Document Type : Original Research Paper


1 Department of Civil Engineering, National Institute of Technology Hamirpur, Himachal Pradesh, India

2 Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India


An earthquake is a random occurrence that can happen anytime in highly seismic active areas. Therefore, it might happen even when the metro-train is moving. In such a scenario, the vibrations produced by the dynamic loading of a moving metro-train and the dynamic loading due to an earthquake will impact the dynamic response of underground metro-tunnels. In this work, an effort is made to comprehend how the Delhi Metro's underground tunnels will respond to the combined dynamic loading from the earthquake and the running train. Therefore, the dynamic response of underground metro-tunnels is primarily influenced by the vibrations generated due to the dynamic loading of a running metro-train and the dynamic loading due to an earthquake. Both these loadings cause vibrations at the ground surface and the tunnel utilities. In this paper, an attempt is made to understand the response of Delhi metro-underground tunnels to the combined dynamic loading due to the earthquake and the train's motion. Two-dimensional and three-dimensional finite element analyses are carried out using the Plaxis software. The research work finds that the overall response at the ground surface increases due to the combined dynamic loading of the train and earthquake compared to the train's or the earthquake's sole dynamic loading. Maximum displacements in the soil-the tunnel system and forces in RC liners are found to be more significant for the combined loading of the earthquake and the train motion than those due to individual loadings.


[1]. Kalantarian, S.H. and Dehghani, M. (2014). Review on the dynamic vibrations relationship in the metro tunneling. Int. J. of Science and Engineering Investigations. 3 (27): 23-27.
[2]. De-yun, D., Wei-ning, L., Gupta, S., Lombaert, G., and Degrande, G. (2010). Prediction of vibrations from underground trains on Beijing metro line 15. J. Cent. South Univ. Technology, 17, 1109−1118.
[3]. Nicolosia. V., D'Apuzzob, M., and Bogazzi, E. (2012). A Unified approach for the prediction of vibration induced by underground metro. Procedia - Social and Behavioral Sciences, 53, 62 – 71.
[4]. Nejati, H.R., Ahmadi, M., Hashemolhosseini, H., and Hayati, M. (2012a). Probabilistic analysis of ground surface vibration due to train movement, a case study on Tehran metro line 4. Geotech. Geology Engg. 30 (5): 1137–1146. 
[5]. Wu, D., and Gao, B. (2013). Dynamic analysis of the tunnel entrance under the effect of Rayleigh wave.  EJGE, 18, 4231-4246.
[6]. Metrikine, A.V. and Vrouwenvelder, A.C. W.M. (2000). Surface ground vibration due to a moving train in a tunnel: two-dimensional model. J. of Sound and vibration. 234 (1): 43–66.
[7]. Gardien, W. and Stuit, H. G. (2003). Modelling of soil vibrations from railway the tunnels.  J. Sound and Vibration. 267 (3): 605–619.
[8]. Hall, L. (2003). Simulations and analyses of train-induced ground vibrations in finite element models. Soil Dynamics and Earthquake Engineering. 23 (5): 403–413.
[9]. Sheng, X., Jones, C.J.C., and Thompson, D.J. (2004). A theoretical study on the influence of the track on train-induced ground vibration. J. of Sound and Vibration. 272 (3-5): 909–936.
[10]. Sheng, X., Jones, C.J.C., and Thompson, D.J. (2006). Prediction of ground vibration from trains using the wavenumber finite and boundary element methods.  J. of Sound and Vibration. 293 (3-5): 575–586.
[11]. Forrest, J.A. and Hunt, H.E.M. (2006). A three-dimensional the tunnel model for calculation of train-induced ground vibration. J. of Sound and Vibration. 294 (4-5): 678–705.
[12]. Forrest, J.A. and Hunt, H.E.M. (2006b). Ground vibration generated by trains in underground tunnels.  J. of Sound and Vibration. 294 (4-5): 706–736.
[13]. Andersen, L., and Jones, C.J.C (2006). Coupled boundary and finite element analysis of vibration from railway the tunnels-a comparison of two- and three-dimensional models. J. of Sound and Vibration. 293 (3-5): 611–625.
[14]. Hussein, M.F.M. and Hunt, H.E.M. (2007).  A numerical model for calculating vibration from a railway the tunnel embedded in a full-space. J. of Sound and Vibration. 305 (3): 401–431.
[15]. Ma, M., Markine, V., Liu, W., Yuan, Y., and Zhang, F. (2011). Metro train-induced vibrations on historic buildings in Chengdu. China. J. Zhejiang Univ. – Sci. A (Applied Phys & Eng). 12 (10): 782-793.
[16]. Wolf, S. (2003). Potential low frequency ground vibration (f = 63 Hz) impacts from underground LRT operations. J. of Sound and Vibration, 267, 651–661.
[17]. Taiyue, Q.I. and Gao, B. (2011). Strata consolidation subsidence induced by metro tunneling in saturated soft clay strata. J. of Modern Transportation. 19 (1): 35-41.
[18]. Mazek, S.A. and Almannaei, H.A. (2013). Finite element model of Cairo metro tunnel-Line 3 Performance. Ain Shams Engineering Journal, 4(4): 709–716.
[19]. Yaylacı, E.U., Yaylacı, M., Ölmez, H., and Birinci, A. (2020). Artificial neural network calculations for a receding contact problem. Computers and Concrete, An International Journal. 25 (6): 551-563.
[20]. Yaylaci, M., Yayli, M., Uzun Yaylaci, E. O lmez, H., and Birinci, A. (2021b).  Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron. Struct. Eng. Mech. 78 (5): 585-597.
[21]. Birinci, A., Adıyaman, G., Yaylacı, M., and Öner, E. (2015). Analysis of continuous and discontinuous cases of a contact problem using analytical method and FEM. Latin American Journal of Solids and Structures, 12, 1771-1789.
[22]. Oner, E., Yaylaci, M., and Birinci, A. (2015). Analytical solution of a contact problem and comparison with the results from FEM. Structural engineering and mechanics: An international journal. 54 (4): 607-622.
[23]. Yaylacı, M., Eyüboğlu, A., Adıyaman, G., Yaylacı, E.U., Öner, E., and Birinci, A. (2021). Assessment of different solution methods for receding contact problems in functionally graded layered mediums. Mechanics of Materials, 154, 103730.
[24]. Öner, E., Yaylacı, M., and Birinci, A. (2014). Solution of a receding contact problem using an analytical method and a finite element method. Journal of Mechanics of Materials and Structures. 9 (3): 333-345.
[25]. Yaylaci, M., Adiyaman, G., Oner, E., and Birinci, A. (2020). Examination of analytical and finite element solutions regarding contact of a functionally graded layer. Structural Engineering and Mechanics. 76 (3): 325-336.
[26]. Yaylaci, M. (2022). Simulate of edge and an internal crack problem and estimation of stress intensity factor through finite element method. Advances in nano research. 12 (4): 405-414.
[27]. Adıyaman, G., Birinci, A., Öner, E., and Yaylacı, M. (2016). A receding contact problem between a functionally graded layer and two homogeneous quarter planes. Acta Mechanica. 227 (6): 1753-1766.
[28]. Yaylaci, M., Adiyaman, G., Oner, E., and Birinci, A. (2021). Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM. Computers and Concrete. 27 (3): 199-210.
[29]. Yaylaci, M. and Birinci, A. (2013). The receding contact problem of two elastic layers supported by two elastic quarter planes. Structural engineering and mechanics: An international journal. 48 (2): 241-255.
[30]. Yaylacı, M. (2016). The investigation crack problem through numerical analysis. Structural Engineering and Mechanics, An Int'l Journal. 57 (6): 1143-1156.
[31]. Yaylaci, M., Abanoz, M., Yaylaci, E. U., Olmez, H., Sekban, D. M., and Birinci, A. (2022). The contact problem of the functionally graded layer resting on rigid foundation pressed via rigid punch. Steel and Composite Structures. 43 (5): 661–672
[32]. Öner, E., Şengül Şabano, B., Uzun Yaylacı, E., Adıyaman, G., Yaylacı, M., and Birinci, A. (2022). On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 102 (2): e202100287.
[33]. Yaylaci, M., Sabano, B.S., Ozdemir, M.E., and Birinci, A. (2022). Solving the contact problem of functionally graded layers resting on a HP and pressed with a uniformly distributed load by analytical and numerical methods. Structural Engineering and Mechanics. 82 (3): 401-416.
[34]. Yaylacı, M., Abanoz, M., Yaylacı, E.U., Ölmez, H., Sekban, D.M., and Birinci, A. (2022). Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods. Archive of Applied Mechanics. 92 (6): 1953-1971.
[35]. Nejati, H.R., Ahmadi, M., and Hashemolhosseini, H. (2012b). Numerical analysis of ground surface vibration induced by underground train movement. Tunneling and Underground Space Technology, 29, 1-9.
[36]. Duffy, D.G. (2012). Advanced Engineering Mathematics. CRC Press.
[37]. IS: 1893 – 2002 (Part - 1). Criteria for Earthquake Resistant Design of Structures. Bureau of Indian Standards, Manak Bhawan, New Delhi.
[38]. Singh, M., Viladkar, M.N., and Samadhiya, N.K. (2017). Seismic response of metro underground tunnels. Int. J. of Geotech. Engg. 11 (2): 175-185.
[39]. Sony, S. (2015). Static and dynamic response of Delhi metro tunnels. Ph.D. thesis IIT Delhi.
[40]. Yadav, H.R. (2005). Geotechnical Evaluation of Delhi Metro tunnels. Ph.D. Thesis Department of Civil Engineering, IIT Delhi, India.
[41]. Kuhlemeyer, R. L. and amp; Lysmer, J. (1973). Finite element method accuracy for wave propagation problems. Journal of the Soil Mechanics and Foundations Division. 99 (5): 421-427.
[42]. Cen, S., and amp; Shang, Y. (2015). Developments of Mindlin-Reissner plate elements. Mathematica Problems in Engineering, 2015
[43]. Lysmer, J. and Kuhlemeyer, R.L. (1969). Finite dynamic model for infinite media. Journal of the engineering mechanics division. 95 (4): 859-877.
[44]. IS: 456 (2000). Plain and reinforced concrete-Code of Practice. Bureau of Indian Standards, New Delhi, India.