Application of the endurance time method to the seismic analysis and damage evaluation of a continuous rigid-frame bridge
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摘要: 探討了在真實成橋內力狀態下，耐震時程法(Endurance time method，ETM)評估連續剛構橋地震反應與損傷的準確性和有效性. 以一座典型非規則連續剛構橋為背景，采用MIDAS/Civil模擬實際施工過程，經施工階段分析得到10 a收縮徐變下的成橋內力狀態，再借助等效荷載法建立考慮成橋內力狀態的OpenSees動力分析模型；通過與天然地震動下的增量動力分析(Incremental dynamic analysis，IDA)結果相對比，驗證了采用ETM可快速準確地得到地震反應的適用性；通過該方法分析了墩頂位移、梁端位移及碰撞力等地震反應，并采用位移延性系數和Park?Ang損傷指數對橋墩損傷進行了量化分析與評估. 結果表明：ETM可以有效地預測真實成橋內力狀態下連續剛構橋達到某一損傷程度的時間；耐震時間較短時主橋橋墩較引橋橋墩的損傷要小，耐震時間較長時則反之.Abstract: The endurance time method (ETM) is a novel dynamic analysis method in which artificially intensified accelerograms characterized by the increase in seismic intensity with time are used as loading inputs. In this method, various dynamic responses, i.e., ranging from elastic to failure, under seismic excitations of different intensity levels are estimated with a reduced dynamic calculation effort. Based on these merits, this study investigated the accuracy and effectiveness of ETM in predicting the seismic responses and damage to continuous rigid-frame bridges considering the real internal force state (called element initial strain state) of the completed bridge. In detail, first, a typical irregular continuous rigid-frame bridge was selected as the target of the analysis, and its finite element model considering the real construction process was established by MIDAS/Civil. Then, the real internal force state considering the 10-year concrete shrinkage and creep was determined through construction phase analysis, and a dynamic analysis model considering the real internal force state was built via OpenSees utilizing the equivalent load method. Subsequently, the incremental dynamic analysis results under natural ground motions were obtained and compared with the results of the ETM, and the applicability of the ETM to obtain seismic responses rapidly and accurately was verified. Finally, the seismic responses of pier displacement, girder displacement, and pounding force were analyzed using the ETM, and the damage to piers was evaluated using the displacement ductility factor and Park–Ang damage index. The results indicate that ETM can predict the time when a continuous rigid-frame bridge reaches a certain damage status under the real internal force state of the completed bridge. Moreover, the damage to the main-bridge pier is smaller than that of the approach-bridge pier when the endurance time is short. However, when the endurance time is long, the opposite is true.
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圖 1 3條ETA曲線(a)及其加速度反應譜曲線(b)
Figure 1. Three ETA curves (a) and corresponding acceleration response spectra (b)
圖 2 7條天然地震動反應譜及其與目標反應譜的對比
Figure 2. Comparison for individual, mean and target response spectra of seven natural ground motions
圖 3 大跨高墩連續剛構橋的構造形式與截面尺寸(單位：cm)
Figure 3. Structural forms and section details of a long-span continuous rigid-frame bridge with high piers (unit: cm)
圖 6 3#墩處墩梁相對位移時程曲線
Figure 6. Relative displacement–time history between pier and girder at pier 3#
圖 8 橋墩位移時程曲線. (a) 1#墩；(b) 6#墩
Figure 8. Displacement–time history of piers: (a) pier 1#; (b) pier 6#
圖 9 梁端位移時程曲線. (a)主橋；(b)引橋
Figure 9. Displacement–time history of the top of the girders: (a) main bridge; (b) approach bridge
圖 10 伸縮縫處碰撞力時程曲線. (a) 3#墩；(b) 7#臺
Figure 10. Pounding force–time history of the expansion joints: (a) pier 3#; (b) abutment 7#
圖 11 橋墩位移延性系數. (a)1#墩；(b)6#墩
Figure 11. Displacement ductility factors of piers: (a) pier 1#; (b) pier 6#
圖 12 橋墩Park?Ang損傷指數. (a)1#墩；(b)6#墩
Figure 12. Park–Ang damage index of piers: (a) pier 1#; (b) pier 6#
表 1 前5階自振周期
Table 1. First five-order natural vibration periods s
Modal order TM TO Mode description 1 4.10 3.91 The main bridge vibrates along the transverse bridge direction 2 3.40 3.25 The whole bridge vibrates along the longitudinal bridge direction 3 2.64 2.55 Second-order vibration of the main bridge along the transverse bridge 4 2.45 2.47 The approach bridge vibrates along the longitudinal bridge direction 5 1.83 1.86 The main bridge and approach bridge vibrate in different directions along the longitudinal bridge 
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