A semi-analytical solution for modelling the impact on the water table at the pumping well location due to the influence of a finite-sized underground physical barrier in an inclined, homogenous and infinite aquifer

In hydrogeology, an underground physical barrier with partial lateral occultation refers to a low-permeability screen constructed across groundwater flow without reaching the lateral limits of the aquifer, and whose objective is to modify the elevation of the water table. Due to the complexity of the hydraulic-head distribution associated, several practical design issues arise if the exploitation of the resource is to be ensured. Transient and steady-state semi-analytical solutions, based on the method of fundamental solutions, are proposed for evaluating the hydraulic-head distribution caused by a semi-permeable rectangular barrier that fully penetrates an infinite, homogeneous and sloping aquifer, with or without a pumping well. Based on hundreds of simulations with different aquifer, pumping and barrier characteristics, a set of type curves was produced for evaluating i) the duration of equilibrium of the water-table, ii) the length of the barrier to optimize the pumping rate of a given well or its location, and iii) the hydraulic conductivity and width of the barrier. Type curves are used to explain the time-variations in water-table induced by the construction of a railway station basement, and to design a hypothetical underground barrier to raise the water-table level at the location of a pumping well. The variability of barrier characteristics introduced by uncertainty in hydrogeological parameters is also addressed. The analysis of developed solutions includes sensitivity tests and satisfactory comparisons with numerical modelling. Solutions and type-curves can be implemented as operational tools for improving the design of such structures and are meant to supplement existing hydrogeological models.