# 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 measured data changes can be seen in Figure 15. Six settlement measurement points are arranged on the same side of the pilot tunnel axis, with the horizontal distance at the tunnel's longitudinal axis being 0 m. The first measurement point directly above the pilot tunnel shows a measured settlement of \(-\)6.13 mm, the maximum value of this measurement line. At a horizontal distance of 5.1 m to the right along the cross-section, the second settlement point reveals a rapid transition from settlement to heave, with a measured surface heave of 2.42 mm--an 8.55 mm difference from the first point, resulting in a surface tilt toward the axis of 1.68 mm/m. From the second to the third settlement point, the surface heave value increases rapidly, reaching a maximum of 10.62 mm at 10 m horizontal distance (8.2 mm larger than the second point), with the same tilt direction and a tilt value of 1.64 mm/m. Thereafter, the heave value decreases rapidly to 5.58 mm at 15.4 m and 4.02 mm at 20.6 m, inducing a surface tilt away from the axis--an uncommon feature in shallow-buried tunnel settlement troughs. Analyzing the third to fifth points away from the pilot tunnel axis, the rate of heave decrease gradually slows, with the surface tilt rate reducing from \(-\)0.93 mm/m to \(-\)0.3 mm/m. Subsequently, the heave value slightly rebounds to 5.47 mm at 23.7 m, causing the surface tilt rate to turn positive, with a tilt toward the axis of 0.47 mm/m. Overall, the observations show that settlement is largest  
Figure 15: Comparison of measured and calculated ground settlements for Beijing Pilot Tunnel. above the pilot tunnel axis, decreasing rapidly and transitioning to heave when far from the axis. The change rate peaks at 1.68 mm/m, with heave deformation peaking at 2.5 times the tunnel width from the axis, decreasing rapidly and then rebounding again at 5 times the tunnel width. Figure 15 demonstrates that the theoretical calculations in this study align with the measured data in terms of overall trend. However, stochastic medium theory predicts a maximum settlement of \(-4.23\) mm directly above the axis, exceeding the measured values. Beyond this point, the settlement transitions to heave, decreasing radially at a rate of 1.41 mm/m. The ground surface tilts toward the axis, with the heave magnitude peaking at 10.19 mm (10.2 m from the axis). Subsequently, the heave diminishes rapidly at a reduction rate of 0.67 mm/m, reaching 1.04 mm at 23.7 m from the axis. Beyond this distance, the surface tilt direction reverses, pointing away from the axis. The theoretical calculation yields an error of 1.9 mm at the axis, slightly larger than the measured value. Along the direction away from the axis, the error decreases, reaching 0 mm at a horizontal distance of 4.2 m. At 5.1 m, the calculated value is slightly smaller than the measured value by 1.0 mm, with an error of \(-1.8\) mm at 10 m. The absolute error first decreases then increases away from the axis, reaching 3.7 mm at 15.4 m. The maximum error occurs at the edge, with a value of \(-4.4\) mm at 23.7 m. Overall, stochastic medium theory shows strong correlation with the measured data. Within a 10 m horizontal distance, the maximum relative error is 17.2%; the correlation is moderate at 10-23.7 m, with absolute errors fluctuating between 0 and 4.4 mm. The highest correlation occurs within 5 m of the axis, corresponding to the stage of surface settlement decrease. The theoretical calculation exhibits a similar pattern to the field measurements: the rate of surface heave increase is approximately twice that of the decrease stage, and the surface tilt during heave decrease shows a higher correlation with the actual measurements. The theoretical calculation curve in Figure 15 is symmetrically redrawn to obtain Figure 16. The lateral ground subsidence induced by ultra-shallow-buried excavation differs from the traditional bell-shaped settlement trough.