粗糙裂隙非线性渗流特征参变量泛化统计预测模型构建及主控因子识别&#x0002A;

王思渝; 曲辞晓; 王明玉

doi:10.7523/j.ucas.2026.035

中国科学院大学学报 >

2026 2026031

DOI: https://doi.org/10.7523/j.ucas.2026.035

粗糙裂隙非线性渗流特征参变量泛化统计预测模型构建及主控因子识别^*

王思渝 ,
曲辞晓 ,
王明玉

展开

中国科学院大学资源与环境学院,北京 101408

收稿日期: 2026-03-10

修回日期: 2026-05-20

网络出版日期: 2026-06-03

基金资助

^*国家自然科学基金（42207106、42477092）和国家重点研发计划项目（2024YFC3712702）资助

收起

Establishing generalizable statistical prediction models and identifying primary controlling factors for nonlinear flow characteristic parameters in rough fractures

WANG Siyu ,
QU Cixiao ,
WANG Mingyu

Expand

College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 101408, China

Received date: 2026-03-10

Revised date: 2026-05-20

Online published: 2026-06-03

Fold

摘要

岩体裂隙是地下水渗流与污染物运移的主要通道之一。受隙宽、粗糙度及相交构型等几何特征与水力梯度共同控制,天然粗糙裂隙整体渗流可能偏离传统立方定律,并呈现出可由Forchheimer方程描述的非线性特征。针对典型粗糙圆盘裂隙,本文构建了影响渗流的裂隙几何特征与水动力参数集,并通过正交试验设计确定代表性参数组合。本文利用功率谱密度（power spectral density, PSD）控制的随机方法生成粗糙裂隙面,并结合数值模拟仿真获取了162个典型情景下的渗流相关参数。基于Forchheimer非线性渗流拟合方程,本文建立了非线性渗流特征参变量（线性项系数A非线性项系数B与非线性效应因子E）的全因子回归预测模型,并进一步通过逐步回归与方差分析（analysis of variance, ANOVA）识别其主控因子。结果表明,裂隙尺寸、出口交线长度和平均隙宽是影响非线性渗流行为的关键因素。数值模拟仿真数据验证结果表明,本文所建立的非线性渗流特征参变量统计预测模型具有较好的泛化能力,可为典型粗糙裂隙非线性渗流特征参变量的快速预测与量化表征提供参考。

关键词： 粗糙圆盘裂隙; 裂隙相交几何构型; 非线性渗流; 统计回归; 泛化预测模型

本文引用格式

王思渝 , 曲辞晓 , 王明玉 . 粗糙裂隙非线性渗流特征参变量泛化统计预测模型构建及主控因子识别^*[J]. 中国科学院大学学报, 2026 : 2026031 . DOI: 10.7523/j.ucas.2026.035

Abstract

Rock fractures are one of the main pathways for groundwater seepage and contaminant transport. Under the combined control of geometric characteristics such as aperture, roughness, and intersection configuration, as well as hydraulic gradient, the overall seepage in natural rough fractures may deviate from the traditional cubic law and exhibit nonlinear characteristics that can be described by the Forchheimer equation. For typical rough disc-shaped fractures, this study constructed a set of fracture geometric characteristics and hydrodynamic parameters affecting seepage, and determined representative parameter combinations through an orthogonal experimental design. Rough fracture surfaces were generated using a stochastic method controlled by power spectral density (PSD), and seepage-related parameters under 162 representative scenarios were obtained through numerical simulations. Based on the Forchheimer nonlinear seepage fitting equation, full-factor regression prediction models were established for nonlinear seepage characteristic parameters, including the linear coefficient A, nonlinear coefficient B, and nonlinear effect factor E. Furthermore, their primary controlling factors were identified through stepwise regression and analysis of variance (ANOVA). The results show that fracture size, outlet intersection-line length and mean aperture are key factors affecting nonlinear seepage behavior. The validation results based on numerical simulation data indicate that the statistical prediction models established in this study for nonlinear seepage characteristic parameters have good generalization capability, providing a reference for the rapid prediction and quantitative characterization of nonlinear seepage characteristic parameters in typical rough fractures.

Key words： rough disc-shaped fractures; fracture intersection configuration; nonlinear flow; statistical regression; generalizable prediction model

参考文献

[1] Hu M S, Rutqvist J.Numerical manifold method modeling of coupled processes in fractured geological media at multiple scales[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2020, 12(4): 667-681. DOI:10.1016/j.jrmge.2020.03.002.
[2] Pyrak-Nolte L J, Nolte D D. Approaching a universal scaling relationship between fracture stiffness and fluid flow[J]. Nature Communications, 2016, 7: 10663. DOI:10.1038/ncomms10663.
[3] 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.
[4] 徐添阳,琚宜文,黄骋,等. 四川盆地南缘五峰—龙马溪组海相页岩压缩变形试验与破裂模式研究[J]. 中国科学院大学学报, 2018, 35(4): 561-568.
[5] 刘庆哲. 圆盘裂隙模型渗流与溶质运移规律的模拟研究及应用探讨[D]. 北京: 中国科学院大学, 2020.
[6] 蔡佳豪,郤保平,董赟盛,等. 粗糙交叉裂隙非线性渗流特性研究[J]. 矿业安全与环保, 2025, 52(2): 145-152. DOI:10.19835/j.issn.1008-4495.20240012.
[7] 胡少华,周佳庆,陈益峰,等. 岩石粗糙裂隙非线性渗流特性试验研究[J]. 地下空间与工程学报, 2017, 13(1): 48-56. DOI:10.20174/j.juse.2017.01.008.
[8] 张莉丽. 裂隙岩体渗透典型单元体存在性[D]. 北京: 中国地质大学(北京), 2011.
[9] Wong D L Y, Doster F, Geiger S, et al. Fluid flow characterization framework for naturally fractured reservoirs using small-scale fully explicit models[J]. Transport in Porous Media, 2020, 134(2): 399-434. DOI:10.1007/s11242-020-01451-8.
[10] 王明玉,刘庆哲,曲辞晓,等. 基于圆盘裂隙物理模型的岩体单一裂隙渗流规律试验研究[J]. 岩土力学, 2020, 41(11): 3523-3530. DOI:10.16285/j.rsm.2020.0250.
[11] 刘华梅,王明玉. 三维裂隙网络渗流路径识别算法及其优化[J]. 中国科学院研究生院学报, 2010, 27(4): 463-470.
[12] Zhang Y, Chai J R.Effect of surface morphology on fluid flow in rough fractures: A review[J]. Journal of Natural Gas Science and Engineering, 2020, 79: 103343. DOI:10.1016/j.jngse.2020.103343.
[13] 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.
[14] Zhang Z Y, Nemcik J.Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J]. Journal of Hydrology, 2013, 477: 139-151. DOI:10.1016/j.jhydrol.2012.11.024.
[15] 刘日成,蒋宇静,李树忱,等. 交叉裂隙水力学开度的计算及非线性水力特性研究[J]. 岩土力学, 2015, 36(6): 1581-1590. DOI:10.16285/j.rsm.2015.06.008.
[16] 朱寅斌,李长冬,周佳庆,等. 粗糙岩石单裂隙非达西流动的试验和数值模拟研究[J]. 岩土工程学报, 2023, 45(6): 1278-1284.
[17] 尹乾,靖洪文,刘日成,等. 不同侧压力系数下裂隙网络岩体非线性渗流特性[J]. 岩土力学, 2019, 40(2): 592-600. DOI:10.16285/j.rsm.2018.0018.
[18] 吴兵,盛建龙,叶祖洋,等. 单裂隙岩体非线性渗流-法向应力耦合模型研究[J]. 岩土力学, 2025, 46(8): 2495-2504. DOI:10.16285/j.rsm.2024.1172.
[19] 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, 3312. DOI:10.16285/j.rsm.2016.2623.
[20] 周新,盛建龙,叶祖洋,等. 岩体粗糙裂隙几何特征对其Forchheimer型渗流特性的影响[J]. 岩土工程学报, 2021, 43(11): 2075-2083. DOI:10.11779/CJGE202111014.
[21] 曲辞晓. 离散圆盘裂隙网络组构对渗流与溶质运移的控制过程及规律研究[D]. 北京: 中国科学院大学, 2021.
[22] Qu C X, Wang M Y, Wang P.Experimental and numerical investigation of groundwater head losses on and nearby short intersections between disc-shaped fractures[J]. Journal of Groundwater Science and Engineering, 2022, 10(1): 33-43. DOI:10.19637/j.cnki.2305-7068.2022.01.004.
[23] Quinn P M, Cherry J A, Parker B L.Relationship between the critical Reynolds number and aperture for flow through single fractures: Evidence from published laboratory studies[J]. Journal of Hydrology, 2020, 581: 124384. DOI:10.1016/j.jhydrol.2019.124384.
[24] Geng S Y, Zhou Y H, Geng M, et al.New insights into the identification and characterization of Darcy-to-Forchheimer flow transitions in rough fractures[J]. Journal of Hydrology, 2025, 659: 133252. DOI:10.1016/j.jhydrol.2025.133252.
[25] 马亚楠,杨志兵,熊小锋,等. 粗糙裂隙各向异性对非达西渗流特性的影响[J]. 人民长江, 2023, 54(1): 233-239, 244. DOI:10.16232/j.cnki.1001-4179.2023.01.033.
[26] 刘殷彤,毛灵涛,程建超,等. 岩石粗糙裂隙渗流逾渗机制[J]. 岩石力学与工程学报, 2026, 45(1): 118-143. DOI:10.3724/1000-6915.jrme.2025.0438.
[27] 张戈,田园,李英骏. 不同JRC粗糙单裂隙的渗流机理数值模拟研究[J]. 中国科学: 物理学力学天文学, 2019, 49(1): 30-39.
[28] 佴宇鏖,周佳庆,李长冬,等. 基于裂隙网络几何特征参数的岩体溶质传输过程预测模型研究[J]. 岩土工程学报, 2025, 47(8): 1641-1652. DOI:10.11779/CJGE20240355.
[29] 毋振华,王者超,郭玟志,等. 平面交叉裂隙非线性渗流模型参数人工神经网络预测[J]. 工程地质学报, 2020, 28(5): 982-988. DOI:10.13544/j.cnki.jeg.2020-184.
[30] Qu C X, Sun M N, Wang M Y.Establishing generalizable and practicable models of flow regime classifying via mechanism-enhanced machine learning for various rough fractures[J]. Rock Mechanics and Rock Engineering, 2026: 1-24. DOI:10.1007/s00603-026-05433-y.
[31] 刘杰,钟伦伟,钟振,等. 恒定法向刚度边界条件下受剪岩石裂隙非线性渗流特性的数值模拟研究[J]. 岩土力学, 2025, 46(6): 1919-1933. DOI:10.16285/j.rsm.2024.1023.
[32] Li B, Wang J F, Liu R C, et al.Nonlinear fluid flow through three-dimensional rough fracture networks: Insights from 3D-printing, CT-scanning, and high-resolution numerical simulations[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(5): 1020-1032. DOI:10.1016/j.jrmge.2021.04.007.
[33] Wanniarachchi W A M, Ranjith P G, Perera M S A, et al. An integrated approach to simulate fracture permeability and flow characteristics using regenerated rock fracture from 3-D scanning: A numerical study[J]. Journal of Natural Gas Science and Engineering, 2018, 53: 249-262. DOI:10.1016/j.jngse.2018.02.033.
[34] Brown S R.Fluid flow through rock joints: The effect of surface roughness[J]. Journal of Geophysical Research: Solid Earth, 1987, 92(B2): 1337-1347. DOI:10.1029/JB092iB02p01337.
[35] Ogilvie S R, Isakov E, Glover P W J. Fluid flow through rough fractures in rocks. II: A new matching model for rough rock fractures[J]. Earth and Planetary Science Letters, 2006, 241(3/4): 454-465. DOI:10.1016/j.epsl.2005.11.041.
[36] Matsuki K, Chida Y, Sakaguchi K, et al.Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(5): 726-755. DOI:10.1016/j.ijrmms.2005.12.001.
[37] Bear J.Dynamics of Fluids in Porous Media[M]. New York: American Elsevier Pub. Co, 1972.
[38] He S Q, Feng B, Zhu J S, et al.A 3D analysis of the occurrence of fractures in hot dry rock reservoirs based on the spatial distribution of natural fractures[J]. Energy Geoscience, 2023, 4(4): 100165. DOI:10.1016/j.engeos.2023.100165.
[39] Hadgu T, Karra S, Kalinina E, et al.A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock[J]. Journal of Hydrology, 2017, 553: 59-70. DOI:10.1016/j.jhydrol.2017.07.046.
[40] Luo Z W, Zhang R, Xie J, et al.A new approach for 3D structure characterization of rock mass using an improved elliptical discrete fracture network model[J]. Engineering Geology, 2024, 339: 107661. DOI:10.1016/j.enggeo.2024.107661.
[41] Zhang Y S, Chen J P, Zhou F J, et al.A novel approach to investigating 3D fracture connectivity in ultrahigh steep rock slopes[J]. International Journal of Rock Mechanics and Mining Sciences, 2023, 161: 105291. DOI:10.1016/j.ijrmms.2022.105291.
[42] Singh J, Pradhan S P, Vishal V, et al.Characterization of a fractured rock mass using geological strength index: A discrete fracture network approach[J]. Transportation Geotechnics, 2023, 40: 100984. DOI:10.1016/j.trgeo.2023.100984.
[43] Li W, Wang Z C, Qiao L P.Determination of REV size and equivalent permeability coefficient of fractured rock masses from the perspective of fracture network connectivity[J]. Computers and Geotechnics, 2024, 173: 106590. DOI:10.1016/j.compgeo.2024.106590.
[44] Huang N, Liu R C, Jiang Y J, et al.Development and application of three-dimensional discrete fracture network modeling approach for fluid flow in fractured rock masses[J]. Journal of Natural Gas Science and Engineering, 2021, 91: 103957. DOI:10.1016/j.jngse.2021.103957.
[45] Wang Y P, Zhou J W, Chen J L, et al.Integration of automatic discontinuity identification and multi-scale hierarchical modeling for stability analysis of highly-jointed rock slopes[J]. International Journal of Rock Mechanics and Mining Sciences, 2024, 184: 105955. DOI:10.1016/j.ijrmms.2024.105955.
[46] Yan J S, Wu Y W, Gao Q R, et al.Tunable discrete fracture network for dynamic analyses of rock landslides by material point method[J]. Computers and Geotechnics, 2025, 182: 107154. DOI:10.1016/j.compgeo.2025.107154.
[47] Gottron D, Henk A.Upscaling of fractured rock mass properties-An example comparing Discrete Fracture Network (DFN) modeling and empirical relations based on engineering rock mass classifications[J]. Engineering Geology, 2021, 294: 106382. DOI:10.1016/j.enggeo.2021.106382.
[48] Pang Y T, Qu C X, Wang M Y.Efficient quantification via statistical surrogate models for LNAPL migration in typical saturated intersecting fractures[J]. Journal of Hazardous Materials, 2026, 505: 141517. DOI:10.1016/j.jhazmat.2026.141517.

Options

文章导航

摘要

本文引用格式

Abstract

参考文献

访问统计

联系我们

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献

访问统计

联系我们