A Ground Settlement Prediction Model for Shield Tunneling in Sandy Strata Incorporating Depth-to-Diameter Ratio and Density

【Objective】The classical Peck formula exhibits limited accuracy in predicting ground settlement induced by tunneling in sandy strata, primarily due to its neglect of key influencing factors.【Methods】To address this limitation, this study conducted a series of orthogonal physical model tests to investigate shield tunneling-induced settlement. The experiments were designed with varying sand densities (1.35, 1.40, 1.45 kg/dm³) and tunnel depth-to-diameter ratios (C/D = 0.6, 1.2, 1.8, 2.4, 3.0). Ground loss was simulated using a combination of concentric tubes (outer diameter D=11cm; inner diameters of 3cm and 9cm). High-resolution 3D laser scanning was employed to capture surface settlement cloud data. Based on the experimental results, the Peck formula was inversely modified, leading to a new predictive model that incorporates the depth-to-diameter ratio as a key factor.【Results】The findings indicate: (1) Settlement trough geometry is significantly influenced by the coupling effect of sand density and depth-to-diameter ratio, with the latter being the dominant controlling factor. (2) The revised model demonstrates superior performance, reducing the relative error in predicting maximum settlement to within 10% across various scenarios, a marked improvement over the original formula. (3) Even under over-excavation conditions, the new model maintains a stable prediction error within 20%.【Conclusion】This study confirms that the proposed model, which accounts for the depth-to-diameter ratio, can effectively predict settlement trough characteristics in sandy strata and provides a more reliable theoretical basis for shield tunneling engineering.