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Study on flow regimes and seepage models through open rough-walled rock joints under high hydraulic gradient

  • Xin Qian
  • Caichu XiaEmail author
  • Yang Gui
  • Xiaoqing Zhuang
  • Qiangfeng Yu
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Abstract

Little attention has been paid to non-Darcy fluid flow through rough-walled rock joints under high hydraulic gradient. Water fluid flow through splitting granite joints was tested beyond the range of previously tested conditions by using an experimental apparatus designed for this study. This apparatus facilitated the quantification of the effects of joint surface roughness and aperture on fluid flow properties. Experimental results showed that Forchheimer’s law could provide an excellent description of the nonlinear relationship between hydraulic gradient and flow velocity, and the variations of Forchheimer coefficients with joint surface roughness and aperture were further explored. In this work, the Reynolds numbers varied between 2,881 and 290,338, and greatly exceeded the critical value of 2,300. Moreover, the fluid flow entered the turbulent flow regime. In accordance with the discriminant factor α = 0.9 on the basis of Forchheimer’s law, the fluid flow regimes were further divided into two categories: weak turbulence and fully developed turbulence. The corresponding critical Reynolds numbers were obtained and ranged from 17,169 to 94,385. Finally, a new seepage calculation formula for fluid flow through open rough-walled rock joints was established and verified by experimental observations and other formulae. Through a comprehensive consideration of the joint surface roughness and the uneven aperture distribution, the proposed formula could reflect the real fluid flow situation. The findings may prove beneficial for improving understanding of the nonlinear fluid flow in jointed rocks.

Keywords

Laboratory experiments/measurements Rough-walled rock joint Groundwater flow Flow regime Seepage model 

Etude des régimes d’écoulement et des modèles d’infiltration à travers les joints ouverts d’une roche, à surface rugueuse, sous un fort gradient hydraulique

Résumé

Peu d’attention a été porté à l’écoulement non darcyen de fluides à travers les joint d’une roche, à surface rugueuse, sous un fort gradient hydraulique. L’écoulement d’un fluide aqueux à travers les joints de clivage d’un granite a été testé au-delà des conditions d’essais précédents, en utilisant un appareil expérimental élaboré pour cette étude. Cet appareil a facilité la quantification des effets de la rugosité de surface des joints et leur ouverture sur les propriétés d’écoulement du fluide. Les résultats expérimentaux ont montré que la loi de Forchheimer pouvait permettre une excellente description de la relation non linéaire entre le gradient hydraulique et la vitesse du fluide, et les variations des coefficients de Forchheimer avec la rugosité de surface des joints et leur ouverture ont été étudiés plus avant. Dans ce travail, les nombres de Reynolds ont varié entre 2,881 et 290,338, et ont largement dépassé la valeur critique de 2,300. De plus, l’écoulement du fluide est entré en régime turbulent. Conformément au facteur de discrimination α = 0.9 sur la base de la loi de Forchheimer, les régimes d’écoulement du fluide ont été ensuite divisés en deux catégories : une turbulence faible et une turbulence pleinement développée. Les nombres de Reynolds critiques correspondant ont été obtenus et classés de 17,169 à 94,385. Finalement, une nouvelle formule de calcul d’infiltration de l’écoulement du fluide à travers les joints d’une roche, à surface rugueuse, a été établie et vérifiée par des observations expérimentales et par d’autres formules. Grâce à la prise en compte de la rugosité de surface des joints et de la distribution irrégulière du degré d’ouverture, la formule proposée pourrait refléter la réalité de l’écoulement du fluide. Ces découvertes devraient démontrer les bénéfices d’une meilleure compréhension de l’écoulement non linéaire de fluides au sein de roches fissurées.

Estudio los regímenes de flujo y de los modelos de infiltración a través de diaclasas abiertas de paredes rugosas con un alto gradiente hidráulico

Resumen

Se ha prestado poca atención al flujo de fluidos, que no pertenece a Darcy, a través de diaclasas de pared rugosa con un alto gradiente hidráulico. El flujo de fluido de agua a través de la separación entre las diaclasas en un granito se probó, por encima del rango de las condiciones testeadas previamente, mediante el uso de un aparato experimental diseñado para este estudio. Este aparato facilitó la cuantificación de los efectos de la rugosidad de la superficie de la diaclasa y la apertura en las propiedades de flujo del fluido. Los resultados experimentales mostraron que la ley de Forchheimer podría proporcionar una excelente descripción de la relación no lineal entre el gradiente hidráulico y la velocidad del flujo, y se analizaron las variaciones de los coeficientes de Forchheimer con la rugosidad de la superficie de la diaclasa y la apertura. En este trabajo, los números de Reynolds variaron entre 2,881 y 290,338, y superaron ampliamente el valor crítico de 2,300. Además, el flujo de fluido entró en el régimen de flujo turbulento. De acuerdo con el factor discriminante α = 0.9 sobre la base de la ley de Forchheimer, los regímenes de flujo de fluidos se dividieron en dos categorías: turbulencia débil y turbulencia completamente desarrollada. Los números de Reynolds críticos correspondientes se obtuvieron y oscilaron entre 17,169 y 94,385. Finalmente, mediante observaciones experimentales y otras fórmulas se estableció y verificó una nueva fórmula de cálculo de infiltración para el flujo de fluidos a través de diaclasas abiertas de paredes rugosas. A través de una consideración integral de la rugosidad de la superficie de la diaclasa y la distribución desigual de la abertura, la fórmula propuesta podría reflejar la situación real del flujo de fluido. Los hallazgos pueden resultar beneficiosos para mejorar la comprensión del flujo de fluido no lineal en rocas diaclasadas.

粗糙岩石节理高水力梯度下渗流流态和渗流模型的研究

摘要

粗糙岩石节理高水力梯度下的非达西流研究成果较少。本文在自行研制的试验装置上开展人工劈裂花岗岩节理的渗流试验,分析了节理粗糙度和隙宽对节理渗流特性的影响。试验结果表明:Forchheimer方程可以很好的描述水力梯度和节理渗流流速之间的非线性关系,并深入探讨了Forchheimer系数随节理粗糙度和隙宽的变化规律。本文试验工况下节理渗流的雷诺数范围为2,881~290,338,其值已高于节理临界雷诺数2,300,水流进入了紊流状态。基于Forchheimer方程,采用非线性渗流流态临界判别因子α = 0.9,将粗糙岩石节理非线性渗流流态分为弱紊流和完全发展紊流两个阶段,并得到两阶段临界雷诺数的范围为17,169 to 94,385。最后建立了高水力梯度下考虑节理粗糙度和不均匀隙宽的新型岩石节理渗流计算公式,并将试验值和其他公式计算值与本文提出公式的计算结果比较,发现本文提出的渗流计算公式更能反映岩石节理的真实渗流情况。研究结果将有助于增加节理岩体非线性渗流的认识。

Estudo dos modelos de regime de vazão e fluxo através de fraturas abertas em rocha com superfície áspera sujeito a alto gradiente hidráulico

Resumo

Pouca atenção tem sido dada ao fluxo não Darciano de fluídos através de fraturas em rocha com superfície áspera sujeitas a alto gradiente hidráulico. O fluxo de água através de fraturas em granito foi testado além das condições previamente testadas usando um aparato experimental desenvolvido para este estudo. Este aparato facilitou a quantificação dos efeitos das superfícies ásperas da fratura e sua abertura nas propriedades do fluxo. Os resultados experimentais mostraram que a lei de Forchheimer pode resultar em uma excelente descrição da relação não linear entre o gradiente hidráulico e a velocidade de fluxo, e as variações dos coeficientes de Forchheimer com fraturas de superfícies áspera e abertura foram exploradas em detalhe. Neste trabalho, os números de Reynolds variaram entre 2,881 e 290,338, e excedem o valor crítico de 2,300. Além do mais, o fluxo de fluído entrou no regime de fluxo turbulento. De acordo com o fator discriminante α = 0.9 baseado na lei de Forchheimer, os regimes do fluxo de fluídos foram divididos em duas categorias: turbulência fraca e turbulência inteiramente desenvolvida. Os números de Reynolds correspondentes foram obtidos e variaram de 17,169 até 94,385. Finalmente, uma nova fórmula de cálculo do fluxo de fluídos através de fraturas abertas em rocha com superfície áspera foi estabelecida e verificada por observações experimentais e outras fórmulas. Através de uma ampla consideração das superfícies ásperas de fraturas e sua distribuição de aberturas variáveis, a fórmula proposta pode refletir a situação real do fluxo de fluídos. As descobertas podem provar-se benéficas para melhorar o entendimento do fluxo de fluídos não linear em rochas fraturadas.

Notes

Funding information

This work was supported by the National Natural Science Foundation of China (No. 41327001)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xin Qian
    • 1
  • Caichu Xia
    • 1
    • 2
    Email author
  • Yang Gui
    • 1
  • Xiaoqing Zhuang
    • 1
  • Qiangfeng Yu
    • 1
  1. 1.Department of Geotechnical EngineeringTongji UniversityShanghaiChina
  2. 2.Department of Civil EngineeringShaoxing UniversityShaoxingChina

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