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(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)

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.

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.