對大跨徑的橋梁而言，預應力系統為重要的受力部分，橋體的變位量往往與預應力的損失有關。而預應力的損失原因除了乾縮潛變、錨定端滑移等，裂縫的擴展也可能造成預應力的損失。裂縫的生成擴展方向及速度，源自許多因素。本研究透過相關數值模擬，以及預應力混凝土梁振型模態。利用監測數據之變位曲線，再與數值模擬進行比對，透過反算分析估算出劣化箱型梁之剩餘預力。用利用估算出之現有預力值及呆載重使用裂縫擴展模擬判斷現場結構裂縫劣化主要原因。

For the long-span bridge, the prestressed system is an important part of the force, and the displacement of the bridge body is often related to the loss of prestress. In addition to shrinkage and creep, the cause of the loss of prestressing, the direction and speed of the formation and expansion of the slip crack at the anchor end are derived from many factors. In this study, the relevant numerical simulation and the vibration mode of the prestressed concrete beam are adopted. Then compare with the numerical simulation, through the inverse calculation analysis to decompose the prestressed of the extension box-girder. The crack propagation simulation is used to judge the cracks of the on-site structure by using the existing prestressed value and the dead load.

〔1〕 林樹柱，預力混凝土設計及施工，第十版，弘揚圖書有限公司，台北，第120-154 頁(2009)。
〔2〕 Newson, N.R., Prestressed Concrete Bridges: Design and Construction, ThomasTelford Ltd, London (2003).
〔3〕 Collins, M. P., and Mitchell, D., Prestressed Concrete Structures, Prentice Hall, New Jersey, Englewood Cliffs, pp. 168-240 (1991).
〔4〕 Moës, N., Dolbow, J., and Belytschko, T., “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, vol. 46, pp. 131–150, 1999.
〔5〕 Zehnder, A. T., Fracture Mechanics, Springer, 2012
〔6〕 Griffith, A. A. "The phenomena of rupture and flow in solids," Philosophical Transactions of the Royal Society of London, Series A, vol. 221, pp. 163-198, 1921.
〔7〕 FischerCripps, A. C., Nanoindentation, Springer, 2002
〔8〕 Irwin, G. R., Fracture, encyclopaedic of physicics. Berlin: Springer-Verlag, 1958.
〔9〕 Belytschko, T., et al., “A review of extended/generalized finite element methods for material modeling,” Modelling Simul. Mater. Sci. Eng., vol. 17, pp. 43001–43024, 2009.
〔10〕 Abaqus theory manual, Version 6.10, Stimula, 2009.
〔11〕 Yan, Y. and Park, S.H. “An extended finite element method for modeling near-interfacial crack propagation in a layered structure,” International Journal of Solids and Structures, vol. 45, pp.4756-4765, 2008.
〔12〕 Zamani, A. and Eslami, M. R. “Implementation of the extended finite element method for dynamic thermoelastic fracture initiation,” International Journal of Solids and Structures, vol. 47, pp.1392-1404, 2010.
〔13〕 Golewski, G.L., Golewski, P.T., Sadowski, “Numerical modeling crack propagation under Mode II fracture in plainconcretes containing siliceous fly-ash additive using XFEM method,” Computational Materials Science, vol. 62, pp.75-78, 2012.
〔14〕 Shen, F., Xheng, M., and Shi, D. F. et al. Using the cross-correlation technique to excitation modal parameters on response-only data[J]. Joumal of Sound and Vibration , 2003 , 259 (5) : 1163-1179
〔15〕 James, G. H., Carne, I. T. and Lauffer, J. P. “The natural excitation technique (NExT) for modal parameters extraction from operation wind turbines[J]”. Sandia Report , 1993
〔16〕 Brincker Rune , Zhang Lingmi , Andersen Pallle. Modal identification from ambient responses using frequency domain decompositionp [C]. Proc. Of the 18th International Modal Analysis Conference , San Antonio , Texas , USA. 2000: 625-630
〔17〕 Gade, S., Moller, N. B. and Herlufsen, H. et al. Frequency domain techniques for operational modal analysis[C]. 1st IOMAC Conference,2005.
〔18〕 Jacobsen, N. J., Andersen, P. and Brincker, R. Application of frequency domain curve-fitting in the EFDD technique[C]. In Conference Proceedings: IMAC-XXVI Conference.
〔19〕 Saiidi, M., Douglas, B. and Feng, S. "Prestress Force Effect on Vibration Frequency of Concrete Bridges," Journal of Structural Engineering, vol. 120, no. 7, pp. 2233-2241,1994.
〔20〕 Vecchio, F.J. and Shim, W. “Experimental and Analytical Reexamination of Classic Concrete Beam Tests”
〔21〕 Du, G.C. and Tao, X.K. “Ultimate Stress of Unbonded Tendons in Partially Prestressed Concrete Beams”
〔22〕 陸景文，「台灣地區混凝土橋梁溫度、彈性應變、潛變及乾縮特性之整合研究」，博士論文，台灣大學土木工程研究所，89 學年度。
〔23〕 ACI Committee 209, "Guide for Modeling and Calculating Shrinkage ./ and Creep in Har~ened Concrete", ACI 209.2R-08.
〔24〕 Baˇzant, Zdenˇek P. and Sandeep Baweja, "Creep and Shrinkage Prediction Model for Analysis and Design of Concrete Structures: Model B3, " 2000
〔25〕 Zhen, ZhongDu "eXtendedFinite Element Method (XFEM) in Abaqus "http://www.simulia.com/download/rum11/ UK/Advanced-XFEM-Analysis.pdf.
〔26〕 ABAQUS Ver. 6.10, Abaqus Analysis User's Manual.
〔27〕 加藤達也、辻英雄，「∼平成の大改修∼「浜名大橋」橋梁補強について」，平成 23 年度国土交通省国土技術研究會，2011.10。
〔28〕 黃炳勳、吳弘明、劉珊、蘇彥彰“國內大跨徑預力梁橋面臨之問題與因應對策探討”Vol. 45, No. 5 October 2018 土木水利第四十五卷第五期
〔29〕 Bazant, Z.P., Li, G.H., Yu, Qiang Gary Klein and Vladimir Kriıstek “Explanation of Excessive Long-Time Deflections of Collapsed Record-Span Box Girder Bridge in Palau” Infrastructure Technology InstituteMcCormick School of Engineering and Applied ScienceNorthwestern UniversityEvanston, 2008.09
〔30〕 Ru, Zhongliang, Zhao, Hongbo and Zhu, Chuanrui " Crack Propagation Analysis of Concrete Beam Subjected to Three-Point Bending Using XFEM" Applied Mechanics and Materials Vols. 94-96 (2011) pp 1655-1658
〔31〕 川上隆三、堂田忠，「一般国道 53 号那岐大橋上部工の損傷原因及び補修方法」，平成27年9月 土木学会第70回年次学術講演会，2015.09
〔32〕 齋藤玄、宮下孝、小林憲一、大平英生「妙高大橋のＰＣケーブル損傷における調査結果と今後の対応について」，平成23年度國土交通省北陸地方整備局事業研究發表會
〔33〕 今村隆浩「熊本地震により被災した阿蘇長陽大橋の復旧」，一般社團法人 九州地方計畫協會，2018.03