颗粒离散元分层建模法及颗粒尺寸效应

陈龙; 吴顺川; 金爱兵

doi:10.3969/j.issn.0258-2724.20210023

颗粒离散元分层建模法及颗粒尺寸效应

doi: 10.3969/j.issn.0258-2724.20210023

陈龙^1,,
吴顺川^{1, 2},
金爱兵^1, ,

1.
北京科技大学金属矿山高效开采与安全教育部重点实验室，北京 100083
2.
昆明理工大学国土资源工程学院，云南昆明 650093

基金项目: 国家自然科学基金（51774020，51934003）

详细信息

作者简介:
陈龙(1995—)，男，博士研究生，研究方向为岩石力学与数值模拟，E-mail：2488726214@qq.com

通讯作者:
金爱兵(1974—)，男，教授，博士，研究方向为岩石力学与工程，E-mail：jinaibing@ustb.edu.cn

中图分类号: TD315
计量
- 文章访问数: 410
- HTML全文浏览量: 416
- PDF下载量: 53
- 被引次数: 0
出版历程
- 收稿日期: 2021-01-11
- 修回日期: 2021-05-16
- 网络出版日期: 2022-07-11
- 刊出日期: 2021-09-07

Particle Discrete Element Layered Modeling Method and Particle Size Effect

CHEN Long^1
,,
WU Shunchuan^{1, 2},
JIN Aibing^{1
, ,}

1.
Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine, University of Science and Technology Beijing, Beijing 100083, China
2.
Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China

摘要

摘要:
离散元分析方法是研究岩石力学行为、完善岩石力学基础理论的重要工具之一，为提高颗粒离散元法模拟室内岩石力学及大规模工程尺度试验的精确度，提出分层建模法，该方法对岩石或岩体关注区域采用小尺寸颗粒进行精细化模拟，外侧非重点关注区域采用大尺寸颗粒建模以扩大计算区域. 采用分层建模法进行单轴压缩、巴西劈裂试验并与常规建模计算结果进行对比，初步验证了分层建模法模拟室内力学试验的可行性. 研究结果表明：分层建模法与常规建模一样受颗粒尺寸效应影响，但可以减少颗粒流模型中的颗粒数量，计算效率提高50%以上；分层模型的单轴抗压强度和起裂应力分别与外层对应的常规模型相比，最多仅减小2.7%和1.9%，匹配单轴抗压强度时可先以外层材料常规模型作参照，单轴抗压强度和起裂应力的变异系数（coefficient of variation，COV）普遍大于常规模型，但依然在2%的可接受范围内；分层模型中粒径分布的不均匀性对模型弹性阶段的变形性质影响较小，分层模型的弹性模量与外层对应的常规模型相比减小1.3% ~ 2.3%；分层模型的巴西劈裂抗拉强度与外层对应的常规模型增大了1.32% ~ 2.35%，宏观破裂特征与小粒径常规模型相似，但在加载板附近有更多的裂纹.
- 分层建模法 /
- 离散元 /
- 颗粒尺寸 /
- 三维建模
Abstract:
Discrete element analysis method is one of the important tools for studying rock mechanics behavior and refining the basic theory of rock mechanics. In order to improve the accuracy of the particle discrete element method to simulate indoor rock mechanics and large-scale engineering scale tests, a layered modeling method is proposed. This method adopts small-size particles for fine simulation of the rock or key rock mass area, and large-size particles for the outside area to expand the calculation area. The layered modeling method is used to carry out uniaxial compression and Brazilian splitting tests, and compared with the conventional modeling calculation results, which preliminarily verifies its feasibility to simulate indoor mechanical tests. The results show that the layered modeling method is affected by the particle size like conventional modeling, but it can reduce the number of particles in the particle flow code model and increase the calculation efficiency by more than 50%. The uniaxial compressive strength and crack initiation stress of the layered model are reduced by only 2.7% and 1.9% at most, compared with those of the conventional model with the corresponding outer layer. The coefficient of variation (COV) of uniaxial compressive strength and crack initiation stress is generally larger than that of the conventional model, but it is still within the acceptable range of 2%. The inhomogeneity of particle size distribution in the layered model has minor effect on the deformation properties of the model at the elastic stage, and the elastic modulus of the layered model is reduced by 1.3%−2.3% compared with the conventional model with the corresponding outer layer. The overall Brazilian splitting tensile strength of the layered model is increased by 1.32%−2.35% compared to that of the conventional model with the corresponding outer layer, and the macroscopic fracture characteristics are similar to those of the conventional small-particle model, but there are more cracks near the loading plate.
- layered modeling method /
- discrete element method /
- particle size /
- 3D modeling

HTML全文

图 1 分层建模法示意

Figure 1. Schematic of layered modeling method

下载: 全尺寸图片幻灯片

图 2 单轴压缩试验模型

Figure 2. Uniaxial compression test model

下载: 全尺寸图片幻灯片

图 3 分层模型与常规模型应力-应变曲线对比

Figure 3. Comparison of stress-strain curves between layered model and conventional model

下载: 全尺寸图片幻灯片

图 4 σ_ucs和COV的计算结果

Figure 4. Calculation results of σ_ucs and COV

下载: 全尺寸图片幻灯片

图 5 σ_cis和COV的计算结果

Figure 5. Calculation results of σ_cis and COV

下载: 全尺寸图片幻灯片

图 6 E和COV的计算结果

Figure 6. Calculation results of E and COV

下载: 全尺寸图片幻灯片

图 7 巴西劈裂试验分层模型

Figure 7. Layered model for Brazilian splitting test

下载: 全尺寸图片幻灯片

图 8 σ_bt和COV的计算结果

Figure 8. Calculation results of σ_bt and COV

下载: 全尺寸图片幻灯片

图 9 巴西圆盘宏观破坏

Figure 9. Macroscopic damage of Brazilian disc

下载: 全尺寸图片幻灯片

图 10 深部岩体工程中的分区破裂现象

Figure 10. Zonal disintegration in deep rock mass projects

下载: 全尺寸图片幻灯片

表 1 FJM3D各细观力学参数取值

Table 1. FJM3D meso-mechanical parameters

细观力学参数	数值
安装间距比 g_ratio	0.3
类型 B 单元比例 φ_B	0.9
类型 S 单元比例 φ_S	0.1
接触单元数 N/个	3
颗粒的有效模量 ${{{E}_{\rm c}} }$/GPa	30
黏结的有效模量${\overline {{E}}_{\rm c } }$/GPa	30
颗粒的法向与切向刚度比 $ k_{\rm{n}}/k_{\rm{s} }$	1.9
黏结的法向与切向刚度比$\overline k_{\rm{n}}/ \overline k_{\rm{s} }$	1.9
摩擦系数 μ₁	0.3
黏结张拉强度平均值和标准偏差 σ_b/MPa	3.5, 0
黏结内聚力平均值和标准偏差 c_b/MPa	36, 0
摩擦角 Ф_b/ （°）	10

下载: 导出CSV

表 2 单轴压缩模型粒径设置

Table 2. Particle size setting for uniaxial compression model

模型	组号	d_min/mm	d_max/mm	d /mm	L/d	备注
常规	1	1.50	2.50	2.00	25.00
	2	1.88	3.12	2.50	20.00
	3	2.26	3.74	3.00	16.67
分层	4	1.50	2.50	2.00	25.00	内层
	4	1.88	3.12	2.50	20.00	外层
	5	1.50	2.50	2.00	25.00	内层
	5	2.26	3.74	3.00	16.67	外层
	6	1.88	3.12	2.50	20.00	内层
	6	2.26	3.74	3.00	16.67	外层

下载: 导出CSV

表 3 巴西劈裂模型粒径设置

Table 3. Particle size setting for Brazilian splitting model

模型	组号	d_min/mm	d_max/mm	d/mm	L/d	备注
常规	1	1.13	1.87	1.50	33.33
	2	1.50	2.50	2.00	25.00
	3	1.88	3.12	2.50	20.00
	4	2.26	3.74	3.00	16.67
分层	5	1.13	1.87	1.50	33.33	内层
	5	1.50	2.50	2.00	25.00	外层
	6	1.13	1.87	1.50	33.33	内层
	6	1.88	3.12	2.50	20.00	外层
	7	1.13	1.87	1.50	33.33	内层
	7	2.26	3.74	3.00	16.67	外层

下载: 导出CSV

表 4 分层模型与常规模型颗粒数、计算时长对比

Table 4. Comparison of particle number and calculation time between layered model and conventional model

模型	d/mm	颗粒数/ 个	计算时长/h	计算时长降低率/%
单轴压缩	2.00	27 324	9.57	0
	2.00（内），2.50（外）	15 721	4.72	50.68
	2.00（内），3.00（外）	10 622	2.98	68.86
巴西劈裂	1.50	16 966	5.02	0
	1.50（内），2.00（外）	11 085	2.28	54.58
	1.50（内），2.50（外）	8 994	2.24	55.38
	1.50（内），3.00（外）	8 042	2.13	57.57

下载: 导出CSV

参考文献(22)

[1]	CUNDALL P A. The measurement and analysis of acceleration on rock slopes[D]. London: University of London, 1971.
[2]	CUNDALL P A. UDEC—a generalized distinct element program for modelling jointed rock, peter cundall associates[R]. [S.l.]: European Research Office, 1980
[3]	CUNDALL P A, STRACK O D L. A discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65.
[4]	ZHANG X P, WONG L N Y. Cracking processes in rock-like material containing a single flaw under uniaxial compression:a numerical study based on parallel bonded-particle model approach[J]. Rock Mechanics and Rock Engineering, 2012, 45(5): 711-737.
[5]	DUAN K, KWOK C Y, MA X. DEM simulations of sandstone under true triaxial compressive tests[J]. Acta Geotechnica, 2017, 12(3): 495-510. doi: 10.1007/s11440-016-0480-6
[6]	CAI M, KAISER P K. Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and rocks with pre-existing cracks[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41: 478-483. doi: 10.1016/j.ijrmms.2004.03.086
[7]	JIANG M J, LEROUEIL S, KONRAD J M. Insight into shear strength functions of unsaturated granulates by DEM analyses[J]. Computers and Geotechnics, 2004, 31(6): 473-489. doi: 10.1016/j.compgeo.2004.07.001
[8]	刘宁,张春生,褚卫江,等. 锦屏二级水电站深埋隧洞开挖损伤区特征分析[J]. 岩石力学与工程学报,2013,32(11): 2235-2241. LIU Ning, ZHANG Chunsheng, CHU Weijiang, et al. Excavation damaged zone characteristics in deep tunnel of Jinping Ⅱ hydropower station[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(11): 2235-2241.
[9]	李涛,朱连华,李彬如,等. 深基坑开挖土拱效应影响因素研究[J]. 中国矿业大学学报,2017,46(1): 58-65. doi: 10.13247/j.cnki.jcumt.000626 LI Tao, ZHU Lianhua, LI Binru, et al. Study of the influence factors of soil arching effect for deep foundation pit excavation[J]. Journal of China University of Mining & Technology, 2017, 46(1): 58-65. doi: 10.13247/j.cnki.jcumt.000626
[10]	WU S C, CHEN L, CHENG Z Q. Macro and meso research on the zonal disintegration phenomenon and the mechanism of deep brittle rock mass[J]. Engineering Fracture Mechanics, 2019, 211: 254-268. doi: 10.1016/j.engfracmech.2019.02.023
[11]	刘春,乐天呈,施斌,等. 颗粒离散元法工程应用的三大问题探讨[J]. 岩石力学与工程学报,2020,39(6): 1142-1152. doi: 10.13722/j.cnki.jrme.2019.0977 LIU Chun, LE Tiancheng, SHI Bin, et al. Discussion on three major problems of engineering application of the particle discrete element method[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(6): 1142-1152. doi: 10.13722/j.cnki.jrme.2019.0977
[12]	POTYONDY D O, CUNDALL P A. A bonded-particle model for rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(8): 1329-1364. doi: 10.1016/j.ijrmms.2004.09.011
[13]	YANG B D, JIAO Y, LEI S T. A study on the effects of microparameters on macroproperties for specimens created by bonded particles[J]. Engineering Computations, 2006, 23(6): 607-631. doi: 10.1108/02644400610680333
[14]	YOON J. Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation[J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 871-889. doi: 10.1016/j.ijrmms.2007.01.004
[15]	DING X B, ZHANG L Y, ZHU H H, et al. Effect of model scale and particle size distribution on PFC3D simulation results[J]. Rock Mechanics and Rock Engineering, 2014, 47(6): 2139-2156. doi: 10.1007/s00603-013-0533-1
[16]	XU X L, WU S C, GAO Y T, et al. Effects of micro-structure and micro-parameters on Brazilian tensile strength using flat-joint model[J]. Rock Mechanics and Rock Engineering, 2016, 49(9): 3575-3595. doi: 10.1007/s00603-016-1021-1
[17]	POTYONDY D O. PFC3D flat joint contact model[R]. Minneapolis: ITASCA Consulting Group, 2013.
[18]	WU S C, XU X L. A study of three intrinsic problems of the classic discrete element method using flat-joint model[J]. Rock Mechanics and Rock Engineering, 2016, 49(5): 1813-1830. doi: 10.1007/s00603-015-0890-z
[19]	SUITS L D, SHEAHAN T C, FUENKAJORN K, et al. Laboratory determination of direct tensile strength and deformability of intact rocks[J]. Geotechnical Testing Journal, 2011, 34(1): 103134. doi: 10.1520/GTJ103134
[20]	MA J, WU S C, ZHANG X P, et al. Modeling acoustic emission in the Brazilian test using moment tensor inversion[J]. Computers and Geotechnics, 2020, 123: 103567. doi: 10.1016/j.compgeo.2020.103567
[21]	NAKASHIMA S, TAGUCHI K, MORITOSHI A, et al. Loading conditions in the Brazilian test simulation by DEM[C]//47th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association. San Francisco: [s.n.], 2013: 1833-1838.
[22]	XU X L, WU S C, JIN A B, et al. Review of the relationships between crack initiation stress, mode I fracture toughness and tensile strength of geo-materials[J]. International Journal of Geomechanics, 2018, 18(10): 04018136.1-04018136.20.