The identification of the subsidence stage is vital for the surface infrastructure protection above underground mining panels, while prior studies have only focused on shallow mining with large interpanel pillars. In this study, we aimed to develop a new model to identify the initiation of subcritical subsidence in deep pillarless mining. The key stratum theory was used to transform the problem of stage identification for surface subsidence into the primary key stratum (PKS) failure. The findings show that the PKS in deep mining can remain stable after a single panel is extracted. The narrow pillar gradually loses its structural integrity and fails to isolate the movement of PKS above two panels as the second panel passes it. Consequently, the PKS above two panels integrally fails as an L-shaped plate, causing the transition from super-subcritical to subcritical subsidence stage. According to these findings, the L-shaped PKS model was developed using the theory of elastic plates to determine the critical span of PKS failure and identify the occurrence of subcritical subsidence in pillarless mining. The model was validated using a three-year field measurement data on surface subsidence in Longtan coal mine. This study contributes to the understanding of subsidence mechanism in deep pillarless mining and provides new insight into designing pillarless mining with surface subsidence control.

沉降阶段的识别对于地下采矿面板上方的地表基础设施保护至关重要，而先前的研究仅关注具有大型面板间支柱的浅层采矿。在这项研究中，我们旨在开发一种新模型来识别深部无柱采矿中亚临界沉降的开始。利用关键地层理论将地表沉降阶段识别问题转化为主关键地层（PKS）破坏。研究结果表明，在提取单个面板后，深度挖掘中的 PKS 可以保持稳定。当第二个面板通过它时，狭窄的支柱逐渐失去其结构完整性，并且无法隔离 PKS 在两个面板上方的运动。因此，两个面板上方的 PKS 整体失效为 L 形板，导致从超亚临界向亚临界沉降阶段过渡。根据这些发现，利用弹性板理论开发了 L 形 PKS 模型，以确定 PKS 失效的临界跨度，并识别无柱采矿中亚临界沉降的发生。该模型使用龙潭煤矿地表沉降的三年现场测量数据进行了验证。这项研究有助于理解深部无柱采矿中的沉降机制，并为设计具有地表沉降控制的无柱采矿提供新的见解。该模型使用龙潭煤矿地表沉降的三年现场测量数据进行了验证。这项研究有助于理解深部无柱采矿中的沉降机制，并为设计具有地表沉降控制的无柱采矿提供新的见解。该模型使用龙潭煤矿地表沉降的三年现场测量数据进行了验证。这项研究有助于理解深部无柱采矿中的沉降机制，并为设计具有地表沉降控制的无柱采矿提供新的见解。