Journal of Shandong University(Engineering Science) ›› 2019, Vol. 49 ›› Issue (4): 70-77.doi: 10.6040/j.issn.1672-3961.0.2018.533

• Civil Engineering • Previous Articles     Next Articles

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)

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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

CLC Number: 

  • U43

Fig.1

Collation of friction factor λ for single fracture flow investigations"

Table 1

Comparison of single fracture flow investigations"

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

Fig.2

Rock fracture flow experiment device and schematic diagram"

Fig.3

Schematic diagram of rough fracture model"

Table 2

Geometric parameters of experiment cases"

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

Fig.4

Comparison of experiment data and fitting curves"

Fig.5

Schematic diagram of fracture flow"

Fig.6

Velocity distribution in the fracture flow"

Fig.7

Schematic diagram of Newton′s law of internal friction"

Table 3

Fitting coefficients of experiment cases"

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

Fig.8

Trend of non-Darcy coefficient β of rough fractures"

Fig.9

Critical Reynolds number of each experiment case"

Fig.10

Relation between E and Re"

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
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