## 5 Numerical Modeling
### Model and Material Properties  
A large span underground subway station with relatively limited size has three-dimensional characteristics. Therefore, to numerically study the general performance of the suggested support system, a full three-dimensional model of the station construction was established using FLAC3D 5.0 software (2012, Itasca Consulting Group, Minneapolis MN, USA). The dimension of the numerical model was selected 120 m \(\times\) 39 m \(\times\) 50 m to include most of the soil affected by the excavation, as shown in Figure 23. The bottom boundary of the model was entirely fixed in the whole directions. The horizontal displacements were fixed in the left and upright sides, while vertical movements were free. The top boundary was free to move in all directions. A surcharge of 20 kPa was applied on the top surface to simulate surface loads [36]. The diameter of the cylindrical steel columns is 0.8 m, the distance between cylindrical steel columns is 8.5 m, the length of the feet-lock bolt is 2.5 m, and the distance between the feet-lock bolts is 1.0 m in the model, in accordance to the real structure. Beam and pile elements are adopted to simulate the temporary steel supports and feet-lock bolt, respectively. Different materials were assigned to the different soil layers and different components of the STS structure as seen in Figure 20b. Line and shell elements were used to simulate the cylindrical steel column and the primary lining, respectively. In total, 315,055 zones and 323,540 nodes were used, meanwhile the maximum element size is 6 m \(\times\) 4 m \(\times\) 1 m, and the minimum element size is 0.25 m \(\times\) 0.25 m \(\times\) 1 m. For simplicity, the Mohr-Coulomb model was adopted to define the behavior of the natural and improved soil in the numerical analyses, the parameters of soil were shown in Table 2. The cohesions and friction angles of sandy soils were obtained according to the recommended relationship between the strength parameter and DPSH value from the scientific references. Besides, in the Shenyang area, the cohesions (c) are usually negligible based on engineering experience and some scientific references. But for the numerical simulation software, c = 0 may cause some options performing hardly, even calculation non-convergence. Therefore, the cohesions of sandy soils are generally assumed to be 1 kPa in the numerical analysis [37; 38; 39]. STS structure elements, primary lining, beam and columns are deemed to have a liner-elastic behavior. Material properties used for the numerical simulations are listed in Table 3.  
As for the initial condition, the initial stress field of the soil is generated by balancing the gravity of the soil. In the initial stage of the model calculation, and the initial displacement is reset to zero. Meanwhile, based on the construction experience of Shenyang and the relevant research, it is proved that dewatering has little influence on soil deformation. So hydrostatic or geostatic condition is generally ignored. Figure 23: The 3-D difference model of the station construction: (**a**) Numerical model of the station construction; (**b**) Details of the support structure in the numerical model.