New Analytical Solutions for Phreatic Darcian Flows Over Non-Planar Bedrocks

Abstract

Assessment of recharge zones of strategic aquifers in Northern Oman calls for quantification of groundwater hydraulics in alluvial fans with a subjacent bedrock of various geometry. Unlike standard analytical solutions to a 2-D unconfined flow over a tilted bedrock and a common Dupuit–Forchheimer approximation we derive novel analytical solutions for subjacent confining layer of a non-constant slope or a bedding inconformity. We use a genuine 2-D flow model, conformal mappings and inverse boundary-value problems methods. For flow over an arbitrary corner the vertex is either a stagnation point or point of infinite Darcian velocity. The hodograph domain (a circular triangle) is mapped onto a complex potential strip via an auxiliary half-plane. A non-planar aquifuge is also reconstructed as a streamline, along which an additional “control” boundary condition holds (pore pressure as a function of an auxiliary variable).