孔隙介质的时域BEM计算

根据Biot饱和孔隙介质动力方程，结合快、慢纵波解耦法得到时域Green函数U-P表达以及Somigliana表象积分，采用BEM分析了集中力作用下饱和孔隙介质时域动力响应.详细论述了孔隙介质时域边界积分方程的离散化方法与形式，它的Stokes状态解答和借用已有技术成果对计算奇异性的处理.在无量纲材料参数的数值分析计算中，以图表形式给出结果.由于孔隙介质的时域BEM计算在相关文献中较为罕见，因此文中结果会对两相饱和介质动力响应特性等相关研究提供一些新的途径.

Time-Domain BEM Calculation for Porodynamics

The boundary element method (BEM) in time domain was employed for the dynamic analysis of saturated porous media subjected to external forces. Based on Biot’s porodynamic equations, the U-P formulation of Green’s function obtained through decoupling of the fast and slow dilational waves, the transformation of Stokes’state as well as Somigliana’s representation, the discretization forms of the boundary integration equations in time domain were discussed in detail. Specially, with the aid of achievement for a single-phase medium, the singularity in the integration of the BEM for a porous medium was successfully treated in numerical implementation. Finally, in several examples, the response results of the displacements and pore pressures from numerical calculation with dimensionless material parameters were presented. Since the time-domain BEM calculation is hardly found in porodynamics as yet, the proposed method makes a new way for the research of dynamic response of 2 phase saturated porous media.