NEW ANALYTICAL SOLUTIONS FOR ONE DIMENSIONAL STEADY STATE FLOW IN AN UNCONFINED AQUIFER WITH A SLOPING BASE

Loose sediments with a gentle-inclined impermeable base are widespread in nature. Therefore studies of seepage flows in this kind of sedimentary formation is of critical importance in many hydraulic engineering practices. The most famous analytical solution for this problem is Pavlovskii's method. However it is only applicable to the aquifer of a small slope angle and a small head difference between two boundaries because of its assumption that the divergence angle flow lines should be small. This paper presents a new analytical method for an aquifer with a downward-and counter-sloping base. An appropriate coordinate system was first chosen to divide the aquifer into two parts, one above and another below the x axis. A total differential equation was derived according to equivalent flux across the interface between two parts and the principle of mass conservation(continuity).Analytical solution was then obtained by solving the total differential equation with specified boundary conditions. The method was used in four examples taken from literatures. The results were compared with Pavlovskii's solutions. The discharge is almost identical, but the difference of phreatic surfaces between two methods increases as the slope angle rises and the head difference become larger(expressed as hydraulic slope, related to the divergence and convergence angles of streamlines).Based on analysis of hydraulic mechanisms, the new method presented in this paper provides higher accuracy for calculating phreatic surface than the Pavlovskii's method. It can also be applied to an aquifer with a higher slope angle of the base and greater head difference between boundaries(affecting convergence and divergence angles of streamlines).