**1. Background Introduction**

Owing to the breakthroughs in and the considerable development of mechanical equipment design and the manufacturing industry, as well as developments in the theory of mine pressure mechanics in recent decades, coal mining equipment is being developed towards a large-scale, heavy, and intelligent design. Thick and extra-thick coal seams that used to rely only on layered mining can now be recovered by using large-miningheight comprehensive mechanized mining or large-mining-height fully mechanized caving mining technology. Compared with the traditional layered mining method, the increase in the mining height has the characteristics of high resource recovery rates and significant reductions in the number of driving and moving operations. Additionally, large-miningheight coal mining technology is also faced with increases in the disturbance range of the roof and floor; the obvious ground pressure appearance and the movement of the roof and the top coal have significantly different movement evolution and interaction relations. Based on the provisions and assumptions of rock fracture mechanics and material mechanics for beam components with one end fixed and one end simply supported, we established a mechanical model of direct roof top coal body boundary interaction, transferred the results of direct roof rock beam movement under the basic roof to the top coal in different areas, and calculated three different types of direct roof top coal interaction relationships: the bench vertical interaction relationship, the rotation action relationship of the short cantilever beam, and the horizontal action relationship of the long cantilever beam.

**Citation:** Li, L.; Zhang, X.; Luo, J.; Hu, B. Theoretical Analysis of the Movement Law of Top Coal and Overburden in a Fully Mechanized Top-Coal Caving Face with a Large Mining Height. *Processes* **2022**, *10*, 2596. https://doi.org/10.3390/ pr10122596

Academic Editor: Baisheng Nie

Received: 5 October 2022 Accepted: 22 November 2022 Published: 5 December 2022

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The movement of the roof structure and the displacement of overburden caused by mining are some of the important factors that lead to the communication of aquifers, the appearance of strong ground pressure in the working face, and the instability of coal pillars in stopes. Since the end of the 20th century, the overlying rock movement caused by mining operation disturbances has mostly used the masonry beam [1–3] theory, and the transmission of rock beam theory [4,5] is often used for calculations and solutions. For the integral calculation principle of bearing pressure and the establishment of the beam model, refer to Brauner, G et al. [6], Barczak T.M. et al. [7], and Goodman R. E. et al. [8]. To date, the above achievements have opened up the research field of roof rock pressure control in the field of coal mining engineering, and great progress has been made on this basis by experts and scholars in China and abroad, providing a solid mechanical theoretical basis for large-scale mining equipment, the simultaneous improvement of the recovery rate of thick coal seams and even extra-thick coal seams, the rapid advancement of ultra-long working faces, and the emergence of intelligent roof control systems.

In the past decade, with the gradual entry of mines into the deep mining stage, the increase in the mining height and the gradual enrichment of the research regarding the mechanism of the short-distance coal seam and the steep coal seam groups, mining engineers have frequently faced extremely complex conditions. The calculation results obtained using the traditional empirical calculation formula and the analytical formula obtained under relatively simple hypothetical conditions are difficult to adapt to on-site phenomena. In theoretical and scientific research, because it is difficult to make adaptions between the solid mechanical boundary and the bulk top-coal boundary, the upper boundary is often conditioned by the free surface in the process of similar simulations and numerical simulations of top-coal caving mining, and the influence of the roof fracture movement and pressure change process on the top-coal fracturing movement release process is often ignored. The traditional numerical simulation method is widely based on the "continuum hypothesis" for research of roof fracture movement. In the Flac3D software (HydroChina—ITASCA R&D Center, Hangzhou, China), which uses the finite element method, the elastic–plastic ideal model, the strain-softening plastic model, and the elastic–plastic damage model take the equivalent stress, plastic zone, or damage zone as the criteria for the position of the roof occurrence span. In addition, numerous scholars use the discrete element PFC software to simplify the coal–rock unit into a rectangular block based on the discrete block hypothesis. Spherical blocks are endowed with mechanical properties such as contact stiffness and surface roughness.

The authors of this paper established a fracture mechanical model of roof overburden direct roof top coal with a large mining height based on field investigations; we also studied the mechanical state of the coal–rock interface boundary in depth, and preliminarily designed a similar simulation experimental device to modify the parameters of the numerical simulation experiment to simulate and study the evolutionary law of roof fractures. This research method is of great significance in improving the recovery rate of top coal, controlling the mine pressure, and improving the support conditions.
