Multiple Scattering of P1 Waves by Arbitrarily Arranged Cavities in Saturated Soils

Abstract

Based on Biot’s saturated soil wave theory, using wave function expansion method, theoretical solutions of multiple scattering of plain P1 waves are achieved by rows of cavities as barrier with arbitrarily arranged cavities in saturated soil. Undetermined complex coefficients after wave function expansion are obtained by cavities-soil stress and displacement free boundary conditions. Numerical examples are used to investigate variation of dimensionless displacement amplitude at the back and force of cavities barrier under P1 wave incident, and it is also discussed that the main parameters influenced isolation effect such as scattering orders, separation of cavities, distances between cavity rows, numbers of cavities, and arrangement of barriers. The results clearly demonstrate optimum design proposals with rows of cavities: with the multiple scattering order increases, the displacement amplitude tends to converge and the deviation caused by subsequent scattering cannot be neglected; it will obtain higher calculation accuracy when the order of scattering is truncated at m=4; it is considered to select 2.5≤sp/as≤3.0 and 2.5≤h/as≤3.5, while designing cavity spacing and row-distance, respectively. The isolation properties of elastic waves with rectangular arrangement (counterpoint) are weaker than that with hexagonal arrangement (counterchanged) when the row-distance of barrier is uniform.