Identification of deformed configurations of segmental tunnel rings based on measured convergences

Abstract

If convergences grow so large that the serviceability of a tubbing ring is lost, remedial measures must be taken. In this context, it is useful to reconstruct the displacement history of the tunnel ring in order to gain insight into the evolution of the structural behavior that has led to the current configuration. This challenge is tackled with the help of measured convergences and rigid body kinematics. The latter are sufficient, because the deformations of tubbings, resulting from normal forces and bending moments, do not contribute significantly to the displacements of segmental rings. The analysis is focused on convergences measured during a real-scale test of a symmetric tunnel ring. It consists of six tubbings and has three kinematic degrees of freedom. Deformed configurations are reproduced by optimizing the three scalar components of one symmetric and two antisymmetric modes of rigid body displacements. This problem is under-determined, because convergences are routinely measured in two directions only. Its solution is obtained in two steps. At first, the component of the symmetric mode of rigid body displacements is identified such that the measured convergences are reproduced in the best-possible fashion. Thereafter, the remaining differences between measured and modeled convergences are reduced to zero by optimizing the components of the two antisymmetric modes. This kind of structural analysis starts with the most recent set of measured convergences. It proceeds, in a step-by-step manner backwards in time to older sets of monitored data. It is shown that the developed method allows for a satisfactory reproduction of the displacement history of the tested tubbing ring, making use of measured vertical and horizontal convergences. The obtained visualization of the displacement history of the entire tunnel ring provides more insight into the structural behavior than diagrams showing only the evolution of single convergences.