# Hybrid Simulation of Seismic Responses of a Typical Station with a Reinforced Concrete Column
## 5 Hybrid Simulation Process
### Structural Response  
To evaluate the accuracy of the hybrid test, the results of the analytical model and hybrid simulation are plotted in the same figure. In the case with the peak ground acceleration of 0.01 g, the time histories of drift responses and shear forces at the control point of the hybrid model are given in Figure 8. The good correspondence between the hybrid simulation result and the analytical model result validated the accuracy of the test method at the elastic stage.  
[PERSON] [24] proposed nine indexes to evaluate the accuracy of the hybrid simulation process. As shown in Equations (7) and (8), \(J_{2}\) and \(J_{3}\) could be applied to evaluate the test results in this paper. To be specific, \(J_{2}\) is the standardized RMS error, which could describe the fitness between experimental displacement and analytical displacement in the whole test process. \(J_{3}\) is the standardized peak error, which could describe the error at the peak response and illustrate the fitness between experimental displacement and analytical displacement at the peak response,  
\[J_{2}=\sqrt{\frac{\sum\limits_{i=1}^{N}\left[\mathrm{x}_{\mathrm{m}}(i)- \mathrm{y}_{\mathrm{n}}^{(1)}(i)\right]^{2}}{\sum\limits_{i=1}^{N}\left[ \mathrm{y}_{\mathrm{n}}^{(1)}(i)\right]^{2}}}\times 100\% \tag{7}\]  
Figure 8: Test results of the 0.01 g case.  
Figure 7: Overview of the test setup.  
\[J_{3}=\frac{\max\left|x_{\mathrm{m}}(i)-y_{\mathrm{n}}^{(1)}(i)\right|}{\max\left|y_ {\mathrm{n}}^{(1)}(i)\right|}\times 100\% \tag{8}\]  
where \(x_{\mathrm{m}}(i)\) is the test result at time \(i\) and \(y_{\mathrm{n}}^{(1)}(i)\) is the numerical result at time \(i\). In the displacement result depicted in Figure 8, \(J_{2}\) was computed as 12.4%, whilst \(J_{3}\) was computed as 4.7%. The accuracy of such test method would be verified with the results of \(J_{2}\) and \(J_{3}\).  
As the PBA increased, the RC column specimen reached its plastic state, which is shown in Figures 9 and 10. The stiffness degradation of the specimens during the loading process was described by the secant stiffness trend. The peak-to-peak secant stiffness of the load-displacement hysteretic response was applied to define the secant stiffness trend. This parameter is calculated as:  
\[K_{i}=\frac{F_{i}{}^{+}-F_{i}{}^{-}}{D_{i}{}^{+}-D_{i}{}^{-}} \tag{9}\]  
where \(K_{i}\) is the secant stiffness, \(F_{i}{}^{+}\) and \(F_{i}{}^{-}\) are the peak loads in the positive and negative loading directions, respectively, and \(D_{i}{}^{+}\) and \(D_{i}{}^{-}\) are the corresponding displacements in the positive and negative loading directions, respectively.  
Figure 9: Test results of 0.1 g, 0.22 g, and 0.58 g case. PBA, peak base acceleration.  
In the 0.10 g case, 0.22 g case, and 0.58 g case, the lateral stiffnesses of the specimen were 3.37 kN/mm, 2.53 kN/mm, and 2.37 kN/mm. Therefore, the reductions in the lateral stiffness of the specimen were 24.9% and 29.7% compared to the initial stiffness. The experimental substructure could accurately capture the mechanical behaviors of the RC specimen. Compared with the analytical results, the decrease of the peak shear force and the increase of the peak drift were caused by the reduction of the specimen stiffness.  
Based on the test results mentioned above, it could be concluded that the computer hardware (OpenSEES, OpenFresco) and loading hardware (MTS actuator with a 150 kN capacity) could be applied to fulfill the hybrid simulation process to evaluate the seismic performance of the typical station. Followed by the quasi-static test, the ultimate displacement and load capacity of the specimen are discussed to illustrate the mechanical behavior of the central column after the earthquake excitation.