Analysis on Settlement of Existing Tunnel Induced by Twin Tunneling Underneath Based on Energy Method

A study is conducted on the complex impact of twin tunneling. Utilizing the energy method, a calculation method is developed to assess the settlement of an existing tunnel induced by the excavation of twin tunnels below, considering variations in ground loss. This method integrates the modification factor for soil displacement above the twin tunnel construction, as proposed by Hunt, to account for the influence of ground loss differences based on the classical theories of Peck and Mair. The method combined the Rayleigh–Ritz method and elastic foundation beam theory to derive several expressions for energy and work within the entire system, and these are employed to establish the total potential energy equation. The method for calculating the settlement of the existing tunnel due to the twin tunneling underneath is obtained by solving the total governing equation using the variational method. The results are then compared to the measured data from an engineering case published in the literature. In an example where twin tunnels undercross existing tunnels, a parameter analysis is conducted, including the center-to-center distance between the twin tunnels, the diameter of the new tunnels, and the apparent distance between the new and existing tunnels. The research results showed that the calculated values generally align with the measured data in terms of overall trends, confirming the validity of the proposed method. The asynchronous construction of twin tunnels significantly impacts the settlement of the existing tunnel. As the center-to-center distance between the twin tunnels and the apparent distance between the new and existing tunnels increases, the settlement of the existing tunnel decreases. In contrast, as the diameter of the new tunnel increases, the settlement rises, and the impact of the subsequent undercrossing construction becomes more pronounced. The proposed method provides a quick and accurate evaluation of the longitudinal response of existing tunnels to new tunnel crossings, offering a theoretical foundation and practical guidance for related twin tunnel construction projects.