任意排列的空心管桩屏障对SH波的多重散射

提出1种可计算任意排列、任意圆截面尺寸的多排空心管桩对平面SH波多重散射的理论求解方法。考虑第1重散射即为通常所谓的单重散射,对特定管桩第2重散射的入射波为在各管桩所受的第1重散射波之和,亦即第1重散射所激发的次生波源,以此类推至第m重散射。假设每重散射在桩-土边界以及管桩内部均满足弹性边界条件,将入射波、散射波及透射波采用波函数展开,并运用Graf加法定理移轴获得待定的各重散(透)射复系数,得到总散射及管桩内部透射波场的理论解。算例中讨论了散射重数、桩径与桩(排)间距之比、桩-土剪切模量之比、管桩内外径之比以及多排管桩的几何参数等对屏障隔离效果的影响,结果表明,管桩可取得比实心桩更好的屏蔽效果,同时对管桩非连续屏障的工程设计提供了有价值的理论参考依据。

Multiple scattering of SH waves by rows of arbitrarily arranged tubular piles

A theoretical methodology which can calculate multiple scattering of plane SH waves by arbitrarily arranged and configuration of multi-row tubular piles is achieved. It can be considered the commonly so-called single scattering as the first order of multiple scattering. The second order of scattering of certain tubular pile is derived from incident waves which are excited from the first order of scattering by all tubular piles, which are also be regarded as the secondary waves by the first scattering. The rest scattering process of multiple order can be considered in the same manner. Assuming that every scattering order at pile-soil interface and interior of tubular pile are satisfied the elastic boundary conditions, the incident, scattering and transmitted waves are expanded in wave functions with Graf’s addition theorem so that the undetermined scattering (transmitted) complex coefficients are obtained. Theoretical solutions of total scattering and transmitted wave fields inside the tubular piles are achieved. The influences of multiple scattering orders, ratios of the pile radius and distance between piles (or pile rows), shear modulus ratios of pile and soil, ratios of internal and external radius of tubular piles, geometric parameters of multi-row tubular piles etc. on screening effectiveness is discussed with numerical examples. The results show that tubular piles can achieve better screening effects than solid piles do. Several valuable reference bases of engineering design with discontinuous barriers made by tubular piles are delivered consequently.