Abstract
Based on Biot’s saturated soil wave theory, using wave function expansion method, theoretical solutions of multiple scattering of plain P1waves 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 P1wave 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 atm=4; it is considered to select2.5≤sp/as≤3.0and2.5≤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.
Highlights
With the accelerated process of urbanization, cities have been expanding continuously
The screening effectiveness of P1 waves by single and multirow cavities has been calculated in numerical analysis, which concludes that
(1) Multiple scattering assumption compensates the defects of ignoring the wave coherent phenomenon of subsequent scattering in former analysis for it regarding the y/as
Summary
With the accelerated process of urbanization, cities have been expanding continuously. On account of its inaccuracy to assume the actual soil as monophasic medium, Cai et al [17, 18] theoretically solved elastic wave scattering problem by single-row discontinuous barrier in full space using Biot’s saturation equation. Xia et al [26, 27] proposed theoretical solutions of body waves’ scattering by arbitrarily arranged and shaped discontinuous barriers (solid and hollow piles) in singlephase medium by introducing the multiple scattering method firstly. Based on Biot’s poroelastic theory [28, 29] and multiple scattering method [23], with wave function expansion, this paper proposes the theoretical solution of multiple scattering under plane P1 wave incident when it confronts with arbitrarily arranged and arbitrary radius cavities in saturated soil. The normalized displacement amplitude behind the cavity barrier is numerically analyzed, which has certain engineering guiding significance for vibration isolation
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