# Prediction of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel Construction
## 1 Introduction
[PERSON] [19] introduced a fixed-base assumption, combining the gap parameter concept from small-hole expansion theory to argue that the circular section should not shrink symmetrically from the center but maintain fixed contact with the soil at the bottom, deriving a modified vertical displacement formula. [PERSON] first regarded the final shrinkage shape as a combination of multiple deformations, proposing a step-by-step uniform convergence model for tunnel excavation and suggesting that shield tunnels undergo overall subsidence after shrinkage [20]. Following this, [PERSON] et al. [21] derived boundary conditions for complex sections (e.g., horseshoe-shaped tunnels) based on non-uniform convergence modes. Additionally, collated measured data show that [PERSON]'s formula becomes less applicable with decreasing burial depth, and can be viewed as a special case of the stochastic medium formula. [PERSON] [22] established a non-uniform convergence model for mined tunneling, comparing the differences between mined and shield methods from the soil deformation mechanism, and proposed two suitable non-uniform convergence modes, which have been widely applied. [PERSON] [23] proposed a double-clearance non-uniform convergence correction model for circular and horseshoe sections, using an annealing genetic algorithm to find the optimal parameter combination. [PERSON] et al. [24] considered the influence of variable tunnel cross-sections and existing structures based on traditional stochastic medium theory, treating ground loss at tunnel connections as a linear transition and introducing the concept of a variable cross-section linear transition section. [PERSON] et al. [25] established an analytical solution for surface settlement prediction based on stochastic medium theory, studying 103 groups of monitoring data on surface settlements caused by shield construction in sandy pebble strata using back-analysis, and proposed an empirical prediction formula by analyzing the statistical characteristics of maximum settlement, settlement trough width and ground loss. [PERSON] et al. [26] used stochastic medium theory to study the surface heave mechanism of ultra-shallow pipe-roof freezing method tunnels, proposing that the surface turns to heave when the frozen wall development depth exceeds the overburden thickness. However, current studies on stochastic medium theory rarely distinguish between burial depths. Convergence modes are mostly superimposed based on two categories--shield construction and shallow-buried excavation--with deep-buried theories being more widely applied. The horseshoe cross-section is often simplified as a circle, and no theoretical study has addressed ultra-shallow-buried conditions. Therefore, this study develops a ground deformation prediction model for ultra-shallow-buried pilot tunnels based on the non-uniform superimposed convergence mode of stochastic medium theory, verifying its scientific validity and practicality through engineering cases to improve the theory's applicability in ultra-shallow environments. Calculation Theory of Lateral Ground Settlement Caused by Ultra-Shallow-Buried Pilot Tunnel Construction