Introduction. Prediction of excavations stability is an important step towards ensuring geo-mechanical safety during their construction. A reliable prediction of the stability of excavations includes such factors as the initial stress state, physical and mechanical characteristics of rocks, rock mass fracturing, and a number of others. These factors should be considered when performing calculations. The geo-mechanical conditions of the Apatite deposits are different, rock pressure can manifest itself in the form of brittle fracture of rocks, limited displacement of the rock contour, the formation of local rock failures or arching. In this paper, we consider only areas of the rock mass, where the loss of stability of the excavation contour is associated with the formation of brittle fracture zones. An analysis of methods for predicting brittle fracture zones suggests that they are devoted to their formation in the vicinity of single excavation and do not consider the formation of brittle fracture zones in the areas of excavation junctions. Despite the fact that a significant number of research papers are devoted to the formation of plastic deformation zones and the assessment of the excavation contour stability, they mainly consider two forms of geo-mechanical processes - rock failure along fractures and rock contour deformations. At the same time, little attention is paid to the formation of brittle fracture zones in the areas of excavation junctions in rocks predisposed to the development of such geo-mechanical processes. Considering the conditions of the Apatite deposits, it can be noted that the values of deformational and strength characteristics of rocks are very high. The rock mass is different in fracturing characteristics, however, the volume of rocks with excavations, which can be classified as weakly fractured, is very significant. The initial stress state of rock mass is characterized by the tectonic nature, where the magnitudes of the largest horizontal stresses are several times greater than the vertical stress component. All this makes it possible to classify the conditions of Apatite deposits as very difficult and rock burst hazardous. Methods and materials. To assess the correctness of the numerical modeling using model of brittle fracture of rocks, the following typical problems are considered: forecasting the development of brittle fracture zones in the vicinity of excavations of research laboratory in Canada; forecast of zones of brittle fracture of rocks for mining-geological and geo-mechanical conditions of the Apatite enterprises. Numerical modeling and the stress-strain state prediction in the vicinity of excavations was carried out in a generalized plane-strain formulation (three-dimensional formulation with the assignment of appropriate boundary conditions). An analysis of numerical simulation results suggests that the increase in the size of the brittle fracture zone is that greater, the larger the junction span. This effect was obtained for all four variants of excavation junction. The following results of the stress-strain state formation in rock mass in the vicinity of excavation junctions were obtained: the size of the brittle fracture zone as a whole tends to increase in the areas of excavation junctions, while the type of junction plays a significant role in its size; the higher the value of the σmax index, the more clearly the influence of the junction type on the size of the brittle fracture zone is manifested, while at the ratio σmax/σc < 0.8, the difference in the sizes of the zones in the junction and the extended section of the excavation is not significant. It was noted that the excavation junction has an impact not only on the size of the brittle fracture zone, but also on the nature of this zone formation. There is a “flow” of the brittle fracture zone from the junction area directly to the single excavation, the direction of which coincides with the direction of the maximum principal stresses. Thus, it is possible to form rock failure in the excavation located in a moderately stressed rock mass; The proposed model for predicting brittle fracture zones based on setting the functions of hardening/softening of the medium, makes it possible to effectively predict brittle fracture zones in the vicinity of excavation junctions. In general, the research results confirm the patterns of brittle fracture zones development in the vicinity of excavation junctions obtained by the authors, however, an improved model for describing the development of geo-mechanical processes in rocks prone to brittle fracture made it possible to significantly increase the reliability of predicting the shape of the brittle fracture zone near the excavation.
