###### Abstract  
Mining operations disrupt the structure of rock layers, leading to surface deformations and potential mining damage. This issue has been extensively studied since the 19 th century using various analytical, geometric-integral, and stochastic methods. Since the 1990s, numerical methods have been increasingly applied to determine changes in the stress and strain states of rock masses due to mining activities. These methods account for numerous additional factors influencing surface deformation, offering significant advantages over classical approaches. However, modelling rock masses presents challenges, particularly in calibrating the mechanical parameters of rock layers, an area extensively researched with numerous publications. In this study, we determined the mechanical parameter values of rock layers at the advancing mining front using a custom Python script and Finite Element Method (FEM) numerical models. We also introduced a modification to evaluate the error of the estimated parameter values. Numerical analyses were conducted for the Piasti-Ziemowit mine region in Poland, utilizing mining, geological, and surveying data. Our results demonstrate that accurate calibration of mechanical parameters is crucial for reliable predictions of surface deformations. The proposed methodology enhances the precision of numerical models, providing a more robust framework for assessing the impact of mining activities on rock layers. FEM; coal mining; surface deformation; strong layer; Python +
Footnote †: journal: Applied sciences
Meanwhile, in parallel, since the 1990s, there has been a significant increase in interest in using solutions based on numerical methods [12; 13; 14] to determine changes in the state of stress and strain of the rock mass caused by underground mining operations. The authors of these solutions used a variety of numerical methods and physical and mathematical models [15; 16; 17]. These methods allow taking into account many additional factors affecting the nature and development of surface deformation [12; 18; 19; 20; 21; 22; 23], which is largely an advantage over classical computational methods. However, attention should also be paid to the problems that occur during rock mass modelling. One of the main problems, in addition to the selection of the material law and the size of the model, the density of the elements, and the compensation of numerical disturbances, is the proper calibration of the mechanical parameters of the rock layers. The first work on this topic was based on mapping the rock mass with isotropic elastic models [24; 25; 26], which, however, due to their nature, showed the correctness of the subsidence trough calculations only in terms of the vertical displacement index. A further attempt to use elastic models modified in terms of not transferring tensile stresses by the modeled elements to predict land sur-face deformations in the mining area was conducted by [PERSON] [27]. She used these elements for the weakening zone whose geometry was determined a priori. Some scientists used elastic-plastic models to describe the impact of exploitation on the surface. Adopting this model in a physical sense has greater understanding because rocks exhibit elastic properties only to a very small extent. However, studies conducted by [PERSON] [28], [PERSON] and [PERSON] [29], [PERSON] and [PERSON] [13], and [PERSON] [30] showed that the modeled subsidence trough has a much larger extent than indicated by surface observations. In parallel, work was carried out on the use of transversally isotropic models to analyze the impact of exploitation on the land surface. In 1964, [PERSON] [31] was the first to notice the advantages of using this type of models to limit the width of the modeled trough. Further research presented by [PERSON] [25] and [PERSON] [32] confirmed the validity of the adopted model. In 2019, [PERSON] [33] conducted analyses for several constitutive models: Mohr-Coulomb and modified Hoek-Brown.