Demonstrates the accuracy of an analytical solution in predicting displacements in circular tunnels, indicating its utility in tunnel design.
An analytical solution for predicting the ground displacements and lining internal forces of circular shield tunnels was presented using the complex variable solution. In this method, the complex variable solution is obtained considering the interaction between surrounding ground and tunnel lining under the influence of gravity and non-uniform deformation. The presented analytical solution is applied to several classical tunnel cases, and the results obtained from the near end of the tunnel are in good agreement with the measured data on site, with a maximum settlement relative error of no more than 5%, and compared with empirical formulas or numerical simulation results, the predicted values of analytical solutions have better consistency with on-site measured data. Based on the case study results, formula for calculating the tunnel ellipticity and for determining the tunnel ellipticity monitoring point are proposed, respectively. Although analytical solutions are always limited to elasticity, the presented analytical solution can serve as a rapid and simple tool for predicting the ground and structure response in the preliminary design of circular tunnels.
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Fu et al. (2026) studied this question.
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