基于物质点方法饱和多孔介质动力学模拟(Ⅲ)--两相物质点方法

Material point method for dynamic analysis of saturated porous media (Ⅲ): two-phase material point method

在传统物质点方法的基础上发展了用于饱和多孔介质动力学分析的两相物质点方法(two-phase material point method,tMPM)。由于饱和多孔介质由固体骨架与孔隙流体组成,两相物质点方法通过引入两套物质点,分别表征固体骨架变形与孔隙流体流动。应用饱和多孔介质u-U形式控制方程,推导了两相物质点方法控制方程离散形式,以固相与液相位移作为基本未知量。采用同传统物质点方法相同的时间积分形式,两相物质点方法成功模拟了饱和多孔介质中固体骨架与孔隙流体间的相互作用;并且通过数值算例中两相物质点方法解与有限元参考解的比较验证了两相物质点方法的正确性。

Under the framework of the original material point method（MPM）,a two-phase MPM（tMPM） is proposed to predict the dynamic response of saturated porous media.Because the saturated porous media are composed of solid skeleton and pore fluid,two sets of material points are invoked in the tMPM,which represent the deformation of solid skeleton and pore fluid flow respectively.Based on the u-U form governing equations for saturated porous media,the discrete form of the tMPM is derived explicitly.Adopting the same time integration scheme as that used in the original MPM,the tMPM simulates the coupling behavior of saturated porous media successfully.Compared with the reference solution of the conventional FEM,the validity of the tMPM is demonstrated by the good agreement shown in numerical examples.