Abstract
The mining-induced failure zone is one of the main water flow channels. Due to the complexity of fracture distribution and groundwater flow in the fractures, calculating the water conductivity of fractures in the mining failure zone is a hot and difficult research topic at present. In order to simultaneously simulate the permeability of the complete rock mass of the floor and the hydraulic conductivity of the fractures, a numerical simulation model of pore-fracture porous media was established to study the influence of different fracture structure parameters in the coal seam floor on the hydraulic conductivity of the floor. The spatial distribution of water pressure and water flow velocity under the conditions of different fracture structure parameters and permeability was studied. The simulation results show that the floor pressure distribution is consistent with the actual situation. The distribution of water pressure at the fracture location presents a downward trend. The pressure gradient in the fracture is smaller than that in the fracture’s surrounding porous rock mass. The model can not only simulate and calculate the resistance of complex pore-fracture media to fluid, but also simplify the calculation, providing a new method for the simulation and calculation of the hydraulic conductivity of the floor fracture zone.
1 Introduction
Mine water disaster is one of the major hazards threatening the safe production of coal mines in China (; ; ). With the gradual depletion of shallow coal resources, the depth of coal mining in China has been continuously increasing in recent years. Deeply buried lower coal seams are in complex geological environments with high in situ stress and high water pressure (; ). The basic theoretical research on the mechanism of mine floor water inrush is an interdisciplinary technical problem involving fluid mechanics, rock mechanics, hydrogeology and other disciplines (; ). Chinese experts and scholars have carried out a lot of in-depth research (, and put forward a series of theoretical systems for floor water disaster prevention and control, including the “Lower Three Zones” Theory (), the Water Inrush Coefficient Method (; ), and the Key Stratum Theory (; ). These theoretical results have laid a solid foundation for the prediction and prevention of mine floor water inrush, and made important contributions to the development of safe mining theories and technologies for coal resources under aquifers.
Two necessary conditions for the occurrence of mine floor water inrush are the existence of a reliable water source and an effective water-conducting pathway (). Groundwater in confined aquifers is the main water source for floor water inrush disasters (), and the aquifer water pressure deter-mines whether groundwater can migrate to the mining face through the water-conducting pathway (; ). The failure zones in underground rock masses, including structural fractures such as faults and collapse columns and mining-induced failure zones, are the main water-conducting pathways (; ), and their water conductivity is closely related to fracture structural parameters such as fracture aperture and fracture density. Numerical study of mechanical properties and microcrack evolution of double-layer composite rock specimens with fissures under uniaxial compression (). Grouting optimization for tunnel water-inrush disaster mitigation in jointed rock masses using discrete fracture network modeling (). Fractures can become the main water-conducting channels essentially because the flow resistance of ground-water in fractures is lower than that in the low-permeability aquiclude porous rock mass (), and this resistance directly determines the magnitude of fracture water conductivity. Groundwater needs to overcome its own gravity and the flow resistance along the path when migrating from the aquifer to the mining face through the fracture pathway, and the driving force for migration comes from the aquifer water pressure (). Therefore, it is essential to study the quantitative relationship between water pressure and fracture structural parameters to accurately assess the risk of floor water inrush.
Since fractures are embedded in the porous rock matrix, it is necessary to calculate the groundwater flow parameters in fractures and the surrounding porous media at the same time (). The complex flow behavior of fluid in porous media is usually analyzed by the volume-averaging method, which converts the physical quantities of fluid into average parameters, while the fluid parameters in fractures can be obtained by solving the momentum conservation equation. Due to the differences between the two calculation methods, it is quite difficult to calculate the flow resistance in fractures and porous rock masses simultaneously, resulting in relatively limited research on the spatial distribution characteristics of groundwater flow velocity and water pressure in coal seam floor fractures and surrounding rock masses (; ).
To address the above research gaps, this study uses COMSOL numerical simulation software to couple Darcy’s Law based on the volume-averaging method with the fluid momentum conservation equation, and establishes a pore-fracture porous media numerical model that can simultaneously calculate the groundwater flow parameters in fractures and the surrounding porous media. By comparing with the pore-type porous media numerical model, the in-fluence mechanism of different fracture structural parameters (fracture quantity, aperture, dip angle) on the water-conducting capacity of the coal seam floor fracture zone is systematically studied, and the disaster-inducing mechanism of floor water inrush from the perspective of fluid flow resistance is revealed, providing a theoretical basis and numerical method for the accurate prediction and prevention of mine floor water inrush.
2 Methods
2.1 Governing equations
Underground coal and rock masses are classified as porous media, and fluid flow within such media is highly complex. In practice, the actual flow parameters (e.g., physical velocity) at the pore scale are not directly analyzed; instead, the volume averaging method is used to transform physical velocity into seepage velocity. The seepage velocity derived from Darcy’s experiments is a typical averaged velocity, which is expressed as ():where: is Darcy velocity of the fluid, is permeability of the porous medium, is dynamic viscosity of the fluid, is pore water pressure, is fluid density, is gravitational acceleration vector.
The continuity equation for fluid flow in porous media is given by ():where is porosity of the porous medium.
Combining Equations 1, 2 yields the governing equation for porous media seepage: Fluid flow in fractures of underground coal-rock masses is commonly studied via two approaches: Equating fractures to pores and applying Darcy’s Law, consistent with porous media flow analysis; Directly characterizing the actual flow state in fractures, which is governed by the fluid momentum conservation equation (see Equation 3, ):where is physical velocity of fluid within fractures.
For porous rock masses, the momentum conservation equation reduces to the Brinkman equation (see Equation 4):
By using the Brinkman physical field interface in COMSOL, the fracture area is defined as fracture flows, and other areas are defined as porous media. To calculate mining induced damage zones in the roof and floor of coal seams, porous media are typically assumed to be elastic. Based on the generalized Hooke’s Law and accounting for external stresses (e.g., pore fluid pressure, thermal stress), the constitutive equation is written as (see Equation 5):where is body force vector.
For fractured rock masses, a rock damage variable is adopted to quantify the degree of rock failure and its evolutionary process. The nonlinearity of rock stress–strain curves is generally attributed to progressive damage, microcrack initiation, and propagation under loading-rather than plastic deformation—especially under tensile stress, where brittle behavior is pronounced. Therefore, the constitutive relation of elastic damage mechanics is suitable for describing the mechanical properties of rock meso-elements ().
Since the 1980s, scholars worldwide have proposed various damage models (elastic damage, elastoplastic damage, etc.). Based on the strain equivalence principle-which states that the strain induced by stress on damaged material is equivalent to that induced by effective stress on intact material defined the following damage variables (see Equations 6–8, ):where: is damage variable, is uniaxial tensile strength, is uniaxial compressive strength, is maximum principal tensile strain at tensile damage initiation, is maximum principal compressive strain at shear damage initiation, is coefficient describing element damage evolution (taken as = 2), , are stress state functions for damage judgment based on the maximum tensile stress criterion and Mohr-Coulomb criterion, respectively. Tensile damage occurs at , and shear damage at .
Incorporating the above damage variable, the permeability of a failed intact rock layer can be expressed as (see Equation 9, ):where is permeability influence coefficient due to damage (taken as 5 in this study).
2.2 Pore-fracture type numerical simulation model
The pore-type porous media numerical model simulates the pore characteristics and permeability of coal seam floors by assigning distinct porosity and permeability values. When fractures exist in the floor, a pore-fracture model is required to simultaneously represent the permeability of porous media and the water-conducting capacity of fractures. To clarify the effects of fracture structural parameters on floor water conductivity and highlight differences from the pore-type model, both pore-type and pore-fracture porous media numerical models are established.
2.2.1 Pore-type porous media model
2.2.1.1 Geometric model
The pore-type model characterizes pore structure via porosity, converting physical fluid velocity to the product of seepage velocity and porosity using the volume-averaging method; explicit pore geometry is therefore unnecessary. As shown in the Supplementary Figure S1, the model consists of a 3 m-thick coal seam, a 20 m-thick floor aquiclude, and a 5 m-thick basal aquifer, with a total model width of 30 m.
2.2.1.2 Boundary conditions
To quantify flow resistance (required water pressure) in the aquiclude under varying seepage velocities, the lower boundary of the aquifer is set as a velocity inlet (with variable velocity per simulation scheme), the upper boundary of the mining face as a pressure out-let (0 Pa), and all other boundaries as zero-velocity boundaries.
2.2.1.3 Material parameters
Key parameters include groundwater density (1 × 10 3 kg/m3), dynamic viscosity (1 × 10–3 Pa⋅s), aquiclude permeability (1 × 10–15 m2), and aquifer permeability (1 × 10−12 m2).
2.2.2 Pore-fracture type porous media model
The pore-fracture model comprises porous rock masses and discrete fractures. Porous media are defined by porosity (no explicit pore geometry), and fractures penetrate the aquiclude to connect the aquifer and mining face. As can be seen in the Supplementary Figure S2, the model dimensions are 30 m (width) × 28 m (height), with a 3 m coal seam, 20 m aquiclude, and 5 m aquifer. Fracture structural parameters are adjusted per simulation scheme.
2.2.3 Pore-fracture type porous media model
Spatial pressure distributions for intact (fracture-free) and fractured floors are presented in Figures 1a,b (fracture aperture = 20 mm, inlet velocity = 3 × 10–5 m/s). The fractured case simulates a single fracture (aperture 20 mm, dip 18°) embedded in porous media with permeability matching the pore-type model.
FIGURE 1
Horizontal direction: Pressure is uniform in the intact floor, but exhibits a con-cave-down distribution in the fractured floor (low pressure at fractures, high pressure in adjacent rock). This arises because flow resistance is uniform in the homogeneous aquiclude, but lower within fractures than in surrounding porous media.
Vertical direction: Pressure gradient is uniform in the intact floor, but smaller within fractures than in adjacent rock. Uniform permeability yields consistent vertical flow resistance in the intact floor, while reduced resistance in fractures lowers the local pressure gradient.
Velocity distributions for intact and fractured floors are shown in Figures 1c,d (single fracture, aperture 200 mm, dip 18°, inlet velocity = 3 × 10–5 m/s). In the intact floor, seepage velocity is spatially uniform (3 × 10–5 m/s) due to homogeneous permeability, consistent pressure gradients, and mass conservation. In the fractured floor, flow velocity within fractures is drastically higher than in surrounding rock, as groundwater preferentially migrates through low-resistance fracture pathways.
Along the measurement line at x = 2 m (Figure 2a), seepage velocity in the aquifer is greater than in porous media adjacent to fractures. By mass conservation, total inflow from the aquifer equals outflow from the aquiclude; most flow is concentrated in fractures, leading to higher velocity in the aquifer than in the surrounding porous rock.
FIGURE 2
To isolate fracture resistance, hydrostatic pressure is excluded from analysis. As shown in Figure 2b (inlet velocity from 3 × 10–8 m/s to 4 × 10–5 m/s, aperture 5 mm–200 mm), average water pressure at the fracture inlet differs by approximately six orders of magnitude between 5 mm and 200 mm apertures. Larger fracture apertures reduce along-path flow resistance, lowering the required aquifer pressure. Inlet velocity is positively correlated with fracture inlet pressure.
Water conductivity of fracture zones is closely related to fracture density. Pressure distributions for 3 and 5 fractures (aperture 40 mm, inlet velocity 1 × 10–5 m/s) are plotted in the Supplementary Figures S3, S4. Similar to single-fracture behavior, pressure exhibits a concave-down distribution at fracture locations, with intermediate zones also showing reduced pressure due to hydraulic interaction between adjacent fractures.
As fracture quantity increases from 1 to 5 (Figure 3), average pressure at the aquifer in-let decreases monotonically. Increased fracture density expands the total cross-sectional flow area, reducing overall flow resistance of the fracture zone. This confirms that greater fracture development enhances water conductivity, reduces required pressure for a given flow rate, and elevates water inrush risk.
FIGURE 3
2.3 Pore-stochastic fracture hydro-mechanical-damage (HMD) coupling model
Mining-induced deformation and failure of mine roof and floor strata form water-conducting pathways (e.g., roof water-conducting fracture zones and floor mining-induced failure zones). Groundwater flow in fractures approximates pipe flow, while flow in surrounding rock follows porous media seepage. To accurately simulate dual flow regimes, the momentum conservation equation and porous media seepage equation must be solved simultaneously. The pore-fracture model established above captures both fracture pipe flow and intact rock seepage, realistically reproducing groundwater flow in mining-damaged zones.
To further simulate mining-induced damage, stress and damage equations are coupled into the model. Stochastic fracture networks are introduced to better represent natural fracture distributions in coal seam roofs and floors. Thus, a pore-stochastic fracture hydro-mechanical-damage (HMD) coupling model is developed, with a working Face of a Coal Mine as the engineering case.
2.3.1 Overview of the working face
The average vertical depth of the Working Face is 617 m. The No.2 coal seam has an average thickness of 9.3 m and a dip angle of 4°–6°.
2.3.2 Establishment of the pore-stochastic fracture HMD coupling model
As can be seen in Supplementary Figure S5, a geometric model is constructed based on engineering geological conditions: length 745 m, height 662 m, coal seam thickness 9.3 m, working face inclined length 241 m, with stochastic fracture networks assigned to the roof and floor.
Mining-induced damage zones in the roof and floor are shown in the Supplementary Figure S6. Under hydro-mechanical-damage coupling, damage propagates around fractures and interconnects discrete fractures, forming continuous water-conducting pathways.
Seepage velocity distributions under aquifer pressures of 0, 1, 2, and 3 MPa (outlet pressure = 0 MPa) are plotted in Figure 4. Velocity is zero at 0 MPa. With increasing aquifer pressure, groundwater flows preferentially through interconnected damaged fracture zones, and maximum seepage velocity rises from 5.51 × 10–4 m/s to 1.67 × 10–3 m/s. Roller support is applied on both sides of the model, fixed constraints are applied on the lower boundary, and uniformly distributed loads are applied on the upper boundary. The model adopts an unstructured model mesh.
FIGURE 4
For the pore-type control model (inlet pressure 3 MPa, Figure 4), maximum seepage velocity is 3.02 × 10−4 m/s significantly lower than the pore-fracture model. This is because the pore-fracture model treats fractures as discrete pipe-flow pathways (low resistance) rather than homogeneous porous media (high resistance), yielding higher over-all permeability and flow velocity in damaged zones. The pore-fracture framework there-fore better reflects in situ geological and hydraulic conditions.
3 Conclusions and discussions
Based on porous media seepage and fluid mechanics, a pore-fracture numerical model is developed to simultaneously simulate fracture pipe flow and seepage in surrounding porous rock. The model quantifies spatial distributions of groundwater pressure and velocity under varying fracture structural parameters.
Simulated distributions agree with field observations: flow resistance in surrounding rock exceeds that in fractures, creating a concave-down horizontal pressure profile and smaller vertical gradient within fractures. Flow velocity in fractures is far higher than in intact rock. Water conductivity increases with aperture and quantity, reducing the required pressure for a given flow rate and increasing inrush risk with greater fracture development.
The proposed model couples Darcy’s Law with the fluid momentum conservation equation, improving physical realism in both intact rock and fracture zones. It accurately reproduces flow resistance in complex pore-fracture media while simplifying computations for dual flow regimes, providing a novel numerical approach for evaluating the water-conducting capacity of coal seam floor fracture zones.
The model assumes that the failure area of the coal seam roof and floor is equivalent to random fractures, and modeling should be based on actual situations in future research.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
Author contributions
LS: Data curation, Writing – original draft. WL: Methodology, Writing – review and editing. DM: Resources, Writing – review and editing. HL: Conceptualization, Methodology, Writing – review and editing. ZM: Data curation, Investigation, Writing – review and editing. XZ: Software, Visualization, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This research was funded by the Joint Special Project for the “Double First-Class” Construction of Kunming University of Science and Technology - General Project (No. 202401BE070001-063), the National Natural Science Foundation of China (No. 51874192), and the Basic Research Program of Yunnan Provincial Science and Technology Department - General Program, grant number (No. 202501CF070134).
Acknowledgments
We express our gratitude to the editors and reviewers for their dedication and hard work.
Conflict of interest
Authors LS, HL, and ZM were employed by China Zuoquan Wulihou Coal Industry Co., Ltd., Shanxi Lu’ an Group.
Author XZ was employed by Xinjiang Kalatongke Mining Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2026.1819926/full#supplementary-material
References
1
CaoZ.GuQ.HuangZ.FuJ. (2022). Risk assessment of fault water inrush during deep mining. Int. J. Min. Sci. Technol.32 (2), 423–434. 10.1016/j.ijmst.2022.01.005
2
GuY. L.ZhaoJ. Y.KongD. B.JiG. Q.ShiL. H.LiH. T.et al (2026). Numerical study on the permeability evolution within fault damage zones. Water18, 134. 10.3390/w18010134
3
HaoQ.WuX.MuW. P.ZhangC. (2020). Identification of mine water inrush sources based on random forest model. Sci. Technol. Eng.20, 6411–6418.
4
HuangD.JinQ.ZhengW. (2025). Grouting optimization for tunnel water-inrush disaster mitigation in jointed rock masses using discrete fracture network modeling. Geohazard Mech.3 (4), 261–271. 10.1016/j.ghm.2025.11.001
5
JinD. W.DuanJ. H.LiL. C.ZhangC. (2021). Study on the expansion of mining-induced floor fractures and identification of water-conducting channels based on microseismic technology. J. Eng. Geol.29, 962–971. 10.13544/j.cnki.jeg.2021-0330
6
KongX. Y.LiD. L.XuX. Z.LiuY. (2005). Study on mathematical models of fluid-solid-thermal coupling seepage. J. Hydrodyn.17, 269–275. 10.16076/j.cnki.cjhd.2005.02.020
7
LiW.LiuY.QiaoW.ZhaoC.YangD.GuoQ. (2017). An improved vulnerability assessment model for floor water bursting from a confined aquifer based on the water inrush coefficient method. Mine Water Environ.37 (1), 196–204. 10.1007/s10230-017-0463-3
8
LiL.XieD.WeiJ.YinH.LiG.ManX.et al (2020). Analysis and control of water inrush under high-pressure and complex karstic water-filling conditions. Environ. Earth Sci.79 (21), 493. 10.1007/s12665-020-09242-6
9
LiQ.MengX.LiuY. (2022). Sensitivity analysis of water inrush evaluation model based on the theory of water resistant key strata: a case study in a coal mine, China. Earth Sci. Inf.15 (4), 2481–2494. 10.1007/s12145-022-00851-2
10
LiangZ.SongW.LiuW. (2020). Theoretical models for simulating the failure range and stability of inclined floor strata induced by mining and hydraulic pressure. Int. J. Rock Mech. Min. Sci.132, 104382. 10.1016/j.ijrmms.2020.104382
11
LiuR.ZhiG.YangS.XuX. (2023). Investigation on mining-induced floor water inrush from column and its control based on microseismic monitoring. Adv. Civ. Eng.2023, 1–16. 10.1155/2023/3754079
12
MaQ.LiuX.TanY.ElsworthD.ShangJ.SongD.et al (2023). Numerical study of mechanical properties and microcrack evolution of double-layer composite rock specimens with fissures under uniaxial compression. Eng. Fract. Mech.289, 259535448. 10.1016/j.engfracmech.2023.109403
13
MuW.WuX.DengR.HaoQ.QianC. (2020). Mechanism of water inrush through fault zones using a coupled fluid–solid numerical model: a case study in the beiyangzhuang coal mine, northern China. Mine Water Environ.39 (2), 380–396. 10.1007/s10230-020-00689-4
14
OgataS.YasuharaH.KinoshitaN.CheonD.-S.KishidaK. (2018). Modeling of coupled thermal-hydraulic-mechanical-chemical processes for predicting the evolution in permeability and reactive transport behavior within single rock fractures. Int. J. Rock Mech. Min. Sci.107, 271–281. 10.1016/j.ijrmms.2018.04.015
15
ShengJ. C. (2006). Fully coupled mathematical model and numerical simulation of fluid-solid-thermal three-field interaction in porous media. Chin. J. Rock Mech. Eng.25 (S1), 3028–3033.
16
ShiS.WeiJ.XieD.YinH.LiL. (2019). Prediction analysis model for groundwater potential based on set pair analysis of a confined aquifer overlying a mining area. Arabian J. Geosciences12 (4), 115. 10.1007/s12517-019-4267-6
17
SunD.HouX.YangT.ZhaoY.ZhangP.YangB.et al (2022). Calibration of water inrush channel and numerical simulation of water inrush process in coal mine roof. Front. Earth Sci.10, 931508. 10.3389/feart.2022.931508
18
SunW.LiuH.CaoZ.YangH.LiJ. (2023). Mechanism analysis of floor water inrush based on criteria importance though intercrieria correlation. Water15 (2), 232. 10.3390/w15020232
19
WangP.ZhaoY.RenQ.JiangY.ZhangC.GaoY. (2022). Floor failure characteristics in deep island longwall panel: theoretical analysis and field verification. Geofluids2022, 1–14. 10.1155/2022/1851899
20
XueY.LiuY.DangF.LiuJ.MaZ.ZhuL.et al (2019). Assessment of the nonlinear flow characteristic of water inrush based on the brinkman and forchheimer seepage model. Water11 (4), 855. 10.3390/w11040855
21
YanM.ZhuS.DuanH. (2021). Risk assessment of water inrush from Ordovician limestone based on analytic hierarchical process modelling and water resistance. Arabian J. Geosciences14 (24), 2733. 10.1007/s12517-021-09119-3
22
YinL.MaK.ChenJ.XueY.WangZ.CuiB. (2019). Mechanical model on water inrush assessment related to deep mining above multiple aquifers. Mine Water Environ.38 (4), 827–836. 10.1007/s10230-019-00623-3
23
ZhangS. (2021). Mechanism of water inrush of a deep mining floor based on coupled mining pressure and confined pressure. Mine Water and the Environment40 (2), 366–377. 10.1007/s10230-020-00743-1
24
ZhangS.GuoW.LiY. (2017). Experimental simulation of water-inrush disaster from the floor of mine and its mechanism investigation. Arabian J. Geosciences10 (22), 503. 10.1007/s12517-017-3287-3
25
ZhuW.TangC.YangT.LiangZ. (2003). Constitutive relationship of mesoscopic elements used in RFPA2D and its validations. Chin. J. Rock Mech. Eng.22 (1), 24–29.
Summary
Keywords
coal mine, fracture, porous media, seepage, water inrush
Citation
Shi L, Liu W, Mu D, Li H, Mao Z and Zhang X (2026) Study on hydraulic properties in a pore-fracture coupled model for predicting water inrush from mine floors. Front. Earth Sci. 14:1819926. doi: 10.3389/feart.2026.1819926
Received
28 February 2026
Revised
07 April 2026
Accepted
14 April 2026
Published
11 May 2026
Volume
14 - 2026
Edited by
Eungyu Park, Kyungpook National University, Republic of Korea
Reviewed by
Jinhao Wen, Qingdao University of Technology, China
Li Qiang, Xinjiang Institute of Engineering, China
Updates
Copyright
© 2026 Shi, Liu, Mu, Li, Mao and Zhang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Weitao Liu, skdlwt@126.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.