## 1 Introduction
The hybrid method, first proposed in [34; 35] and further generalized in [13], is an effective and reliable mode for the analysis of the structural behavior of segmental tunnel linings. It is based on transfer relations which are analytical solutions of the linear theory of circular arches [34]. The analysis is hybrid because it is based on two types of input, namely the experimental data of the displacements measured during the test and the external loading. In symmetric problems, the measured circumferential displacements at the outer and inner surfaces of the segmental joints were employed to estimate, at first, the relative rotations at the segmental joints by means of the Bernoulli-Euler hypothesis. The estimated relative rotations were then improved by a strategy that involves symmetric rigid-body displacements. In this strategy, the relative rotations are assumed to be symmetric with respect to the vertical axis of the lining [34; 35]. However, in asymmetric problems, the relative rotations, which were originally estimated by the Bernoulli-Euler hypothesis, were improved by a strategy that involves generalrigid-body displacements. In the simulations, not only the measured circumferential displacements at the joints but also the measured convergences were employed [13]. The symmetric strategy was validated by a full-scale bearing capacity test [36] documented in [34; 35], and the general strategy was validated by \begin{table}
\begin{tabular}{l c c c c} \hline class & A & B & C & D \\ serviceability & excellent & good & endangered & violated \\ criterion & \(C\leq 0.8\%D_{o}\) & \(0.8\%D_{o}<C\leq 1.2\%D_{o}\) & \(1.2\%D_{o}<C\leq 2.0\%D_{o}\) & \(C>2.0\%D_{o}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Classification of convergence-related serviceability of circular shield tunnels according to [12; 13]. two full-scale bearing capacity tests [13]. The general strategy is more time-consuming than the symmetric strategy because an incremental-iterative process needs to be employed to obtain the solution. However, the range of applicability of the general strategy is greater than that of the symmetric strategy. The motivation for this work stems from three full-scale tests on the segmental tunnel rings used for the metro system in Shanghai, China. Test 1 was a bearing capacity test on a segmental tunnel lining without strengthening [36]. Tests 2 and 3 were two-phase tests. Phase 1 referred to a nominal repetition of Test 1 up to the convergences reached with serviceability class C. The serviceability of the linings was endangered. Afterwards, the tests were interrupted and the structures were strengthened by means of a half steel ring in Test 2 [37] and a full steel ring in Test 3. Experimental data from and the analysis of the latter test are the original contributions to this paper. Phase 2 of Tests 2 and 3 referred to the increase in the loading of the strengthened structures up to their bearing capacities. Initially, the deformation states of the three tests are symmetric. Thus, theoretically, the strategy for the consideration of symmetric rigid-body displacements should be suitable for the general hybrid analysis. However, it was found that, for Tests 2 and 3, the symmetric strategy resulted in accurate convergences before reaching serviceability class C but failed to produce accurate results for larger convergences. The structures in these two tests were strengthened by steel rings. Thus, it is important to reproduce the deformation states of non-strengthened structures to provide the basis for the analysis of strengthened structures. In this paper, a third class of the given structural problem is described in addition to the two classes introduced before. Although the structural behavior is symmetric, the strategy based on symmetric rigid-body displacements, developed in [35], is not able to simulate the deformed configurations accurately when the structure enters serviceability class C. This class of the underlying structural problems will be defined by error indices.