Analytical solutions for analysing pumping tests in a sub-vertical and anisotropic fault zone draining shallow aquifers

We present new analytical solutions for examining the influence, during a pumping test in a well, of an infinite linear and anisotropic strip-aquifer that drains shallow aquifers of different diffusivity and thickness. The whole system is confined and the aquifer geometry can be represented by a ‘T’, an aquifer geometry resembling a sub-vertical fault or a sub-vertical vein cross-cutting shallower aquifers. The proposed solutions are based upon an unconventional application of well-image theory, without limitation of the diffusivity contrast between the three domains. Solutions for drawdown were developed for the three domains, i.e. the strip-aquifer and the two shallow compartments, and flow signatures are discussed in detail and compared to numerical modelling. The proposed solutions are not shown to be exact solutions to the appropriate partial differential equation, but very good and useful approximations. The solutions were applied to a 63-day pumping test in a steep fault zone in crystalline aquifer rock of Brittany, France. After that, the flow contributions of the fault zone and of the shallow aquifers deduced from groundwater dating were compared to analytical solutions. The solutions and theoretical type-curve examples can help in understanding flow processes from tests conducted in settings that are similar to such a conceptual model.