@ARTICLE{Misa_Rafał_Knothe’s_2023,
 author={Misa, Rafał},
 volume={vol. 39},
 number={No 4},
 journal={Gospodarka Surowcami Mineralnymi - Mineral Resources Management},
 pages={157-180},
 howpublished={online},
 year={2023},
 publisher={Komitet Zrównoważonej Gospodarki Surowcami Mineralnymi PAN},
 publisher={Instytut Gospodarki Surowcami Mineralnymi i Energią PAN},
 abstract={The theory of Professor Stanislaw Knothe, known as Knothe’s Theory, has been the foundation for practical predictive calculations of the impacts of exploitation for many years. It has enabled the large-scale extraction of coal, salt and metal ores located in the protective pillars of cities and prime surface structures. Knothe’s Theory has been successfully applied in Polish and global mining for over seventy years, making it one of the most well-known and recognized achievements in Polish mining science. Knothe’s Theory provides a temporal-spatial description of subsidence that relies on four essential parameters: the vertical scale parameter a, the horizontal displacement parameter λ, the horizontal range scale parameter cotβ and the time scale parameter c. This article characterizes the parameters of Knothe’s Theory used in various current applications for calculating subsidence, surface and rock uplift, and other applications of the theory, even beyond its classical form. The presented solutions are based on a mathematical model of the interaction of a complex element and cover topics such as subsidence during full exploitation with roof collapse and full exploitation with backfilling, pillar-room mining, the effect of salt caverns on the surface and salt rock, and fluid deposits and surface uplift caused by changes in the water level within closed coal mines. The article also discusses the evolution of the range angle of the main influences and presents Knothe’s solutions related to time, describing the horizontal displacement parameter λ.},
 type={Article},
 title={Knothe’s theory parameters – computational models and examples of practical applications},
 URL={http://journals.pan.pl/Content/129740/PDF/Misa.pdf},
 doi={10.24425/gsm.2023.148164},
 keywords={Knothe’s theory, salt caverns, uplift, surface movement, post-mining},
}