## 1 Introduction  
The extensive mining of coal resources has led to the fracturing of key strata within the overlying strata, resulting in surface subsidence [1, 2]. This, in turn, has caused significant degradation of the ecological environment. The conflict between economic development and the imperative for green and sustainable environmental practices has become an urgent challenge in need of strategic planning and resolution [3, 4, 5]. This contradiction is particularly pronounced in the case of shallow coal seams, where surface subsidence is an inherent outcome of mining activities. The manifestation of fractured bearing structuresin the key strata of the overlying layers on the surface represents the primary issue left unresolved by mining operations [6,7]. This situation has the potential to trigger a chain reaction, posing unpredictable threats to field production, and has consequently become a central focus for both researchers and industry operators [8, 9, 10]. At the same time, some scholars, focusing on mining subsidence as their research background, have studied its associated hazards and preventive measures, obtaining relevant results on surface subsidence caused by coal seam mining [11, 12, 13]. Building on this foundation, their in-depth research on key strata and surface subsidence has become crucial for assessing and managing the ecological environment. This research offers effective methods to address certain mining disasters and the chain reactions they may trigger. At present, a substantial amount of research has been conducted on key strata and surface subsidence in shallow coal seam mining. Numerous scholars have investigated the mechanical structure of overlying strata and surface subsidence under various mining conditions, primarily analyzing stress characteristics, rock fracture patterns, and subsidence parameters, providing valuable guidance for subsequent research [14, 15, 16]. Based on the geological characteristics of shallow coal seams, it has been found that after coal seam extraction, the overlying strata can fracture to form hinged rock beam structures and step rock beam structures. Hinged rock beam structures exhibit stable load-bearing capabilities, while step rock beam structures have reduced load-bearing capacities [17, 18, 19]. The fractured overlying strata play a role in inhibiting and weakening surface subsidence [20]. Step rock beam structures lead to surface subsidence in a step manner and the formation of vertical fault fissures on the surface [4,21, 22]. When fractured overlying strata form hinged rock beam structures, the surface subsides uniformly, creating tensional fissures [23,24]. Surface subsidence, as a representation of the fracture pattern of key strata-bearing structures, to some extent, reflects the type of load-bearing structure. Scholars have made significant progress in this area, forming a system of surface subsidence studies [25, 26, 27]. Through comprehensive research on surface subsidence, factors such as mining thickness, burial depth, and dip angle have been identified as influencing surface subsidence [28, 29, 30]. Currently, researchers have predominantly conducted separate studies on key strata fracture-bearing structures and surface subsidence [31, 32]. While the results of these studies provide guidance for field production, they are constrained by the complexity and variability of geological strata [33, 34, 35]. The organic correlation between key strata-bearing structures and surface subsidence, as influenced by mine extraction, has not been thoroughly explored and requires continuous research. Therefore, research on the mechanisms governing the rock displacement of key strata-bearing structures and the evolution of surface subsidence in shallow coal seam mining should focus on the interactive mechanisms of key strata fracture-bearing structures and surface subsidence.