Predicting Vertical Earth Pressure in High-Fill Cut-and-Cover Tunnels Using Relative Differential Settlement

In high-fill load reduction cut-and-cover tunnels (HFLRCCTs), the vertical earth pressure (VEP) after load reduction cannot be accurately determined using conventional methods. This study employs discrete element method (DEM) simulation to analyze the load reduction mechanism of expanded polystyrene (EPS). A mechanical analysis model is established, from which a VEP calculation method is derived. Then, based on the concept of relative differential settlement (RDS), a simplified VEP calculation method is proposed as a more practical alternative. The results indicate that the average VEP above the cut-and-cover tunnel (CCT) is smaller when the cross-section is rectangular, and the optimal load reduction effect occurs at a slope angle of 60–70°. Quantitatively, the inclusion of EPS reduces the VEP by 60–70%. Based on the DEM results, the RDS in the top section of the EPS layer (δ0) exhibits a strong linear correlation with the upward additional VEP (p2) (R2 > 0.99). The optimal load reduction effect occurs at H/h = 9/2. Thicker EPS layers enhance load reduction (increasing the thickness from 0.10 m to 0.15 m improves the load reduction rate by 8%), while a lower EPS density (12–20 kg/m3) provides better performance. The proposed RDS-based formula predicts the VEP with errors of 0.43–4.58% compared with cases reported in the literature (max error 1.10 kPa, RMSE = 0.51 kPa, MAPE = 4.18%). Compared with the elasticity-based method, the RDS-based method is simpler and more intuitive for engineering practice. However, this study has some limitations: the use of the two-dimensional DEM is not applicable to the case of tunnel portals and has not been verified in practical engineering.