## 2 Analysis of Overburden Load Transfer Mechanical Model
### Example Analysis of Overburden Load Transfer  
In order to more intuitively reflect the evolution process of load transfer in the deep high-stress stop, this simulation takes the three stages of beam, plate, and arch as an example, in which the load transfer of beam structure can be analyzed through the load transfer process of the plate structure. The expressions of the internal force bending moment of beam-slab structure and arch structure of the main roof under the condition of three-side fixed support and one-side simple support, and three-side simple support and one-side fixed support are established, respectively. On the basis of theoretical analysis of overburden load transfer, Matlab's powerful data processing and numerical fitting software is used to perform linear fitting and numerical analysis on the mechanical expressions established under different mining stages of the working face by using typical case calculation methods. Through linear data regression and image visualization processing, the three-dimensional deformation surface diagram of load distribution under different mining stages of the deep high-stress stope is obtained.  
2.1 Trilateral Fixed Support and One-Side Simply Supported Beam Plate Structure Internal Force Distribution  
Plate length \(a=100\) m, plate width \(2a=50\) m, plate thickness \(s=4\) m, Poisson's ratio \(\mu=0.25\), elastic modulus \(E=30.3\) GPa. By calculating the bending moment values of the beam-slab structure surface in x and y directions under this boundary condition, the contour map of the internal force distribution of the three-dimensional surface is made by using Matlab numerical fitting software, as shown in Figure 9:  
Figure 9: Three-dimensional surface contour map of internal force distribution of three-sided fixed supported and one-sided simply supported plate. (**a**) Diagram of bending moment \(M_{x}\); (**b**) \(M_{x}\) stress isoline diagram; (**c**) Diagram of bending moment \(M_{y}\); (**d**) My stress isoline diagram.  
Through the analysis of the curved surface image, it can be seen that the roof fracture trend is a process from edge to surface, that is, the conversion process from beam to plate. It is not difficult to see from the size of the bending moment, at the beginning of mining, the load on the roof is transmitted from the center of the plate to the periphery and is transferred to the lower coal body through the beam (fixed long side) until the beam structure breaks and loses its load capacity. By calculating the ultimate span of the beam structure, the ultimate span of the beam is 45.28 m under the stress state. When the bending moment of the lower beam of the roof reaches its maximum, the beam breaks. The bending moment distribution in the x and y directions of the simply supported plate with three edges clamped, and one edge simply supported is 'wavy'. The maximum point of the bending moment of the thin plate is located near the center of the long edge of the fixed support. The bending moment value decreases in turn from 'fixed long edge-fixed short edge-plane center-simple short edge'. The long fixed edge is broken first, and then the fixed short edge is broken. After all the fixed edges are broken, the cracks gradually develop and connect with the broken boundary of the simply supported edge to form an 'O'-shaped broken ring. After that, cracks are generated in the center of the plate and extended to the surrounding areas to develop 'X'-shaped breaking, that is, 'O-X'-shaped breaking. Its development model is in good agreement with the theoretical analysis results, and its breaking evolution process is shown in the following Figure 10: