Structural importance analysis and key chambers identification for chain instability of chamber group in coal mine

Accurately locating the weak links in chamber group is crucial for achieving targeted and directional control for its surrounding rock. In this paper, the topological structure of the chamber group was first established, which divided the chambers into important chambers and general chambers. The chain instability inertia I was defined as the ratio of important chambers m to all chambers n, which can reflect the difficulty of chain instability for chamber group. On this basis, two-chamber, three-chamber, and four-chamber group were analyzed respectively, the topological structure evolution of chamber group were revealed. The concept of structural importance was introduced, which was used to quantitatively characterize the influence of micro-state of each chamber on macro-state of chamber group. Finally, a method of key chambers identification was proposed. When I = 0, there are no key chambers; when I = 1/n, the important chamber is the key chamber; and when I > m/n, chamber with the maximum key coefficient is the key chamber. Moreover, key chambers identification should follow four principles of structure, diversity, dynamic and priority. This research established a quantitative and effective framework for the stability control of chamber group.