Studies On Effective Phase Velocity Of Surface Waves

In this paper, the dispersions and displacements of modes of Rayleigh waves for a layered half space system are calculated from eigenvalue analysis of the assembly stiffness matrix of the layered system with a rigid base. The thickness of mini layers and position for the rigid base are related to the minimum and maximum of the interested wavelength range respectively. The criteria for filtering out Rayleigh wave modes from surface wave modes of the layered system with the rigid base are given. Influences of the layered soil properties such as shear velocity; thickness; density; Poisson's ratio and damping coefficient on dispersions of Rayleigh wave modes are discussed. The phase velocities approach to the shear velocity of the bottom layer for lower frequencies and to the shear velocity of the softest layer for higher frequencies. The approximation is analyzed by the rate of energy transmission in layer.The discrete solution of displacement is expressed in the form of Hankel and Bessel functions under harmonic loading for axisymmetric case. The conditions for forming the harmonic mode waves are analyzed from approximation expressions of Bessel and Hankel functions. If propagating distance is greater than the wavelengths of mode waves, the mode waves are harmonic. The phase velocities obtained from surface wave testing are actually the phase velocities of superposition of the different mode waves. The superposition waves are not harmonic even if the mode waves are harmonic, the effective phase velocities of superposition waves vary with propagation distance. Based on the analytical displacement solution of surface particles, the effective phase velocities are derived from spectral analysis of surface waves. The relationship between the effective velocity and the soil layer properties, positions for the source and transducers is established, and influences of these parameters on the effective velocities are discussed. Different from the approach of phase velocities of mode waves, the effective velocities approach the shear velocity of surface layer in high frequencies, that is, the properties of the deeper layers have less influence on the effective velocities in high frequencies. The approach is analyzed from energy distribution of the superposition waves in layers. Compared with the effective velocity analysis on wave theory, the experience analyses such as the half wavelength technique are discussed. In conventional testing of surface waves, data are analyzed on plane wave theory. The source and the transducers are set in some ways, and data are filtered by some criteria. Dependence on the data filtering criteria can be reduced or even avoided with the effective velocity calculation on axisymmetric wave field. The analysis is examined with the finite element simulation, and feasibility is confirmed. The analysis is also applied to in-situ testing of surface waves.Finally, influences of frequency resolution and wave reflection on phase velocity calculation are discussed. The frequency zooming and reflection cutting techniques are presented. Influences of frequency-amplitude and frequency-phase characters of transducer on the spectral analysis are analyzed. The rectifying method for phase velocity curve is presented when data quality is poor in lower frequencies...