Analytical solution for long lined tunnels subjected to travelling loads |
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| Affiliation: | 1. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China;2. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;3. Department of Mathematics, Tongji University, Shanghai 200092, China;4. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;1. Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran;2. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;1. Institute of Mineral Resources Engineering, National Taipei University of Technology, Taipei, Taiwan;2. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan;3. Department of Geotechnical Engineering, CECI Engineering Consultants, Inc., Taipei, Taiwan;1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China;3. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;1. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China;2. Beijing City Traffic Collaborative Innovation Center, Beijing University of Technology, Beijing 100124, China;3. Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu, SiChuan, China;4. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Dongsan Rd. 1, Chenghua District, Chengdu City, China;1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;2. Shanghai Construction No.4(Group) Co., Ltd., Shanghai 201103, China;3. China Construction Second Engineering Bureau Ltd. East China Company, Shanghai 200135, China;4. Department of Civil Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;5. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China |
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| Abstract: | An analytical solution is derived for dynamic response of long lined tunnels subjected to travelling loads. For the derivation, the long lined tunnel is assumed to be infinitely long with a uniform cross-section resting on a viscoelastic foundation. Fourier and Laplace transforms are utilized to simplify the governing equation of the tunnel to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of tunnel responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The proposed solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. Further parametric analysis, such as the influence of wave velocity and frequency on dynamic responses of the tunnel is presented with the analytical solution. These relationships can be an effective tool for practitioners. |
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| Keywords: | Long lined tunnel Travelling loads Dynamic response Integration transform Convolution theorem |
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