Skip to main content
SpringerLink
Log in

Influence of contact characteristics on nonlinear flow and eddy development in three-dimensional fractures under normal stress

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

In this study, a three-dimensional (3D) contact fracture model with different normal stresses is established by using artificial rough fractures. To investigate the influence of fracture void and contact changes caused by stress variation on the nonlinear fluid flow process, smooth and hypothetical fractures with the same mechanical aperture are constructed for comparative analysis. The results show that the direct numerical solution of the 3D Navier–Stokes equation is consistent with the experimental results of stress-seepage flow. Compared with the smooth and hypothetical fractures, the contact rate evolution caused by stress changes enhances the nonlinearity of fluid flow in the 3D fractures. The pressure boundary, high-velocity catastrophe area, and eddy distribution area in the contact area are highly consistent. Eddy appears in the backflow area around the contact area and increases with the contact rate and flow rate increase. The critical Reynolds number increases with the increase in the contact ratio, indicating the presence of local effects in the development of eddy, leading to a lag in the appearance of nonlinear flow state. The multi-vortex system operates in an unclosed “8” shape between two pairs, and there is competition but no exchange between the vortices. Finally, it is proposed that the volume average value of vorticity can effectively characterize the variation trend of vorticity with contact rate in the fractures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author, Shuhong Wang, upon reasonable request.

References

  • Abdelghani FB, Aubertin M, Simon R, Therrien R (2015) Numerical simulations of water flow and contaminants transport near mining wastes disposed in a fractured rock mass. Int J Min Sci Technol 25(1):37–45

    Article  Google Scholar 

  • Arianfar A, Ramezanzadeh A, Khalili M (2021) Numerical modeling of closure effect of natural fracture surfaces of rock on behavior of fluid flow. Bull Eng Geol Env 80:2335–2348

    Article  Google Scholar 

  • Briggs S, Karney BW, Sleep BE (2017) Numerical modeling of the effects of roughness on flow and eddy formation in fractures. J Rock Mech Geotech Eng 9(1):105–115

    Article  Google Scholar 

  • Brown SR, Stockman HW, Reeves SJ (1995) Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys Res Lett 22(18):2537–2540

    Article  Google Scholar 

  • Cao C, Xu Z, Chai J, Li Y (2019) Radial fluid flow regime in a single fracture under high hydraulic pressure during shear process. J Hydrol 579(2019):124142

    Article  Google Scholar 

  • Cappa F, Scuderi MM, Collettini C, Guglielmi, Y Avouac JP (2019) Stabilization of fault slip by fluid injection in the laboratory and in situ. Sci adv 5(3):eaau4065

  • Chen Y, Zhao Z (2020) Heat transfer in a 3D rough rock fracture with heterogeneous apertures. Int J Rock Mech Min Sci 134:104445

    Article  Google Scholar 

  • Chen Y, Selvadurai A, Zhao Z (2021) Modeling of flow characteristics in 3D rough rock fracture with geometry changes under confining stresses. Comput Geotech 130:103910

    Article  Google Scholar 

  • Faivre M, Paul B, Golfier F, Giot R, Massin P, Colombo D (2016) 2D coupled HM-XFEM modeling with cohesive zone model and applications to fluid-driven fracture network. Eng Fract Mech 159:115–143

    Article  Google Scholar 

  • Forchheimer P (1901) Wasserbewegung durch boden. Z Ver Deutsch Ing 45(1901):1782–1788

    Google Scholar 

  • Gangi A (1978) Variation of whole and fractured porous rock permeability with confining pressure. Int J Rock Mech Min Sci Geomech Abstr. Pergamon 15(5):249–257

  • Ge S (1997) A governing equation for fluid flow in rough fractures. Water Resour Res 33(1):53–61

    Article  Google Scholar 

  • Guo P, Gao K, Wang M, Wang Y, He M (2022) Numerical investigation on the influence of contact characteristics on nonlinear flow in 3D fracture. Comput Geotech 149(2022):104863

    Article  Google Scholar 

  • Hakami E, Larsson E (1996) Aperture measurements and flow experiments on a single natural fracture. Int J Rock Mech Min Sci Geomech Abstrs. Pergamon 33(4):395–404

  • Han W, Wang S, Liu W, Sun W, Hou Q, Zhang S, Wei W (2022) Crack analysis using a hybrid numerical manifold method with node-based strain smoothing and double-interpolation. Eng Fract Mech 273:108685

    Article  Google Scholar 

  • He L, Xiao H, Cui Y, Liu S, Chen J (2021) Review of visualisation methods of studying the seepage mechanism in fractured rocks. Geomech Geophys Geo-Energy Geo-Resour 7(4):1–25

    CAS  Google Scholar 

  • Huang N, Liu R, Jiang Y (2017) Numerical study of the geometrical and hydraulic characteristics of 3D self-affine rough fractures during shear. J Nat Gas Sci Eng 45(2017):127–142

    Article  Google Scholar 

  • Izbash S (1931) O Filtracii v Kropnozernstom Materiale. USSR (in Russian), Leningrad

    Google Scholar 

  • Javadi M, Sharifzadeh M, Shahriar K, Mitani Y (2014) Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour Res 50(2):1789–1804

    Article  Google Scholar 

  • Javanmard H, Saar MO, Vogler D (2022) On the applicability of connectivity metrics to rough fractures under normal stress. Adv Water Resour 161(2022):104122

    Article  Google Scholar 

  • Khirevich S, Patzek TW (2019) Three-dimensional simulation of tracer transport dynamics in formations with high-permeability channels or fractures: estimation of oil saturation. Phys Fluids 31(11):113604

    Article  Google Scholar 

  • Kim D, Yeo I (2022) Flow visualization of transition from linear to nonlinear flow regimes in rock fractures. Water Resour Res 58(11):e2022WR032088

  • Koyama T, Neretnieks I, Jing L (2008) A numerical study on differences in using Navier-Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear. Int J Rock Mech Min Sci 45(7):1082–1101

    Article  Google Scholar 

  • Kulatilake PH, Du S-G, Ankah MLY, Yong R, Sunkpal DT, Zhao X, Liu G-J, Wu R (2021) Non-stationarity, heterogeneity, scale effects, and anisotropy investigations on natural rock joint roughness using the variogram method. Bull Eng Geol Env 80(8):6121–6143

    Article  Google Scholar 

  • Kumara C, Indraratna B (2017) Normal deformation and formation of contacts in rough rock fractures and their influence on fluid flow. Int J Geomech 17(1):04016022

    Article  Google Scholar 

  • Kundu P, Cohen I, Dowling D (2015) Fluid mechanics. Academic press

  • Lee SH, Yeo IW, Lee KK, Detwiler RL (2015) Tail shortening with developing eddies in a rough-walled rock fracture. Geophys Res Lett 42(15):6340–6347

    Article  Google Scholar 

  • Liu R, He M, Huang N, Jiang Y, Yu L (2020) Three-dimensional double-rough-walled modeling of fluid flow through self-affine shear fractures. J Rock Mech Geotech Eng 12(1):41–49

    Article  Google Scholar 

  • Liu G, Zhao Z, Chen Y, Ma F, Wang G (2021) Comparison between typical numerical models for fluid flow and heat transfer through single rock fractures. Comput Geotech 138:104341

    Article  Google Scholar 

  • Ma G, Ma C, Chen Y (2022) An investigation of nonlinear flow behaviour along rough-walled fractures considering the effects of fractal dimensions and contact areas. J Nat Gas Sci Eng 104(2022):104675

    Article  Google Scholar 

  • Makino S, Iwamoto K, Kawamura H (2008) Turbulent structures and statistics in turbulent channel flow with two-dimensional slits. Int J Heat Fluid Flow 29(3):602–611

    Article  CAS  Google Scholar 

  • Nicholl M, Rajaram H, Glass R, Detwiler R (1999) Saturated flow in a single fracture: Evaluation of the Reynolds equation in measured aperture fields. Water Resour Res 35(11):3361–3373

    Article  Google Scholar 

  • Rasoulzadeh M, Yekta A, Deng H, Ghahfarokhi BR (2020) Semi-analytical models of mineral dissolution in rough fractures with permeable walls. Phys Fluids 32(5):05200

    Article  Google Scholar 

  • Renshaw CE (1995) On the relationship between mechanical and hydraulic apertures in rough-walled fractures. J Geophys Res: Solid Earth 100(B12):24629–24636

    Article  Google Scholar 

  • Rong G, Hou D, Yang J, Cheng L, Zhou C (2017) Experimental study of flow characteristics in non-mated rock fractures considering 3D definition of fracture surfaces. Eng Geol 220:152–163

    Article  Google Scholar 

  • Rong G, Tan J, Zhan H, He R, Zhang Z (2020) Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture. J Hydrol 589:125162

    Article  Google Scholar 

  • Schädle P, Zulian P, Vogler D, Bhopalam SR, Nestola MG, Ebigbo A, Krause R, Saar MO (2019) 3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers. Comput Geosci 132:42–55

    Article  Google Scholar 

  • Shahbazi A, Saeidi A, Chesnaux R, Rouleau A (2023) Effects of fracture-system geometrical parameters on the inflow rate into a tunnel in rock: a numerical modelling experiment. Q J Eng Geol Hydrogeol 56(2):qjegh2021–128

  • Sun C, Zheng H, Liu WD, Ma H (2020) Study on dynamic propagation of hydraulic fractures in enhanced thermal reservoir. Eng Fract Mech 236:107207

    Article  Google Scholar 

  • Vogler D, Settgast RR, Annavarapu C, Madonna C, Bayer P, Amann F (2018) Experiments and simulations of fully hydro-mechanically coupled response of rough fractures exposed to high-pressure fluid injection. J Geophys Res: Solid Earth 123(2):1186–1200

    Article  Google Scholar 

  • Wang M, Chen Y-F, Ma G-W, Zhou J-Q, Zhou C-B (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Adv Water Resour 96(2016):373–388

    Article  Google Scholar 

  • Wang Z, Su T, Konietzky H, Tan Y, Zhou G (2021) Hydraulic properties of Beishan granite after different high temperature treatments. Bull Eng Geol Env 80:2911–2923

    Article  Google Scholar 

  • Whitaker S (2013) The method of volume averaging. (vol. 13). Springer Science & Business Media

  • Witherspoon PA, Wang JS, Iwai K, Gale JE (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024

    Article  Google Scholar 

  • Xiong X, Li B, Jiang Y, Koyama T, Zhang C (2011) Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. Int J Rock Mech Min Sci 48(8):1292–1302

    Article  Google Scholar 

  • Xiong F, Jiang Q, Ye Z, Zhang X (2018) Nonlinear flow behavior through rough-walled rock fractures: the effect of contact area. Comput Geotech 102(2018):179–195

    Article  Google Scholar 

  • Yang T, Selvadurai P, Wang P, Wang S, Liu H (2022) Hydro-mechanical coupling of rough fractures that exhibit dilatancy phenomena. Bull Eng Geol Env 81(10):433

    Article  Google Scholar 

  • Yang T, Wang P, Wang S, Liu H, Zhang Z (2023) Experimental study on shear-seepage coupling characteristics of single fractured rock mass under cyclic loading and unloading. Rock Mech Rock Eng 56(3): 2137-2156.

  • Yao C, Shao Y, Yang J, Huang F, He C, Jiang Q, Zhou C (2020) Effects of fracture density, roughness, and percolation of fracture network on heat-flow coupling in hot rock masses with embedded three-dimensional fracture network. Geothermics 87(2020):101846

    Article  Google Scholar 

  • Yin Q, Jing H, Liu R, Su H, Yu L, Han G (2020) Pore characteristics and nonlinear flow behaviors of granite exposed to high temperature. Bull Eng Geol Env 79:1239–1257

    Article  Google Scholar 

  • Zambrano M, Pitts AD, Salama A, Volatili T, Giorgioni M, Tondi E (2019) Analysis of fracture roughness control on permeability using SfM and fluid flow simulations: implications for carbonate reservoir characterization. Geofluids 2019

  • Zhang Q, Ju Y, Gong W, Zhang L, Sun H (2015) Numerical simulations of seepage flow in rough single rock fractures. Petroleum 1(3):200–205

    Article  Google Scholar 

  • Zhang A, Yang J, Cheng L, Ma C (2022a) A simulation study on stress-seepage characteristics of 3D rough single fracture based on fluid-structure interaction. J Petrol Sci Eng 211(2022):110215

    Article  CAS  Google Scholar 

  • Zhang Z, Wang S, Yin H, Yang T, Wang P (2022b) Fracture seepage and the temperature field distribution of rocks surrounding high-temperature tunnels: a numerical analysis. Geomech Geophys Geo-Energy Geo-Resour 8(4):1–30

    Google Scholar 

  • Zhou J-Q, Hu S-H, Fang S, Chen Y-F, Zhou C-B (2015) Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading. Int J Rock Mech Min Sci 80(2015):202–218

    Article  Google Scholar 

  • Zhou S, Luo X, Jiang N, Zhang S, Lei Y (2021) Ground vibration characteristics of carbon dioxide phase transition fracturing: an in situ test. Bull Eng Geol Env 80:9029–9047

    Article  Google Scholar 

  • Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23(1):1–30

    Article  CAS  Google Scholar 

  • Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Non-linear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(3):163–169

    Article  Google Scholar 

  • Zoorabadi M, Saydam S, Timms W, Hebblewhite B (2015) Non-linear flow behaviour of rough fractures having standard JRC profiles. Int J Rock Mech Min Sci 76(2015):192–199

    Article  Google Scholar 

  • Zou L, Jing L, Cvetkovic V (2017) Shear-enhanced nonlinear flow in rough-walled rock fractures. Int J Rock Mech Min Sci 97(2017):33–45

    Article  Google Scholar 

Download references

Funding

This work was conducted with supports from the National Natural Science Foundation of China (Grant Nos. U1602232 and 51474050), Liaoning Science and Technology Project (2019JH2/10100035).

Author information

Authors and Affiliations

  1. School of Resources and Civil Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Ze Zhang, Shuhong Wang, Furui Dong, Zehui Gao & Dongsheng Wang

  2. School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, 211816, Jiangsu, China

    Tianjiao Yang

Authors
  1. Ze Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuhong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tianjiao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Furui Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zehui Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Dongsheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Ze Zhang: data curation, results and discussion, writing—original draft. Shuhong Wang: conceptualization, methodology, funding acquisition, resources. Tianjiao Yang: final editing, writing—review and editing. Furui Dong: writing—review and editing. Zehui Gao: project administration. Dongsheng Wang: writing—review and editing.

Corresponding author

Correspondence to Shuhong Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Wang, S., Yang, T. et al. Influence of contact characteristics on nonlinear flow and eddy development in three-dimensional fractures under normal stress. Bull Eng Geol Environ 83, 129 (2024). https://doi.org/10.1007/s10064-024-03644-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10064-024-03644-7

Keywords

Search

Navigation