Lorenzo Panzeri, Alessio Fumagalli, Laura Longoni, Monica Papini, Diego Arosio
{"title":"Sensitivity analysis with a 3D mixed-dimensional code for DC geoelectrical investigations of landfills: synthetic tests","authors":"Lorenzo Panzeri, Alessio Fumagalli, Laura Longoni, Monica Papini, Diego Arosio","doi":"arxiv-2409.10326","DOIUrl":null,"url":null,"abstract":"Electrical resistivity tomography is a suitable technique for non-invasive\nmonitoring of municipal solid waste landfills, but accurate sensitivity\nanalysis is necessary to evaluate the effectiveness and reliability of\ngeoelectrical investigations and to properly design data acquisition. Commonly,\na thin high-resistivity membrane in placed underneath the waste to prevent\nleachate leakage. In the construction of a numerical framework for sensitivity\ncomputation, taking into account the actual dimensions of the electrodes and,\nin particular, of the membrane, can lead to extremely high computational costs.\nIn this work, we present a novel approach for numerically computing sensitivity\neffectively by adopting a mixed-dimensional framework, where the membrane is\napproximated as a 2D object and the electrodes as 1D objects. The code is first\nvalidated against analytical expressions for simple 4-electrode arrays and a\nhomogeneous medium. It is then tested in simplified landfill models, where a 2D\nbox-shaped liner separates the landfill body from the surrounding media, and 48\nelectrodes are used. The results show that electrodes arranged linearly along\nboth sides of the perimeter edges of the box-shaped liner are promising for\ndetecting liner damage, with sensitivity increasing by 2-3 orders of magnitude,\neven for damage as small as one-sixth of the electrode spacing in diameter.\nGood results are also obtained when simulating an electrical connection between\nthe landfill and the surrounding media that is not due to liner damage. The\nnext steps involve evaluating the minimum number of configurations needed to\nachieve suitable sensitivity with a manageable field effort and validating the\nmodeling results with downscaled laboratory tests.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10326","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.