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Abstract 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.

Based on a large number of field investigations and the analysis of the "analogous hyperbolic" overall movement model proposed by the author, this paper further extends it to three-dimensional space, and proposes a full-space "analogous hyperboloid"three-dimensional movement model of the mining strata.There are two types of hyperboloids, "quasi-single-leaf"and "quasi-double-leaf", which can approximately describe the three-dimensional movement and surface subsidence characteristics of full-space mining strata under different lithological conditions.The "analogous single leaf hyperboloid" model is a horizontal moving boundary model of the spatial rock layer, which is implicit in the thick loose layer overlying rock; the "analogous double leaf hyperboloid" model is the vertical movement of the spatial surface subsidence and the overlying fissure arch and caving arch.The boundary models are approximately symmetrical with the "origin" in the main key layer, and are embodied in external forms such as surface subsidence under mining disturbance and arch caving of the surrounding rock in the stope. Through theoretical analysis, similar model test and 3DEC numerical simulation, this paper deduces and proves in detail the "analogous hyperboloid" model of spatially mined rock strata movement and surface subsidence under the condition of near-horizontal coal seam mining in thick loose layers.At the same time, this study analyzed the composition conditions, influencing factors and overall migration law of the co-asymptotic conical surface "analogous hyperboloid" model.Results show that under the condition of near-horizontal coal seam mining with thin bedrock and thick loose layer, the "quasi-hyperboloid" theoretical model is in good alignment with the 3DEC simulation results, indicating that the overlying rock migration and surface subsidence in space mining are "analogous hyperboloid" feature.