# Model Test on Excavation Face Stability of Shallow-Buried Rectangular Pipe Jacking in Sand Layer
## 3 Results and Analysis
### Deep Soil Deformation Process  
Taking medium-dense soil as an example, Figure 6 illustrates the progressive instability mechanisms of soil mass under varying overburden ratios (Z/H) with increasing relative displacement (\(\Delta\)s). Figure 5: The difference between Pmin and Ps. As shown in Figure 6, all tested overburden conditions exhibited consistent evolutionary patterns, successively experiencing no deformation, slight deformation, local instability, and overall instability. The ultimate failure configuration comprised two distinct features: (1) triangular shear zones in front of the excavation face and (2) vertical shear planes extending to the ground. As shown in Figure 6a, under the condition of \(Z/H=0.5\), when \(\Delta s=0.2\%\), there is no deformation. When \(\Delta s=0.3\%\), minor deformations occur and triangular + arched shear zones appear, which are the same as the shear band morphology in the circular excavation face test and numerical simulation [18; 19; 20]. When \(\Delta s=0.4\%\), the soil in the arched shear zone is locally unstable. When \(\Delta s=0.5\%\), the arched shear zone extends to the ground, forming a vertical shear zone, and the overall overlying soil on the excavation face becomes unstable. As the relative displacement continues to increase (\(\Delta s=0.9\%\), \(1\%\), \(1.5\%\), \(2\%\)), the deformation of the soil in the shear zone also increases, but the range of the vertical shear zone no longer expands. It can be seen that even when the burial depth is relatively small, there is a weak soil arching effect. However, due to the fact that the full development of the soil arching effect requires a certain burial depth, its stability is relatively poor and it soon develops into a vertical shear zone. As shown in Figure 6b, under the condition of \(Z/H=1\), there is no deformation when \(\Delta s=0.3\%\). When \(\Delta s=0.4\%\), slight deformation occurs, but only triangular shear bands appear. When \(\Delta s=0.7\%\), the displacement of the triangular shear band further increases and an arched shear band appears. However, when \(\Delta s=0.9\%\), the arched shear zone does not directly extend to the ground as \(Z/H=0.5\) but undergoes local instability and generates a loose failure zone. As the relative displacement continues to increase, the original soil arch is damaged when \(\Delta s=1\%\), \(2\%\), and \(3\%\), forming a new arched shear zone. It does not extend to the ground until \(\Delta s=4\%\), forming a vertical shear zone. As shown in Figure 6c,d, the instability process under the conditions of \(Z/H=1.5\), \(2\), and \(3\) is similar to that of \(Z/H=1\), with only the difference in the relative displacement \(\Delta s\). Meanwhile, during the instability process, the angle between the triangular shear zone and the horizontal line (i.e., the failure angle) remains basically unchanged, indicating that the failure angle under the same overburden ratio and density is independent of the relative displacement. Figure 6: _Cont._  
Figure 6 demonstrates the progressive evolution of shear bands in overlying soils during excavation face instability, transitioning from an arch-shaped pattern to vertical alignment. This development mechanism parallels observations from trapdoor tests [21; 22]. Notably, the triangular shear zone ahead of the excavation face governs the width of the \"trapdoor\" mechanism through its slippage extent. Experimental results in Figure 7 reveal consistent failure angles under varying overburden ratios with equivalent densities, indicating the independence of triangular shear zone slippage from burial depth. Conversely, maintaining constant overburden ratio while increasing soil density results in progressive enlargement of failure angles and corresponding reduction in shear zone slippage. Figure 8 illustrates that rectangular excavation faces exhibit failure angles approaching \(2\varphi\), significantly exceeding the theoretical value of \(45^{\circ}+\varphi/2\). This discrepancy amplifies with increasing soil density.