Asymmetric serviceability limit states of symmetrically loaded segmental tunnel rings: Hybrid analysis of real-scale tests

Abstract

Serviceability limit states (SLS) of segmental circular tunnel rings, subjected to symmetric loading, may experience asymmetric deformations. This is investigated herein, based on real-scale experiments and structural analysis. Single segmental rings, consisting of six tubbings and six joints, were subjected to 24 point loads, simulating ground pressure until convergence-related SLS were reached. Structural analysis is based on transfer relations, representing analytical solutions of the linear theory of thin circular arches. One symmetric mode and two antisymmetric modes of rigid-body displacements of the investigated segmental rings are described analytically. The vertical-to-horizontal convergence ratio of the symmetric mode is compared with convergence ratios, measured close to the SLS obtained in the tests. This allows for categorization of the tests as symmetric and asymmetric problems. The structural behavior of two asymmetric tests is analyzed by means of a generalized hybrid method. The term “hybrid” applies insofar as the external loading and the data from monitoring of the displacements during the tests are used as input. It is “generalized” in order to allow for consideration of the asymmetric structural behavior, thus abandoning the restriction to symmetry. The relative rotations of the joints are determined such that they refer to symmetric and antisymmetric rigid-body displacements and that the simulated convergences reproduce the measured values. Applying this concept to the two tests, it is shown that the asymmetry develops in a progressive rather than in a stepwise fashion. It refers to different forms of structural behavior of joints that nominally transmit the same normal forces and bending moments. It is concluded that the asymmetry results from small initial imperfections rather than from asymmetric external loading.