Estimation of effective damping ratio for cast-in-place tunnel-form system and evaluation of its role in performance point prediction

Abstract

The extensive time and computational effort are primary challenges in nonlinear dynamic analysis of tunnel-form concrete systems. These challenges lead engineers to resort to simpler, pushover-based analyses, inherently based on estimating the seismic performance point of the system. Technical literature review indicates that no study has yet rigorously evaluated the accuracy of existing methods for estimating the performance point of tunnel-form systems. To eliminate potential ambiguities, in this study, the seismic performance point of the system under design basis earthquake (with a 475-year return period) has been calculated using three different methods (i.e., displacement coefficient, capacity spectrum, and displacement amplification factor), and compared with the results of accurate nonlinear time-history analysis. In the range of 5-, 7-, and 10-story models studied, the results indicate the inefficiency and insufficiency of the mentioned methods. Investigations reveal that while the capacity spectrum method provides better results, but its process is lengthy, and the displacement coefficient method significantly overestimates the performance point (with more than 80 % error). It was also evident that the displacement amplification factor underestimates the performance point and contradicts the direction of confidence. Based on observations, the use of all three methods for the tunnel-form system requires modifications. The calculated values of effective damping ratio for the tunnel-form system explicitly indicate type A behavior according to the ATC-40 classification. By presenting this parameter in a multi-level format, the shortcomings of both capacity spectrum and displacement coefficient methods are easily addressed. Referring to the results, the calculated value of the displacement amplification factor in the system exceeds the recommended value by the seismic design code, and by adjusting it, satisfactory responses can be obtained in the method based on the displacement amplification factor. Finally, introducing the “probable performance interval” parameter, recommending its use instead of the “performance point” parameter in assessments by pushover analysis is suggested. This parameter is applicable with all three mentioned methods and has been introduced in this study as a desirable factor in compensating for inherent uncertainties related to future earthquakes.