## 3 Case Study
### Compaction Characteristic Parameters of Filling Materials  
The accuracy of numerical simulation results is dependent on the rationality of the constitutive model used. Given that fly ash filling is a granular material, its stress-strain characteristics markedly differ from those of rock materials. Therefore, it is necessary to investigate the compression characteristics of fly ash filling under grouting into overburden separation conditions.  
During the grouting process, the fly ash slurry, as it moves through the separation, experiences continuous water drainage due to pressure and seepage within the rock layers, ultimately resulting in a compacted filling body. To simulate this real-world condition in a laboratory setting, a fly ash slurry compressor, which emulates a confined environment, is used. This apparatus allows for the replication of both the stress experienced by the filling slurry and the water loss processes occurring within rock layers [13]. The schematic diagram of this slurry compact is presented in Figure 9. The compactor consists of an outer cylinder that acts as a closed system with an inner cavity at the bottom connected to a water outlet. Equipped with a sieve plate and filter screen, the device effectively simulates the ongoing water loss during the slurry consolidation process. Prior to starting  
Figure 8: Layout diagram of grouting holes and surface subsidence monitoring stations for work face.  
Figure 7: Project overview. (**a**) Location of the research mine; (**b**) surface and underground features of the working face [33].  
the experiment, lubricating oil is applied between the piston and the barrel wall to reduce friction. During the experiment, pressure is exerted on the slurry by a press machine acting on the piston, mimicking the gravitational force of the overlying strata. Both the pressure and the displacement experienced by the fly ash filling body are recorded in real time. The sample used in this experiment was sourced from fly ash utilized in the grouting operations at the Wuyang Coal Mine in Changzhi City, Shanxi Province, China. The water-to-ash ratio used was \(1.15\):\(1\), mirroring the specifications employed on-site for engineering purposes.  
The double-yield constitutive model is particularly effective for simulating the behavior of compacted bodies made from granular materials [34]. To determine the parameters for this model, the confined compression test was numerically simulated. The simulation involved a unit block configured as a \(1\) m cube, with displacement constraints fixed at the periphery and the bottom edge of the model, while a fixed vertical velocity was applied to the top. Material parameters for the model were established through a trial-and-error inversion method. This approach facilitated the fine-tuning of parameters to best match the observed experimental data. The comparison of the final simulation results with actual experimental data is depicted in Figure 10. Additionally, the mechanical properties derived from the experiments on the fly ash filling body used in overburden separation are detailed in Table 1.  
Figure 10: Stress–strain relationship curve of fly ash filling body.  
Figure 9: Diagram of fly ash slurry compressor and its working principle.