高鐵以及捷運在世界上使用的比例越來越高，為了節省行駛時間及增加效率，他們追求更高的營運速度。但是列車發生脫軌的案例一直都在發生，往往會造成人員及財物的損失，所以必須加以討論。最容易發生脫軌的區塊是彎曲軌道的部分，因此彎曲軌道的影響對研究脫軌相當重要。軌道有許多會影響脫軌的設計參數，例如超高、摩擦係數以及速度，他們彼此之間的關係也是探討脫軌的一個重點。
本文利用有限元素法開發了一種軌道模型，其中包含了克羅梭曲線段。設計軌道的參數是參考台灣交通部的規範，將軌道設計分為捷運軌道以及高鐵軌道。本文分別設計不同列車在捷運軌道及高鐵軌道行駛，透過改變列車的行駛速度來觀察不同的超高和摩擦係數對於脫軌的影響。將脫軌分為滑動以及翻覆來討論，在發生滑動之後，若離心力繼續增加，則有可能會發生翻覆現象。利用有限元素法模擬出會發生脫軌的臨界半徑值，並將有限元素法的模擬結果與理想的理論公式進行比較，以驗證有限元素法的結果是否準確。結果顯示，模擬的結果與理論公式的差異值很小，因此可以將此軌道模型應用在其他具有彎曲軌道的案例當中使用。

High-Speed Rail (HSR) and Mass Rapid Transit (MRT) are used increasingly in the world. In order to save driving time and increase efficiency, they pursue higher running velocity. However, cases of train derailment have always occurred, resulting in loss of personnel and property, so the issue of derailment must be discussed. The most prone to derailment is the part of the curved rail, so it is the part of interest in the study of derailment. There are many design parameters that affect the derailment of the rail, such as the cant, the friction coefficient and the velocity, and their relationship with each other is also an important point to discuss derailment.
In this thesis, a finite element method (FEM) is used to develop the rail model, which contains clothoid curve segments. The parameters of the design rail refer to the specifications of the Ministry of Transportation and Communication R.O.C (MOTC), and the rail is designed as MRT rails and HSR rails. In this thesis, different trains are designed to travel on MRT rails and HSR rails, and the effect of different cant and friction coefficient on derailment is observed by changing the running velocity of trains. The derailment is divided into sliding and overturning to discuss. The FEM model is used to simulate the critical radius value that will derail, and the simulation results of FEM are compared with the ideal theoretical formula to verify whether the results of FEM are accurate. The results show that the difference between the simulation results and the theoretical formula is very small, so the rail model can be used in other cases with curved rails.

Adrema, M. D., Newton-Euler Dynamics. (2005).
Antolín, P., Zhang, N., Goicolea, J. M., Xia, H., Astiz, M. Á., Oliva, J., Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways. Journal of Sound and Vibration, (2013), 332(5), 1231-1251.
Chen, C. C., Dzeng, R. J., Huang, S. F., Decision Support System for Railway Alignment Design. (2011).
Du, X. T., Xu, Y. L., & Xia, H., Dynamic interaction of bridge-train system under non-uniform seismic ground motion. Earthquake Engineering & Structural Dynamics, (2011), 41(1), 139-157.
Hibbeler, R. C., Engineering Mechanics : Dynamics, 14th Edition. (2016).
Jazar, R. N., Advanced Dynamics : Rigid Body, Multibody, and Aerospace Applications. (2011).
Ju, S. H., A cubic-spline contact element for frictional contact problems. Journal of the Chinese Institute of Engineers, (1998), 21(2), 119-128.
Ju, S. H., A frictional contact finite element for wheel/rail dynamic simulations. Nonlinear Dynamic, (2016), 85, 365-374.
Ju, S. H., A simple finite element for nonlinear wheel/rail contact and separation simulations. Journal of Vibration and Control, (2014), 20(3), 330-338.
Ju, S. H., Derailment of trains moving on lead rubber bearing bridges under seismic loads. Journal of Vibration and Control, (2020), 0(0), 1-10.
Ju, S. H., Nonlinear analysis of high-speed trains moving on bridges during earthquakes. Nonlinear Dynamics, (2011), 69(1-2), 173-183.
Ju, S. H., Stone, J. J., Rowlands, R. E., A new symmetric contact element stiffness matrix for frictional contact problems. Computers and Structures, (1996), 54(2), 289-301.
Kalker, J. J., Survey of Wheel—Rail Rolling Contact Theory. Vehicle System Dynamics, (1979), 8(4), 317-358.
Pfeiffer, F., Glocker, C., Multibody Dynamics with Unilateral Contacts. (1996).
Shabana, A. A., Zaazaa, K. E., Sugiyama, H., Railroad Vehicle Dynamic A Computational Approach. (2008).
Xia, H., Han, Y., Zhang, N., & Guo, W., Dynamic analysis of train–bridge system subjected to non-uniform seismic excitations. Earthquake Engineering and Structural Dynamics, (2006), 35(12), 1563–1579.
Yang, Y. B., Wu, Y. S., Dynamic stability of trains moving over bridges shaken by earthquakes. Journal of Sound and Vibration, (2002), 258(1), 65–94.
Yang, Y. B., Yau, J. D., Vehicle-Bridge Interaction Element For Dynamic Analysis. Journal of Structural Engineering, (1997), 123(11), 1512-1518.
Yang, Y. B., Yau, J. D., Wu, Y. S., Vehicle-Bridge Interaction Dynamics With Applications to High-Speed Railways. (2004).
Zhang, N., Xia, H., & Guo, W., Vehicle–bridge interaction analysis under high-speed trains. Journal of Sound and Vibration, (2008), 309(3-5), 407–425.
Zeng, Q., Analysis and Simulation of the Vehicle-Bridge-Interaction in Horizontally Curved Railway Bridges. (2016).
Zeng, Q., Dimitrakopoulos, E. G., A three-dimensional dynamic analysis scheme for the interaction between trains and curved railway bridges. Computers and Structures, (2015), 149, 43-60.
Zeng, Q., Dimitrakopoulos, E. G., Seismic Response Analysis of an Interacting Train-Bridge System considering Derailment. 16th World Conference on Earthquake Engineering, 16WCEE, (2017).
Zeng, Q., Dimitrakopoulos, E. G., Vehicle–bridge interaction analysis modeling derailment during earthquakes. Nonlinear Dynamics, (2018), 93(4), 2315-2337.
Zeng, Q., Dimitrakopoulos, E. G., Seismic response analysis of an interacting curved bridge–train system under frequent earthquakes. Earthquake Engineering and Structural Dynamics, (2016), 45(7), 1129-1148.
Zeng, Q., Yang, Y. B., Dimitrakopoulos, E. G., Dynamic response of high-speed vehicles and sustaining curved bridges under conditions of resonance. Engineering Structures, (2016), 114, 61-74.
中華民國交通部，「鐵路修建養護規則」，(2016)。
中華民國交通部工務部，「一四三五公厘軌距鐵路長銲鋼軌鋪設及養護規範」，(2006)。
中華民國交通部工務部，「鐵路橋梁設計規範」，(2004)。
中華民國交通部工程設計部，「捷運系統建設技術標準規範」，(2006)。
中華民國交通部工程設計部，「高速鐵路建設技術標準規範」，(2018)。
中華民國交通部車輛設計部，「捷運軌道車輛技術標準規範-高運量鋼軌車輛規劃基準」，(2013)。
中華民國交通部車輛設計部，「高速鐵路車輛技術標準規範」，(2019)。
包志強、「中華技術72期-列車運轉理論及模擬分析」，(2006)。
台灣世曦工程顧問股份有限公司，「中華技術113，永續的綠色運輸捷運工程」，(2017)。
理查曼，「鐵路養護作業大意」，(2017)。
許博士、羅吉特、胡劭安，「大眾捷運概論」，(2018)。
陳精微，「克羅梭緩和曲線應用手冊」，(1995)。
黃民仁、張欽亮，「新世紀鐵路工程」，(2017)。
薄志毅，「關於緩和曲線平行線的探討」，測繪通報第1期，(1998)。