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工程科学与技术:2022,54(2):141-149
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单排水孔轴对称填充流场解析解
张帅1,2, 叶飞1,2, 胡超1,2, 郑双1,2, 符文熹1,2
(1.四川大学 水利水电学院, 四川 成都 610065;2.四川大学 水力学与山区河流保护国家重点实验室, 四川 成都 610065)
Analytical Solution to Flow Field Around an Axisymmetric Filled Drainage Hole
(1.College of Water Resource & Hydropower, Sichuan Univ., Chengdu 610065, China;2.State Key Lab. of Hydraulics and Mountain River Eng., Sichuan Univ., Chengdu 610065, China)
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投稿时间:2021-04-08    修订日期:2021-09-03
中文摘要: 工程中通常布置排水孔以降低岩体内部渗流压力。在运行过程中,充填物堵塞排水孔会限制排水能力,威胁工程安全。目前,对于填充排水孔的分析,主要考虑非填充区域的纯流体运动,却鲜有同时考虑填充区域和非填充区域的水流运动。鉴于此,建立自由流-渗流耦合理论模型,分析岩体内轴对称填充排水孔的流速分布,该理论模型中,排水孔中非填充区域纯水流运动遵循Navier?Stokes方程,填充介质中渗流运动可由Darcy?Brinkman方程描述;结合速度连续和应力跳跃的界面边界条件,推导出流场流速分布和泄流量解析解;流速理论解与4阶Runge?Kutta方法数值解结果吻合良好。参数敏感性分析结果表明:流场流速与达西数和空隙相对开度呈正相关,与黏度比和应力跳跃系数呈负相关;当应力跳跃系数小于0时,上述参数变化对流速分布的影响更为显著,此时黏度比对模型计算结果的影响不能忽略。随着空隙相对开度增加,当达西数等于1时,界面速度逐渐减小;当达西数等于0.1时,界面速度先增大后减小;当达西数小于0.1时,界面速度逐渐增大。研究成果可为部分堵塞排水孔泄流能力计算提供理论依据,对于完善和发展排水孔自由流-渗流耦合理论具有重要意义,可为后续排水孔加压清淤提供参考。
Abstract:Drainage holes are usually arranged to reduce the seepage pressure inside rock mass. The partial blockage of the drainage hole will limit the drainage capacity and threaten the safety of an engineering project. At present, the analysis of the filled drainage hole only considers the fluid movement in the unfilled area, and there are few theoretical studies that consider the flow in both the filled and unfilled regions. In view of this, a clear-seepage flow coupled theoretical model was presented to study the velocity distribution of the drainage hole with axisymmetric filled medium in the rock mass. In the model, the Navier-Stokes equation was adopted to describe the motion of the clear water in the hole, and the Darcy-Brinkman equation was employed to describe the movement of the seepage water in the filled medium. The analytical solutions of velocity distribution and discharge were derived under the shear stress jumping interface boundary condition, and the results of analytical solution for velocity shown good agreement with that of the numerical solution obtained by the fourth order Runge-Kutta method. Parameter sensitivity analyses shown that the flow velocity had a positive relation with the Darcy number (Da) and the relative thickness of the open region, and a negative relation with the ratio of viscosity and the stress jump coefficient. The flow velocity was more sensitive to the variation of the typical parameters and the influence of viscosity ratio on the velocity distribution could not be neglected when the stress jump coefficient is less than 0. Furthermore, with the increase of the relative thickness of the open region, the interface velocity gradually decreases when Da=1, while it firstly increases and then decreases when Da=0.1, and it gradually increases when Da<0.1. The research results of this paper can provide a theoretical basis for the calculation of the drainage capacity of the partially filled drainage hole. It is of great significance for developing the clear-seepage flow coupled theory of drainage holes and can provide a reference for the follow-up drainage hole dredging.
文章编号:202100297     中图分类号:O35    文献标志码:
基金项目:国家自然科学基金项目(42107172;41772321);四川省科技计划项目(2020YFS0361);中央高校经费资助(2021SCU12035)
作者简介:第一作者:张帅(1996-),男,硕士生.研究方向:地下水渗流与岩土体稳定.E-mail:zzs9616@163.com;通信作者:叶飞,E-mail:yefei16scu@163.com
引用文本:
张帅,叶飞,胡超,郑双,符文熹.单排水孔轴对称填充流场解析解[J].工程科学与技术,2022,54(2):141-149.
ZHANG Shuai,YE Fei,HU Chao,ZHENG Shuang,FU Wenxi.Analytical Solution to Flow Field Around an Axisymmetric Filled Drainage Hole[J].Advanced Engineering Sciences,2022,54(2):141-149.