# Structural Responses of a Superall Building Subjected to a Severe Typhoon at Landfall
## 4 Results and Discussion
### Identification of Modal Parameters
#### 4.3.2 Amplitude-Dependence of Natural Frequency and Damping Ratio  
Although natural frequencies and damping ratios are conventionally regarded as constant for a given mode of the studied dynamic system, results from numerous field studies reveal that the values of these parameters may vary noticeably with the vibration amplitude of building structures [22]. The amplitude-dependence of modal parameters, particularly of the damping ratio, sheds new light on the intrinsic properties of the buildings' dynamics.  
Figure 13 and Table 5 show the values of natural frequency and damping ratio for the first three modes along the two measurement directions via the SSI method based on field records collected at the 56 th floor during the three selected periods. As expected, the values of natural frequency and damping ratio for the same mode varied among different periods. The natural frequencies decreased slightly, while the damping ratios increased significantly when the typhoon got nearest to the study site and the building vibrated most severely. By contrast, when the typhoon moved far away from the study site and the building vibrated moderately, the natural frequencies increased while the damping ratios decreased, respectively.  
Figure 12: Correlation between the building fundamental frequencies with building height and existing prediction models.  
Figure 13: Natural frequencies and damping ratios at three periods during the passage of Mangkhut. (**a**) Dir-X; (**b**) Dir-Y.  
Great efforts have been made to explore the mechanisms for the amplitude dependence of damping ratio. Typically, [PERSON] [46; 47] proposed a three-staged model of damping ratio for building structures. According to this theory, at quite low amplitudes, only large structural components have relative motions, typically at junction points, and the damping at this stage is relatively stable and small. As the building's vibration amplitude increases, increasingly more small units tend to participate in such relative movements. Accordingly, the damping increases continuously. Finally, when all possible mechanisms are activated, the damping remains constant, even throughout the increase of amplitude.  
To further explore the amplitude-dependence of modal parameters, Figure 14 plots the variations of damping ratios and natural frequencies with continuously increasing acceleration response for the first swaying and torsional modes in the two orthogonal directions. As depicted, the natural frequencies decreased gradually with the increase of vibration amplitudes, from 0.185 to 0.175 Hz for the first swaying mode, from 0.435 to 0.425 Hz for the first torsional mode, and from 0.70 to 0.65 Hz for the second swaying mode. On the other hand, results of damping ratio demonstrated slight fluctuations, but an increasing trend could be observed when the amplitude reached a certain level, beyond which, the damping ratio values tended to level off. Overall, the damping ratios for both the swaying modes and the torsional mode were in a range of 0.5-1.2%, which were a bit smaller the typical value of 1.0-1.5% as recommended in codes and standards.