Coupled effects of fracture spatial distribution and rock matrix permeability on tunnel water inflow: An embedded discrete fracture model based investigation

Abstract

Groundwater inflow constitutes a critical challenge in rock tunnel engineering. This study systematically investigates the coupled effects of fracture spatial distribution and rock matrix permeability on tunnel water inflow using a novel embedded discrete fracture model based method. A set of quadratic regression models is established to delineate the relationship between inflow rate and fracture distribution parameters over a wide range of fracture-to-matrix permeability ratios (k_{\mathrm{f}}/k_{\mathrm{m}}). Results demonstrate that fracture aperture, spacing, and their interaction dominate the inflow across all permeability ratios. Analysis of variance further reveals a threshold-dependent behavior: coupled effects are significant below a critical k_{\mathrm{f}}/k_{\mathrm{m}} value but decay markedly above it. This threshold decreases with larger aperture and increases with wider spacing, yet remains nearly independent of fracture dip angle. Moreover, when k_{\mathrm{f}}/k_{\mathrm{m}} is below the threshold, aperture and spacing exert greater influence on tunnel inflow at lower permeability ratios, while k_{\mathrm{f}}/k_{\mathrm{m}} gains influence under larger apertures and smaller spacings. Finally, a case study of Nanwan Tunnel shows that matrix permeability plays a dual role—increasing the mean inflow rate while reducing uncertainty from stochastic fracture distribution.

Graphical abstract

Keywords

tunnel water inflow / fractured rock tunnel / fracture spatial distribution / rock matrix permeability / embedded discrete fracture model / fracture-to-matrix permeability ratio

References

[1] Palmstrom A , Stille H . Ground behavior and rock engineering tools for underground excavations. Tunnelling and Underground Space Technology, 2007, 22(4): 363–376

[2] Zhu Y M , Zhou J J , Zhang B , Wang H C , Huang M Q . Statistical analysis of major tunnel construction accidents in China from 2010 to 2020. Tunnelling and Underground Space Technology, 2022, 124: 104460

[3] Liu J H , Li X J . Analytical solution for estimating groundwater inflow into lined tunnels considering waterproofing and drainage systems. Bulletin of Engineering Geology and the Environment, 2021, 80(9): 6827–6839

[4] Gong C J , Cheng M J , Fan X , Peng Y C , Ding W Q . Hydraulic fracturing-based analytical method for determining seepage characteristics at tunnel-gasketed joints. Journal of Central South University, 2025, 32(4): 1520–1534

[5] Gokdemir C , Li Y D , Rubin Y , Li X J . Stochastic modeling of groundwater drawdown response induced by tunnel drainage. Engineering Geology, 2022, 297: 106529

[6] Xu H , Li X J , Gokdemir C . Modeling and assessing the impact of tunnel drainage on terrestrial vegetation. Tunnelling and Underground Space Technology, 2021, 116: 104097

[7] Pujades E , Jurado A . Groundwater-related aspects during the development of deep excavations below the water table: A short review. Underground Space, 2021, 6(1): 35–45

[8] Shahbazi A , Saeidi A , Chesnaux R , Rouleau A . Effects of fracture-system geometrical parameters on the inflow rate into a tunnel in rock: A numerical modeling experiment. Quarterly Journal of Engineering Geology and Hydrogeology, 2023, 56(2): 618850

[9] Bi J F , Jiang H . Water infiltration in drained circular tunnels: An analytical solution and its simplification. Geotechnique, 2025, 75(2): 180–191

[10] Sun H Y , Le L , Dai Y M , Rui Y , Zhu H H , Li X J , Li X H , Xue G W . Groundwater environmental effects risk evaluation in mountain tunnel construction: A dynamic decision support system based on fuzzy two-dimensional cloud probability model. Tunnelling and Underground Space Technology, 2025, 156: 106276

[11] Farhadian H , Katibeh H , Huggenberger P , Butscher C . Optimum model extent for numerical simulation of tunnel inflow in fractured rock. Tunnelling and Underground Space Technology, 2016, 60: 21–29

[12] Javadi M , Sharifzadeh M , Shahriar K . Uncertainty analysis of groundwater inflow into underground excavations by stochastic discontinuum method: Case study of Siah Bisheh pumped storage project, Iran. Tunnelling and Underground Space Technology, 2016, 51: 424–438

[13] Sharifzadeh M , Karegar S , Ghorbani M . Influence of rock mass properties on tunnel inflow using hydromechanical numerical study. Arabian Journal of Geosciences, 2013, 6(1): 169–175

[14] Shahbazi A , Saeidi A , Chesnaux R , Rouleau A . An index based on fracture length and aperture to predict groundwater inflow rates in tunnels excavated in fractured-rock. Transportation Geotechnics, 2024, 45: 101217

[15] Shahbazi A , Chesnaux R , Saeidi A . A new combined analytical-numerical method for evaluating the inflow rate into a tunnel excavated in a fractured rock mass. Engineering Geology, 2021, 283: 106003

[16] Cesano D , Bagtzoglou A C , Olofsson B . Quantifying fractured rock hydraulic heterogeneity and groundwater inflow prediction in underground excavations: The heterogeneity index. Tunnelling and Underground Space Technology, 2003, 18(1): 19–34

[17] Bang S H , Jeon S W , Kwon S K . Modeling the hydraulic characteristics of a fractured rock mass with correlated fracture length and aperture: Application in the underground research tunnel at KAERI. Nuclear Engineering and Technology, 2012, 44(6): 639–652

[18] Rong G , Peng J , Wang X Z , Liu G , Hou D . Permeability tensor and representative elementary volume of fractured rock masses. Hydrogeology Journal, 2013, 21(7): 1655–1671

[19] Wang C C , Liu X L , Wang E Z , Wang M Y , Liu C . Dependence of connectivity dominance on fracture permeability and influence of topological centrality on the flow capacity of fractured porous media. Journal of Hydrology, 2023, 624: 129883

[20] Romano V , Bigi S , Carnevale F , Hyman J D , Karra S , Valocchi A J , Tartarello M C , Battaglia M . Hydraulic characterization of a fault zone from fracture distribution. Journal of Structural Geology, 2020, 135: 104036

[21] He CYao CShao Y LFan HZhou C B. Effective permeability of three-dimensional fractured rock with low fracture densities. Journal of Tsinghua University (Science and Technology), 2021, 61(8): 827–832 (in Chinese)

[22] Regnet J B , David C , Robion P , Menéndez B . Microstructures and physical properties in carbonate rocks: A comprehensive review. Marine and Petroleum Geology, 2019, 103: 366–376

[23] Huang Y , Yu Z B , Zhou Z F . Simulating groundwater inflow in the underground tunnel with a coupled fracture-matrix model. Journal of Hydrologic Engineering, 2013, 18(11): 1557–1561

[24] Ma L , Gao D , Qian J Z , Han D , Xing K , Ma H C , Deng Y P . Multiscale fractures integrated equivalent porous media method for simulating flow and solute transport in fracture-matrix system. Journal of Hydrology, 2023, 617: 128845

[25] Zhang K , Xue Y G , Xu Z H , Su M X , Qiu D H , Li Z Q . Numerical study of water inflow into tunnels in stratified rock masses with a dual permeability model. Environmental Earth Sciences, 2021, 80(7): 260

[26] Flemisch B , Berre I , Boon W , Fumagalli A , Schwenck N , Scotti A , Stefansson I , Tatomir A . Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources, 2018, 111: 239–258

[27] COMSOL Multiphysics. Version 6.3. Stockholm: COMSOL. 2024

[28] 3DEC: Three-Dimensional Distinct Element Code. Version 7.0. Minneapolis, MN: Itasca Consulting Group, Inc. 2020

[29] Hokr M , Škarydová I , Frydrych D . Modeling of tunnel inflow with combination of discrete factures and continuum. Computing and Visualization in Science, 2012, 15(1): 21–28

[30] Yan C Z , Wang Y X , Xie X , Ali S , Sheng Z G . A 2D continuous-discrete mixed seepage model considering the fluid exchange and the pore pressure discontinuity across the fracture for simulating fluid-driven fracturing. Acta Geotechnica, 2023, 18(11): 5791–5810

[31] Zhao L H , Di Y T , Shao L Y , Mao J . An immersed finite-discrete element method (IFDEM) framework for water entry with fracture dynamics. Computer Methods in Applied Mechanics and Engineering, 2025, 442: 118026

[32] Ren F , Ma G W , Wang Y , Li T , Zhu H H . Unified pipe network method for simulation of water flow in fractured porous rock. Journal of Hydrology, 2017, 547: 80–96

[33] Yan X , Yu H T . Numerical simulation of hydraulic fracturing with consideration of the pore pressure distribution based on the unified pipe-interface element model. Engineering Fracture Mechanics, 2022, 275: 108836

[34] Ma G W , Wang H D , Fan L F , Chen Y . A unified pipe-network-based numerical manifold method for simulating immiscible two-phase flow in geological media. Journal of Hydrology, 2019, 568: 119–134

[35] Lee S H , Lough M F , Jensen C L . Hierarchical modeling of flow in naturally fractured formations with multiple length scales. Water Resources Research, 2001, 37(3): 443–455

[36] Hajibeygi H , Karvounis D , Jenny P . A hierarchical fracture model for the iterative multiscale finite volume method. Journal of Computational Physics, 2011, 230(24): 8729–8743

[37] Moinfar A , Varavei A , Sepehrnoori K , Johns R T . Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs. SPE Journal, 2014, 19(2): 289–303

[38] Fumagalli A , Pasquale L , Zonca S , Micheletti S . An upscaling procedure for fractured reservoirs with embedded grids. Water Resources Research, 2016, 52(8): 6506–6525

[39] Rao X , Cheng L S , Cao R Y , Jia P , Wu Y H , He Y M , Chen Y . An efficient three-dimensional embedded discrete fracture model for production simulation of multi-stage fracture horizontal well. Engineering Analysis with Boundary Elements, 2019, 106: 473–492

[40] Zhang YRui YLi Z FLv Y YLi X J. Computing water inflow into fractured rock tunnels based on embedded discrete fracture model. Journal of Tongji University (Natural Science), 2025, 53(11): 1691–1701 (in Chinese)

[41] Jobson J D. Analysis of variance and experimental design. In: Jobson J D, ed. Applied Multivariate Data Analysis: Regression and Experimental Design. New York, NY: Springer, 1991

[42] Jiang X W , Wan L , Yeh T C J , Wang X S , Xu L . Steady-state discharge into tunnels in formations with random variability and depth-decaying trend of hydraulic conductivity. Journal of Hydrology, 2010, 387(3–4): 320–327

[43] Chen Z Q , He C , Zhang Y H , Xu Z Y , Li Z , Yu B X . The impact of formation heterogeneity on water discharge and groundwater depletion of an excavated tunnel. Journal of Hydrology, 2023, 627: 130403

[44] Nikvar Hassani A , Farhadian H , Katibeh H . A comparative study on evaluation of steady-state groundwater inflow into a circular shallow tunnel. Tunnelling and Underground Space Technology, 2018, 73: 15–25

[45] Atangana A. Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology. Amsterdam: Elsevier Inc., 2018

[46] Snow D T . Anisotropie permeability of fractured media. Water Resources Research, 1969, 5(6): 1273–1289

[47] Blazek J. Principles of grid generation. In: Blazek J, ed. Computational Fluid Dynamics: Principles and Applications. 3rd Ed. Amsterdam: Elsevier, 2015

[48] Møyner O , Lie K A . A multiscale two-point flux-approximation method. Journal of Computational Physics, 2014, 275: 273–293

[49] Wong DDoster FGeiger S. Chapter 9: Embedded discrete fracture models. In: Advanced Modelling with the MATLAB Reservoir Simulation Toolbox. Cambridge: Cambridge University Press, 2021

[50] El Tani M . Circular tunnel in a semi-infinite aquifer. Tunnelling and Underground Space Technology, 2003, 18(1): 49–55

[51] Farhadian H , Katibeh H , Huggenberger P . Empirical model for estimating groundwater flow into tunnel in discontinuous rock masses. Environmental Earth Sciences, 2016, 75(6): 471

[52] ISRM (International Society for Rock Mechanics) . Suggested methods for the quantitative description of discontinuities in rock masses. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1978, 15(6): 319–368

[53] Rong G , Tan J , Zhan H B , He R H , Zhang Z Y . Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture. Journal of Hydrology, 2020, 589: 125162

[54] Peng L B , Lu Z , Lei T , Jiang P . Dual-structure elements morphological filtering and local Z-score normalization for infrared small target detection against heavy clouds. Remote Sensing, 2024, 16(13): 2343

[55] MATLAB . Version R2023b. Santa Clara, CA: The MathWorks, Inc. 2023

[56] Sanderson D J , Nixon C W . Topology, connectivity and percolation in fracture networks. Journal of Structural Geology, 2018, 115: 167–177

[57] China Railway 14th Bureau Group Co.Ltd. Guanyue Road & Bridge Co.Guangdong Ltd . Monitoring and Measurement Plan for Nanwan Tunnel. 2013 (in Chinese)

[58] Gómez S , Sanchidrián J A , Segarra P , Bernardini M . A non-parametric discrete fracture network model. Rock Mechanics and Rock Engineering, 2023, 56(5): 3255–3278

[59] Hyman J D . Flow channeling in fracture networks: Characterizing the effect of density on preferential flow path formation. Water Resources Research, 2020, 56(9): e2020WR027986

[60] de Dreuzy J R , Méheust Y , Pichot G . Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN). Journal of Geophysical Research: Solid Earth, 2012, 117: B11207

[61] Xiong FJiang Q HChen S YHu X C. Modeling of coupled Darcy–Forchheimer flow in fractured porous media and its engineering applications. Chinese Journal of Geotechnical Engineering, 2021, 43(11): 2043 (in Chinese)

[62] Sadeghnejad S , Masihi M , King P R . Dependency of percolation critical exponents on the exponent of power law size distribution. Physica A, 2013, 392(24): 6189–6197

[63] Huang N , Liu R C , Jiang Y J , Cheng Y F . Development and application of three-dimensional discrete fracture network modeling approach for fluid flow in fractured rock masses. Journal of Natural Gas Science and Engineering, 2021, 91: 103957

RIGHTS & PERMISSIONS

Higher Education Press