Contents -- Foreword -- Preface -- 1 Introduction -- 1.1 Ground-Borne Vibrations -- 1.2 Analytical Approaches -- 1.2.1 Classical theory of wave propagation -- 1.2.2 Elastic medium subjected to moving loads -- 1.2.2.1 Elastic unbounded body subjected to a moving point load -- 1.2.2.2 Elastic half-space subjected to a moving line load -- 1.2.2.3 Elastic half-space subjected to a moving point load -- 1.2.3 Beam on elastic half-space subjected to moving loads -- 1.2.4 Tunnel structure subjected to moving loads -- 1.2.5 Load generation mechanism -- 1.3 Field Measurement -- 1.4 Empirical Prediction Models -- 1.5 Numerical Simulation -- 1.5.1 Two-dimensional modeling -- 1.5.2 2.5-dimensional modeling -- 1.6 Isolation of Ground Vibrations -- 1.6.1 Trenches -- 1.6.2 Wave impeding block -- 1.6.3 Floating slab track -- 1.7 Evaluation Criteria of Vibration -- 1.8 Concluding Remarks -- 2 Elastic Waves in Half-Space Due to Vehicular Loads -- 2.1 Introduction -- 2.2 Fundamentals of the Problem -- 2.2.1 Equation of motion -- 2.2.2 Triple Fourier transform -- 2.3 Solution for the Soil Response -- 2.3.1 Boundary conditions -- 2.3.2 Steady state response in time domain -- 2.4 Loading Functions for Moving Loads of Different Forms -- 2.4.1 General loading function of a moving train -- 2.4.2 Distribution function f(z) of the loading -- 2.4.2.1 Single point load -- 2.4.2.2 A uniformly distributed wheel load -- 2.4.2.3 An elastically distributed wheel load -- 2.4.2.4 A sequence of wheel loads -- 2.4.3 Interaction forces between wheels and rails -- 2.4.4 Calculation of inverse Fourier transform -- 2.5 Numerical Studies and Discussions -- 2.5.1 Verification of the present approach -- 2.5.2 Single moving point load -- 2.5.3 A uniformly distributed moving wheel load -- 2.5.4 An elastically distributed moving wheel load -- 2.5.5 A sequence of moving wheel loads.

2.6 Concluding Remarks -- 3 2D Finite/Infinite Element Method -- 3.1 Introduction -- 3.2 Formulation of the Problem -- 3.3 Shape Functions and Matrices of Infinite Element -- 3.3.1 Shape functions -- 3.3.2 Element matrices -- 3.3.3 Damping property of materials -- 3.3.4 Method of numerical integration -- 3.3.5 Selection of amplitude decay factor a -- 3.3.6 Selection of wave number k -- 3.4 Mesh Range and Element Size -- 3.5 Mesh Expansion by Dynamic Condensation -- 3.6 Numerical Examples -- 3.7 Concluding Remarks -- 4 Characteristics of Foundation Vibrations -- 4.1 Introduction -- 4.2 Dynamic Stiffness and Compliance of Foundation -- 4.3 Vibration of a Massless Rigid Strip Foundation -- 4.3.1 Effect of bedrock depth (H/B) -- 4.3.2 Effect of shear modulus ratio (G1/G2) of soil layers -- 4.3.3 Effect of Poisson's ratio -- 4.3.4 Effect of material damping ratio -- 4.4 Vibration of Rails and Ground under Harmonic Loads -- 4.5 Applications to Practical Problems -- 4.5.1 Problem 1: Uniform half-space -- 4.5.2 Problem 2: Soil deposit resting on bedrock -- 4.6 Concluding Remarks -- 5 Wave Barriers for Vibration Isolation of Foundations: Parametric Study -- 5.1 Introduction -- 5.2 Considerations in Parametric Studies -- 5.3 Vibration Isolation by Elastic Foundation -- 5.3.1 Young's modulus ratio (Es /Ee) -- 5.3.2 Mass density ratio ( rs / re) -- 5.3.3 Poisson's ratios ( ne, n) -- 5.3.4 Material damping ratio ( b) -- 5.3.5 Normalized dimensions (T, E) -- 5.3.6 Bedrock depth H -- 5.4 Vibration Isolation by Open Trenches -- 5.4.1 Distance L between the railway and open trench -- 5.4.2 Depth D and width W of open trench -- 5.5 Vibration Isolation by In-Filled Trenches -- 5.5.1 Distance L between the railway and in-filled trench -- 5.5.2 Material damping ratio b -- 5.5.3 Shear modulus ratio (Gsb/Gss) -- 5.5.4 Mass density ratio ( rb/ ).

5.5.5 Poisson's ratios ( nb, ns) -- 5.5.6 Depth D and width W of in-filled trench -- 5.6 Effect of Frequencies of Traffic Loads -- 5.7 Concluding Remarks -- 6 Vibration Reduction of Buildings Located Alongside Railways -- 6.1 Introduction -- 6.2 Problem Formulation and Basic Assumptions -- 6.3 Scheme for Generating Finite/Infinite Element Mesh -- 6.4 Parametric Studies for Open Trenches -- 6.4.1 Normalized distance L from the structure -- 6.4.2 Normalized depth D and width W of trench -- 6.5 Parametric Studies for In-Filled Trenches -- 6.5.1 Normalized distance L from the structure -- 6.5.2 Normalized depth D and width W of trench -- 6.5.3 Impedance ratio of in-filled trench -- 6.5.4 Poisson's ratios ( nb, ns) -- 6.6 Effect of Frequencies and Soil Conditions -- 6.6.1 Soil with no bedrock -- 6.6.2 Soil with bedrock -- 6.7 Concluding Remarks -- 7 2.5D Finite/Infinite Element Method -- 7.1 Introduction -- 7.2 Formulation of the Problem and Basic Assumptions -- 7.3 Procedure of Derivation for Finite/Infinite Elements -- 7.4 Wave Numbers for the Case with Moving Loads -- 7.5 Shape Functions of Infinite Element -- 7.6 Wave Propagation Properties for Different Vehicle Speeds -- 7.7 Selection of Element Size and Mesh Range -- 7.8 Selection of Wave Number k -- 7.9 Selection of Amplitude Decay Factor a of Displacement -- 7.10 Verification of the Present Approach -- 7.10.1 Responses in frequency domain for moving loads at sub-, trans- and super-critical speeds -- 7.10.2 Responses in frequency domain for moving loads with self oscillation -- 7.10.3 Effectiveness and accuracy of condensation procedure -- 7.10.4 Responses in time domain for sub-critical speed case -- 7.10.5 Responses in time domain for trans-critical speed case -- 7.11 Case Study -- 7.12 Concluding Remarks -- 8 Ground Vibration Due to Moving Loads: Parametric Study -- 8.1 Introduction.

8.2 Measurement of Vibration Attenuation for Soils -- 8.3 Problem Description and Element Meshes -- 8.4 Parametric Study for a Uniform Half-Space -- 8.4.1 Effect of shear wave speed -- 8.4.2 Effect of Poisson's ratio -- 8.4.3 Effect of damping ratio with no self oscillation -- 8.4.4 Effect of damping ratio for different oscillation frequencies -- 8.5 Parametric Study for Single Soil Layer Overlying a Bedrock -- 8.5.1 Effect of stratum depth for a quasi-static moving load -- 8.5.2 Effect of stratum depth for a moving load with self oscillation -- 8.5.3 Effect of self oscillation frequency -- 8.5.4 Effect of load-moving speed -- 8.6 Parametric Study for Multi Soil Layers -- 8.6.1 Effect of soil layers for a quasi-static moving load -- 8.6.2 Effect of soil layers for a moving load with self oscillation -- 8.6.3 Effect of load-moving speed for multi-layered soils -- 8.7 Concluding Remarks -- 9 Wave Barriers for Reduction of Train-Induced Vibrations: Parametric Study -- 9.1 Introduction -- 9.2 Major Considerations in Parametric Studies -- 9.3 Vibration Reduction by Open Trenches -- 9.3.1 Moving loads with no self oscillation -- 9.3.1.1 Effect of load-moving speed -- 9.3.1.2 Effect of trench depth -- 9.3.1.3 Effect of trench width -- 9.3.2 Moving loads with self oscillation -- 9.4 Vibration Reduction by In-Filled Trenches -- 9.4.1 Moving loads with no self oscillation -- 9.4.1.1 Effect of load-moving speed -- 9.4.1.2 Effect of trench depth -- 9.4.1.3 Effect of trench width -- 9.4.1.4 Effect of shear wave speed of trenches -- 9.4.2 Moving loads with self oscillation -- 9.5 Vibration Reduction by Wave Impeding Block -- 9.5.1 Moving loads with no self oscillation -- 9.5.1.1 Effect of load-moving speed -- 9.5.1.2 Effect of depth of WIB -- 9.5.1.3 Effect of thickness of WIB -- 9.5.1.4 Effect of shear wave speed of WIB -- 9.5.2 Moving loads with self oscillation.

9.6 Comparison and Discussion -- 9.7 Concluding Remarks -- 10 Soil Vibrations Caused by Underground Moving Trains -- 10.1 Introduction -- 10.2 Problem Formulation and Basic Assumptions -- 10.3 Formulation of 2.5D Finite/Infinite Element Method -- 10.4 Verification of the Present Approach -- 10.5 Numerical Modeling and Related Considerations -- 10.6 Parametric Study for an Underground Moving Train -- 10.6.1 Effect of number of carriages -- 10.6.2 Effect of load-moving speed -- 10.6.3 Effect of bedrock depth H -- 10.6.4 Effect of damping ratio -- 10.6.5 Effect of tunnel lining thickness -- 10.6.6 Effect of tunnel depth -- 10.7 Concluding Remarks -- Appendix Steady-State Response in Finite Integrals by Eason (1965) -- Bibliography -- Author Index -- Subject Index.