Discrete element modeling of a cross-river tunnel under subway train operation during peak and off-peak periods

  • Zhihua Zhang
  • Xiedong Zhang
  • Yifei CuiEmail author
  • Hongsheng Qiu
Original Paper


In China, a large number of passengers during peak period are a key problem issue that results in a peak load on the subway tunnel. The irregular vibration due to the overloading of train will cause critical damage to rail track and foundations. Due to the lack of field monitoring data, the effects of trainload-induced irregular vibration to the stability of concrete foundation and surrounding area remain a crucial scientific challenge. In current study, a cross-river tunnel in Wuhan subway 2nd line was selected as a case study. The numerical model was developed by using the discrete element method with the consideration of rail track, sleeper, concrete lining, and surrounding strata. Irregular vibration levels induced by train operation with different loads, which included the normal load and peak load, were applied to the rail. Stress, vertical and radial displacement, and particle acceleration in the rail, sleeper, concrete lining, and surroundings were calculated during the numerical simulation. The results revealed that with the increasing of trainload, the settlement of the rail track increases linearly. The symmetrical position on both sides of the concrete lining was compared and showed that the radial displacement and hoop stress of the particles are evenly distributed. The vibrational frequency of the concrete lining was closely associated with the load frequency. The symmetrical trend of radial displacement of particles in the surroundings showed that the value decreased with increasing distance from the outer edge of the lining. The effective distance of train irregular vibration load in the horizontal path is more than 4.0 m, which should be considered when an adjacent tunnel is constructed simultaneously.


Cross-river tunnel Irregular vibration levels Peak load Subway Radial displacement Discrete element method 


Funding information

The project was financially supported by the Fundamental Research Funds for the Central Universities (2017-YB-014) and the National Natural Science Foundation of China (NO. 51408450). The authors are also grateful for financial support from the theme-based research grant T22-603/15-N provided by the Research Grants Council of the Government of Hong Kong SAR, China, and the Opening Fund of State Key Laboratory of Hydraulics and Mountain River Engineering (SKHL1609).


  1. Alice JC, Hélio AN, Luben CG (2016) Damping coefficient and contact duration relations for continuous nonlinear spring-dashpot contact model in DEM. Powder Technol 302:462–479CrossRefGoogle Scholar
  2. Bagnoli P, Bonfanti M, Vecchia GD, Lualdi M, Sgambi L (2015) A method to estimate concrete hydraulic conductivity of underground tunnel to assess lining degradation. Tunn Undergr Space Technol 50:415–423CrossRefGoogle Scholar
  3. Bian XC, Jiang HG, Chang C, Hu J, Chen YM (2015) Track and ground vibrations generated by high-speed train running on ballastless railway with excitation of vertical track irregularities. Soil Dyn Earthq Eng 76:29–43CrossRefGoogle Scholar
  4. Brady BHG, Brown ET (2004) Rock mechanics for underground mining. 3rd edn. pp 173–175Google Scholar
  5. Colaço A, Costa PA, Connolly DP (2016) The influence of train properties on railway ground vibrations. Struct Infrastruct Eng 12(5):517–534CrossRefGoogle Scholar
  6. Connolly DP, Kouroussis G, Laghrouche O, Ho CL, Forde MC (2015) Benchmarking railway vibrations-track, vehicle, ground and building effects. Constr Build Mater 92:64–81CrossRefGoogle Scholar
  7. Cui Y, Nouri A, Chan D, Rahmati E (2016) A new approach to DEM simulation of sand production. J Pet Sci Eng 147:56–67CrossRefGoogle Scholar
  8. Cui Y, Chan D, Nouri A (2017a) Discontinuum modeling of solid deformation pore-water diffusion coupling. Int J Geomech 17(8):04017033CrossRefGoogle Scholar
  9. Cui Y, Chan D, Nouri A (2017b) Coupling of solid deformation and pore pressure for undrained deformation – a discrete element method approach. Int J Numer Anal Methods Geomech 41(18):1943–1961CrossRefGoogle Scholar
  10. Fan ZY, Zhang DM, Huang HW (2008) Safety analysis on longitudinal settlement and crack width of shield tunnel segments in operation period. Proceedings of international symposium on safety. Sci Technol 7:2249–2252Google Scholar
  11. Fryba L (1999) Vibration of solids and structures under moving loads, 3rd edn. Thomas Telford, WestminsterCrossRefGoogle Scholar
  12. Gao WL, Yang MS, Zhao BM (2012) Seismic response analysis of large span tunnel across the river under earthquake. Highway 5:344–349Google Scholar
  13. Gong JZ, Chen WL, Liu YS, Wang JY (2014) The intensity change of urban development land: implications for the city master plan of Guangzhou, China. Land Use Policy 40:91–100CrossRefGoogle Scholar
  14. Gu X, Lu L, Qian J (2017) Discrete element modeling of the effect of particle size distribution on the small strain stiffness of granular soils. Particuology 32:21–29CrossRefGoogle Scholar
  15. ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15:99–103CrossRefGoogle Scholar
  16. Jiang Y, Gao Y, Wu X (2016) The nature frequency identification of tunnel lining based on the microtremor method. Undergr Sp 1(2):108–113CrossRefGoogle Scholar
  17. Kang C, Chan D (2017) Modelling of entrainment in debris flow analysis for dry granular material. Int J Geomech (ASCE) 17(10):1–20Google Scholar
  18. Kang C, Chan D (2018) Numerical simulation of 2D granular flow entrainment using DEM. Granul Matter 20(13).
  19. Kouroussis G, Connolly DP, Verlinden O (2014) Railway induced ground vibrations-a review of vehicle effects. Int J Rail Transp 2(2):69–110CrossRefGoogle Scholar
  20. Kouroussis G, Florentin J, Verlinden O (2016) Ground vibrations induced by InterCity/InterRegion trains: a numerical prediction based on the multibody/finite element modeling approach. J Vib Control 22(20):4192–4210CrossRefGoogle Scholar
  21. Laryea S, Baghsorkhi MS, Ferellec JF, Mcdowell GR, Chen C (2014) Comparison of performance of concrete and steel sleepers using experimental and discrete element methods. Transport Geotech 1(4):225–240CrossRefGoogle Scholar
  22. Lee I, Nam S (2001) The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels. Tunn Undergr Space Technol 16:31–40CrossRefGoogle Scholar
  23. Li GC, Ding LY, Wu XG, Luo HB, Li XQ (2007) Ground settlement prediction during construction of Wuhan Yangtze River tunnel. Chin J Rock Mech Eng 26(Supp. 2):3631–3638Google Scholar
  24. Li YJ, Zhang DL, Fang Q, Yu QC, Xia L (2014) A physical and numerical investigation of the failure mechanism of weak rocks surrounding tunnels. Comput Geotech 61:292–307CrossRefGoogle Scholar
  25. Li PF, Zhao Y, Zhou XJ (2016) Displacement characteristics of high-speed railway tunnel construction in loess ground by using multi-step excavation method. Tunn Undergr Space Technol 51:41–55CrossRefGoogle Scholar
  26. Liu Z, Koyi HA (2013) Kinematics and internal deformation of granular slopes: insights from discrete element modeling. Landslides 10(2):139–160CrossRefGoogle Scholar
  27. Lu M, McDowell G (2010) Discrete element modelling of railway ballast under monotonic and cyclic triaxial loading. Geotechnique 60(6):459–467CrossRefGoogle Scholar
  28. Lu JF, Zhang CW, Jian P (2017) Meso-structure parameters of discrete element method of sand pebble surrounding rock particles in different dense degrees, Proceedings of the 7th international conference on discrete element methods 188:871–879Google Scholar
  29. Ma L, Liu W (2018) A numerical train-floating slab track coupling model based on the periodic-Fourier-modal method. P I Mech Eng F-J Rai 232(1):315–334Google Scholar
  30. Min FL, Zhu W, Han XR, Zhong XC (2010) The effect of clay content on filter cake formation in highly permeable gravel. Geotech Spec Publ 204:210–215Google Scholar
  31. Mostafa S, Rahman D, Mohsen SB (2012) Design of sequential excavation tunneling in weak rocks through findings obtained from displacements based back analysis. Tunn Undergr Space Technol 28(1):10–17Google Scholar
  32. Picandet V, Khelidj A, Bellegou H (2009) Crack effects on gas and water permeability of concretes. Cem Concr Res 39:537–547.CrossRefGoogle Scholar
  33. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 4:1329–1364CrossRefGoogle Scholar
  34. Ricci L, Nguyen VH, Sab K, Duhamel D, Schmitt L (2005) Dynamic behaviour of ballasted railway tracks: a discrete/continuous approach. Comput Struct 83(28–30):2282–2292CrossRefGoogle Scholar
  35. Shamy UE, Zamani N (2012) Discrete element method simulations of the seismic response of shallow foundation including soil-foundation-structure interaction. Int J Numer Anal Methods Geomech 36:1303–1329CrossRefGoogle Scholar
  36. Shi XS, Herle I (2017) Numerical simulation of lumpy soils using a hypoplastic model. Acta Geotech 11:349–363CrossRefGoogle Scholar
  37. Shi XS, Yin J (2018) Consolidation behavior for saturated sand–marine clay mixtures considering the intergranular structure evolution. J Eng Mech 144(2):04017166CrossRefGoogle Scholar
  38. Shi XS, Herle I, Yin JH (2017) Experimental and theoretical investigation on the compression behavior of sand-marine clay mixtures within homogenization framework. Comput Geotech 90:14–26CrossRefGoogle Scholar
  39. Shi XS, Herle I, Muir Wood D (2018) A consolidation model for lumpy composite soils in open-pit mining. Geotechnique 68(3):189–204CrossRefGoogle Scholar
  40. Standard of Environmental Vibration in Urban Area (1988) State Department of Environmental Conservation of the People’s Republic of China: GB-10070Google Scholar
  41. Standard of metro gauges (2003) Ministry of Construction of the People’s Republic of China: CJJ-96, China Building Industry PressGoogle Scholar
  42. Tang Y, Chan DH, Zhu DZ (2017a) A coupled discrete element model for the simulation of soil and water flow through an orifice. Int J Numer Anal Methods Geomech 41(10):1477–1493CrossRefGoogle Scholar
  43. Tang Y, Zhu DZ, Chan DH (2017b) Experimental study on submerged sand erosion through a slot on a defective pipe. J Hydraul Eng 143(9):04017026CrossRefGoogle Scholar
  44. Usman M, Galler R (2013) Long-term deterioration of lining in tunnels. Int J Rock Mech Min Sci 64:84–89CrossRefGoogle Scholar
  45. Vogiatzis K (2010) Noise and vibration theoretical evaluation and monitoring program for the protection of the ancient “Kapnikarea church” from Athens subway operation. Int Rev Civil Eng 1:328–333Google Scholar
  46. Vogiatzis K (2012) Protection of the cultural heritage from underground subway vibration and ground-borne noise in Athens centre: the case of the Kerameikos archaeological museum and Gazi cultural centre. Int J Acoust Vib 17:59–72Google Scholar
  47. Voit K, Zimmermann T (2015) Characteristics of selected concrete with tunnel excavation material. Constr Build Mater 101:217–226CrossRefGoogle Scholar
  48. Wang Y (2008) Research on ground subsidence caused by shield-driven construction and buildings protection. Thesis of Huazhong University of Science and Technology. (in Chinese)Google Scholar
  49. Wang J, Gutierrez M (2010) Discrete element simulations of direct shear specimen scale effects. Géotechnique 60(5):395–409CrossRefGoogle Scholar
  50. Wu SM, Wang Z, Wang LZ (2013) Monitoring and analysis of force and deformation of large section crossing-river tunnel during operation period. J Zhejiang Univ (Eng Sci) 47(4):595–608 (in Chinese)Google Scholar
  51. Xia X, Li HB, Li JC, Liu B, Yu C (2013) A case study on rock damage prediction and control method for underground tunnels subjected to adjacent excavation blasting. Tunn Undergr Space Technol 35:1–7CrossRefGoogle Scholar
  52. Xu W-J, Hu L-M, Gao W (2016) Random generation of the meso-structure of a soil-rock mixture and its application in the study of the mechanical behavior in a landslide dam. Int J Rock Mech Min Sci 86:166–178CrossRefGoogle Scholar
  53. Xue F (2017) Dynamic responses of subway tunnel in clay stratum to moving loads. Arab J Sci Eng 42(3):1327–1340CrossRefGoogle Scholar
  54. Zhang Z, Zhang X, Qiu H, Daddow M (2016) Dynamic characteristics of track-ballast-silty clay with irregular vibration levels generated by high-speed train based on DEM. Constr Build Mater 125:564–573CrossRefGoogle Scholar
  55. Zhang Z, Cui Y, Chan DH, Taslagyan KA (2018a) DEM simulation of shear vibrational fluidization of granular material. Granul Matter 20(4).
  56. Zhang Z, Zhang X, Tang Y, Cui Y (2018b) Discrete element analysis of a cross-river tunnel under random vibration levels induced by trains operating during the flood season. J Zhejiang Univ Sci A 19(5):346–366CrossRefGoogle Scholar
  57. Zhou GGD, Sun QC (2013) Three-dimensional numerical study on flow regimes of dry granular flows by DEM. Powder Technol 239:115–127CrossRefGoogle Scholar
  58. Zhou YF, Su K, Wu HG (2015) Hydro-mechanical interaction analysis of high pressure hydraulic tunnel. Tunn Undergr Space Technol 47:28–34CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.School of TransportationWuhan University of TechnologyWuhanChina
  2. 2.Changjiang River Scientific Research Institute of Changjiang Water Resources CommissionWuhanChina
  3. 3.Department of Civil and Environmental EngineeringHong Kong University of Science and TechnologyClear Water BayHong Kong

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