PFC2D学习指南：入门到进阶

PFC2D

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"PFC2D学校笔记：一个优秀的PFC2D初学者教程，包含对增强鱼缸（Augmented Fish Tank）的介绍及其在PFC2D中的应用" 本文档是针对PFC2D（Particle Flow Code in 2 Dimensions）的入门教程，适合初学者学习。PFC2D是一款基于离散元素方法（DEM，Discrete Element Method）的二维颗粒流模拟软件，用于模拟颗粒系统的力学行为，广泛应用于地质工程、矿业、材料科学等领域。在PFC2D中，"增强鱼缸"（Augmented Fish Tank）是一组由Itasca公司开发的内部算法集合，自1995年版本1.1发布以来，一直在其咨询项目中使用。这个工具的主要功能包括： 1. **创建合成固体**：通过将颗粒相互连接形成一个代表固体的颗粒集合，实现基于颗粒的建模。 2. **确定宏观性质**：通过对合成固体进行模拟实验测试，计算其相关的宏观物理属性。 3. **施加应力场**：在固体内部安装预设的应力场或在固体边界上施加应力条件。 4. **监测与可视化损伤**：监控并可视化固体内部的损伤形成过程。增强鱼缸提供这些算法服务，主要是因为大多数用户可能没有足够的时间或专业知识来自己构建类似的函数集。用户可以将它作为一个起点，专注于将基于颗粒的模型应用于特定的应用场景。这些算法的设计目标是面向熟悉计算机编程并对使用PFC2D解决实际问题感兴趣的用户。使用增强鱼缸，用户可以更高效地进行以下操作： - 创建复杂的颗粒结构模型，模拟真实世界的颗粒系统。 - 通过模拟实验，研究颗粒材料在不同加载条件下的行为，如应力、应变、破坏模式等。 - 实现动态加载和边界条件，以研究瞬态响应。 - 通过损伤和破坏的可视化，理解和解释实验结果。 PFC2D学校笔记通过介绍增强鱼缸这一核心组件，帮助初学者快速掌握PFC2D的基本用法和高级特性，为进一步深入研究颗粒系统的行为提供了一个实用的平台。通过不断实践和学习，用户将能够利用PFC2D解决各种工程问题，并对颗粒材料的力学性能有更深入的理解。

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3 - 16 FISH in PFC

(a)

(b)

Figure 3.2 Parallel-bond idealization (a), and forces carried in the bond ma-

terial (b)

A parallel bond is deﬁned by the following ﬁve parameters: normal and shear stiffnesses

and

[stress/displacement] (PROPERTY pb kn =

pb ks =

); normal and shear strengths ¯σ

and

¯τ

[stress] (PROPERTY pb nstr = ¯σ

pb sstr = ¯τ

); and bond radius

R. The bond radius is set by

specifying

λ (PROPERTY pb

radius =

λ) such that

R =

λ min



[A]

[B]



(3.13)

When either ¯σ or ¯τ exceeds the corresponding strength, the bond breaks.

The macroresponse of a parallel bond can be related to that of an elastic beam subject to pure axial

and pure shear loading. The beam cross-sectional area and moment of inertia can be expressed as

A =



Rt, (PFC

)

, (PFC

)

I =



t(2

, (PFC

)

3 π

, (PFC

)

(3.14)

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3 - 18 FISH in PFC

3.3.2.2 Strength

The values of parallel-bond normal and shear strengths, ¯σ

and ¯τ

, are speciﬁed in stress units.

Thus, there is a direct one-to-one correspondence between parallel-bond strengths and material

strengths. A scaling relation of the form of Eq. (3.10) is not necessary. It should be borne in mind

that a parallel bond can carry load in bending. The bending strength does not enter directly into the

parallel-bond formulation. Instead, bending load contributes to the maximum ﬁber stress carried

by the bond, and can thus induce a normal-mode failure. This bending-load contribution scales as

bond radius.

3.3.2.3 Microparameter Speciﬁcation

In addition to the deformability and strength microparameters, a parallel bond is also characterized

by its bond radius,

R. As the bond radius is reduced, the parallel bond experiences a decrease

in stiffness. Thus, reducing

R mimics the effect of reducing the amount of cement-like material

joining the two bonded particles.

The complete set of microparameters that characterizes a parallel-bonded material are given by

¯σ

(mean & std. dev.)

¯τ

(mean & std. dev.)

(parallel-bonded material) (3.17)

in which

λ is the radius multiplier used to set the parallel-bond radii via Eq. (3.13); E

is the

Young’s modulus at each particle-particle contact; k

is the ratio of particle normal to shear

stiffness;

is the Young’s modulus of each parallel bond;

is the ratio of parallel bond

normal to shear stiffness; µ is the particle friction coefﬁcient; and ¯σ

and ¯τ

are the normal and

shear strengths, respectively, of the cement-like material represented by a parallel bond. Note that

the three microparameters for particle-particle contact (E

, k

and µ) must also be speciﬁed in

addition to the ﬁve parallel-bond microparameters to characterize a parallel-bonded material.

The overall modulus at a parallel-bonded contact (at which the two bonded particles have a nonzero

overlap) is the sum of E

and

. When a parallel bond breaks, the overall modulus at the contact

is reduced by

. One can deﬁne a modulus-damage index as

PFC

Version 3.0

AUGMENTED FISHTANK 3-19

χ =

(3.18)

such that χ is a local measure of the damage, in terms of modulus reduction, that occurs when a

parallel bond breaks.

One can estimate the relation between the deformability microparameters and the macroscopic

modulus of a complete assembly using the relation

E =

(3.19)

in which ζ and

ζ are the ratios of micromodulus to macromodulus contribution for the particle-

particle contacts and the parallel bonds, respectively, and E is the macroscopic modulus. These

ratios can be estimated for a given particle system in which the majority of particles possess two

or more contacts to inhibit rolling of contact-bonded particle pairs, as follows. First, assign only

contact bonds (in which case,

= 0) and measure the modulus to obtain an estimate of ζ . Next,

assign only parallel bonds and measure the modulus to obtain an estimate of

ζ .

3.3.3 Unbonded Material Behavior

Particle-particle contact is characterized using a soft-contact approach in which a ﬁnite stiffness is

takento represent the measurable stiffnessthat existsat a contact. The deformability of an unbonded

material is described by the relations in Section 3.3.1.1. The strength of an unbonded material is

controlled by the particle size distribution, the material porosity and the particle friction coefﬁ-

cients. No general relation exists between particle friction angle and overall material friction angle.

However, the particular relation for a given particle assembly can be determined by performing a

set of biaxial tests upon the synthetic material.

The complete set of microparameters that characterizes an unbonded (granular) material are given

(unbonded material) (3.20)

in which n is the material porosity; E

is the Young’s modulus at each particle-particle contact;

is the ratio of particle normal to shear stiffness; and µ is the particle friction coefﬁcient.

(Alternatively, one can specify a Hertz-Mindlin contact law that enforces a nonlinear contact for-

mulation and is characterized by a different set of microparameters — see Section 2.1.2 in Theory

and Background.)

PFC

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3 - 20 FISH in PFC

3.3.4 Specimen-Genesis Procedure

The specimen-genesis procedure produces a rectangular specimen containing either a densely-

packed, bonded particle assembly with low locked-in stress or an unbonded particle assembly. The

microparameters used to characterize the short-term response of the synthetic material are given by

Eqs. (3.11), (3.17) and (3.20). The inputs to the specimen-genesis procedure can be divided into

those that control the specimen-genesis procedure (see Table 3.1), and those that deﬁne the PFC

material (see Eqs. (3.21) to (3.23) and Tables 3.2 to 3.4). The material strengths are picked from a

Gaussian (normal) distribution and are speciﬁed in terms of a mean and a standard deviation.

Note that the specimen porosity cannot be speciﬁed when creating bonded assemblies because it

is set automatically for such assemblies in the ﬁrst stage of the specimen-genesis procedure (see

below). The porosity of bonded assemblies can be increased by deleting particles from the densely-

packed specimen produced by these procedures. See ec

porosify in the ﬁle “et2.FIS” for an

examplethat creates discrete pore spaces within a densely-packedspecimen. Thespecimen porosity

can be speciﬁed when creating unbonded assemblies.

The naming convention for the sequence of models produced by the example driver ﬁles is shown in

Example 3.4. Three example data ﬁles that produce gross-resolution instances of contact-, parallel-

and un-bonded material-A are provided. All three ﬁles produce a PFC

specimen containing

539 particles and having a height of 63.4 mm and a width of 31.7 mm (see Figure 3.4). The

specimenhasa uniform particle-sizedistributionboundedby R

min

andR

max

, withR

max

= 1.66R

min

and R

min

= 0.75 mm. The “Agc.DVR” ﬁle (Example 3.5) creates a contact-bonded material,

the “Agp.DVR” ﬁle (Example 3.6) produces a parallel-bonded material, and the “Agu.DVR” ﬁle

(Example 3.7) produces an unbonded material. The material properties are chosen such that all

models should exhibit approximately the same initial modulus and both bonded models should

exhibit approximately the same peak strength. Thus, all materials are referred to as material-A.

Table 3.1 Parameters that control the specimen-genesis procedure

parameter description FISH name

h sample height [m] et2

ylen

w sample width [m] et2

xlen

min

minimum ball radius [m] et2 rlo

max

min

ball size ratio, uniform distribution [ ] et2

radius ratio

β wall normal stiffness multiplier [ ] md wEcfac

◦

locked-in isotropic stress [Pa] tm req isostr

min. number of contacts to be a non-ﬂoater [ ] flt def

/N remaining ﬂoaters ratio [ ] flt remain

PFC

Version 3.0

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