# Prediction of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel Construction
## 3 Case Validation of Deformation Predictions in Shallow-Buried Tunnels
### Analysis of Results
#### 4.2.1 Vertical Surface Deformation
The most significant difference is the pronounced surface heave at 2.5 times the pilot tunnel width from the centerline, a feature absent in classic bell-shaped profiles. This phenomenon arises because the secondary lining has low stiffness before gaining sufficient strength. Under surrounding rock pressure, soil on both sides of the pilot tunnel is horizontally extruded. As this soil moves laterally, it squeezes the undisturbed dense soil below, generating an upward stress component. In deeply buried tunnels, a natural soil arch forms in the overburden and the self-weight stress fully offsets the upward stress, preventing surface heave. By contrast, ultra-shallow burial depths are insufficient to form a natural arch, so the self-weight stress is less than the upward stress, causing partial surface heave. The horizontal expansion of the initial support has limited disturbance, only inducing heave over a localized surface area that diminishes with distance from the axis. Overall, the surface deformation curve is M-shaped, characterized by maximum settlement above the excavation center, a rapid transition from settlement to heave from the axis to the edge, and a subsequent rapid decrease in heave magnitude. Ultra-shallow-buried pilot tunnel excavation induces surface tilting and warping due to uneven heave and settlement, collectively termed vertical surface deformation. As shown in Figure 17, the ground surface near the pilot tunnel centerline on both sides exhibits tilted deformation toward the axis. The positive/negative values in the figure denote the tilt direction: the normal to the tilted plane aligns with the positive x-axis (positive), and vice versa (negative). The surface tilt curve is centrally symmetric, featuring three zero points and four extreme values within the plotted range. The zero points occur at horizontal distances of \(-12.9\) m, \(0\) m and \(+12.9\) m, corresponding to the three extreme points of the settlement curve: maximum settlement at 0 m and peak heave at \(\pm\)12.9 m. As the horizontal distance approaches infinity, the surface tilt tends to zero. The tilt curve has four extreme points, corresponding to the four inflection points (reverse bends) on the surface settlement curve. The distances from these inflection points to the pilot tunnel axis are denoted as i\({}_{1}\) and i\({}_{2}\). Starting from the origin, as the distance x from the tunnel axis increases, the surface tilt value gradually rises, reaching a maximum at x = \(\pm\)i\({}_{1}\) and then decreasing. For a typical shallow-buried tunnel, the tilt curve would converge to zero at this stage, whereas the ultra-shallow-buried tunnel's tilt curve crosses the zero point after a reverse increase, reaching a secondary maximum at x = \(\pm\)i\({}_{2}\) and then decreasing to zero. Analyzing the positive x-axis alone, inflection point i\({}_{1}\) is at 5.8 m, where the surface tilt reaches a maximum of \(-\)1.79 mm/m, corresponding to the steepest increase in surface heave on the settlement curve. Inflection point i\({}_{2}\) is at 19.4 m, where the tilt reaches the next highest value of 1.11 mm/m, aligning with the fastest reduction rate of surface heave. As shown in Figure 18, the surface curvature deformation curve exhibits axisymmetric distribution, with an extreme value of 0.48 \(\times\) 10\({}^{-3}\) m\({}^{-1}\) directly above the pilot tunnel axis. The curvature curve follows the same variation pattern along both the positive and negative x-axes. For the positive x-axis, as the distance x from the pilot tunnel center increases, surface curvature gradually decreases. When x reaches x = i\({}_{1}\), the curvature deformation first drops to zero, coinciding with the maximum surface tilt. As x continues to increase, the curvature deformation increases negatively, reaching a negative maximum of \(-\)0.35 \(\times\) 10\({}^{-3}\) m\({}^{-1}\) at x = 11.4 m. For a typical shallow-buried tunnel, the surface curvature  
Figure 16: Surface settlement of Beijing Pilot Tunnel. Figure 17: Beijing Pilot Tunnel surface tilt.