Vibration Reduction with Rows of Arbitrarily Arranged Elastic Piles in Saturated Soil by Multiple Scattering Method

Abstract

An analytical solution of elastic waves scattered by a series of arbitrarily arranged cylindrical piles in saturated soils is achieved based on Biot’s poroelastic theory and multiple scattering method in acoustics and electromagnetics. The elastic waves are expanded by cylindrical functions with undetermined complex coefficients, and the first order of scattering is satisfied with the boundary conditions at the certain pile; therefore, the coefficients of the first-order scattering are obtained. Subsequently, regarding the first order of scattering waves as the secondary excitation to the remaining piles, it is also contented with required boundary conditions; thus, the second order of undetermined complex coefficients are acquired by generalized Graf’s addition theorem. The successive scattering could be repeated as the same manner. The vibration reduction of elastic waves by rows of piles is calculated. The numerical results demonstrate that the defection of neglecting subsequent scattering waves’ coherence has been corrected by considering scattering waves as every secondary wave source in multiple scattering theory. It is also discussed the main parameters influencing the vibration reduction effect such as scattering orders, separations between piles, distances between pile rows, shear modulus ratio of pile and soil and barrier size, and several significant suggestions of optimal design are concluded.