# Model Test on Excavation Face Stability of Shallow-Buried Rectangular Pipe Jacking in Sand Layer
## 3 Results and Analysis  
### Support Pressure Variation Law  
Figure 3 presents the normalized support pressure evolution curve characterized by two dimensionless parameters: relative displacement \(\Delta\)s (ratio of actual displacement to pipe height H) and support pressure ratio P (ratio of measured pressure to initial pressure). It can be found that as \(\Delta\)s increases, the variation law of P under different overburden ratios and densities is basically consistent, which can be divided into 4 stages:  
1. Pressure rapid decline stage: Small relative displacement causes significant support pressure drop. This stage mainly involves soil elastic deformation and gradual mobilization of sand shear strength, with the support pressure reaching failure value P1. 2. Pressure slow decline stage: Reduced pressure reduction rate. Mainly soil plastic deformation occurs, while soil arching effect develops. Upon reaching limit equilibrium state at certain displacement, the support pressure reaches minimum Pmin. 3. Pressure slow rise stage: Pressure shows gradual increase as displacement continues. Soil ahead reaches ultimate shear strength, arching effect diminishes, and local shear failure occurs. 4. Pressure stabilization stage: Support pressure stabilizes, remaining constant with displacement increase, while the support pressure reaches stable value Ps. Figure 4a shows Pmin under different overburden ratios and densities. It can be found that higher density leads to tighter particle packing, stronger arching effects, and more pressure redistribution, resulting in lower Pmin. Among them, the support force can be  
Figure 3: Normalized supporting pressure–displacement curve. reduced to 0.39-0.58 of the initial pressure in a loose state, 0.38-0.49 in a medium-dense state, and 0.1-0.37 in a dense state. Notably, when overburden ratio < 1.5, Pmin decreases with depth increase. When >1.5, Pmin remains stable. This is because soil arching requires certain burial depth, that is, there is a critical overburden ratio. Circular face tests show critical ratio = 1 [18; 19], indicating rectangular geometry's reduced arching efficiency, requiring greater depth to develop equivalent stress redistribution. Figure 4: Pmin variation law. The exertion of the soil arching effect requires a certain soil burial depth, that is, there exists a critical overburden ratio [18; 19]. [PERSON] et al. [19] carried out the circular excavation face model test. In this paper, the test results under the same density (1.65 g/cm\({}^{3}\)) are selected for comparison. As shown in Figure 4b, the critical ratio of the circular face test is 1 [19]. This rule is not obvious in this study, indicating that rectangular geometry's reduced arching efficiency, requiring greater depth to develop equivalent stress redistribution. The evolution of soil arching effects can be characterized by the critical support pressure parameters Pmin and Ps. When the support pressure decreases to Pmin, the soil arching mechanism reaches full activation but subsequently deteriorates until complete shear failure occurs at Ps. The pressure differential (Ps--Pmin) quantitatively represents the arching effect intensity. As shown in Figure 5, the difference between the two is positively correlated with the soil density and overburden ratio. As the density and burial depth increase, the soil arch bears more pressure. After the soil arch of the overlying soil fails and is completely sheared, the degree of rebound of the support force in the slow rise stage will be greater. This mechanical behavior implies two distinct operational scenarios for rectangular pipe jacking projects:  
In deep-buried, high-density soil conditions, minimal support pressure (approaching Pmin) suffices to maintain face stability through effective soil arching. The relatively large pressure margin (Ps--Pmin) provides substantial operational flexibility during the progressive failure process, enhancing excavation face control.