非连续群桩屏障对平面P、SV波的隔离效应:二维宽频带间接边界积分方程法模拟

Isolation effect of discontinuous pile-group barriers on plane P and SV waves: Simulation based on 2D broadband indirect boundary integration equation method

采用一种高精度的间接边界积分方程法(IBIEM),对二维非连续群桩屏障对平面P、SV波的隔振效果进行宽频带计算分析。该方法基于单层位势理论,通过在非连续屏障交界面附近引入虚拟波源,分别用以构造散射体内、外散射场,继而由边界条件建立方程并求解得到虚拟波源密度,外部的总波场可由散射场和自由场叠加而得到。精度检验表明,该方法能够精确高效地求解任意排桩的宽频隔振问题。进而以圆柱实心桩为例,通过定量化频谱分析,揭示了P、SV波入射时排桩对不同频段弹性波的隔振差别,探讨了不同波速比、桩间距、桩排数对隔振效果的影响规律,研究结果表明:(1)隔振效果存在最优无量纲频段,宜优化设计桩径和桩间距以达到最佳效果;(2)场地土愈软,隔振效果愈佳。相比P波,SV波对于桩间距更为敏感;(3)低频波宜采用多排桩,但对高频波,采用三排以上的桩屏障对隔振效果的提升则不再显著。

An indirect boundary integration equation method（IBIEM） of high precision is used to analyze the vibration isolation effect of the two-dimensional discontinuous pile-group barriers on plane P and SV waves within a broad band of frequency. This method is based on the single layer potential theory, and the scattered field in vivo and vitro of the scatterer is constructed using the fictitious wave sources close to the surfaces of discontinuous barriers. The magnitude of the fictitious wave sources are determined by boundary conditions, while the total response can be obtained by the superposition of free field and scattered field. It is shown that the proposed method has excellent numerical accuracy in solving broadband isolation vibration problems related to arbitrary arranged piles. For the elastic cylindrical solid pile, the frequency spectrum is quantitatively analyzed, showing that different vibration isolation effects of elastic rowed piles are associated with different ranges of frequency with the incidence of P and SV waves. The vibration isolation effect for different wave velocity ratios, different distances of piles and different rows of piles are discussed, and it is shown that： 1） there exist optimal dimensionless frequencies for prominent vibration isolation effect; and thus it is necessary to carry out optimization design of pile diameter and pile spacing; 2） for softer soil, the isolation effect becomes better, and compared to P wave, SV waves is more sensitive to the pile spacing; 3） Multiple rows of piles should be adopted for low frequency waves, but for the high frequency wave, more than three rows of piles will not lead to significant improvement on the vibration isolation effect.