Asymmetric analogous hyperbola model of overburden movement and its verification.

The extraction of underground coal resources induces the fracture and movement of overlying strata, leading to geological hazards such as surface deformation, cracks, and even subsidence. Utilizing the analogous hyperbola model of overlying strata movement, we conducted a mechanical analysis to examine the asymmetric fracture mechanism resulting from coal seam mining in thick loose strata. An asymmetric analogous hyperbola model was established by introducing distinct virtual half-axis lengths (b). The thickness impact of thick loose layers (H) and bedrock layer (h) on the asymmetric movement of overlying rock during mining was also discussed. Similarity model tests were conducted to research the migration characteristics and surface subsidence patterns of overburdened rock and thick loose layers at different mining stages and validate the hypothesis of asymmetric overburdened rock migration. Additionally, the discrete element numerical model for thick and loose layers mining was established by using UDEC and discussed the asymmetric analogous hyperbola behaviour of overburden movement and surface subsidence. The comparison results show that the established asymmetric hyperbolic model can effectively predict the movement law of overlying strata and surface subsidence characteristics. Therefore, the proposed model can provide valuable theoretical support for predicting the movement patterns of overburden under thick loose layers and mitigating surface subsidence disasters.