Mathematical Model of Forecasting the Formation of Sinkhole Using Salustowicz’s Theory / Model Matematyczny Prognozowania Zapadlisk Przy Wykorzystaniu Teorii Sklepienia Ciśnień Sałustowicza

Abstract

Abstract In area affected by old, shallow extraction in some cases sinkholes are formed, causing security issues in urbanized areas. Problem of working out deterministic forecast of this threat seems to be important and up-to-date. Mathematical model presented in this work let us predict the possibility of sinkhole formation. That prediction is essential for analyzing possibility of investments in such areas. Basing on presented work, it is also possible to determine dimensions of sinkhole. Considerations are based on known from literature Sałustowicz’s theory, which is utilises Huber’s solution of equation describing the stress state around elliptic void made in flat plate