# An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel
## 2 The Dynamic Zoning Method
### Numerical Modeling of Longwall Mining Based on the FDM  
The four zones are developed during the actual mining process, and the mechanical properties in different zones correspondingly change. Therefore, the proposed dynamic zoning method considers the mechanical parameter adaptation of disturbed rock masses in the progressive mining process. More specifically, according to the simplified complete stress-strain curve, the zoning criteria are established by considering the deformation and failure characteristics of the disturbed rock masses, and the mechanical parameters of the disturbed rock masses are adaptively adjusted. On those bases, the dynamic zoning of the disturbed rock mass in the mining process is simulated, and the dynamic development characteristics of the four zones are obtained.  
This paper simulates the underground longwall mining process with FLAC\({}^{\text{3D}}\) by means of step-by-step excavation. More details of the simulation process are introduced as follows (Figure 7):  
Step 1. Mining with a distance of L in each step.  
L is determined according to the actual mining schedule; in this paper, L = 10 m.  
Step 2. Adaptively adjusting the parameters of the overlying disturbed rock masses and dynamically zoning by looping over all the elements of the computation model.  
For each element, it is first necessary to determine whether the element yields. If not, then the element is in the elastic deformation stage; otherwise, the element needs to be further checked according to the failure type and plastic strain of the element to determine which stage it is in (the post-peak softening stage, the residual strength stage, or the caved material deformation stage). Second, by exploiting the principles of adaptively adjusting the mechanical parameters of rock masses in different stages, the cohesion \(c\) and the friction angle \(\varphi\) of the element are adjusted correspondingly. Finally, by following the zoning criteria, it must be determined which zone the element belongs to.  
Step 3. Checking whether the numerical computation reaches computational balance after N iterations (in this paper, N = 100).  
Figure 7: Flowchart for the simulation of longwall mining and dynamic zoning processes.  
If the computation is balanced (i.e., the maximum unbalanced force ratio is less than \(1\times 10^{-5}\)), then it should further conduct mining with distance L and repeat Step 2; otherwise, it needs to repeat Step 2 directly until the computation is balanced.  
Step 4. Proceeding to the next step of mining and repeating Steps 1-3.  
The mechanical parameters of the disturbed rock masses are dynamically adjusted, and the scope of the four zones is updated in real time until the end of the mining.  
The program code of the algorithm (Figure 7) is written by using the FISH language in FLAC3D software, and it is embedded in the numerical simulation calculation process to realize the dynamic adjustment of the mechanical parameters of the disturbed strata. See Appendix A for the algorithm code.  
Additionally, the following methods are used to simulate coal-seam mining: first, before FLAC3D simulation mining, the interfaces are set at the contact surface between the coal seam and the roof, which can avoid the dragging effect on the contact surface when the coal seam is mined, and prevent the distortion of the grid displacement data near the interface, so as to realize the full collapse of the coal-seam roof and the natural collapse to the floor and ensure the numerical simulation effect. Then, according to the coal-seam mining step, the coal-seam units within the step are emptied (that is, set to null model) to simulate the coal-seam excavation in the current step. Finally, it is iterated to the equilibrium state (the maximum unbalance ratio is less than \(1\times 10^{-5}\)), the calculation model is saved, and the next mining step according to the above method is then simulated until the coal-seam excavation of the working face is completed.