论文总字数：79771字

摘 要

随着计算机技术的不断进步，越来越多的采用不同计算原理的数值计算方法被应用到了实际工程中。有限元连续方法计算速度快，但不能完全准确反映岩土类材料性质，颗粒离散元非连续方法对岩土类材料模拟更准确，但计算规模大、运行效率低。将离散元与有限元模型协同，在不同区域采用不同的模拟方法，能够减少以上两种模拟方法缺点的影响，同时使二者的优点互补。通过接触界面协同连续-非连续模型，可以充分利用离散元大变形分析特点，也可借助有限元法的计算效率减少了模拟计算的时间成本。

本文提出了一种能够适用于复杂协同接触界面的三维连续（有限差分法FLAC^3D）-非连续（颗粒离散元方法PFC^3D）数值模型协同计算方法。首先总结了有限差分法和颗粒离散元法的计算原理，提出了复杂协同界面上离散元颗粒和有限差分单元表面接触力的计算方法。整理归纳了协同计算的流程与算法要求，针对软件特点设计了模型间数据的通信协议。实现了全域搜索、局域搜索和复杂协同界面上接触力分配三个基本模块。全域搜索模块完成了空间网格的划分，建立了能够快速检索的数据结构。局域搜索基于全域搜索建立的空间网格信息，完成了颗粒与差分单元表面的接触判断。提出了复杂协同界面条件下接触力计算与分配方法。进一步将协同算法在PFC^3D和FLAC^3D软件中用FISH语言实现与验证。建立单颗粒模型验证了法向接触力和切向接触力计算的准确性，模拟竖向加载试验验证了力的传递，建立柱形界面模型验证了复杂协同界面上两种模型变形的协调性。

关键词：数值模拟，颗粒离散元，有限差分法，协同计算，复杂接触界面

Abstract

With the continuous advancement of computer technology, more and more numerical calculation methods using different calculation principles have been applied to practical engineering. The finite element continuous method has a fast calculation speed, but it cannot completely reflect the properties of geotechnical materials. The particle discrete element discontinuous method is more accurate for simulating geotechnical materials, but the calculation scale is large and the operation efficiency is low. Combining discrete elements with finite element models and using different simulation methods in different regions can reduce the effects of the two simulation methods’ disadvantages, and at the same time complement the advantages of the two. Through the contact interface collaborative continuous-discontinuous model, the discrete element large deformation analysis characteristics can be fully utilized, and the computational efficiency of the finite element method can be used to reduce the time cost of the simulation calculation.

This paper proposes a three-dimensional continuous (finite difference method FLAC^3D)-discontinuous (particle discrete element method PFC^3D) numerical model collaborative calculation method that can be applied to complex collaborative contact interfaces. Firstly, the calculation principles of finite difference method and particle discrete element method are summarized. The calculation method of surface contact force between discrete element particles and finite difference elements on complex cooperative interface is proposed. The process and algorithm requirements of collaborative computing are summarized and the communication protocol of data between models is designed for the characteristics of software. Three basic modules of contact force distribution on global search, local search and complex collaborative interface are realized. The global search module completes the division of the spatial grid and establishes a data structure that can be quickly retrieved. The local search is based on the spatial grid information established by the global search, and the contact judgment between the particles and the surface of the differential unit is completed. A method for calculating and distributing contact force under complex collaborative interface conditions is proposed. The collaborative algorithm is further implemented and verified in the FFC language in PFC3D and FLAC3D software. The single particle model was established to verify the accuracy of the normal contact force and the tangential contact force calculation. The vertical load test was used to verify the force transfer. The cylindrical interface model was established to verify the coordination of the two models on the complex collaborative interface.

KEY WORDS: numerical simulation, particle discrete element, finite difference method, cooperative calculation, complex contact interface

目 录

摘 要 I

Abstract II

第一章 绪论 1

1.1 引言 1

1.2 国内外研究现状 2

1.2.1 数值模拟技术在岩土工程中的应用 2

1.2.2 有限元方法的发展 2

1.2.3 离散元算法的发展 2

1.2.4 连续-非连续协同模型与协同计算 3

1.2.5 离散元算法的基本原理 3

1.3 论文主要内容及技术路线 4

1.3.1 论文主要内容 4

1.3.2 技术路线 5

第二章 PFC3D与FLAC3D协同算法 6

2.1 理论基础 6

2.1.1 软件介绍 6

2.1.2 协同计算基础 6

2.2 算法分析 6

2.2.1 协同计算流程 6

2.2.2 算法要求 8

2.2.3 模型通信协议 9

2.3 离散元与有限元协同算法 10

2.3.1 全域搜索 10

2.3.2 局域搜索 15

2.3.3 颗粒与有限差分单元表面的接触力 21

第三章 算法验证 29

3.1 单颗粒算法验证 29

3.1.1 法向接触力验证 29

3.1.2 切向接触力验证 31

3.2 竖向加载试验验证 33

3.3 柱形截面协同模拟 36

第四章 总结与展望 40

4.1 成果总结 40

4.2 展望 41

4.2.1 存在的问题 41

4.2.2 改进方向 41

参考文献 43

附录：程序代码 45

致谢 64

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