## 1 Introduction
Significant and uneven ground subsidence can also be observed when the movement is transmitted to the land  
Figure 1: Types of induced earthquakes and the proportion of mining-induced earthquakes ([[https://inducedearthquakes.org/](https://inducedearthquakes.org/)]([https://inducedearthquakes.org/](https://inducedearthquakes.org/)) accessed on 5 November 2023). surface, which has an adverse impact on the surrounding environment, such as agricultural activities and above-ground structures. The cumulative change of the stress state of the rock mass can result in new fractures or the reactivation of pre-existing faults and hence induce seismicity [18; 19; 20; 21]. In 1996, [PERSON], [PERSON] et al. [22] defined the key strata and later proposed a theory related to this concept. When there are multiple layers of hard rock in the overlying strata of the mining site, the rock layers that play a decisive role in all or partial rock activity are called key layers. The former can be called the key layer of rock movement, and the latter can be called the sub-critical layer. The breakage of key strata can control the whole or local failure of the overburden above [23]. In addition, ground stress, hydrogeological conditions, and properties of the surrounding rock have an impact on overburden behavior, as confirmed in previous research [24; 25]. Therefore, studies considering multiple factors and their interactions are very necessary. Theoretical, experimental (or field), and numerical analyses are three main tools to find the key strata and investigate the induced seismicity. (1) The theoretical method often requires a significant simplification, carrying several assumptions. [PERSON] [26] established a roof strata model to study the relationship between mechanical properties and the stability of the covering layer. [PERSON], [PERSON] et al. [27] investigated the effects of mining height and face advance length on rock overburden failure and fracture development in the rock strata. Fault sliding is closely related to the position relationship of the slope, the mining speed, and the mechanical properties of the fault [28]. (2) The validity of the theory and the more complicated scenarios need experimental and field studies to verify. Based on physical model experiments, [PERSON], [PERSON] et al. [29] analyzed the physical and mechanical properties and microstructural characteristics of weakly cemented overburden and overburden failure and pointed out that the failure mode of ultra-thick and weakly cemented overburden cover is \"beam-arch-semi-arch shell\", and the failure boundary is arch-fractured. (3) Due to the technical limitation, numerical simulation can further enrich the experimental scene and obtain more comprehensive and repeatable data [30; 31; 32; 33; 34]. [PERSON], [PERSON] et al. [35] used the numerical simulation software FLAC3D to simulate the failure process of the roof overburden of the 1308 working face, and the results showed that the mining depth and the working face advance distance were the two most influential factors of the failure height of the roof cover. [PERSON], [PERSON] et al. [36] determined the reasonable length of working face under similar geological conditions based on comprehensive research methods such as numerical simulation, theoretical analysis, and on-site exploration. As the distance from the top of the coal seam increases, the stress in the rock gradually shifts upward to the overlying formation, and the scale of this stress transfer gradually decreases. Building on existing research, this study addresses the limitations of prior work that often focused on isolated phenomena related to mining-induced seismicity. Previous studies have insufficiently considered the complex interactions among multiple factors, such as the combined effects of mechanical properties, excavation geometry, and mining rates, on overburden failure.