## 4 Numerical Simulation Based on MIDAS FE Platform  
Based on MIDAS 6.71 FE platform, Huangsha Harbor Bridge is simulated using 58 beam elements with 63 nodes with the help of the modeling assistant module provided by the platform. We admit that the simplified beam FE models cannot satisfactorily simulate all the geometric details of the structures, and, therefore, inevitably contain model structure errors [20]. According to our experiences, their errors can hardly be completely eliminated  
Figure 8: Stress sequences measured on location and predicted by GM (1,1) models. (**a**) B-B cross-section. (**b**) C-C cross-section. through traditional parameter identification. However, MIDAS is a specialized FE platform oriented to bridge engineering, and the beam elements provided by the MIDAS platform are different from those provided by other general FE software, which can accurately reflect the realistic sectional properties of the structure. Therefore, the inherent uncertainties associated with the beam model established are greatly reduced on the MIDAS platform. For the reduced modeling workload and the computing efficiency, we finally chose to use the beam model established on the MIDAS platform. The numerical simulation procedure sequentially includes the basic information (the elevation geometry, the material properties, the division of the structure for construction, and the construction duration) input, the cross-section geometry input and the steel strand information input. The geometry of the structure is modeled in detail in accordance with Figures 1 and 2, and the concrete material model adopted is the uniaxial compression and tension linear elastic constitutive relation. To take into account the influences of the steel strand pre-stressing, the shrinkage and the creep of the concrete, and other effects during the construction stages on the mechanical state of the constructed structure, the model of Huangsha Harbor Bridge is established progressively reflecting each constructional state in time order, including the concrete pouring of the piers, the concrete pouring of the 0 blocks above the piers, the carriage traveling, the concrete pouring and the steel strand tensioning for 1-8 blocks, the closure of T-shaped structures and the structural system transformation. Therefore, the process accurately considers the cumulative influences of the multiple constructional effects. The FE model established for Huangsha Harbor Bridge after concrete segment 5 is poured and the FE model of the finally built Huangsha Harbor Bridge are shown in Figures 9 and 10, respectively. This initial model employs the design parameters of the structure, which might deviate from their actual values. Taking the model updating for the stage where pre-stresses are applied to segments 1 as an example, the applied pre-stresses are uniformly set at five points in the interval (0.5\({}^{\circ}\)design value, 1.5\({}^{\circ}\)design value) (i.e., 6.52 \(\times\) 10\({}^{8}\) N/m\({}^{2}\), 9.78 \(\times\) 10\({}^{8}\) N/m\({}^{2}\), 1.30 \(\times\) 10\({}^{9}\) N/m\({}^{2}\), 1.63 \(\times\) 10\({}^{9}\) N/m\({}^{2}\), and 1.96 \(\times\) 10\({}^{9}\) N/m\({}^{2}\)), and the stresses on the top of the B-B and the C-C cross-sections are calculated using the initial FE model with different applied pre-stresses. The obtained results are 2.56 MPa, 3.11 MPa, 3.66 MPa, 4.21 MPa, and 4.77 MPa, respectively, for the above-mentioned five points of applied pre-stresses. Then, a linear surrogate model reflecting the relationship between the stress on the top of the B-B (or the C-C) cross-section and the applied pre-stress to the segment 1 can be established based on the regression technique using the data obtained above, which can be written as y \(=-8.64011\)E\(8+592.02909*\) x, in which x is the stress on the top of the B-B (or the C-C) cross-section (in Pa) and y is the applied pre-stress to the segment 1 (in Pa).