Criterion of local energy release rate of gob instability in deep mines considering unloading stress path

The stress path characteristics of surrounding rock in the formation of gob were analyzed and the unloading was solved. Taking Chengchao Iron Mine as the engineering background, the model for analyzing the instability of deep gob was established based on the mechanism of stress relief in deep mining. The energy evolution law was analyzed by introducing the local energy release rate index (LERR), and the energy criterion of the instability of surrounding rock was established based on the cusp catastrophe theory. The results show that the evolution equation of the local energy release of the surrounding rock is a quartic function with one unknown and the release rate increases gradually during the mining process. The calculation results show that the gob is stable. The LERR per unit volume of the bottom structure is relatively smaller which means that the stability is better. The LERR distribution showed that there was main energy release in the horizontal direction and energy concentration in the vertical direction which meets the characteristics of deep mining. In summary, this model could effectively calculate the stability of surrounding rock in the formation of gob. The LERR could reflect the dynamic process of energy release, transfer and dissipation and that provided an important reference for the study of the stability of deep mined out area.