一种模拟土体流动的连续体数值方法

Continuum approach for modelling soil flow in geotechnical engineering

介绍了一种先进的能够处理土体流动问题的连续体数值模拟方法——粒子有限元法(PFEM)。这一方法不仅继承了传统有限元法扎实的数学理论基础(即每一个增量步分析均为经典拉格朗日有限元分析过程),同时还能绕开在大变形情况下由于固定网格拓扑结构带来的计算困难。详细阐述了粒子有限元法的基本思想以及如何基于已有的有限元法程序发展粒子有限元法,并揭示了粒子有限元法中的几个关键性技术。为验证粒子有限元法的准确性并展示其先进性,采用粒子有限元法模拟了准静态和动态颗粒柱的坍塌问题以及边坡稳定性问题。模拟结果表明:粒子有限元法特别适合于模拟包含岩土材料流固转换行为的大变形工程问题。

A novel continuum approach called particle finite element method（PFEM） which is capable of modelling soil flow in geotechnical engineering is introduced. This approach inherits the solid mathematical foundation of the traditional finite element method in the sense that each incremental analysis is conducted via the classical Lagrangian finite element procedure and also circumvents the computational difficulties resulting from the meshes with fixed geometric topology in the case of large deformations. This paper details the fundamental idea of the PFEM as well as how to develop the PFEM based on an existing finite element program with some key technologies being discovered. To verify its correctness and exhibit its advantages, the PFEM is utilized to simulate the quasi-static and dynamic collapse of granular columns and slope stability problems. It is shown that the PFEM is particularly suitable for the simulation of engineering problems involving solid-fluid transitional behaviour of geomaterials.