An Iterative Calculation Method for Internal Forces and Deformation of Curved Tunnel Lining

The accurate prediction of lining forces and deformations is crucial for the design of arched tunnel lining. However, in traditional tunnel structural mechanics methods, the distribution shape of the surrounding rock elastic resistance (SRER), as well as the zero point and maximal point locations of SRER, are not clearly defined. In this paper, an iterative calculation method is proposed based on the gradual convergence of the unitized values of SRER and total displacement (TD) of the lining, and the one-to-one functional relationship between the two in the stability process of the surrounding rock and lining. In this method involves using the initial displacement caused by the pressure of the surrounding rock pressure is used to initiate the iterative process, and iterative calculation is carried out until the errors between the unitized value of SRER and the unitized value of TD of the lining structure meet the error requirements. This enables precise determination of the SRER and TD. In order to verify the effectiveness of the proposed method, a case study is conducted on the tunnel of Lianghe Expressway tunnel in Yunnan province, China. The results showed that when the semi-lining structure is divided into unit blocks and the average error of consistency is required to be less than 1e-3, it takes about 20 iterations are needed to meet the error requirement. Furthermore, the accuracy of the calculated results is verified through site-measuring experiments. This method provides an effective tool for failure analysis of arched tunnel lining structures.