# Model Test on Excavation Face Stability of Shallow-Buried Rectangular Pipe Jacking in Sand Layer
## 2 Experimental Design
### Materials and Methods  
According to scaling principles in geotechnical modeling, the deformation trend of soil particles is basically consistent with prototype soil when the scale ratio between model dimensions and particle sizes exceeds 175 [17]. For the current experimental configuration with a 0.10 m \(\times\) 0.16 m pipe model, this criterion dictates that the maximum particle diameter should be less than 0.57 mm. As shown in Figure 2, The selected medium sand (Figure 2) exhibits the following: (1) a small coefficient of uniformity (Cu = 2.07); (2) a steep gradation curve (91.7% soil particles \(\leq\) 0.57 mm), collectively ensuring proper scaling fidelity and particle size compliance. The experimental matrix systematically investigates two key parameters: (1) overburden ratios (Z/H = 0.5, 1.0, 1.5, 2.0) and (2) soil compactness (loose, medium-dense, and dense). Standard compaction and volumetric methods were employed to establish the soil's maximum and minimum dry densities. Based on these benchmarks, three characteristic densities were selected as follows: 1.56 g/cm\({}^{3}\) (loose), 1.65 g/cm\({}^{3}\) (medium-dense), and 1.80 g/cm\({}^{3}\) (dense), corresponding to distinct compactness states as summarized in Table 1. The model test of this study is the unstable deformation of the soil at the excavation face under the action of self-weight, as well as the density and internal friction angle meet the similarity ratio requirements. Figure 2: The grain size distribution curve. The experimental procedure comprised seven sequential phases:  
1. Instrument Configuration (Shanghai Saisu Motor Technology Co., Ltd., Shanghai, China)
2. Stereo cameras were configured for 1 Hz image acquisition over 5 s intervals. 3. Calibrated thin-film pressure sensors were surface-mounted on the moving panel with 10 Hz sampling. 4. Terrestrial laser scanning resolution was set to 0.025 mm. 5. Stepper motor displacement rate was programmed at 0.16 mm/s (0.1%H/s) through closed-loop control. 6. Specimen Preparation  
Employing the sand raining technique, the predetermined soil mass was deposited layer-wise to achieve target density profiles corresponding to specific overburden ratios and soil compactness. 7. Baseline Measurement  
Following 24 h pressure stabilization, initial condition documentation included the following:  
* Initial deep soil images. * Support pressure baseline values. * Reference ground topography. 8. Kinematic Testing  
Synchronized data acquisition commenced with motor activation, maintaining constant face retreat velocity while monitoring the following:  
* Temporal pressure fluctuations. * Progressive soil displacement fields. 9. Intermittent Scanning  
Automated test pauses at 0.5% displacement intervals enabled intermediate ground deformation quantification using a 3D laser scanner. 10. Termination Criteria  
Cyclic testing continued until ground subsidence exceeded 5%H or catastrophic collapse morphology developed. 11. Post-processing
12. Particle Image Velocimetry (PIV) analysis was performed using MATLAB (R2022a)-integrated PIVlab plugin to quantify soil displacement fields during instability progression. High-resolution 2D image sequences were processed to generate time-dependent displacement contour maps. 13. Single point pressure test system SPM-8 was employed to process pressure-time histories. \begin{table}
\begin{tabular}{c c c c} \hline
**Soil Compactness** & **Loose** & **Medium-Dense** & **Dense** \\ \hline Relative density D\({}_{\mathrm{r}}\) & 0.2–0.33 & 0.33–0.67 & 0.67–1 \\ Dry density pd (g/cm\({}^{3}\)) & 1.53–1.57 & 1.57–1.68 & 1.68–1.80 \\ Experimental control density (g/cm\({}^{3}\)) & 1.56 & 1.65 & 1.8 \\ Internal friction angle \(\varphi\) (\({}^{\circ}\)) & 31.8 & 36.4 & 40 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the test soils.