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Mathematical Model for Establishing the Time-Dependent Behavior of Rocks by the Gradient Method

In the underground activity domain, most problems related to mining pressure and mining stability need to be solved by taking into account the time behavior of rocks through an approach of the interaction amidst the rock massif, support system, time through the elastic, viscous and plastic models, namely a rheological approach. In order to choose a rational support system, one needs to know the sustainment solicitation at different time intervals. The change in the sustainment in time is emphasized only in the analytical research in which the massif is studied and characterized in terms of the rheological behavior. The gradient method applied in this regard is based on the evolution of the final deformations at a given time, compared to their previous evolution. The paper is structured into two parts, the experimental and interpretation of the experimental data, showing the author’s methodology to assess the rheological behavior of analyzed andesite, the result of the theoretical and experimental research being carried out on the analyzed rock types. Based on the deformation and the time curve of the horizontal mining work contour, the mathematical function was established, which expresses the law of sought deformation. At the same time, the rheological model capable of describing the behavior under a load and under extremely adverse conditions is proposed.