| Summary: | Mathematical modeling of surface deformations caused by underground mining operation is commonly carried out with use of empirical, numerical or stochastic models. One of the most frequently applied model for prediction of ground deformation in many countries is Knothe model. The model developed by Knothe belongs to the stochastic methods and is based on the influence function. In China a prediction method named Probability Integration Method (PIF) was established by Liu Baochen and Liao Guohua based on the stochastic medium theory. Modified version of that model allows to predict ground movements caused by mining operation in extremely complex technical and geological conditions. That model is commonly applied for coal, metal ore and salt deposits. The article presents several modifications of the mathematical model used in China and Poland. This model is very widespread in the world, therefore the generalizations proposed in the article can be implemented for the purposes of prediction surface deformations for various types of deposits in many countries. The presented generalizations were then tested on specific examples of coal mining, copper ore mining and rock salt deposit. The obtained results indicate high efficiency of methods based on the influence function in complex geological and mining conditions. Keywords: Mining operation, Modeling of surface deformations, Stochastic models, Probability integration method, Influence function, Salt hard coal mining copper ore mining
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