Skip to main content

A Simple Approximate Simulation Using Coupled Eulerian–Lagrangian (CEL) Simulation in Investigating Effects of Internal Blast in Rock Tunnel


The need for faster and safer means of land transportation has increased due to scarcity of land. The number of terror attacks on the underground metro tunnels has increased in the past couple of decades. These events have presented the increased need for blast resistant design of metro tunnels. The stability of underground metro tunnels constructed in the different rocks has been analysed in the present paper. The analysis of impact loading has been carried out using nonlinear finite element technique. The coupled Eulerian–Lagrangian which is an advanced method of modelling for trinitrotoluene (TNT) and air inside the tunnel has been used. The explosive charge has been assumed at the centre of the tunnel having 100 kg mass, and the analysis is carried out for 30 ms of duration. The nonlinear behaviour of TNT has been simulated by using Jones–Wilkins–Lee material model of the equation of state. The nonlinear behaviour of the different rocks, i.e. Quartzite, Quartz-Schist, Sandstone, Shale and Dolomite, has been considered through the Mohr–Coulomb constitutive model. The rock model has 30 m × 30 m × 35 m dimension having an opening of 5 m at the centre of the model. The tunnel has 12.5 m of the depth of overburden and tunnel lining has 0.35 m of thickness. The tunnel lining has been reinforced with steel bars of Fe415 steel grade, and concrete has M30 grade. The rock tunnel constructed in Shale is susceptible to a higher magnitude of damage as compared to other rocks in this paper when exposed to internal blast loading. The Quartzite rock tunnel is the most suitable choice for constructing the blast-resistant tunnel. It has been concluded that Quartzite has higher safety against an internal blast loading caused by 100 kg TNT explosive charge. Heaving has been observed for all the cases on the ground above the location of TNT.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16


  1. Lane KS (2019) Tunnels and underground excavations | History, Methods, Uses, & Facts | Britannica. Accessed 24 May 2020

  2. Richemond-Barak D (2017) Underground warfare. Oxford University Press, Oxford

    Google Scholar 

  3. Balasubramanian A (2014) Tunnels-types and importance

  4. St. Marie J, Tunnelling: Mechanics, methods, and mistakes, (n.d.). Accessed 24 May 2020

  5. Deere DU, Hendron AJ, Patton FD, Cording EJ (1966) Design of surface and near-surface construction in rock

  6. Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech Felsmechanik Mécanique Des Roches 6:189–236.

    Article  Google Scholar 

  7. Hoek E (2001) Big tunnels in bad rock, journal of geotechnical and geoenvironmental. Engineering 127:726–740.

    Article  Google Scholar 

  8. Jia P, Tang CA (2008) Numerical study on failure mechanism of tunnel in jointed rock mass. Tunn Undergr Space Technol 23:500–507.

    Article  Google Scholar 

  9. Yeung MR, Leong LL (1997) Effects of joint attributes on tunnel stability. Int J Rock Mech Min Sci Geomech Abstracts 34:505.

    Article  Google Scholar 

  10. Bhasin R, Grimstad E (1996) The use of stress-strength relationships in the assessment of tunnel stability. Tunn Undergr Space Technol 11:93–98.

    Article  Google Scholar 

  11. Gahoi A, Zaid M, Mishra S, Rao KS (2017) Numerical analysis of the tunnels subjected to impact loading. In: 7th Indian Rock conference, (IndoRock2017), Indorock2017, New Delhi

  12. Sharma H, Mishra S, Rao KS, Gupta NK (2018) Effect of cover depth on deformation in tunnel lining when subjected to impact load. In: ISRM international symposium - 10th Asian Rock Mechanics Symposium, International Society for Rock Mechanics and Rock Engineering, Singapore

  13. Li JC, Li HB, Ma GW, Zhou YX (2013) Assessment of underground tunnel stability to adjacent tunnel explosion. Tunn Undergr Space Technol 35:227–234.

    Article  Google Scholar 

  14. Wu Q, Kulatilake PHSW (2012) Application of equivalent continuum and discontinuum stress analyses in three-dimensions to investigate stability of a rock tunnel in a dam site in China. Comput Geotech 46:48–68.

    Article  Google Scholar 

  15. Zaid M, Shah IA, Farooqi MA (2019) Effect of cover depth in unlined himalayan tunnel: a finite element approach. In: 8th Indian Rock conference, New Delhi, pp 448–454

  16. Zaid M, Mishra S, Rao KS (2020) Finite element analysis of static loading on urban tunnels. In: Gali ML, Rao PR (eds) Geotechnical characterization and modelling, 1st edn. Springer, Singapore, pp 807–823.

    Chapter  Google Scholar 

  17. Naqvi MW, Zaid M, Sadique MR, Alam MM (2017) Dynamic analysis of rock tunnels considering joint dip angle: a finite element approach. In: 13th international conference on vibration problems, indian institute of technology Guwahati, INDIA

  18. Athar MF, Zaid M, Sadique MR (2019) Stability of different shapes of tunnels in weathering stages of basalt. In: Proceedings of national conference on advances in structural technology, NIT Silchar, pp 320–327

  19. Zaid M, Rehan Sadique M (2021) Dynamic analysis of tunnels in western ghats of indian peninsula: effect of shape and weathering. In: Recent trends in civil engineering, Springer, Singapore, pp 763–776.

  20. Zaid M, Mishra S, Rao KS (2019) Stability of different shapes of himalayan tunnels under blast loading. In: 8th Indian Rock conference, New Delhi, pp 375–380

  21. Zaid M, Sadique MR (2019) Effect of joint orientation and weathering on static stability of rock slope having transmission tower. In: 7th Indian young geotechnical engineers conference – 7IYGEC 2019 15–16 March 2019, NIT Silchar, Assam, India SILCHAR, NIT Silchar

  22. Zaid M, Mishra S (2021) Numerical Analysis of Shallow Tunnels Under Static Loading: A Finite Element Approach. Geotech Geol Eng.

    Article  Google Scholar 

  23. Wasif Naqvi M, Akhtar MF, Zaid M, Sadique MR (2021) Effect of Superstructure on the Stability of Underground Tunnels. Transp Infrastruct Geotech 8(1):142–161.

    Article  Google Scholar 

  24. Liu H (2009) Dynamic analysis of subway structures under blast loading. Geotech Geol Eng 27:699–711.

    Article  Google Scholar 

  25. Mussa MH, Mutalib AA, Hamid R, Naidu SR, Radzi NAM, Abedini M (2017) Assessment of damage to an underground box tunnel by a surface explosion. Tunn Undergr Space Technol 66:64–76.

    Article  Google Scholar 

  26. Tiwari R, Chakraborty T, Matsagar V (2016) Dynamic analysis of a twin tunnel in soil subjected to internal blast loading. Indian Geotechn J 46:369–380.

    Article  Google Scholar 

  27. Zaid M, Sadique MR (2020) The response of rock tunnel when subjected to blast loading: finite element analysis. Eng Rep.

    Article  Google Scholar 

  28. Zaid M, Sadique MR (2020) Blast resistant behaviour of tunnels in sedimentary rocks. Int J Protect Struct.

    Article  Google Scholar 

  29. Chakraborty T, Larcher M, Gebbeken N, Khas H, Mechanics S (2014) Performance of tunnel lining materials under internal blast loading. Int J Protect Struct 5:83–96.

    Article  Google Scholar 

  30. D.M.R.C. Limited (2015) Design specifications, Barakhamba road, New Delhi, India

  31. Gschwandtner GG, Galler R (2013) Laugungsversuche als Grundlage zur Stabilitätsuntersuchung von Grubengebäuden in wasserlöslichen GebirgsformationenLeaching Experiments as Basis for the Stability Analysis of Underground Structures in Water-Soluble Rock Formations. BHM Berg- Und Hüttenmännische Monatshefte 158:493–500.

    Article  Google Scholar 

  32. Gupta AS (1997) Engineering behavior and classification of weathering rock. Indian Institute of Technology Delhi, Delhi

    Google Scholar 

  33. Kumar A (2019) Engineering behavior of oil shale under high pressure after thermal treatment. IIT Delhi, Delhi

    Google Scholar 

  34. Mitelman A, Elmo D (2014) Modelling of blast-induced damage in tunnels using a hybrid finite-discrete numerical approach. J Rock Mech Geotechn Eng 6:565–573.

    Article  Google Scholar 

  35. Babanouri N, Mansouri H, Nasab SK, Bahaadini M (2013) A coupled method to study blast wave propagation in fractured rock masses and estimate unknown properties. Comput Geotech 49:134–142.

    Article  Google Scholar 

  36. Hibbitt D, Karlsson B, Sorensen P (2014) ABAQUS User-Manual Release 6.14, Dassault Systèmes Simulia Corp., Providence, RI

  37. Systemes D (2014) Abaqus 6.14 Documentation, Providence, RI: Dassault Systèmes

  38. Lubliner J, Oliver J, Oller S, Onate E (1989) A plastic damage model for concrete. Int J Solids Struct 25:299–329

    Article  Google Scholar 

  39. Lee J, Fenves GL (1998) Plastic-damage model for cyclic loading of concrete structures. J Eng Mech 124:892–900.

    Article  Google Scholar 

  40. Hafezolghorani M, Hejazi F, Vaghei R, Bin Jaafar MS, Karimzade K (2015) Simplified damage plasticity model for concrete. Struct Eng Int.

    Article  Google Scholar 

  41. Dass Goel M, Matsagar V, Marburg S (2011) An abridged review of blast wave parameters. Accessed 28 Nov 2019

  42. Chen X, Zhang L, Chen L, Li X, Liu D (2019) Slope stability analysis based on the Coupled Eulerian–Lagrangian finite element method. Bull Eng Geol Environ 78:4451–4463.

    Article  Google Scholar 

  43. Hamann T, Qiu G, Grabe J (2015) Application of a Coupled Eulerian-Lagrangian approach on pile installation problems under partially drained conditions. Comput Geotech 63:279–290.

    Article  Google Scholar 

  44. Dutta S, Hawlader B, Phillips R (2014) Finite element modeling of partially embedded pipelines in clay seabed using Coupled Eulerian-Lagrangian method. Can Geotech J 52:58–72.

    Article  Google Scholar 

  45. Galeati G, Gambolati G, Neuman SP (1992) Coupled and partially coupled Eulerian-Lagrangian Model of freshwater-seawater mixing. Water Resour Res 28:149–165.

    Article  Google Scholar 

  46. Qiu G, Henke S, Grabe J (2011) Application of a Coupled Eulerian-Lagrangian approach on geomechanical problems involving large deformations. Comput Geotech 38:30–39.

    Article  Google Scholar 

  47. Zaid M, Sadique MR, Samanta M (2020) Effect of unconfined compressive strength of rock on dynamic response of shallow unlined tunnel. SN Appl Sci 2:2131.

    Article  Google Scholar 

  48. Zaid M, Sadique MR, Alam MM (2021) Blast analysis of tunnels in Manhattan-Schist and Quartz-Schist using coupled-Eulerian–Lagrangian method. Innov Infrastruct Solut 6:69.

    Article  Google Scholar 

  49. Wang D, Randolph MF, White DJ (2013) A dynamic large deformation finite element method based on mesh regeneration. Comput Geotech 54:192–201.

    Article  Google Scholar 

  50. Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14:227–253.

    Article  MATH  Google Scholar 

  51. Benson DJ (1992) Computational methods in Lagrangian and Eulerian hydrocodes. Comput Methods Appl Mech Eng 99:235–394.

    Article  MathSciNet  MATH  Google Scholar 

  52. TM5-1300 (1969) Structures to resist the effects of accidental explosions. Department of Army technical manual TM 5-1300, USA

  53. Larcher M, Casadei F (2010) Explosions in complex geometries: a comparison of several approaches. Int J Protect Struct 1:169–195.

    Article  Google Scholar 

  54. Zhao CF, Chen JY (2013) Damage mechanism and mode of square reinforced concrete slab subjected to blast loading. Theor Appl Fract Mech 63–64:54–62.

    Article  Google Scholar 

  55. Banadaki MMD (2010) Stress-wave induced fracture in rock due to explosive action, Doctoral Dissertation, University of Toronto

  56. Wang J, Yin Y, Esmaieli K (2018) Numerical simulations of rock blasting damage based on laboratory-scale experiments. J Geophys Eng 15:2399–2417.

    Article  Google Scholar 

  57. Nicholls H (1971) Blasting vibrations and their effects on structures, U.S. Department of the Interior, Bureau of Mines

  58. Zaid M, Sadique MR, Alam MM, Samanta M (2020) Effect of shear zone on dynamic behaviour of rock tunnel constructed in highly weathered granite. Geomech Eng 23:245.

    Article  Google Scholar 

  59. Zaid M, Sadique MR (2020) Numerical modelling of internal blast loading on a rock tunnel. Adv Comput Des 5:417–443.

    Article  Google Scholar 

Download references


Authors would like to acknowledge Mr Manojit Samanta Senior Scientist (CBRI-CSIR Roorkee, Uttarakhand, India) for assisting in the computational facility.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Md. Rehan Sadique.

Ethics declarations

Conflict of interest

Authors declare that they have no potential conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zaid, M., Rehan Sadique, M. A Simple Approximate Simulation Using Coupled Eulerian–Lagrangian (CEL) Simulation in Investigating Effects of Internal Blast in Rock Tunnel. Indian Geotech J 51, 1038–1055 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Blast
  • Rock
  • Trinitrotoluene
  • Finite element analysis
  • Coupled Eulerian–Lagrangian