PFC3D 3.1 用户指南：三维粒子流代码详解

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"PFC3D 3.1 manual 是一个关于Particle Flow Code in 3 Dimensions (PFC3D) 的在线手册，包含了用户指南、命令参考、FISH语言指南、理论背景以及可选功能的详细内容。" PFC3D是一款强大的颗粒流代码，用于模拟三维环境中的颗粒系统，广泛应用于地质力学、材料科学、矿业工程等领域。这个3.1版本的手册提供了丰富的信息，帮助用户理解和应用该软件。 **用户指南**：手册的用户指南部分包括了对PFC3D的基本介绍、如何开始使用软件以及问题解决策略。Section 1: Introduction 引导用户了解PFC3D的基本概念和目的。Section 2: Getting Started 提供了软件安装、启动和界面导航的步骤。Section 3: Problem Solving with PFC3D 详述了如何利用PFC3D解决实际问题的策略和技巧。 **FISH语言**： FISH是PFC3D内置的一种脚本语言，用于编写控制和分析模型的程序。Section 4:FISH Beginner’s Guide 针对初学者介绍了FISH的基础知识，而Section 1: FISH Reference 则提供了更全面的函数和语法规则。Section 2: FISH Reference 包含了对所有可用FISH命令的详细解释，方便用户编写自定义脚本。Section 3: Augmented Fish Tank 和 Section 4: AC/DC Logic 进一步扩展了FISH的功能，提供了高级逻辑和适应性连续/离散逻辑。 **理论与背景**：这部分深入探讨了PFC3D的理论基础和实现细节。Section 1: General Formulation 描述了PFC3D的通用公式化方法。Section 2: Contact Constitutive Models 解释了接触本构模型，这是模拟颗粒间相互作用的关键。Section 3: Implementation Issues 讨论了在实际应用中可能遇到的问题和解决方法。Section 4: Clump Logic 和 Section 5: General Wall Logic 分别介绍了团簇逻辑和通用壁面逻辑，这些都是处理颗粒系统中复杂几何形状和边界条件的重要工具。 **可选功能**：手册还涵盖了PFC3D的一些高级特性。Section 1: Thermal Option 提供了热力学模拟的指导，Section 2: Fixed Coarse-Grid Fluid Scheme 描述了固定粗网格流体方案，用于处理颗粒与流体的相互作用。Section 3: User-Written C++ Code 说明了如何集成用户编写的C++代码以扩展PFC3D的功能。Section 4: Parallel Processing 介绍了并行处理能力，允许用户在多核或分布式计算环境中加速模拟。Section 5: Writing New Contact Models 指导用户创建自定义的接触模型，以适应特定的应用需求。Section 6: Post-processing 部分则讲述了结果的后处理和可视化方法。 PFC3D 3.1 manual 是一份详尽的参考资料，无论对于初学者还是经验丰富的用户，都能提供宝贵的指导和支持，帮助他们有效地利用PFC3D进行颗粒系统的模拟和分析。

User’s Guide Contents - 7

Figure 3.7 Convergence to an isotropic stress of −1.0 × 10

........................ 3-39

Figure 3.8 Contact logic ........................................................ 3-43

Figure 3.9 Bonding logic ....................................................... 3-43

Figure 3.10 Rolling without slip at a contact bond .................................. 3-44

Figure 3.11 Starting conﬁguration of particles for triaxial test ........................ 3-54

Figure 3.12 Axial deviatoric stress vs axial strain for elastic load/unload test .......... 3-60

Figure 3.13 Volumetric strain vs axial strain for elastic load/unload test ............... 3-61

Figure 3.14 Axial deviatoric stress and conﬁning stress vs axial strain for test on unbonded

granular material .................................................. 3-62

Figure 3.15 Axial deviatoric stress and conﬁning stress vs axial strain for test on bonded

granular material: contact-bond strength = 0.05 MN .................. 3-64

Figure 3.16 Axial deviatoric stress and conﬁning stress vs axial strain for test on bonded

granular material: contact-bond strength = 0.10 MN .................. 3-64

Figure 3.17 Volumetric strain vs axial strain for test on bonded granular material: contact-

bond strength = 0.05 MN .......................................... 3-65

Figure 3.18 Volumetric strain vs axial strain for test on bonded granular material: contact-

bond strength = 0.10 MN .......................................... 3-65

Figure 3.19 Axial deviatoric stress and conﬁning stress vs axial strain for test on bonded

granular material: parallel bonds .................................... 3-67

Figure 3.20 Volumetric strain vs axial strain for test on bonded granular material: parallel

bonds ............................................................ 3-67

Figure 3.21 Single joint with dip angle of -45

◦

, dip direction of 20

◦

and origin at x = 0.0,

y = 0.0, z = 2.0 .................................................... 3-71

Figure 3.22 Multiple joint planes in a PFC

model ................................ 3-72

Figure 3.23 Particle assembly within periodic space ................................. 3-77

Figure 3.24 Time history of isotropic stress ........................................ 3-78

Figure 3.25 Initial conﬁguration under gravity: contact forces shown ................. 3-88

Figure 3.26 Geometry after approximately 0.64 seconds of shaking ................... 3-90

Figure 3.27 Velocity histories at base, midpoint and top vs time ...................... 3-90

Figure 3.28 A small portion of a jointed rock mass .................................. 3-97

PFC

Version 3.1

Contents - 8 User’s Guide

EXAMPLES

Example 2.1 PFC

output from “TEST1.DAT” ................................... 2-9

Example 2.2 Creating and using a plot view ....................................... 2-12

Example 2.3 Specifying view parameters .......................................... 2-13

Example 2.4 Using macros ...................................................... 2-29

Example 2.5 Using line continuations ............................................. 2-30

Example 2.6 Using a named model object ......................................... 2-31

Example 2.7 Illustrating the behavior of RANGE, GROUP and MACRO model objects ... 2-32

Example 2.8 Using macros ...................................................... 2-33

Example 2.9 Creating new commands ............................................ 2-33

Example 2.10 Using different object types to do the same job ......................... 2-34

Example 2.11 Creating named ranges .............................................. 2-34

Example 2.12 Form of BALL command ............................................ 2-37

Example 2.13 Creating a mixture of two discrete particle sizes ........................ 2-39

Example 2.14 Conﬁning particles to an angled region ................................ 2-40

Example 2.15 Generating a hemispherical region of particles ......................... 2-41

Example 2.16 Expanding the radii to create a compacted assembly .................... 2-43

Example 2.17 Numerical test for angle of repose of a slope ........................... 2-48

Example 2.18 Footing composed of 16 balls ........................................ 2-54

Example 2.19 Stepping to initial equilibrium ....................................... 2-56

Example 2.20 Applying a footing load and monitoring the response ................... 2-61

Example 2.21 Excavate an unlined tunnel beneath the footing ........................ 2-64

Example 2.22 Excavate and install a lined tunnel beneath the footing .................. 2-65

Example 2.23 Using comments during model testing ................................ 2-77

Example 2.24 The GUI tutorial ﬁle “TRENCH1.DAT” ............................... 2-78

Example 3.1 Producing a planar hexagonal packing ................................ 3-7

Example 3.2 Creating a model with speciﬁed porosity by radius expansion ........... 3-12

Example 3.3 Creating a model with speciﬁed porosity by explosive repulsion ......... 3-14

Example 3.4 Creating a model with two size distributions by radius expansion ........ 3-16

Example 3.5 Creating clumps .................................................... 3-21

Example 3.6 Identify boundary balls and set their velocities ......................... 3-29

Example 3.7 Apply forces to boundary particles for equilibrium ..................... 3-31

Example 3.8 Apply mixed boundary conditions .................................... 3-33

Example 3.9 Obtaining a given isotropic stress state ................................ 3-36

Example 3.10 Nonlinear variation in friction coefﬁcient .............................. 3-47

Example 3.11 Creation and packing of particles ..................................... 3-51

Example 3.12 Servo-control and initial stress state .................................. 3-55

Example 3.13 Preparation for upcoming tests ....................................... 3-58

Example 3.14 Elastic load/unload test .............................................. 3-60

PFC

Version 3.1

User’s Guide Contents - 9

Example 3.15 Failure test, frictional strength only ................................... 3-61

Example 3.16 Failure test, friction and contact bonds-A .............................. 3-63

Example 3.17 Failure test, friction and contact bonds-B .............................. 3-63

Example 3.18 Failure test, friction and parallel bonds ................................ 3-66

Example 3.19 Create a single joint through sample .................................. 3-69

Example 3.20 Scaling of applied boundary forces ................................... 3-75

Example 3.21 FISH function to ﬁnd total reaction force on controlled particles ........ 3-76

Example 3.22 Creation and packing of particles in periodic space ..................... 3-78

Example 3.23 Obtaining isotropic stress state in periodic space ....................... 3-82

Example 3.24 FISH function to delete escaping particles ............................ 3-85

Example 3.25 Initial static equilibrium of a structure made of “beams” ................ 3-87

Example 3.26 Dynamic excitation of the structure ................................... 3-89

Example 4.1 Deﬁning a FISH function ........................................... 4-2

Example 4.2 Using a variable .................................................... 4-3

Example 4.3 SETting variables ................................................... 4-3

Example 4.4 Test your understanding of function and variable names ................ 4-4

Example 4.5 Capturing the history of a FISH variable .............................. 4-4

Example 4.6 Using symbolic constants in a FISH function .......................... 4-6

Example 4.7 Controlled loop in FISH ............................................ 4-7

Example 4.8 Manipulating variables in a loop construct ............................. 4-8

Example 4.9 Splitting lines ...................................................... 4-8

Example 4.10 Variable types ...................................................... 4-9

Example 4.11 Action of the IF ELSE ENDIF construct ................................ 4-10

Example 4.12 Use of the COMMAND – ENDCOMMAND construct ...................... 4-10

Example 5.1 Benchmark data ﬁle — “timing.DAT” ................................ 5-1

PFC

Version 3.1

INTRODUCTION 1-1

1 INTRODUCTION

1.1 Background and Overview

PFC

models the movement and interaction of spherical particles by the distinct element method

(DEM), as described by Cundall and Strack (1979). The original application of this method was as a

tool to perform research into the behavior of granular material; representative elements containing

several hundred particles were tested numerically. The particle model was used to understand

element behavior (in which conditions are “uniform”), and a continuum method was used to solve

real problems that involve complicated deformation patterns (with the element behavior derived

from the particle-model tests). Two factors have brought about a change in this approach. First, the

task of deriving general constitutive laws from test results on particle assemblies is very difﬁcult.

Second, with thespectacular increase in power ofsmall computers, it is now possible to model entire

problems with particles; the constitutive behavior is built into the model automatically. PFC

designed to be an efﬁcient tool to model complicated problems in solid mechanics and granular

ﬂow.

A physical problem that is concerned with the movement and interaction of spherical particles may

be modeled directly by PFC

. It is also possible to create particles of arbitrary shape by attaching

two or more particles together, such that each group of particles acts as an autonomous object

(using the clump logic described in Section 4 in Theory and Background). PFC

is also able

to model a brittle solid, by bonding every particle to its neighbor; the resulting assembly can be

regarded as a “solid” that has elastic properties and is capable of “fracturing” when bonds break

in a progressive manner. PFC

contains extensive logic to facilitate the modeling of solids as

closely packed assemblies of bonded particles (much of this logic has been implemented in the

Augmented FishTank — a set of functions written in FISH, the PFC

embedded language — see

Section 3 in the FISH volume); the solid may be homogeneous, or it may be divided into a number

of discrete regions or blocks. This type of physical system may also be modeled by the distinct

element programs UDEC (Itasca 2004) and 3DEC (Itasca 2003), which deal with angular blocks.

However, PFC

has three advantages. First, it is potentially more efﬁcient, since contact detection

between circular objects is much simpler than contact detection between angular objects; second,

there is essentially no limit to the magnitude of displacement that can be modeled; and third, it

is possible for the blocks to break (since they are composed of bonded particles), unlike blocks

modeled with UDEC or 3DEC which cannot break. The drawback to modeling a blocky system

with PFC

is that block boundaries are not planar; in exchange for the advantages offered by

PFC

, the user must accept “bumpy” boundaries.

The speciﬁcation of the geometry, properties and solution conditions is not as straightforward in

PFC

as in programs such as FLAC (Itasca 2005) and UDEC. For example, with a continuum

program, a grid is created, initial stresses installed, and boundaries set as ﬁxed or free. In a

particle code such as PFC

, a compacted state cannot be pre-speciﬁed in general, since there is no

unique way to pack a number of particles within a given volume. A process analogous to physical

compaction must be followed until the required porosity is obtained. The initial stress state cannot

be speciﬁed independent of the initial packing since contact forces arise from the relative positions

of particles. Finally, the setting of boundary conditions is more complicated than for a continuum

program because the boundary does not consist of planar surfaces. These issues are all addressed in

PFC

Version 3.1

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