Transient Groundwater Flow in a Sloping Aquifer with Surface Water-Groundwater Interaction

Abstract

The theory of groundwater flow in a sloping aquifer is indispensable to understand water exchange among atmosphere, surface water and an aquifer. However, for various reasons, the theory of groundwater flow in a sloping aquifer is still not understood clearly. In the past decades, several researchers have studied groundwater flow in a sloping aquifer using analytical and numerical methods and laboratory experiments. The purpose of this dissertation is to advance the hydrodynamics of transient groundwater flow in a sloping aquifer with surface water-groundwater interaction. A few new models and their semi-analytical and numerical solutions are developed to study the water table fluctuations and river-aquifer fluxes in the presence of an unconfined sloping aquifer. The first model is built for a sloping aquifer with a river on left side and infinite extent on the other side. The second model is built for a sloping aquifer with two parallel rivers. The two models both provide general considerations about the less permeable sedimentary layer (or clogging layer) between an aquifer and surface water, the time-dependent river stages, and responses of time-dependent recharge by infiltration. Special attention has been paid to the impact of sloping feature, among other parameters, on the evolution of the water table profile and the river-aquifer fluxes. The analytical solutions are developed using a linearized Boussinesq equation modified for a sloping aquifer, and they are compared with a finite element COMSOL program for the same linearized Boussinesq equation. Excellent agreement was found between the analytical solution and the COMSOL program. The analytical solution is subsequently compared with a full scale numerical model using HydroGeoSphere to consider coupled unsaturated-saturated flow process. The result indicates that the linearized analytical solution can serve as a reliable surrogate of the full scale numerical model when the sloping angle is less than 10 degrees. The flow character of a sloping aquifer is quite different from that of a horizontal aquifer, and the variations of river stages will cause much more variations of water table heights and river-aquifer fluxes in a sloping aquifer. In particular, the water table profile in a sloping aquifer shows some unique features that have never been seen in a horizontal aquifer, as the water table profile may evolve from a straight line parallel with the sloping bed at the beginning to a convex shape, even without any recharge/evaporation. Another new model acknowledging the realistic initial conditions and river stage variation is proposed with the help of sequential Sigmoid functions for describing the river stage. One benefit of using the Sigmoid functions is that it allows enough time for the system to reach its pseudo-steady state before the rapid rising or falling of the river stage. Therefore, this avoids the idealized (and often unrealistic) initial condition of a constant water table height above the impermeable base as was assumed by many previous investigations. Finally, the limitations of the study and future work are outlined.