## 3 Comparison between Proposed Full-Ring Model and Experiments  
### Full-Scale Ring Experiment  
Indoor full-scale ring experiments allow for a direct evaluation of the mechanical performance of tunnel linings. The loads exerted on the structure are clearly defined, and the measurement results from this kind of indoor experiments are relatively reliable when compared to those from an in-situ tunnel. Figure 9: Relationship between shear stiffness and compressive force. Full-scale ring experiments have been performed for the Green Heart Tunnel in the Netherlands [38], the Elbe Tunnel in Germany [39], the Shanghai Changjiang Tunnel [40], a water storage and sewage tunnel in Shanghai [41] and special-section tunnels including rectangular tunnels [5] and DOT shield tunnels [3; 42]. In this paper, the results from a full-scale ring experiment are used to verify the applicability of the previously presented incremental model. In the test, a full ring is placed horizontally into a self-balancing steel frame (Figure 10a). Every loading point is equipped with two hydraulic jacks with a maximum load output of 2000 kN. A series of steel balls is deployed under the horizontal ring specimen to provide a test condition with negligible friction. During the loading process, 30 loading points are arranged over the circumference to simulate different kinds of loads, such as soil and water pressure and ground overload. These loading points can be divided into several groups for load applications in different experimental cases. All hydraulic jacks in the same group provide an equal load simultaneously. During the test, the convergence deformations and displacements of the structure are monitored by 46 displacement transducers. The strains on the rebar and concrete are measured by 424 and 224 strain gauges, respectively. Before the formal loading, all loading jacks and measuring meters were calibrated, and a pre-experiment was carried out to eliminate the initial gaps between the segments which might appear during the assembly. After that, an inspection of the bolts was performed to ensure all connections were stable, in order to reduce the initial structural deformation. Three experimental cases are selected to compare the results from experiments and the aforementioned iterative model. In Experimental Cases 1 and 2, the 30 jacks are divided into 3 groups (Figure 10b) while 16 groups are used to simulate the load distribution in Experimental Case 3 (Figure 10c), in which an extra partial offset pressure on the left half side of 30 kPa is simulated. This corresponds to the relatively dangerous design condition of the tunnel going partially under a building or when new construction is taking place close to an existing tunnel. A summary of the design parameters and the experimental loads are presented in Table 2. The strata surrounding the tunnel is mucky clay and mucky silty clay. The unit weight of the soil is 18 kN/m\({}^{3}\). The water level is 0.5 m below the ground. In order to use the 30 loading points to simulate the design condition, the principles for deciding the groups and values of these loading points include both equivalences of the load distributions on the linings and similarity of the internal forces and deformations between experiment and design. Although the real load exerted on the tunnel and the corresponding structural mechanical behavior cannot be exactly simulated by the 30 point loads due to the complexity of the soil-structure interaction, plenty of preliminary calculations were made to ensure the internal forces of key sections and displacement of key deformation points (in Figure 6) in the tested linings are approximately equivalent to those of an actual tunnel structure under the given design conditions. This principle of soil load simulation through separate point loads was also adopted in previous full-scale ring experiments [3; 5; 38; 40; 43; 44].