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

TL;DR

This paper introduces a novel mixed-dimensional numerical approach for sensitivity analysis in 3D geoelectrical landfill investigations, improving computational efficiency and detection accuracy of liner damage.

Contribution

The work develops a mixed-dimensional framework that models the membrane as 2D and electrodes as 1D, reducing computational costs while maintaining accuracy in sensitivity analysis.

Findings

Electrodes along liner edges significantly increase sensitivity to damage.

Sensitivity improves by 2-3 orders of magnitude for small damages.

The approach effectively detects non-damage related electrical connections.

Abstract

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. Commonly, a thin high-resistivity membrane in placed underneath the waste to prevent leachate leakage. 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 2D object and the electrodes as 1D objects. The code is first validated against analytical expressions for simple 4-electrode arrays and a homogeneous medium. It is then tested in simplified landfill models, where a 2D 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 2-3 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 next steps involve evaluating the minimum number of configurations needed to achieve suitable sensitivity with a manageable field effort and validating the modeling results with downscaled laboratory tests.