnesses for Circular Disk.- References.

Blurb

This book contains new results in the area of statics and dynamics of heterogeneous and anisotropic foundations. The book is directed at engineers and scientists in the area of soil mechanics, soil-structures interaction, seismology and geophysics. Some characteristic features of the book are the construction of general solutions of harmonic vibrations in the transversely isotropic half-space and the presentation of new analytic solutions relating to the homogeneous transversely isotropic elastic half-space subjected to the action of external forces or for half-spaces with stiffness varying exponentially with depth. Numerical-analytical methods for the considered problems of static and dynamic interactions between a deformable foundation and structures are presented as well. The book also presents a large number of computational results which give a clear picture of the behavior of the presented rock and soil foundation systems.