## 3 Model Description for Water Conveyance Tunnel
### Finite Element Model Overview  
A full scale, three-dimensional finite element (FE) model of the QWCT tunnel has been constructed according to the geologic circumstance and design materials. The full scale FE model includes soil, tunnel, inner water, work shafts and deformation joints between tunnel and work shafts. The final three-dimensional size of the full scale FE model, which is composed of 1,668,760 elements and 1,913,524 nodes, is 13280 m \(\times\) 5150 m \(\times\) 300 m. Figures 6 and 7 show the three-dimensional view of the established full scale FE model, and some more detailed depictions of the FE model are given in Figure 8. As shown in Figure 7, twenty-four typical cross-sections including IS1-IS9 in the island part, RS1-RS10 in the cross-river part and LS1-LS5 in the land part are chosen as the concerned locations.  
Figure 5: Typical cross-section of the tunnel (cross-river part).  
Figure 6: The whole finite element (FE) model of the tunnel-soil-water coupling system.  
The tunnel is discretized with thick shell elements, the local coordinates of which are determined by the nodes of elements. The tunnel is treated as a homogeneous model, which is considered as an alternative [31] to get the whole responses of the tunnel and determine the dangerous cross-sections  
Figure 8: Details of FE model: (**a**) tunnel and soil; (**b**) tunnel, inner water and null material; (**c**) typical work shaft; (**d**) work shaft and surrounding soil. a, b and c mean the first, second and third deformation joint, respectively; \(A_{i}\) and \(B_{i}\) denote the \(i\)th displacement at the left and right side of the deformation joint, respectively.  
Figure 7: The whole tunnel FE model and positions of the control sections. IS1–IS9, RS1–RS10 and LS1–LS5 depict the chosen control sections in the island, cross-river and land part, respectively.  
while maintaining a moderate system equation for computation. The mesh dimension is determined through a series of mesh sensitivity tests which also assure the accuracy of the results. The work shafts and their details are meshed with eight node hexahedron elements (excluding the pile foundation discretized with beam elements). The inner water is discretized with eight node hexahedron elements with ALE description. The deformation joints are also discretized with thick shell elements. The surrounding soil is established based on the geological data. The soil strata are divided into 10 layers with the elevation of \(-300\) m which is the typical depth of bedrock in Shanghai. The soil model is meshed with eight node hexahedron elements. The whole model is discretized with fine meshes at the core area around the tunnel and coarse meshes at the other areas, and the fine and coarse meshes are coupled by node equivalence. This kind of discretization is considered as a time-saving method for large-scale numerical computation. The element sizes are determined according to the primary frequency of the input seismic wave to reduce the errors caused by model discretization. In this study, six elements per wavelength are adopted. The total number of elements in this study is similar to that of elements used in the previous seismic analysis for the underground tunnel [8].