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Methodological approaches to the selection of ultimate state criteria and strength characteristics of the repeatedly undermined rock massifs were developed. These approaches were designed to provide parametric support to the geomechanical modelling of the massif stress-strain state and the mining systems of the Starobin potash deposit mine fields planned for the additional mining of the mineral reserves left. It was established that a complex criterion must be used to study the massif ultimate state. Determination of such criterion can be carried out using the developed approaches. The first approach is to select several criteria that evaluate the massif ultimate state by certain types of the massif stress-strain state. These criteria are the following: the criterion of the maximum normal stresses, criterion of the maximum linear strains, the criterion of the maximum shear stresses and the Coulomb–Mohr failure criterion. The second approach is to construct an integrated failure state criterion for materials whose ultimate tensile and compressive stresses differ significantly. In this case, parameters characterizing the type of stress state and properties of the material are introduced. These parameters together determine the destruction character – tear or shear. To describe the rocks behavior in the extreme strength stage of deformation, it is proposed to apply deformation theory of strength using the developed strain failure criterion. When calculating the strength characteristics of the repeatedly undermined rock massif, it is recommended to use a structural attenuation coefficient as the product of several factors, taking into account various types of disturbances in the primary undermined massif and the time factor. The Coulomb–Mohr strength condition is recommended to be used taking into account the composite structural attenuation coefficient. Dependencies have been developed to describe the change in the strength characteristics of rocks in the undermined massif, considering the attenuation coefficient.

The geomechanical model is proposed and the technology of numerical simulation is developed. Carried out computer simulation of the geomechanical state of the being undermined repeatedly rock massifs of the 3rd potash level of the Starobin deposit taking into account its structural and strength features, as well as the technological schemes of the primary mining. The regularities of the stress-strain zones formation in the undermined rock mass containing mined out mine workings and inter-panel pillars were determined. It is shown that the stability of the workings located in the undermined areas significantly depends on the time passed since the primary mining and on the location of the workings in the massif relative to the location of the primary mining operations. It is determined that the most dangerous for repeated mining are the areas of generalized shear, since the processes of rock mass movement and failure are most likely to be active in these areas. In the areas of generalized compression, the processes of compaction of caved rock take place. As a consequence, after a considerable period of time, the state of the rock massif in these areas can be treated as approximating to the natural state, without additional structural failures. In such areas, the effective mechanical characteristics of the rock massifs are practically restored. Therefore, the greatest stability of mine workings will be achieved when they are placed in the area of generalized compression stress state in the zone of caved, compacted rocks of the mined out roadways and faces.