Enhancing Underground Cave Stability Assessment through Physically-Based Machine Learning Methods

In recent years, the risk of landslides caused by man-made underground caves has increased on Italian territory, with significant consequences for human life and for the anthropogenic environment. Such artificial caves have generally been dug and subsequently abandoned in very soft porous rock formations, such as calcarenite deposits, even at shallow depths. The low mechanical strength values of such rocks, together with their susceptibility to weathering and consequent loss of strength, make these rock masses prone to sinkhole formation. In order to develop a rapid but mechanically based method to assess the stability of artificial caves based on the geometrical features of the cave and the mechanical properties of the rock, an improved formulation of the abaci, originally proposed by Perrotti et al. (2018), has recently been proposed by Mevoli et al. (2024), which introduces the ability to also assess the range of the cave safety factor. In this perspective, the application of the abaci can be used as a quantitative tool for the preliminary assessment of sinkhole hazards, enabling large scale analyses that can subsequently be followed by a detailed and advanced study at the local scale.A data-driven approach was employed to compare and discuss the results obtained from the direct application of the abaci, based on this newly developed version. The selected method, proposed by Giustolisi and Savic (2006), and known as 'Evolutionary Polynomial Regression', is based on the genetic programming paradigm and returns simple functional relationships, namely polynomials of elementary functions, among the considered physical parameters. In particular, it generates a Pareto front of expressions that considers simplicity and accuracy. This facilitates the interpretation of the results of the data modelling approach, thereby maintaining focus on the physics of the phenomenon under investigation, as outlined by Fazio et al. (2024).The results will also demonstrate the use of these machine learning techniques to provide mathematical formulations that can be readily employed in the field by experts involved in assessing the stability of underground cavities. Perrotti M., Lollino P., Fazio N.L., Pisano L., Vessia G., Parise M., Fiore A., Luisi M. (2018). Finite Element– Based stability Charts for Underground Cavities in Soft Calcarenites. Int. J. Geomechanics, 18(7), DOI: 10.1061/(ASCE)GM.1943-5622.0001175.Mevoli, F.A., Fazio, N.L., Perrotti, M. et al. Assessing the stability of underground caves through iSUMM (innovative, straightforward, user-friendly, mechanically-based method). Geoenviron Disasters 11, 10 (2024). https://doi.org/10.1186/s40677-023-00264-3Giustolisi O., Savic D. A. (2006). A symbolic data-driven technique based on evolutionary polynomial regression." J. of Hydroinformatics, 8 (3), 207-222.Fazio, V., Pugno, N. M., Giustolisi, O., & Puglisi, G. (2024). Physically based machine learning for hierarchical materials. Cell Reports Physical Science, 5(2).