# Stability Analysis of the Exploitation System with Room and Pillar by Analytical Methods
###### Abstract
That is why many concerns are directed in particular towards finding research methods, respectively, appropriate calculations for the problems and precision required by the mining activity [11; 12; 17; 18; 20; 24; 29]; others refer to finding experimental procedures for determining the behavior of underground constructions of all kinds using different modeling systems and in situ measurements [7; 8; 19; 20; 24; 25; 28; 29; 30; 31; 32; 25]. Finding that, in the end, the analytical way is not at all inferior to the experimental one, the analytical and numerical methods of solving the most diverse problems encountered in practice have also seen an exceptional development [34; 35; 36]. However, we specify the fact that the analytical development of determining the stress states and the mode of manifestation of mining pressure was not achieved at the expense of experimental research methods (numerical methods, in situ measurements) and vice versa. Where the mathematical models built for the representation of random processes, no matter how general they are, cannot be sufficient to represent all types of phenomena and processes that we know or that the mining technique imposes on us, experimental research procedures are welcome. From a mathematical point of view, the problem of determining the optimal values consists of the minimization or maximization of certain functions subject to restrictions imposed by the nature of the considered processes based on a certain performance index. In recent times, many of the numerical methods have been abandoned in favor of new methods suitable for the computing technique. This is possible only if \(\sigma\) presents \"finite\" values on the intermediate surfaces of the elements. The problem of the stability of an empty space created underground, respectively the safe and economical dimensioning of the support of mining opening and preparation works, as well as exploitation (in the case of rooms), requires a fair assessment of the stress state created by the displacement phenomenon of the massif-support system, of the effect of the inhomogeneity of these stresses, as well as the influence of the anisotropy factor of heterogeneity and time. This can be conducted analytically by using the finite element method. The salt exploitation method with rooms and pillars forms a unique spatial system. From this, it follows that the necessity of establishing in any concrete situation an optimal correlation between the parameters of the room, the pillar, and the area of the rock massif is certain. Usually, in each specific case, the dimensioning of the most requested element in the system is sought, and depending on its parameters, the other parameters of the system are established. In the case of the exploitation method with rooms and pillars, the most requested elements are the pillars. In the case of the reopening of some mining fields within the salt panels and the exploitation in depth with square pillars, the establishment of the optimal parameters of the elements of the exploitation system requires the establishment of the loads that appear in the surrounding salt massif (the natural stress state); the qualitative-quantitative determination of the way of distribution of the secondary stress state in the pillars; evaluating the bearing capacity of the pillars; and establishing their geometric elements [27; 37; 38; 39]. The way of appearance, distribution, and manifestation of the secondary stress state, as well as its magnitude, is not only a characteristic of the salt massif because it is not dependent only on its quality but is a function of the \"complete and inseparable interaction\" of a complex of natural, technical, mining, and organizational factors [7; 11; 12; 13; 14; 15; 22; 23; 31; 36; 39; 40]. Studies related to the analytical assessment of the stability of the dry rock salt exploitation system with the increase in depth were carried out in the paper [12].