饱和土-结构相互作用稳定两相接触MPM算法
Development of a stable two-phase contact MPM algorithm for saturated soil-structure interaction problems
摘要：
涉及两相材料的土与结构相互作用问题的模拟对岩土工程提出了重大挑战。这些挑战是由于材料刚度的差异、多相之间的相互作用、孔隙流体的高体积模量和低渗透性而出现的。传统的显式时间积分方法受其条件稳定性的限制，需要小的时间步长，并导致快速加载条件下的压力振荡。为了解决这些问题，我们提出了一个稳定的两相接触算法内的物质点法（MPM）框架内的土-结构相互作用问题。我们的算法模拟土壤作为一个完全饱和的多孔介质不可压缩的孔隙流体。我们介绍了传统的MPM方法的三个主要进步。我们采用Chorin的投影方法来解决耦合配方和减少数值振荡。通过隐式处理扩散项，我们的算法允许更大的稳定时间步长，独立于孔隙流体的体积模量和渗透率。最后，我们整合了一个刚性的算法来精确地建立实体模型和一个精确的接触检测算法。我们提供了详细的配方和时间增量过程的两相接触MPM算法。此外，我们比较了所提出的算法与有限元法（FEM）和显式MPM，以评估其精度和性能在模拟耦合流体力学问题。两相接触算法为土-结构相互作用问题的模拟提供了一种更稳定、更有效的方法。
英文摘要：
The simulation of soil-structure interaction problems involving two-phase materials poses significant challenges in geotechnical engineering. These challenges arise due to differences in material stiffnesses, the interaction between multiple phases, high bulk modulus of pore fluid, and low permeability. The conventional explicit time integration scheme is limited by its conditional stability, necessitating small time step sizes and resulting in pressure oscillations under rapid loading conditions. To address these issues, we propose a stable two-phase contact algorithm within the Material Point Method (MPM) framework for soil-structure interaction problems. Our algorithm models the soil as a fully saturated porous media with incompressible pore fluid. We introduce three main advancements over conventional MPM methods. We employ Chorin's projection method to solve coupled formulations and reduce numerical oscillations. By implicitly handling a diffusion term, our algorithm permits larger stable time step sizes, independent of the bulk modulus and permeability of the pore fluid. Lastly, We integrate a rigid algorithm to model solid bodies accurately and a precise contact detection algorithm. We provide detailed formulations and time increment processes of the two-phase contact MPM algorithm. Furthermore, we compare the proposed algorithm with Finite Element Method (FEM) and explicit MPM to assess its accuracy and performance in simulating coupled hydro-mechanical problems. The two-phase contact algorithm offers a more stable and efficient approach to simulate soil-structure interaction problems.
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