Calculation Method for Soil Displacement Caused by Non-horizontal Parallel Double-line Shield Tunnel Construction Based on Modified Loganathan Formula

Objective To investigate the law of surrounding soil displacement induced by construction under the arrangement of non-horizontal parallel double-line shield tunnels, a soil displacement calculation method based on modified Loganathan formula is proposed. Method The Loganathan formula and its relevant assumptions are introduced. Considering the comprehensive effects of ground loss, soil unloading rebound, and variation of soil loss rate along the excavation path caused by shield tunnel excavation disturbance, the Loganathan formula is modified, and a solution for soil displacement around a single-line shield tunnel is established. Then, a calculation method for soil displacement induced by construction in the case of non-horizontal parallel double-line shield tunnels is developed. The engineering applicability of the proposed method is validated through field monitoring and numerical simulation results of actual projects. Result & Conclusion The proposed calculation method can account for factors such as the angle (θ) between the tunnel axis line and the horizontal plane, the radius (R1,R2) of double-line tunnels, the spacing (D) between tunnel axes, and the buried depth (H1,H2) of double-line tunnels, and the influence of construction factors such as ground loss, soil unloading rebound, and variation of soil loss rate along the excavation path caused by shield tunnel construction disturbance on soil displacement. The average errors between theoretical calculation and field monitoring/numerical simulation results for land subsidence and horizontal soil displacement are 5.6% and 0.6%, and 5.5% and 5.3%, respectively. These errors all meet the 20% accuracy requirement specified by engineering experience, demonstrating that the proposed calculation method can effectively address the soil displacement calculation problem induced by the construction of non-horizontal parallel double-line shield tunnels and has good engineering applicability.