Analysis of rock mass destruction processes with different activity diagrams

Abstract

The paper presents the considerations devoted to homomorphism analysis of processes: displacement and medium (rock) vibration, generating physical risk for the area of topological transformations. The aim of the study was to associate interactions: mining induced vibrations and displacement and their temporal relations. The basis for the analysis were both: sets of observed displacements -measured with GPS technology and recordings of acceleration process by using 3D vibration sensors, as well as mathematical modelling of these processes. It has been indicated, that the carrier of a formal process will be the probability space -which implies the stochastic nature of the phenomenon. Measures of the destruction occurrence -a critical process -there are the probability measures. In the estimated moment of time t, the results of observations of both processes -which are sets of real numbers -indicate that objects that are at risk of event are subjected to danger or failure. Fundamental here are mappings, used for modelling of concurrent processes, those communicate with each other. Features of timing relationships are: the structure and dynamics of processes.The emergence of the conflict -the occurrence of a critical event -has been estimated on the basis of the lemma for reaching of the outer extremes, in terms of equivalence relations in a fixed set of circumstances. The structural similarity between the two processes, their predictability and determination of characteristic frequencies was performed with using the relevant statistics, including the so-called Hurst exponent. An important element of proceeding the threats is the relationship in the domain of extreme events as a decisive influence -the difference compared to traditional analysis. The application layer contains specific examples of estimating the risk of a critical event arising.

Lake bottom relief reconstruction and water volume estimation based on the subsidence rate of the post-mining area (Bytom, Southern Poland)

“…The extraction of natural resources, especially hard coal, is an essential factor leading to the subsidence basins formation, and Bytom is one of the cities most affected by this process 12 – 16 , 44 , 51 , 64 , 81 , 82 . Subsidence is accompanied by mine-induced seismicity, typical of the USCB area 23 , 83 – 86 and the formation of fault zones. It leads to an abrupt, temporary increase in the subsidence rate, exceeding the average speed by 20–30 times.…”

Analysis of deflections of reinforced concrete slab in the rectified water-storage tank

“…This problem refers to different types of constructions:, such as residential buildings [3], historic towers [4], churches [5], as well as grain elevators. Vertical deflection of the construction can be also the effect of the non-uniform depression of mining areas [6], which is caused by compression of the voids left after underground extraction works [7]. Deflection can damage constructions with wall building structure [8], frame structures [9], can increase the risk of building operation [10], and the risk of the collapse [11].…”

Computing the value of uneven raising of building consisting of nine segments deflected from vertical due to mining exploitation

“…The inclination of objects can also be the result of earthquakes [8], wind loads [9], as well as the construction of tunnels in their vicinity [10]. In addition, there are numerous cases of buildings tilted as a result of uneven lowering of the mining area [11], which is caused by the tightening of voids left after underground mining of coal seams [12] and tilting caused by the exploitation of natural underground water reservoirs [13]. Inclination can cause damage to objects with a load-bearing wall structure [14], frame structure [15], increase the risk of the object's operation [16], as well as construction disasters [17].…”