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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (2): 348-357    DOI: 10.3785/j.issn.1008-973X.2021.02.015
土木工程、交通工程     
基于FDEM的岩石颗粒破碎后碎片形状的统计分析
周剑1(),马刚1,*(),周伟1,程勇刚1,黄泉水1,曹学兴2
1. 武汉大学 水资源与水电工程科学国家重点实验室，湖北 武汉 430072
2. 华能澜沧江水电股份有限公司，云南 昆明 650214
Statistical analysis of fragment shape of rock grain after crushing based on FDEM
Jian ZHOU1(),Gang MA1,*(),Wei ZHOU1,Yong-gang CHENG1,Quan-shui HUANG1,Xue-xing CAO2
1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2. Huaneng Lancang River Hydropower Inc, Kunming 650214, China
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摘要：

针对碎片尺寸和形状会影响岩石强度和变形的问题，采用三维扫描技术获得真实岩石颗粒的表面点云数据，然后通过数字图像处理技术重构数字颗粒，利用连续-离散耦合方法（FDEM）模拟单个颗粒在平板压缩下的断裂破碎. 识别颗粒破碎后所产生的碎片，并进行碎片形状的表征和量化，分析碎片形状与颗粒初始形状、碎片尺寸的关系. 为了准确描述裂纹尖端的应力梯度和损伤演化，进行颗粒有限元网格密度的敏感性分析，结果表明，断裂过程区至少需要5、6个界面单元以减弱网格尺寸的影响. 本研究关注颗粒破碎后所产生碎片的整体形态，忽略断裂引起的碎片表面局部起伏和粗糙变化. 尽管所研究颗粒的初始形状存在较大差异，仍发现颗粒破碎后所产生碎片的形状指标分布具有一些共性特征. 碎片的圆度、扁平率、Domokos因子和凸度对颗粒初始形状的敏感性逐渐增强，并且除了圆度外，其他形状指标分布与碎片尺寸之间并未发现显著的相关性. 不同粒径组碎片的圆度分布表明，较大的碎片棱角更明显.
关键词： 岩石颗粒;  单颗粒破碎;  连续-离散耦合方法（FDEM）;  内聚力模型;  形状指标    
Abstract:

3D scanning technology was employed to obtain the surface point cloud data of real rock grains and these grains were reconstructed by using digital image processing technology, aiming at the influence of fragment size and shape on the strength and the deformation of crushing rock grain. The combined finite-discrete element method (FDEM) was used to simulate the fracture and fragmentation of single grain under compression of flat plates. The fragment shape was characterized and quantified, and then the relationships between fragment shape and grain shape and size were analyzed by identifying each fragment produced by single grain crushing. The sensitivity analysis of grain finite element mesh density was conducted to accurately describe the stress gradient and damage evolution along the crack tip. Results show that at least 5、6 cohesive interface elements are required in the fracture process zone to reduce the effects of the element size. The overall shape of fragments generated after grain crushing was focused on, while the local undulation and roughness changes of fragment surface caused by fracture were ignored. Although the grains shapes are different, there are some generic features of shape distribution of fragments after crushing. The sensitivity of sphericity, aspect ratio, Domokos shape descriptor, and convexity of fragments to grain shape gradually increases, and no significant correlation was found between the distribution of other shape descriptors and fragment size except sphericity. The sphericity distribution of fragments with different sizes shows that the larger size fragments tend to be more angular.
Key words: rock grain    single grain crushing    finite-discrete element method (FDEM)    cohesive zone model (CZM)    shape descriptor
收稿日期: 2020-07-08 出版日期: 2021-03-09
CLC:  TV 41  
基金资助: 国家自然科学基金资助项目（51825905，U1865204）；华能集团科技资助项目（HNKJ18-H26）
通讯作者: 马刚     E-mail: 604036445@qq.com;magang630@whu.edu.cn
作者简介: 周剑（1994—），男，硕士生，从事水工结构和岩土工程数值仿真分析. orcid.org/0000-0002-0347-0580. E-mail： 604036445@qq.com
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周剑
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引用本文:

周剑,马刚,周伟,程勇刚,黄泉水,曹学兴. 基于FDEM的岩石颗粒破碎后碎片形状的统计分析[J]. 浙江大学学报(工学版), 2021, 55(2): 348-357.

Jian ZHOU,Gang MA,Wei ZHOU,Yong-gang CHENG,Quan-shui HUANG,Xue-xing CAO. Statistical analysis of fragment shape of rock grain after crushing based on FDEM. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 348-357.

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http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.02.015    或    http://www.zjujournals.com/eng/CN/Y2021/V55/I2/348

图 1  棱角状花岗岩颗粒
颗粒编号 $L$/mm $I$/mm $S$/mm ${\rm{EI}}$ ${\rm{FI}}$ ${S_{\rm{f}}}$ ${\psi _{{\rm{3D}}}}$ ${C_{\rm{x}}}$
G1 64.725 55.034 35.883 0.850 0.554 3.274 0.847 0.904
G2 73.791 41.169 35.398 0.558 0.480 3.496 0.787 0.862
G3 84.285 54.624 37.843 0.648 0.449 3.507 0.811 0.928
G4 68.353 55.415 46.224 0.811 0.676 3.117 0.796 0.849
G5 62.311 57.968 48.701 0.930 0.782 3.048 0.808 0.858
G6 63.983 46.226 43.552 0.722 0.681 3.135 0.852 0.921
G7 77.504 48.492 37.44 0.626 0.483 3.436 0.800 0.921
G8 62.171 61.087 39.292 0.983 0.632 3.196 0.838 0.895
G9 61.726 58.954 40.825 0.955 0.661 3.150 0.820 0.884
表 1  棱角状花岗岩颗粒的形状指标
图 2  岩石颗粒FDEM模型
图 3  界面单元本构关系
参数 数值 单位
实体单元 $\; \rho$[1, 19, 25] 2 700 ${{{\rm{kg}}} / {{{\rm{m}}^{\rm{3}}}}}$
$E$[1, 19, 25] 40 ${\rm{GPa}}$
$\nu $[1, 19, 25] 0.2 ?
界面单元 ${k_{\rm{n}}}$ 4.8×1013 ${{\rm{N}} / {{{\rm{m}}^{\rm{3}}}}}$
${k_{\rm{s}}}$ 2.0×1013 ${{\rm{N}} / {{{\rm{m}}^{\rm{3}}}}}$
${f_{\rm{t}}}$[19, 25] 均值为11 ${\rm{MPa}}$,方差为0.5的对数正态分布 ${\rm{MPa}}$
${\varphi _i}$[1, 25] 40 （°）
${\varphi _{\rm{f}}}$[1, 25] 30 （°）
$c$[19, 25] $c = { {15{f_t}\left( {1 - {\rm{sin}}\;{\varphi _i} } \right)} / {\left( {2{\rm{cos}}\;{\varphi _i} } \right)} }$ ${\rm{MPa}}$
$ {G}_{{\rm{I}}}$[25] 100 ${{\rm{N}} / {\rm{m}}}$
$ {G}_{{\rm{II}}}$[25] 500 ${{\rm{N}} / {\rm{m}}}$
接触准则 $\;\mu$[1, 25] 0.577 ?
表 2  FDEM模型计算时输入的参数
图 4  颗粒的4种网格示意图
编号 ${l_{\rm{e}}}$/mm ${n_{\rm{n}}}$ ${n_{\rm{e}}}$ $n_{{\rm{CIE}}}^{\min }$
G-M1 5.18 21 476 13 671 4
G-M2 4.49 31 731 21 064 5
G-M3 3.10 91 751 63 761 7
G-M4 2.21 249 662 176 650 9
表 3  颗粒的4种网格
图 5  典型荷载位移曲线和外力功
图 6  不同网格外力功箱形图
图 7  荷载位移锯齿状曲线
图 8  碎片数量和失效界面单元累积百分数
图 9  大块碎裂后最大的10个碎片
图 10  碎片尺寸累积分布
图 11  加载结束时碎片Domokos因子的概率密度分布
图 12  加载结束时扁平率和圆度的频率分布
图 13  形状指标的累积分布
图 14  荷载位移曲线和碎片数量
图 15  加载结束时碎片形状指标的累积分布
颗粒 ${S_{\rm{f}}}$ ${S / L}$ ${\psi _{{\rm{3D}}}}$ ${C_{\rm{x}}}$
$q$ $a$ $b$ $a$ $b$ $a$ $b$
G1 2.345 0.506 5.248 0.617 12.330 0.828 3.854
G2 1.881 0.503 3.530 0.601 13.200 0.852 2.810
G3 2.402 0.527 4.618 0.604 10.020 0.834 4.289
G4 2.455 0.543 4.213 0.613 10.620 0.811 4.064
G5 2.193 0.518 4.280 0.606 12.730 0.842 4.056
G6 2.292 0.525 4.078 0.609 11.590 0.804 5.400
G7 2.242 0.525 4.300 0.607 9.881 0.809 3.736
G8 2.595 0.557 4.260 0.617 10.990 0.844 4.093
G9 1.907 0.487 4.327 0.596 12.220 0.871 5.366
表 4  不同形状指标累积分布的拟合参数
图 16  加载结束时碎片形状指标的累积分布和函数拟合
图 17  不同粒径组碎片圆度的累积分布和Kruskal - Wallis检验
图 18  粒径组的Zingg分类图
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