移动荷载与土体中孔洞相互作用的2.5D边界元法分析

为了研究具有复杂表面的饱和土体与移动荷载相互作用机理,根据饱和土Biot理论,采用Fourier变换和势函数分解法,推导了饱和土体频域-波数内的Green函数;建立了移动荷载作用下,饱和土体中孔洞动力响应的频域-波数域内边界元法方程(2.5D boundary element methods);利用快速Fourier逆变换法,得到了时间-空间域内饱和土体的动力响应.研究结果表明:在频域内,利用移动荷载方向的一致性建立的频域-波数域内边界积分方程,可将3D空间问题转化为频域-波数域的2D平面问题, 3D边界元简化为2D边界元,使得计算面转换为计算线,减小了计算规模. 

Analysis of Dynamic Interaction between Hole Embedded in Saturated Soil and Moving Loads Using 2.5D Boundary Element Method

To study the mechanism of interaction between the saturated soil with complex surface and moving loads, a specific 2.5D boundary element method (BEM) for the problem of dynamic responses of the hole embedded in the saturated soil under a moving load was derived systematically. Based on Biot's theory, the frequency wave number domain Green's function for saturated porous media was developed using the Fourier transform method and the potential decomposition approach. Then, dynamic responses in the time-space domain solution were further obtained by synthesizing the wave number solution via inverse fast Fourier transform (IFFT). The results show that using the frequency wave-number boundary integrated equations established by the consistency of the directions of moving load, a 3D spatial model for the dynamic interaction between the holes embedded in the saturated soil with moving loads is convertible to a 2D planar model in the frequency domain, and the 3D complex boundary can be simplified to a problem of 2D boundary element. Thus, the complicated boundary planes can be transformed into computed lines using the 2.5D wave number domain BEM formulation, consequently reducing the amount of computation to a manageable size.