Coupled material point method and characteristic finite element method for saturated porous media
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摘要: 物质点法是当下用于分析饱和孔隙介质大变形问题的常用手段。然而，传统的显式物质点法直接采用弱可压缩的泊松方程计算孔隙水压力，存在着孔隙水压力震荡以及压力边界难以施加等问题。鉴于此，提出了一个适用于饱和孔隙介质的耦合物质点-特征有限元方法。该算法将孔隙水视为不可压缩流体，基于特征线分裂算法的思想，将存在对流项的液相动量方程采用特征线法进行时间离散，并利用投影法分步计算固、液相中的压力和速度。应用此算法对一维饱和土柱的固结以及二维弹性地基中波的传播问题进行了数值模拟，所得结果与参考解基本相一致。计算结果表明新算法可以很好地克服显式物质点法在计算固结问题时产生的孔隙水压力震荡现象。Abstract: The material point method (MPM) is a common approach to analyze the large deformation of the saturated porous media. However, the pore pressure oscillations caused by the weak-compressibility fluid, and the complication to apply the pressure boundary are the main challenges in the conventional explicit MPM. In this study, a novel algorithm, which couples the MPM and characteristic finite element method (FEM) for the saturated porous media with the incompressible fluid, is proposed. Inspired by the characteristic-based split (CBS) method, the characteristic-based procedure is applied to the temporal discretion of the fluid momentum equation to avoid the instability induced by the convective term, and the projection method is introduced to split the velocity and pressure in the solid and fluid phases. Several numerical tests, involving the consolidation of one-dimensional saturated soil column and the wave propagation in two-dimensional elastic foundation, are conducted to examine the performance of the proposed method. The simulated results agree with the reference solutions, which indicates that the new algorithm can greatly overcome the water pressure oscillation of the consolidation problem in comparison with the explicit MPM.
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图 2 不同时刻孔隙水压力沿深度的分布
Figure 2. Distribution of pore water pressure along height at different time
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图 3 土柱中部孔隙水压力随时间的消散曲线
Figure 3. Dissipation curves of pore water pressure at middle of soil column
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图 4 大变形条件下孔隙水压力沿深度随时间的分布
Figure 4. Distribution of pore water pressure along height with time under large deformation
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图 5 小渗透系数下初始固结阶段孔压的分布
Figure 5. Distribution of pore pressure at initial consolidation stage with small permeability coefficient
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