# Prediction of Surface Deformation Induced by Ultra-Shallow-Buried Pilot Tunnel Construction
## 1 Introduction  
With the development of urban underground space toward ultra-shallow burial, surface deformation control during mining method tunnel construction faces severe challenges. Although the shallow mining method offers the advantage of non-disruptive traffic, when the burial depth is less than 1.5 times the tunnel diameter--especially during full-face excavation--the stratum stress arching effect is significantly weakened [1], posing safety hazards to adjacent structures. The tunnel-induced ground surface disturbance becomes particularly pronounced under ultra-shallow conditions [2], causing a sharp decline in the prediction accuracy of conventional empirical formulas. For example, [PERSON]'s formula fails to consider the lining force [3], often predicting settlement where the actual surface experiences heave, thus urgently necessitating the establishment of a targeted theoretical prediction model. The system of surface deformation prediction methods primarily comprises four categories: empirical formula methods (e.g., [PERSON]'s formula), elastic-plastic analyticalmethods ([PERSON]'s solution, cavity expansion theory, etc. ), numerical simulation methods and stochastic medium theory. Although [PERSON]'s formula demonstrates high accuracy in deep-buried, small-radius tunnels [4], its Gaussian curve assumption struggles to capture abrupt settlement changes in shallow-buried conditions. Direct analysis of the settlement-time relationship can also be classified as an empirical method. To accurately predict surface settlements induced by shallow-buried metro tunnel construction, [PERSON] et al. [5] proposed a bagging algorithm with an improved combined strategy for base learners. [PERSON] et al. [6] established a surrounding rock prediction model using the SVM information granulation method for vault settlement in shallow tunnels. Elastic-plastic analytical methods have limited adaptability in complex strata. For instance, cavity expansion theory typically ignores soil stress history, initial stress anisotropy and stress-induced fabric anisotropy [7], overestimating deformations in soft soils. The classic Mindlin solution, considering only additional normal stresses, is commonly used for settlement prediction in shield tunneling [8]. When applying complex variable functions, most analyses assume full bonding between the lining and surrounding rock [9], regarding the tunnel as embedded in a linear elastic medium [10], which excels in solving seismic stress responses [11] and time-dependent material effects [12]. Stress functions are more suitable for elastic mechanics problems [13]. Although numerical simulation methods can reproduce the construction process in 3D, they exhibit high parameter sensitivity and require substantial computational time, often used when measured data are scarce. [PERSON] et al. [14] verified the applicability of stochastic medium theory in predicting deep soil settlements caused by shield tunneling in sandy pebble strata through numerical simulation and model tests. Stochastic medium theory has become a research hotspot in recent years due to its clear physical mechanism. First proposed by [PERSON] [15] in the 1950s, this theory treats geotechnical materials as discontinuous media with stochastic movements to construct a surface settlement prediction system. After [PERSON] [16] established a circular shrinkage model, a complete system formed, which has been widely applied to calculate surface settlements from subway excavation. Subsequent scholars have made a series of improvements to address its limitations. Aiming at the difficulty of determining key parameters, [PERSON], [PERSON] [17] proposed using [PERSON]'s optimization program method in back-analysis to determine the main influence angle and uniform radial shrinkage value in [PERSON]'s formula. [PERSON] introduced an elliptical deformation mechanism, suggesting that tunnels undergo elliptical deformation superimposed on uniform radial shrinkage, but did not specify elliptical parameters [18].