Novel method for determining the time coefficient [formula omitted] in Knothe’s function and disappearance time of deformation increase using SAR data

Abstract

This paper presents a novel approach to determining the disappearance time of deformation increase after the conclusion of mining activity using Knothe’s time function and persistent scatterer interferometric synthetic aperture radar (PSInSAR). As a result, a method was proposed for determining a parameter of the function, the time coefficient c, using SAR data. The area of study was a strongly urbanised (city centre) post-mining region within the Upper Silesian Coal Basin (USCB), located in central-eastern Europe (Poland), which was characterised by intense hard coal mining that was concluded in 2015. The study analysed ground displacements generated directly after the conclusion of extraction as well as the time after which the rock mass assumes a relatively calm state. The obtained results were validated based on the results of classic geodesic measurements. The average time coefficient c determined by the developed method was 0.84, while the average time coefficient based on classic geodesic measurements was 1.01. So the theoretical disappearance time of deformation increase was, respectively, 5 years and 6 months and 4 years and 7 months. The research revealed that the developed method is helpful in determining the parameter in Knothe’s function and enables a more accurate definition of the disappearance time of deformation increase after the conclusion of extraction. This has great significance in the context of safety and the potential limitation of damage generated as a result of the negative influence of underground mining on the ground surface as well as for the spatial planning of post-mining areas.