Surface wave propagation along the soil water interface in layered soil deposits overlaid by water was analytically investigated. Theoretical dispersion curves were determined to represent surface wave propagation and applied to interpret Spectral- Analysis-of Surface-Waves (SASW) measurements. Two solutions, the “2-dimensional (2-D)” and “3- dimensional (3-D)” solutions were applied to determine theoretical dispersion curves.
Normal modes of underwater systems assuming plane wave propagation in Cartesian coordinates were computed using the stiffness matrix approach, and referred to as the 2-D solution. Dispersion curves were determines by the modes corresponding to the fundamental Scholte wave. Although the dispersion curves from the 2-D were acceptable in many cases, there were often uncertainties in the 2-D solution for special cases involving the complex determinant, or exhibiting considerable contributions of higher modes to dispersion curves. From the studies examining these uncertainties, it was concluded that the 3-D solution needed to be applied to obtain valid results.
To compute the 3-D solution, waves were assumed to propagate with a curved wave front in cylindrical coordinates. The 3-D solution was then expressed as the inverse Hankel transform integral of the harmonic displacements excited by a disk load at the soil-water interface. The integrals were numerically evaluated using the “fast field” technique. Using the 3-D solution, rigorous dispersion curves were computed which considered contributions of higher modes and the experimental set up used in SASW measurements.
For both example and in situ cases, a series of parametric studies was performed to examine the applicability of each solution, and to study further the uncertainties in the 2-D solution using the 3-D solution. The following key conclusions were drawn based on the results from the parametric studies: (1) the dispersion curves from the 2-D solution were believed to be acceptable in cases where the soil was relatively soft and increased with depth; and (2) for other cases, the dispersion curves determined from the 2-D solution should be examined by the 3-D solution to check their validity.