GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.2 GNGTS 2024 Mixed-dimensional forward-problem solver for the geoelectrical analysis of highly resistve liners in landflls L. Panzeri 1,2 , A. Fumagalli 2 , L. Longoni 1 , M. Papini 1 , L. Zanzi 1 , D. Arosio 3 1 Department of Civil and Environmental Engineering, Politecnico di Milano, Italy 2 Department of Mathematcs, Politecnico di Milano, Italy 3 Dipartmento di Scienze Chimiche e Geologiche, Università degli studi di Modena e Reggio Emilia, Italy To avoid the difusion of the leachate in the subsoil and the possible contaminaton of aquifers, a thin liner of high-density polyethylene (HDPE) is placed underneath the waste in municipal solid waste landflls (MSWLFs). The conditons of the plastc membrane are of paramount relevance but, unfortunately, they are difcult to be assessed due to the locaton of the liner. A 3D code based on a mixed-dimensional mathematcal model has been developed to simulate the fow of the current injected in the geoelectrical surveys to allow a non-destructve analysis of the highly resistve liner (Aguzzoli et al. 2020, Aguzzoli et al. 2021, Fumagalli et al., 2023, Panzeri et al., 2023)). The peculiarity of our approach is to consider the problem as mixed-dimensional. This means that elements of diferent dimensions coexist in the same mesh (Fig.1). Due to their reduced dimension along x and y with respect to z, electrodes have been simulated as 1D elements (Peacemean 1978), while the liner is simulated as a 2D element because of its limited thickness (typically a few millimetres). The new code defnes parallelepipedal boxes around the electrodes and exploits the fnite volume Multpoint Flux Approximaton method (MPFA). These conditons need to be mathematcally expressed in the formulaton of the forward problem also including the interface/ coupling conditons between the elements with diferent dimensions. In this work, the results obtained with our Python code based on Porepy (Keilegavlen et al. 2021) have been compared, frst, with two analytcal solutons. One represents two horizontal layers with diferent conductvity (Sherif et al., 1990), and the other is characterized by the presence of a conductve sphere in an infnite horizontal space (Aldridge and Oldenburg, 1989). Afer that, the results were compared with the outcomes of an open-source library for mult-method modelling and inversion in geophysics named pyGIMLi (Rücker et al. 2017). Finally, to further validate our modelling code, tests were performed with diferent setngs in the laboratory on a homogeneous material (water) placed in a plastc box.