Hillside seepage and the steady water table. I: Theory |
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| Institution: | 1. School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China;2. Centre for Offshore Foundation Systems, School of Civil Environmental and Mining Engineering, The University of Western Australia, Perth 6009, Australia;3. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;4. Rail Transit Engineering Limited Company, The Twenty-three Bureau Group of China Railway Construction, Shanghai 201399, China;1. Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China;2. Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha 410075, China;3. National and Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha 410075, China;1. School of Architecture Engineering and Planning, Jiujiang University, Jiujiang, Jiangxi 332005, PR China;2. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, Jiangxi 330013, PR China;3. Department of Computational Science and Statistics, Nantong University, Nantong, Jiangsu 226019, PR China |
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| Abstract: | Steady seepage through a hillslope aquifer results in the formation of a water table. In this paper, the boundary conditions governing the steady water table location are analysed, and an analytical series method applied to the problem, using eigenfunction expansions. Eigenfunction expansions, modified for non-orthogonal basis functions, provide a conceptually simple, efficient estimation process, that reduces the steady water table problem to a sequence of curve fitting exercises. A rigorous examination of the hodograph relationships reveals the possibility of more than one water table location, for given recharge rate. An elementary analysis reveals that one of these possibilities can always be eliminated. Also, the boundary conditions governing the steady water table are determined at a non-vertical upstream boundary. Hillslopes subjected to low recharge rates can be very difficult to analyse, and appropriate techniques for this case are detailed. In a companion paper (Adv. Water Resour., 19(2) (1996) 75–81), the techniques described in this paper are put to the test, and the upstream boundary conditions are investigated, using the series methods. |
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