A Multi-Arch Analytical Model for Predicting Ground Settlement Induced by Twin Rectangular Tunnels Considering Soil Arching Effects

The intricate influence of soil arching effects on tunnel-soil-tunnel interactions and ground disturbance mechanisms during the construction of twin rectangular tunnels remains a challenge, critically limiting the precision of surface settlement predictions. To address this, an innovative analytical method is proposed for predicting surface settlement induced by twin rectangular tunnels, explicitly incorporating soil arching effects. This method first establishes a “multi-arch model,” comprising an elastic arch and an inter-tunnel friction arch, for which stress evolution equations are derived. Subsequently, analytical stress-strain solutions for rectangular tunnels are formulated using complex variable theory. This foundation is then utilized to refine the Loganathan formula, leading to a tailored settlement prediction model applicable to twin rectangular tunnel scenarios. The proposed method’s predictive capabilities are validated against finite element models (FEM) across various depth-to-spacing ratios (H/S, where S is the net tunnel spacing) and benchmarked against the conventional Peck’s formula, which neglects soil arching. The study reveals a strong correlation between the surface settlement trough morphology and the H/S ratio: a ‘V’-shaped trough is observed for H/S ≤ 1/3 or H/S > 2 (the latter approximating single tunnel behavior); a ‘W’-shape for 1/3 < H/S ≤ 1; and a ‘U’-shape for 1 < H/S ≤ 2. Validation results demonstrate that the proposed method offers superior accuracy in predicting surface settlement under diverse conditions compared to Peck’s formula, particularly in capturing the influence of soil arching. This research provides valuable theoretical insights for the design and construction of urban twin rectangular tunnels.