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*

doi:10.7523/j.ucas.2026.035

摘要/Abstract

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

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

中图分类号:

X523

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, DOI: 10.7523/j.ucas.2026.035.

WANG Siyu, QU Cixiao, WANG Mingyu. Establishing generalizable statistical prediction models and identifying primary controlling factors for nonlinear flow characteristic parameters in rough fractures[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.035.

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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^*

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

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