## 4 Numerical Simulation Study of the Effect of Anchoring on Overburden Rock in Oil Wells  
### Modeling and Scenarios  
The FLAC3D 7.0 numerical simulation software was employed to model and calculate the geomechanical behavior of the system. The overall model dimensions were set as L \(\times\) W \(\times\) H = 150 m \(\times\) 150 m \(\times\) 105 m based on the actual geological conditions of Well No. 1 at Checun Coal Mine. To accommodate the petroleum well casing and its surrounding structures, cylindrical voids with a diameter of 0.93 m were excavated within the stratum.  
After achieving excavation equilibrium, each cylindrical void was filled with cement sheaths represented by annular rings with an outer diameter of 0.50 m and a thickness of 0.25 m, simulating the cementing cement. The cementing material used was Portland cement (API Grade G), a calcium carbonate-silica mixture with minor amounts of iron ore and gypsum, as per industry standards.  
To ensure model accuracy and minimize computational errors, the grid resolution was refined within 50 m of the well complex perimeter. The top boundary of the model was set as a free boundary, while loads were applied based on stratigraphic relationships. Displacement constraints were imposed on all other boundaries. Additionally, to simulate realistic geological conditions, a coal boundary pillar with a width of 50 m was maintained at the x- and y-direction edges of the model, as illustrated in Figure 5.  
The physical-mechanical parameters of the coal rock body listed in Table 1 were obtained from actual field tests and laboratory tests. In the course of the study, the field test data were obtained from the geological exploration and rock mechanics tests conducted on the No. 1 shaft of Checun coal mine in Yan'an City, Shaanxi Province. The laboratory tests, on the other hand, obtained the specific physical-mechanical parameters by conducting a series of mechanical property tests on the collected rock samples, including compression strength, friction angle, shear strength, and so on.  
In the numerical simulation of oil well borehole excavation, the wellbore is first excavated at the surface coordinates of the designated oil well, which serves as the reference point. Subsequently, the borehole is backfilled with a cementing ring of the predetermined dimensions as established in the initial model setup. The simulation process involves excavating the entire oil well borehole, followed by filling it with cementing material once excavation equilibrium is achieved. The detailed procedural workflow is illustrated in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithologic Characters** & **Density** & **Bulk** & **Shear** & **Friction** & **Force of** & **Tensile** \\  & **(kg/m\({}^{3}\))** & **Modulus/GPa** & **Modulus/GPa** & **Angle/(\({}^{\circ}\))** & **Cohesion/MPa** & **Strength/MPa** \\ \hline Silstone mud & 2490 & 2.4 & 1.63 & 35 & 1.56 & 1.92 \\ Fine grained sandstone & 2490 & 3.7 & 2.20 & 35 & 2.12 & 2.43 \\ Muddy Silstone & 2530 & 3.0 & 1.67 & 37 & 1.36 & 2.17 \\ Medium grained sandstone & 2500 & 2.3 & 1.25 & 34 & 2.12 & 3.12 \\
3\# Coal seam & 1400 & 2.2 & 1.30 & 33.5 & 0.9 & 1.63 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of coal rock bodies.  
Figure 5: Three-dimensional view of the model.