# Model Test on Excavation Face Stability of Shallow-Buried Rectangular Pipe Jacking in Sand Layer
## 3 Results and Analysis
### Ground Settlement Characteristics  
Taking medium-dense soil as an example, Figure 9 delineates the evolutionary characteristics of ground settlement under varying overburden ratios, revealing two distinct phases:  
Without settlement phase: During initial face displacement, the soil arching effect remains underdeveloped as arch-shaped shear bands have not propagated to the ground, resulting in negligible ground settlement. Rapid settlement phase: Progressive relative displacement facilitates shear band penetration through the ground, triggering global instability in overburden soils. Initial micro-settlements evolve into rapid linear subsidence with expanding influence zones. The enhanced soil arching effect in circular excavations produces gradual phase transitions. This phenomenon was experimentally verified in shallow sandy strata, identifying four-stage evolution: without settlement, slow linear growth, accelerated nonlinear development, and rapid linear progression [18; 19]. In contrast, rectangular excavations demonstrate abrupt settlement characteristics due to compromised arching capacity. Beyond critical displacement thresholds, both settlement magnitude and rate escalate dramatically, bypassing intermediate transitional phases and indicating catastrophic collapse potential. The critical settlement amount Scr is defined as the settlement at the inflection point between the no-settlement and rapid settlement phases. Figure 10 demonstrates that Scr remains consistent when soil density is unchanged and exhibits minimal dependence on the overburden ratio. However, larger overburden ratios decelerate the propagation of the arched shear zone toward the ground, consequently increasing the incremental settlement \(\Delta\)s required to attain Scr. Beyond Scr, ground settlement progresses linearly at an approximately constant rate. At this stage, soil arching collapses, shear effects diminish, and gravitational acceleration governs the settlement rate. Consequently, settlement rates converge to similar values across varying overburden ratios and densities. As illustrated in Figures 11 and 12, trapezoidal settlement surfaces emerge on the ground under varying overburden ratios and soil densities. Adjacent soils experience stress relaxation and slide along the natural angle of repose, forming arcuate boundary lines. With increasing relative displacement, these trapezoidal surfaces collapse downward while the arcuate boundary line boundaries expand. This demonstrates the three-dimensional nature of soil arching, which manifests both vertically and horizontally within deep soil strata. During excavation-induced displacement, the overburden develops two distinct stress zones: (1) a plastic stress zone within the shear band where soils slide downward, and (2) an elastic stress zone outside the shear band exhibiting negligible deformation. Stress transmission occurs through soil particle interactions. When the soil in the plastic stress zone undergoes stress relaxation, the soil arch effect will occur in the direction perpendicular to it. The soil arch contour of the soil is called the equilibrium arch (i.e., the trapezoidal boundary line) [26]. Soils within the equilibrium arch undergo significant settlement synchronized with excavation displacement, whereas those beyond the arch slide solely under self-weight conditions. This transitional region progressively extends outward toward the elastic stress zone. Figure 12 demonstrates equilibrium arch angles \(\beta\) ranging 41\({}^{\circ}\)-48\({}^{\circ}\), independent of the density and overburden ratio. Centrifuge testing proved an inverse proportionality between \(\beta\) and retaining wall aspect ratio W/H [26]: \(\beta\) = 45\({}^{\circ}\) at W/H = 1.5 and \(\beta\) = 55\({}^{\circ}\) at W/H = 0.5. Interpolation yields \(\beta\) = 47.5\({}^{\circ}\) for the current model's W/H = 1.25, aligning with experimental measurements. Figure 9: _Cont._  
Figure 9: Three-dimensional map of ground settlement (the planar view above the model).