1、PDF外文：http:/ solution for steady-state groundwater inow into a drained circular tunnel in a semi-innite aquifer: A revisit Kyung-HoPark a,*,AdisornOwatsiriwong a,Joo-GongLee b aSchool of Engineering and Technology, Asian Institute of Technology, P.O.Box4, KlongLuang, Pathumthani 12120, Thailand bDOD
2、AM E&C Co.,Ltd., 3F. 799, Anyang-Megavalley, Gwanyang-Dong, Dongan-Gu, Anyang, Gyeonggi-Do, Republic of Korea Received 19 November 2006；received in revised form 13 February 2007；accepted 18 February 2007 Available online 6 April 2007 Abstract This study deals with the comparison of existing anal
3、ytical solutions for the steady-state groundwater inow into a drained circular tunnel in a semi-innite aquifer. Two dierent boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference, used in the existing solutions, are mentioned. Simple
4、closed-form analytical solutions are re-derived within a common theoretical framework for two dierent boundary conditions by using the conformal mapping technique. The water inow predictions are compared to investigate the dierence among the solutions. The correct use of the boundary condition along
5、 the tunnel circumference in a shallow drained circular tunnel is emphasized. 2007 Elsevier Ltd. All rights reserved. Keywords: Analytical solution； Tunnels； Groundwater ow； Semi-innite aquifer 1. Introduction Prediction of the groundwater inow into a tunnel is needed for the design of the tunnel dr
6、ainage system and the estimation of the environmental impact of drainage. Recently, El Tani (2003) presented the analytical solution of the groundwater inow based on Mobius transformation and Fourier series. By compiling the exact and approximate solutions by many researchers (Muscat, Goodmanet al.,
7、 Karlsrud, Rat, Schleiss, Lei, and Lombardi), El Tani(2003) showed the big dierence in the prediction of groundwater inow by the solutions. Kolymbas and Wagner (2007)also presented the analytical solution for the groundwater inow, which is equally valid for deep and shallow tunnels and allows variab
8、le total head at the tunnel circumference and at the ground surface. While several analytical solutions for the groundwater inow into a circular tunnel can be found in the literature,they cannot be easily compared with each other because of the use of dierent notations, assumptions of bo
9、undary conditions, elevation reference datum,and solution methods. In this study, we shall revisit the closed-form analytical solution for the steady-state groundwater inow into a drained circular tunnel in a semi-innite aquifer with focus on two dierent boundary conditions (one for zero water
10、 pressure and the other for a constant total head) along the tunnel circumference, used in the existing solutions. The solutions for two dierent boundary conditions are re-derived within a common theoretical framework by using the conformal mapping technique. The dierence in the water inow predictio
11、ns among the approximate and exact solutions is re-compared to show the range of appli-cability of approximate solutions. 2. Denition of the problem Consider a circular tunnel of radius r in a fully saturated,homogeneous,isotropic,and semi-innite porous aquifer with a horizontal water table (Fig.1).
12、The surrounding ground has the isotropic permeability k and a steady-state groundwater ow condition is assumed. Fig.1.Circular tunnel in a semi-infinite aquifer. According to Darcys law and mass conservation, the two-dimensional steady-state groundwater ow around the tunnel is described by the
13、 following Laplace equation: 02222 yx (1) where =total head (or hydraulic head), being given by the sum of the pressure and elevation heads, or ZpW (2) p =pressure, W =unit weight o
14、f water, Z =elevation head,which is the vertical distance of a given point above or below a datum plane. Here,the ground surface is used as the elevation reference datum to consider the case in which the water table is above the ground surface. Note that E1 Tani (2003) used the water level as the el
15、evation reference datum,whereas Kolymbas and Wagner (2007) used the ground surface. In order to solve Eq. (1),two boundary conditions are needed:one at the ground surface and the other along the tunnel circumference.The boundary condition at the ground surface (y =0) is clearly expressed as Hy ）（ 0
16、 (3) In the case of a drained tunnel, however, two dierent boundary conditions along the tunnel circumference can be found in the literature:(Fig.1) (1)Case 1:zero water pressure, and so total head=elevation head (El T
17、ani,2003) yr )( (4) (2)Case 2:constant total head, ha(Lei, 1999； Kolymbas and Wagner,2007) ar h）（ (5) It should be noted that the boundary condition of Eq.(5) assumes a constant total head, whereas Eq.(4) gives varying total head along the tunnel circumference. By considering these two dierent boundary conditions along the tunnel circumference, two dierent solutions for
