## 3 The Experiment of Similar Physical Models
### Layout of the Monitoring System  
The experimental apparatus incorporates an integrated monitoring framework consisting of DIC instrumentation and distributed optical fiber sensors, synchronized through a high-precision total station measurement system, as depicted in Figure 4. Data acquisition from each monitoring subsystem commences following the face advancement and strata stabilization phases. The surveying apparatus employs a Leica TS02 instrument, establishing 25 monitoring points at 10 cm intervals across the critical stratum surface, intersecting with the optical fiber array to form a horizontal measurement grid. Floor-mounted pressure transducers are installed at the base of the physical model for monitoring the stress evolution and spatial distribution within the goat region. The analysis employs a GOM-aramis digital image correlation apparatus, which acquires surface deformation patterns via dual high-resolution CCD sensors operating at 2648 \(\times\) 2448 pixel definition. Given the insufficient surface contrast of the analogous materials, engineered speckle patterns must be artificially applied. The optimization process determines circular speckle elements of 3 mm diameter, achieving approximately 40% surface coverage density. The correlation window dimensions are established through dual-threshold optimization, with image processing parameters configured at a 30-pixel minimum correlation area and a 15-pixel facet interval. The instrumentation incorporates single-mode compact optical fibers (2000 \(\upmu\)m diameter) selected for their minimal interference with rock mass deformation characteristics. During the installation phase of analogous materials up to the critical stratum position, a calibrated tensile force is applied to the optical sensors to ensure precise linear alignment within the target stratum. The NBX-6055 fiber optic analyzer operates with parameters set to 1 cm sampling intervals, 5 cm spatial resolution, and an averaged sampling frequency of 2 \(\times\) 106 measurements. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Layer** & **Lithology** & **Model Thickness-ness/cm** & **Mix Number** & **Sand/kg** & **Gypsum/kg** & **CaCO3/kg** & **Remarks** \\ \hline
1 & Loess & 3.33 & 1019 & 238.25 & 2.38 & 21.44 & Topsoil \\
2 & mudstone & 10 & 919 & 82.89 & 0.92 & 8.29 & \\
3 & Silstone & 14.66 & 837 & 119.53 & 4.48 & 10.46 & \\
4 & Medium & 20 & 837 & 159.47 & 5.98 & 13.95 & \\
5 & Silstone & 5.33 & 937 & 37.63 & 1.25 & 2.93 & \\
6 & Medium & 6.66 & 828 & 55.24 & 1.38 & 5.52 & \\
7 & Fine & 4.66 & 837 & 36.33 & 1.36 & 3.18 & \\
8 & sandstone & 4 & 828 & 21.08 & 0.53 & 2.11 & \\
9 & Fine & 9.33 & 828 & 61.01 & 1.53 & 6.1 & Key stratum \\
10 & Fine & 8.66 & 937 & 12.13 & 0.27 & 1.08 & Immediate \\  & sandstone & & & & & roof \\
11 & Coal seam & 2 & & 12.48 & 0.47 & 3.12 & coal seam \\
12 & Silstone & 4 & 937 & 19.88 & 0.66 & 1.55 & \\
13 & Fine & 5.33 & 837 & 48.26 & 1.81 & 4.22 & \\  & sandstone & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Similar materials used in the simulation test of the physical and mechanical properties and proportions of various layers. This physical simulation program demonstrates several unique advantages and innovative features in its comprehensive design. The model employs a sophisticated multi-scale approach with carefully calculated similarity ratios (dimensional scaling coefficient of 150 and density similarity constant of 1.56), enabling accurate representation of complex geological conditions while maintaining practical experimental dimensions (3000 mm \(\times\) 200 mm \(\times\) 1140 mm). A key strength lies in its integrated monitoring framework that synergistically combines three advanced measurement technologies: distributed optical fiber sensing, digital image correlation (DIC), and high-precision total station measurements. This multimodal monitoring approach enables unprecedented coverage and cross-validation of deformation measurements.