## 2 Experimental Data from Real-Scale Tests on Segmental Tunnel Linings  
Three real-scale tests, see Figure 1a, are considered in the present paper. The tested rings are symmetrically assembled. They consist of six tubbings; see Figure 1.  
The radius of the axes of the rings, \(R\), amounts to \(2925\,\mathrm{mm}\), the axial length to \(1200\,\mathrm{mm}\), and the radial thickness of the segments, \(t\), to \(350\,\mathrm{mm}\). The bending stiffness, \(EI\), and extensional stiffness, \(EA\), of the rings are \(186\,\mathrm{M}\mathrm{N}\mathrm{m}^{2}\) and \(18,620\,\mathrm{M}\mathrm{N}\), respectively. The segmental joints were positioned at the angular coordinates \(\varphi_{1}=8^{\circ}\), \(\varphi_{2}=73^{\circ}\), \(\varphi_{3}=138^{\circ}\), \(\varphi_{4}=222^{\circ}\), \(\varphi_{5}=287^{\circ}\), and \(\varphi_{6}=352^{\circ}\); see also Table 2. Bolts connected neighboring tubbings; see Figure 1b and [34] for details.  
Figure 1: **(a)** Photo of the testing facility for segmental tunnel linings; (b) symmetric layout and loading of the rings.  
The tested structures were loaded by 24 point loads, provided by 24 hydraulic jacks, which were symmetrically deployed. They included six loads \(P_{1}\), ten loads \(P_{2}\), and eight loads \(P_{3}\); see Figure 1b. Test 1 served as a reference; see [34; 35] for the experimental data and structural analysis. Phase 1 of Tests 2 and 3, at least nominally, repetitions of Test 1; see Figures 2a and 3a for the intensities of the point loads. The experimental data of Test 2 have been published [37], while those of Test 3 are first reported in the present paper. The first ten load steps in both tests referred to the application of the design value of the in situ ground pressure. The next load steps simulated the increase in the ground pressure resulting from the overload above the tunnel. The coefficient of lateral ground pressure amounted to 0.65, i.e., \(P_{1}=0.65P_{2}\). \(P_{3}\) is the mean value of \(P_{1}\) and \(P_{3}\), simulating the ground pressure on the shoulder of the structures. \(P_{1}\), \(P_{2}\), and \(P_{3}\) were increased simultaneously until \(P_{2}\) reached the passive ground pressure, which occurred at load step 18 in Test 2. Thereafter, \(P_{2}\) was kept constant. \(P_{1}\) was further increased and \(P_{3}\) was chosen as \(P_{3}=0.5(P_{1}+P_{2})\).  
During the test, the circumferential displacements of the inner and outer gaps of the six joints as well as the horizontal and vertical convergences, see Figure 4, were measured. The measured data of Test 1 are shown in Figures 3b, 5, and 6 of [35] and those of Test 2 and Test 3 in Figures 2b-d and 3b-d. \(v_{j}^{i}\) and \(v_{j}^{o}\) in Figure 2 are the inner and outer circumferential displacements at the \(j\)th intrasegmental joint, with \(j=1,2,...,6\), respectively. The angular coordinates of the \(j\)th joint are shown in Table 2. As described in the Introduction, the convergence-related categorization of the serviceability of the tested tunnel rings, with 6200 mm as the value of the outer diameter \(D_{o}\), is provided in Table 3. In Test 1, the serviceability was violated because the maximum convergences reached values larger than 125 mm; see Figure 6 in [35]. In Tests 2 and 3, the serviceability was endangered because the maximum convergences reached values larger than 75 mm but smaller than 125 mm; see Figures 2b and 3b.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(R=2925\) mm & \(EI=186\) MNm\({}^{2}\) & \(\varphi_{1}=\) & \(8^{\circ}\) & \(\varphi_{3}=138^{\circ}\) & \(\varphi_{5}=287^{\circ}\) \\ \(t=350\) mm & \(EA=18,620\) MN & \(\varphi_{2}=\) & \(73^{\circ}\) & \(\varphi_{4}=222^{\circ}\) & \(\varphi_{6}=352^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 2: Geometric and mechanical properties of the tested linings.  
Figure 2: Experimental data of Test 2: (**a**) intensities of the point loads; (**b**) measured convergences; (**c**,**d**) refer to measured inner and outer circumferential displacements of the joints, respectively.