Sensitivity analysis with a 3D mixed-dimensional code for direct current geoelectrical investigations of landfills: synthetic tests

Electrical resistivity tomography is a suitable technique for non-invasive monitoring of municipal solid waste landfills, but accurate sensitivity analysis is necessary to evaluate the effectiveness and reliability of geoelectrical investigations and to properly design data acquisition. Typically, a thin high-resistivity membrane is placed underneath the waste to prevent leakage of leachate. In the construction of a numerical framework for sensitivity computation, taking into account the actual dimensions of the electrodes and, in particular, of the membrane, can lead to extremely high computational costs. In this work, we present a novel approach for numerically computing sensitivity effectively by adopting a mixed-dimensional framework, where the membrane is approximated as a two-dimensional object and the electrodes as one-dimensional objects. The code is first validated against analytical expressions for simple four-electrode arrays and a homogeneous medium. Then it is tested in simplified landfill models, where a two-dimensional box-shaped liner separates the landfill body from the surrounding media, and 48 electrodes are used. The results show that electrodes arranged linearly along both sides of the perimeter edges of the box-shaped liner are promising for detecting liner damage, with sensitivity increasing by 2 to 3 orders of magnitude, even for damage as small as one-sixth of the electrode spacing in diameter. Good results are also obtained when simulating an electrical connection between the landfill and the surrounding media that is not due to liner damage. The configurations with the highest sensitivity directly beneath the liner are quadrupoles in which both the current and voltage dipoles have one electrode inside the liner and one electrode outside, and a two-dimensional arrangement of the electrodes. The modelled sensitivity values beneath the liner are close to a minimum sensitivity threshold derived from arbitrary and simplified assumptions. We believe that direct current surveys have the potential to detect liner damage using electrode spreads positioned along the liner perimeter, both inside and outside the landfill. However, down-scaled laboratory tests will be necessary to validate the modelling results and confirm whether the computed sensitivity values are sufficiently high to reliably detect liner damage.