Subsidence process in the rock mass disturbed by mining can be complicated and can be faster or slower depending on the geological structure and physical and mechanical properties of the rock mass, changes in exploitation geometry, and changes in the rate of exploitation. The most frequently, the subsidence process develops over years in a way that is difficult to observe over a short period (days). It has been proven in practice of coal mines in Poland that Knothe’s model describes subsidence process with high accuracy. It is based on treating the rock mass as a stochastic medium and describing subsidence with stochastic equations.

It can be assumed that, the complicated stress field as a result of mining activities induce a series of displacements of different sizes in rock mass. The inelastic deformation in rock mass is accompanied by a microseismicity that can be recorded and processed. We assumed that seismic noise with weak seismic events is a low-energy part of the microseismicity. We proposed an analytical solution to examine the distribution of the energy of the seismic noise during subsidence process development based on Knothe’s model. In general a qualitative method of subsidence process assessment by the registration of the seismic noise was described.

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.