裂隙介质氡迁移的分形离散裂隙网络模型

doi:10.16265/j.cnki.issn1003-3033.2022.11.0284

中国安全科学学报 ›› 2022, Vol. 32 ›› Issue (11): 97-104.doi: 10.16265/j.cnki.issn1003-3033.2022.11.0284

裂隙介质氡迁移的分形离散裂隙网络模型

冯胜洋¹^,²(), 李策¹, 刘永¹^,³^,^**(), 康虔⁴

¹ 南华大学资源环境与安全工程学院,湖南衡阳 421001
² 南华大学安全工程技术中心,湖南衡阳 421001
³ 深圳大学物理与光电工程学院,广东深圳 518060
⁴ 江西理工大学应急管理与安全工程学院,江西赣州341000

收稿日期:2022-06-11 修回日期:2022-09-12 出版日期:2022-11-28 发布日期:2023-05-28
通讯作者: 刘永
作者简介:
冯胜洋 (1985—),男,湖北汉川人,博士,副教授,主要从事铀矿冶安全理论与技术、建筑安全等方面的研究。E-mail:fengshengyang@usc.edu.cn。
基金资助:
国家自然科学基金资助(11705083); 湖南省自然科学基金资助(2019JJ50488); 装备预研领域基金资助(80927015101); 衡阳市科技创新计划项目(202105006)

Study on fractal discrete fracture network model of radon migration in fractured medium

FENG Shengyang¹^,²(), LI Ce¹, LIU Yong¹^,³^,^**(), KANG Qian⁴

¹ School of Resource Environment and Safety Engineering, University of South China, Hengyang Hunan 421001, China
² Safety Engineering Technology Center, University of South China, Hengyang Hunan 421001, China
³ School of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen Guangdong 518060, China
⁴ School of Emergency Management and Safety Engineering, Jiangxi University of Science and Technology, Ganzhou Jiangxi 341000, China

Received:2022-06-11 Revised:2022-09-12 Online:2022-11-28 Published:2023-05-28
Contact: LIU Yong

摘要/Abstract

摘要：

为更有效地开展氡污染防治、氡示踪研究,根据分形理论与离散裂隙网络(DFN)建立裂隙介质氡迁移模型;采用双幂律模型描述裂隙位置与长度,多级联乘方法获得裂隙中心点位置,von Mises-Fisher分布函数确定裂隙方向,对数正态分布方法确定裂隙开度分布;采用自研试验装置验证理论模型,并使用理论模型分析某天然裂隙岩体氡迁移特征。结果表明:理论模型计算氡活度浓度与试验结果相差最大不超过4%,该裂隙岩体的平均氡析出率为0.002 58 Bq/(m²·s),岩体内连通裂隙构成氡迁移的主要通道,裂隙密集处的最大氡通量比裂隙稀疏处的大约3个数量级。裂隙介质平均氡析出率随分形维数的增加而增大,随长度指数的增加而减小,与对流速度呈非线性增加关系。

关键词: 裂隙介质, 氡迁移, 离散裂隙网络(DFN), 氡析出率, 分形维数

Abstract:

In order to effectively carry out radon pollution control and radon tracing research, the fractal theory and DFN were combined to establish a model of radon migration in fractured medium. In the model, the distribution of fracture lengths was obtained by a double-power law model. The location of fracture centers was determined by the multiplicative cascade process method. The von Mises-Fisher method and the lognormal distribution method were used to model fracture orientations and fracture apertures, respectively. The model was verified by using a test device, and a natural fractured rock mass was analyzed by the model. The results show that the maximum difference between the radon activity concentrations calculated by the model and the test is less than 4%. The average radon exhalation rate of the fractured rock mass is 0.002 58 Bq/(m²·s), and interconnected fractures in the rock mass constitute the primary channels for radon migration. The maximum radon flux of the dense fractures is about 3 orders of magnitude higher than that at the sparse fractures. The average radon exhalation rate in fractured medium increases linearly with the fractal dimension, decreases linearly with the length index, and shows a nonlinear increase relationship with the convection velocity.

Key words: fractured medium, radon migration, discrete fracture network (DFN), radon exhalation rate, fractal dimension

冯胜洋, 李策, 刘永, 康虔. 裂隙介质氡迁移的分形离散裂隙网络模型[J]. 中国安全科学学报, 2022, 32(11): 97-104.

FENG Shengyang, LI Ce, LIU Yong, KANG Qian. Study on fractal discrete fracture network model of radon migration in fractured medium[J]. China Safety Science Journal, 2022, 32(11): 97-104.

图/表 14

图1

图2

表1

图3

图4

表2

图5

表3

DFN模型参数

参数	数值	参数	数值
D_f	1.62	b_max/mm	3.6
$β$	1.49	b_min/mm	0.5
α	2.39	$b -$ /mm	1.7
$μ 0$ /(°)	65	h	3
$κ$	2	—

表3

图6

图7

图8

图9

图10

图11

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序号	模型计算氡活度浓度/(Bq·m^-3)	试验测得氡活度浓度/(Bq·m^-3)	相对误差/%
试样1	17 598	17 002	3.5
试样2	21 764	21 035	3.4
试样3	22 103	21 255	4.0

裂隙介质氡迁移的分形离散裂隙网络模型

Study on fractal discrete fracture network model of radon migration in fractured medium

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试样序号	D_f	a	μ₀/(°)	κ	N_t
1	1.6	2.3	45	1	15
2	1.52	2.8	30	2	25
3	1.48	2.5	60	5	30