Prediction method of ground settlement for rectangular tunnel construction

Abstract

In rectangular tunnel construction, the disturbance and damage mechanisms affecting the surrounding strata remain poorly understood, often leading to ground collapses, settlements, and other engineering hazards. Existing theories and methods for predicting ground settlement still lack sufficient accuracy. To address this issue, this paper proposes a prediction method for ground settlement during the construction of rectangular tunnels based on complex functions and the Maxwell–Betti work reciprocity theorem. Based on the Maxwell–Betti work reciprocity theorem, two distinct stress states of a two-dimensional rectangular tunnel are defined, leading to an explicit expression for ground loss. Through conformal transformation using the complex variable functions method, the rectangular tunnel is mapped to a circular tunnel, resulting in an explicit displacement solution for the tunnel body. Additionally, the Loganathan formula has been modified to extend its applicability to rectangular tunnels. By combining our ground loss expression with the Loganathan formula, we can predict the ground settlement caused by rectangular tunnel excavation. Finally, the proposed method was validated by comparing it with the results of four numerical models at different burial depths and other theoretical approaches. The method was also applied to five typical rectangular tunnel projects. By comparing the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) between calculated and measured values, it was found that the predicted values in three of these projects were in closer agreement with the observed data. The results demonstrate that the proposed method can effectively predict ground settlement caused by rectangular tunnel construction and exhibits high reliability in practical engineering applications.