您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(工学版)》

山东大学学报 (工学版) ›› 2019, Vol. 49 ›› Issue (4): 70-77.doi: 10.6040/j.issn.1672-3961.0.2018.533

• 土木工程 • 上一篇    下一篇

岩石粗糙裂隙大范围雷诺数条件下渗流特性

刘杰1(),王者超2,*(),张宇鹏2,孙华阳3   

  1. 1. 山东大学岩土与结构工程研究中心, 山东 济南 250061
    2. 东北大学深部金属矿山安全开采教育部重点实验室, 辽宁 沈阳 110004
    3. 东北大学资源与土木工程学院, 辽宁 沈阳 110004
  • 收稿日期:2018-12-09 出版日期:2019-08-20 发布日期:2019-08-06
  • 通讯作者: 王者超 E-mail:liujiegt@126.com;wang_zhechao@hotmail.com
  • 作者简介:刘杰(1988—),男,山东高唐人,硕士研究生,主要研究方向为岩体裂隙渗流. E-mail:liujiegt@126.com
  • 基金资助:
    国家自然科学基金资助项目(51779045);国家自然科学基金资助项目(51579141)

Flow characteristics of rough rock fractures under wide range of Reynolds numbers

Jie LIU1(),Zhechao WANG2,*(),Yupeng ZHANG2,Huayang SUN3   

  1. 1. Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, Shandong, China
    2. Key laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110004, Liaoning, China
    3. School of Resources and Civil Engineering, Northeastern University, Shenyang 110004, Liaoning, China
  • Received:2018-12-09 Online:2019-08-20 Published:2019-08-06
  • Contact: Zhechao WANG E-mail:liujiegt@126.com;wang_zhechao@hotmail.com
  • Supported by:
    国家自然科学基金资助项目(51779045);国家自然科学基金资助项目(51579141)

摘要:

通过试验和理论分析,研究不同几何参数的岩石粗糙裂隙渗流的非达西系数β、临界雷诺数Rec、非达西效应因子E等变化特性。研制裂隙渗流试验仪器,制作9个不同开度和裂隙粗糙度(joint roughness coefficient, JRC)的单裂隙模型,开展大范围雷诺数Re条件下粗糙裂隙渗流试验。根据渗流试验结果,得到了不同粗糙度(JRC=2~20)单裂隙的渗流特性,显示出粗糙度对裂隙的非线性渗流特性产生显著的影响。结合Forchheimer方程,从理论参数方面,对粗糙度的影响进行量化。研究显示:裂隙粗糙度越大,则越容易引起裂隙渗流的非线性,临界雷诺数越小,非线性作用越强。

关键词: 粗糙裂隙, 渗流试验, 非线性渗流, Forchheimer方程, 临界雷诺数

Abstract:

Through experiments and theoretical analysis, the flow characteristics of rock rough fractures with different geometric parameters were studied, including non-Darcy coefficient β, critical Reynolds number Rec and non-Darcy effect factor E. Testing equipment for fluid flow in fractures was developed and 9 rough single fracture models with different apertures and Joint Roughness Coefficients (JRC) were prepared. Laboratory tests on flow in rough fractures with Reynolds numbers, i.e., from 2 to 5000 were performed. The characteristics of flow in single fractures with different roughness (JRC=2-20) under wide range of Reynolds numbers were obtained. It was shown that fracture roughness had a significant impact on the nonlinear flow characteristics of the fracture. Based on the Forchheimer equation, the effects of fracture roughness on equation parameters were quantitatively studied. The larger fracture roughness was, the more likely it was to cause the nonlinearity of the fracture flow, the smaller critical Reynolds number was, and the stronger non-linear effect would be.

Key words: rough fracture, flow experiment, nonlinear flow, Forchheimer equation, critical Reynolds number

中图分类号: 

  • U43

图1

单裂隙渗流沿程损失系数λ整理"

表1

单裂隙渗流相关研究对比"

文献序号研究方法模型尺寸/(mm×mm)开度范围/mm粗糙度Rec范围模型制作方法
[12]试验、模拟20×200.15粗糙10树脂模型
[14]试验1 000×2504.00~9.00光滑12~86树脂玻璃板
[16]试验6 000×5003.00~13.00光滑/粗糙200~1 000树脂板粘贴凸起网格
[17]试验100×500~0.04JRC=6~12.51~15劈裂花岗岩
[18]试验200×1000.50~2.00JRC=11.2~14.5劈裂花岗岩

图2

岩石裂隙渗流试验装置及原理图 1—变频水泵; 2—水箱; 3—控制阀; 4—压力传感器; 5—涡轮流量计; 6—数据处理显示器; 7—裂隙模型"

图3

粗糙裂隙模型示意图"

表2

各试验工况几何参数"

试验工况长度L/mm宽度w/mm平均开度em/mm水力开度eh/mmJRC
1202500.800.7750~2
2202501.000.9560~2
3202501.321.3650~2
4201500.560.5968~10
5201500.800.8118~10
6201501.201.1828~10
7200500.450.39318~20
8200500.700.69718~20
9200500.950.88518~20

图4

各工况试验数据与拟合曲线对比"

图5

裂隙渗流示意图"

图6

裂隙内流速分布"

图7

牛顿内摩擦定律示意图"

表3

各试验工况拟合系数"

试验工况ABR2
(公式(6))
β
15.86×1044.59×1080.9986.75
22.81×1042.89×1080.9966.47
39.65×1038.38×1070.9983.83
41.16×1053.12×1090.99927.19
54.83×1041.63×1090.99926.26
61.48×1045.44×1080.99918.61
74.04×1051.17×10100.99744.45
87.25×1044.76×1090.99856.67
93.54×1041.97×1090.99837.76

图8

不同粗糙度裂隙中非达西系数β变化趋势"

图9

各工况临界雷诺数"

图10

E与Re的关系"

1 刘日成, 蒋宇静, 李博, 等. 岩体裂隙网络非线性渗流特性研究[J]. 岩土力学, 2016, 37 (10): 2817- 2824.
LIU Richeng , JIANG Yujing , LI Bo , et al. Nonlinear seepage behaviors of fluid in fracture networks[J]. Rock and Soil Mechanics, 2016, 37 (10): 2817- 2824.
2 BERKOWITZ B . Characterizing flow and transport in fractured geological media: a review[J]. Advances in Water Resources, 2002, 25 (8): 861- 884.
3 ZIMMERMAN R W , BODVARSSON G S . Hydraulic conductivity of rock fractures[J]. Transport in Porous Media, 1996, 23 (1): 1- 30.
4 SKJETNE E , HANSEN A , GUDMUNDSSON J S . High-velocity flow in a rough fracture[J]. Journal of Fluid Mechanics, 1999, 383, 1- 28.
doi: 10.1017/S0022112098002444
5 JAVADI M , SHARIFZADEH M , SHAHRIAR K , et al. Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes[J]. Water Resources Research, 2014, 50 (2): 1789- 1804.
doi: 10.1002/2013WR014610
6 蒋宇静, 李博, 王刚, 等. 岩石裂隙渗流特性试验研究的新进展[J]. 岩石力学与工程学报, 2008, 27 (12): 2377- 2386.
doi: 10.3321/j.issn:1000-6915.2008.12.001
JIANG Yujing , LI Bo , WANG Gang , et al. New advances in experimental study on seepage characteristics of rock fractures[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27 (12): 2377- 2386.
doi: 10.3321/j.issn:1000-6915.2008.12.001
7 LIU R C , YU L Y , JIANG Y J . Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures[J]. Rock Mechanics and Rock Engineering, 2016, 50 (4): 1- 9.
8 熊峰, 孙昊, 姜清辉, 等. 粗糙岩石裂隙低速非线性渗流模型及试验验证[J]. 岩土力学, 2018, 39 (9): 3294- 3302.
XIONG Feng , SUN Hao , JIANG Qinghui , et al. Theoretical model and experimental verification on non-linear flow at low velocity through rough-walled rock fracture[J]. Rock and Soil Mechanics, 2018, 39 (9): 3294- 3302.
9 YU L Y , LIU R C , JIANG Y J . A review of critical conditions for the onset of nonlinear fluid flow in rock fractures[J]. Geofluids, 2017, 1- 17.
10 LIU R C , JING H J , HE L X , et al. An experimental study of the effect of fillings on hydraulic properties of single fractures[J]. Environmental Earth Sciences, 2017, 76, 684.
doi: 10.1007/s12665-017-7024-8
11 BRUSH D J , THOMSON N R . Fluid flow in synthetic rough-walled fractures: navier-stokes, Stokes, and local cubic law simulations[J]. Water Resources Research, 2003, 39 (4): 1085.
12 ZIMMERMAN R W , AL-YAARUBI A , PAIN C C , et al. Nonlinear regimes of fluid flow in rock fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41 (3): 163- 169.
13 KONZUK J S , KUEPER B H . Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture[J]. Water Resources Research, 2004, 40 (2): W02402.
14 QIAN J Z , ZHAN H B , CHEN Z , et al. Experimental study of solute transport under non-Darcian flow in a single fracture[J]. Journal of Hydrology, 2011, 399 (3): 246- 254.
15 CHEN Y F , HU S H , HU R , et al. Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash's law-based empirical model[J]. Water Resources Research, 2015, 51 (4): 2096- 2118.
doi: 10.1002/2014WR016458
16 TZELEPIS V , MOUTSOPOULOS K N , PAPASPYROS J N E , et al. Experimental investigation of flow behavior in smooth and rough artificial fractures[J]. Journal of Hydrology, 2015, 521 (2): 108- 118.
17 ZHOU J Q , HU S H , CHEN Y F , et al. The friction factor in the Forchheimer equation for rock fractures[J]. Rock Mechanics and Rock Engineering, 2016, 49 (8): 3055- 3068.
doi: 10.1007/s00603-016-0960-x
18 QIAN X , XIA C C , GUI Y . Quantitative estimates of non-Darcy groundwater flow properties and normalized hydraulic aperture through discrete open rough-walled joints[J]. International Journal of Geomechanic, 2018, 18 (9): 04018099.
doi: 10.1061/(ASCE)GM.1943-5622.0001228
19 王媛, 顾智刚, 倪小东, 等. 光滑裂隙高流速非达西渗流运动规律的试验研究[J]. 岩石力学与工程学报, 2010, 29 (7): 1404- 1408.
WANG Yuan , GU Zhigang , NI Xiaodong , et al. Experimental study of non-Darcy water flow through a single smooth fracture[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29 (7): 1404- 1408.
20 王志良, 申林方, 徐则民, 等. 岩体裂隙面粗糙度对其渗流特性的影响研究[J]. 岩土工程学报, 2016, 38 (7): 1262.
WANG Zhiliang , SHEN Linfang , XU Zemin , et al. Influence of roughness of rock fracture on seepage characteristics[J]. Chinese Journal of Geotechnical Engineering, 2016, 38 (7): 1262.
21 BARTON N , CHOUBEY V . The shear strength of rock joints in theory and practice[J]. Rock Mechanics, 1977, 10, 1- 54.
doi: 10.1007/BF01261801
22 IWAI K. Fundamental studies of fluid flow through a single fracture[D]. California, USA: California University, 1976.
23 FORCHHEIMER P H . Wasserbewegung durch boden[J]. Zeitschrift des Vereins Deutscher Ingenieure, 1901, 45, 1782- 1788.
24 BEAR J . Dynamics of Fluids in Porous Media[M]. New York. USA: American Elsevier, 1972.
25 ZENG Z , GRIGG R A . Criterion for non-Darcy flow in porous media[J]. Transport in Porous Media, 2006, 63 (1): 57- 59.
doi: 10.1007/s11242-005-2720-3
26 CHEN Y F , ZHOU J Q , HU S H , et al. Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures[J]. Journal of Hydrology, 2015, 529, 993- 1006.
doi: 10.1016/j.jhydrol.2015.09.021
27 许凯, 雷学文, 孟庆山, 等. 非达西渗流惯性系数研究[J]. 岩石力学与工程学报, 2012, 31 (1): 164- 170.
doi: 10.3969/j.issn.1000-6915.2012.01.019
XU Kai , LEI Xuewen , MENG Qingshan , et al. Study of inertial coefficient of non-Darcy seepage flow[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31 (1): 164- 170.
doi: 10.3969/j.issn.1000-6915.2012.01.019
28 王者超, 张振杰, 李术才, 等. 基于离散裂隙网络法的地下石油洞库洞室间水封性评价[J]. 山东大学学报(工学版), 2016, 46 (2): 94- 100.
WANG Zhechao , ZHANG Zhenjie , LI Shucai , et al. Assessment of intercavern containment property for underground oil storage caverns using discrete fracture networks[J]. Journal of Shandong University (Engineering Science), 2016, 46 (2): 94- 100.
29 ZHANG Z , NEMCIK J . Friction factor of water flow through rough rock fractures[J]. Rock Mechanics and Rock Engineering, 2013, 46 (5): 1125- 1134.
doi: 10.1007/s00603-012-0328-9
[1] 刘子豪,张建成,张波,范志鑫,李成新,杨惠茗,李景龙. 含水率对土钉锚固土体抗剪性能影响[J]. 山东大学学报 (工学版), 2023, 53(3): 14-22.
[2] 王心泉,王智猛,牛犇,蒋恒,冯春. 8度地震烈度区新民隧道出口处边坡的稳定性[J]. 山东大学学报 (工学版), 2023, 53(3): 23-30.
[3] 刘健,杨浩,崔晓琳. 围压作用下土-结构接触渗流特性[J]. 山东大学学报 (工学版), 2023, 53(3): 60-68.
[4] 肖文斌,谢印标,郑扬,武科,陈榕,李秋雷,程睿哲. 活动断层下城市地铁隧道变形破坏与损伤[J]. 山东大学学报 (工学版), 2023, 53(3): 1-13.
[5] 柴少波,史杰辉,阿比尔的,刘钦,宋浪. P波入射含顺层结构面岩质边坡引起的振动[J]. 山东大学学报 (工学版), 2023, 53(3): 31-40.
[6] 李连祥,李红波,韩刚,郭龙德,赵仕磊. 济南非饱和土基坑支护设计[J]. 山东大学学报 (工学版), 2023, 53(3): 41-49.
[7] 陈榕,魏彤,郝冬雪,武科,郭瑞峰. 重金属Cu(Ⅱ)在球黏土中的吸附特性[J]. 山东大学学报 (工学版), 2023, 53(1): 60-67.
[8] 李连祥,王雷,赵永新,季相凯. 考虑支护结构作用的地下管廊真实受力模型[J]. 山东大学学报 (工学版), 2021, 51(1): 60-68.
[9] 孙连勇,时刚,崔新壮,周明祥,王永军,纪方,闫小东. 饱和地基中单排孔近场隔振的现场试验与数值分析[J]. 山东大学学报 (工学版), 2020, 50(3): 88-97.
[10] 李连祥,白璐,陈天宇,季相凯. 复合地基与临近基坑支护结构之间距离影响规律[J]. 山东大学学报 (工学版), 2019, 49(3): 63-72, 79.
[11] 张建明, 刘泉声, 唐志成, 占婷, 蒋亚龙. 考虑剪切变形历史影响的节理峰值剪切强度准则[J]. 山东大学学报(工学版), 0, (): 77-81.
[12] 王者超,王心语,韦昌富,李崴,段广平,李帅,张春雨. 水化学条件对高岭土压缩性的影响机理[J]. 山东大学学报 (工学版), 2018, 48(5): 109-117.
[13] 白现军,王太兴,卫鑫,赵武胜. 近断层速度脉冲对隧洞工程动力响应的影响规律[J]. 山东大学学报(工学版), 2017, 47(2): 14-19.
[14] 陈恩瑜,邓思文,陈方明,马池帅. 一种基于TBM掘进参数的现场岩石强度快速估算模型[J]. 山东大学学报(工学版), 2017, 47(2): 7-13.
[15] 刘金,李勤昌,马秀媛. 有限元强度折减法在边坡稳定分析中的应用[J]. 山东大学学报(工学版), 2016, 46(4): 83-88.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 孔祥臻,刘延俊,王勇,赵秀华 . 气动比例阀的死区补偿与仿真[J]. 山东大学学报(工学版), 2006, 36(1): 99 -102 .
[2] 来翔 . 用胞映射方法讨论一类MKdV方程[J]. 山东大学学报(工学版), 2006, 36(1): 87 -92 .
[3] 秦通,孙丰荣*,王丽梅,王庆浩,李新彩. 基于极大圆盘引导的形状插值实现三维表面重建[J]. 山东大学学报(工学版), 2010, 40(3): 1 -5 .
[4] 李士进,王声特,黄乐平. 基于正反向异质性的遥感图像变化检测[J]. 山东大学学报(工学版), 2018, 48(3): 1 -9 .
[5] 王伟,毛华永,李国祥,潘世艳,巩厅房,晋世强,郝胜兵 . 一种车用燃油加热器燃烧器的流场数值分析[J]. 山东大学学报(工学版), 2008, 38(3): 64 -68 .
[6] 许延生,刘兴芳 . 模糊聚类迭代模型在水资源承载能力评价中的应用[J]. 山东大学学报(工学版), 2007, 37(3): 100 -104 .
[7] 孙亮. 瞬变电磁对含水层的超前探测效果分析[J]. 山东大学学报(工学版), 2009, 39(4): 50 -52 .
[8] 董彤 袁淑娟 葛军饴 洪芳 郁黎明 曹世勋 张金仓. 磁制冷材料Gd5Ge4中的磁玻璃态[J]. 山东大学学报(工学版), 2009, 39(3): 67 -70 .
[9] 李利平,李术才,徐帮树,丁万涛,蔚立元 . 海底隧道施工设计及其数值优化研究[J]. 山东大学学报(工学版), 2008, 38(4): 63 -68 .
[10] 周咏辉,艾兴,赵军,袁训亮,薛强 . Al2O3/(W, Ti)C纳米复合陶瓷材料的力学性能与强韧化机理[J]. 山东大学学报(工学版), 2008, 38(1): 1 -4 .