Reliability analysis of shield lining sections using Spreadsheet method

The reliability of shield lining sections is calculated using the Spreadsheet method which can avoid independent transformation of related variables and partial derivatives of limit state function over the basic variables. The ultimate limit state functions of eccentric compression failure of normal section and shear failure of oblique section are established. The corresponding reliability indexes are calculated using the Spreadsheet method, and the failure probability of lining sections connected by those two failure modes in series is derived. In addition, the service limit state functions of concrete crack, joint opening and tunnel convergence failures are established, and the corresponding reliability indexes are calculated using the Spreadsheet method. Meanwhile, the Monte Carlo simulation is employed to calculate the reliability indexes of the lining sections under different failure modes. The Monte Carlo simulation results are compared with those of the Spreadsheet method. The maximum difference of reliability index between the two methods is less than 4%, but the Spreadsheet method can save the computing time significantly. Therefore, based on the proposed ultimate limit state and service limit state functions and the Spreadsheet method, the reliability index of shield tunnel lining sections can be analyzed quickly, accurately and conveniently.