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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。
A two-phase material point method (tMPM) for dynamic analysis of saturated porous media was developed on the basis of traditional material point methods. As the saturated porous media consists of a solid framework and pore fluid, the two-phase material point method characterizes the deformation of the solid skeleton and the flow of the pore fluid by introducing two sets of material points. Using the governing equations of the u-U form of saturated porous media, the discrete form of the governing equations of the two-phase material point method is deduced, taking the solid and liquid displacements as the basic unknowns. By using the same method of time integration as the traditional material point method, the two-phase material point method successfully simulates the interaction between the solid skeleton and pore fluid in saturated porous media. And by the method of two-phase material point method and the finite element reference Solution comparison verifies the correctness of the two-phase material point method.