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

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.

Figures (8)

• Figure 1: Examples of computational grids for the mixed dimensional model: 3D tetrahedral elements in grey, 2D triangular elements of the liner in red and 1D electrodes in yellow. a) 48 electrodes around the box-shaped liner; b) 24 electrodes outside the liner and 24 electrodes inside, a hole in the bottom surface of the liner with its vertical walls not in contact with the top boundary of the domain. The liner has dimensions $1[m]\times1[m]\times0.1[m]$.
• Figure 2: Vertical slices of sensitivity values for Wenner-alpha a)-b) and dipole-dipole c)-d) arrays and a homogeneous half-space. a)-c) show plots of the analytical expression \ref{['eq:sensi']}, while b)-d) show the modelled results. Both arrays have total length of $2[m]$.
• Figure 3: Images of computed sensitivity for case 1) with a $0.1[m]$ diameter hole in the bottom surface of the liner. From top-left, clockwise: top view, zoomed top view, volume below the box-shaped liner with 3 depth slices, vertical cut. See text for details.
• Figure 4: Zoomed top view of the computed sensitivity for case 3) with a hole in the middle of the liner.
• Figure 5: Sensitivity values along horizontal lines at different depths for the Wenner-alpha array. Vertical dashed lines indicate the positions of the electrodes (from right: C1-P1-P2-C2). a) Analytical values; b) modelled values.