Abstract
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.
















References
Lane KS (2019) Tunnels and underground excavations | History, Methods, Uses, & Facts | Britannica. https://www.britannica.com/technology/tunnel. Accessed 24 May 2020
Richemond-Barak D (2017) Underground warfare. Oxford University Press, Oxford
Balasubramanian A (2014) Tunnels-types and importance
St. Marie J, Tunnelling: Mechanics, methods, and mistakes, (n.d.). http://umich.edu/~gs265/tunnel.htm. Accessed 24 May 2020
Deere DU, Hendron AJ, Patton FD, Cording EJ (1966) Design of surface and near-surface construction in rock
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. https://doi.org/10.1007/BF01239496
Hoek E (2001) Big tunnels in bad rock, journal of geotechnical and geoenvironmental. Engineering 127:726–740. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:9(726)
Jia P, Tang CA (2008) Numerical study on failure mechanism of tunnel in jointed rock mass. Tunn Undergr Space Technol 23:500–507. https://doi.org/10.1016/j.tust.2007.09.001
Yeung MR, Leong LL (1997) Effects of joint attributes on tunnel stability. Int J Rock Mech Min Sci Geomech Abstracts 34:505. https://doi.org/10.1016/S1365-1609(97)00286-4
Bhasin R, Grimstad E (1996) The use of stress-strength relationships in the assessment of tunnel stability. Tunn Undergr Space Technol 11:93–98. https://doi.org/10.1016/0886-7798(95)00047-X
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
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
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. https://doi.org/10.1016/j.tust.2012.07.005
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. https://doi.org/10.1016/j.compgeo.2012.05.013
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
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. https://doi.org/10.1007/978-981-15-6086-6_64
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
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
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. https://doi.org/10.1007/978-981-15-5195-6_57
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
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
Zaid M, Mishra S (2021) Numerical Analysis of Shallow Tunnels Under Static Loading: A Finite Element Approach. Geotech Geol Eng. https://doi.org/10.1007/s10706-020-01647-1
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. https://doi.org/10.1007/s40515-020-00119-6
Liu H (2009) Dynamic analysis of subway structures under blast loading. Geotech Geol Eng 27:699–711. https://doi.org/10.1007/s10706-009-9269-9
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. https://doi.org/10.1016/j.tust.2017.04.001
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. https://doi.org/10.1007/s40098-016-0179-5
Zaid M, Sadique MR (2020) The response of rock tunnel when subjected to blast loading: finite element analysis. Eng Rep. https://doi.org/10.1002/eng2.12293
Zaid M, Sadique MR (2020) Blast resistant behaviour of tunnels in sedimentary rocks. Int J Protect Struct. https://doi.org/10.1177/2041419620951211
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. https://doi.org/10.1260/2041-4196.5.1.83
D.M.R.C. Limited (2015) Design specifications, Barakhamba road, New Delhi, India
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. https://doi.org/10.1007/s00501-013-0202-4
Gupta AS (1997) Engineering behavior and classification of weathering rock. Indian Institute of Technology Delhi, Delhi
Kumar A (2019) Engineering behavior of oil shale under high pressure after thermal treatment. IIT Delhi, Delhi
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. https://doi.org/10.1016/j.jrmge.2014.09.002
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. https://doi.org/10.1016/j.compgeo.2012.11.008
Hibbitt D, Karlsson B, Sorensen P (2014) ABAQUS User-Manual Release 6.14, Dassault Systèmes Simulia Corp., Providence, RI
Systemes D (2014) Abaqus 6.14 Documentation, Providence, RI: Dassault Systèmes
Lubliner J, Oliver J, Oller S, Onate E (1989) A plastic damage model for concrete. Int J Solids Struct 25:299–329
Lee J, Fenves GL (1998) Plastic-damage model for cyclic loading of concrete structures. J Eng Mech 124:892–900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
Hafezolghorani M, Hejazi F, Vaghei R, Bin Jaafar MS, Karimzade K (2015) Simplified damage plasticity model for concrete. Struct Eng Int. https://doi.org/10.2749/101686616X1081
Dass Goel M, Matsagar V, Marburg S (2011) An abridged review of blast wave parameters. https://www.researchgate.net/publication/257811909. Accessed 28 Nov 2019
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. https://doi.org/10.1007/s10064-018-1413-4
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. https://doi.org/10.1016/j.compgeo.2014.10.006
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. https://doi.org/10.1139/cgj-2014-0045
Galeati G, Gambolati G, Neuman SP (1992) Coupled and partially coupled Eulerian-Lagrangian Model of freshwater-seawater mixing. Water Resour Res 28:149–165. https://doi.org/10.1029/91WR01927
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. https://doi.org/10.1016/j.compgeo.2010.09.002
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. https://doi.org/10.1007/s42452-020-03876-8
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. https://doi.org/10.1007/s41062-020-00446-0
Wang D, Randolph MF, White DJ (2013) A dynamic large deformation finite element method based on mesh regeneration. Comput Geotech 54:192–201. https://doi.org/10.1016/j.compgeo.2013.07.005
Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14:227–253. https://doi.org/10.1016/0021-9991(74)90051-5
Benson DJ (1992) Computational methods in Lagrangian and Eulerian hydrocodes. Comput Methods Appl Mech Eng 99:235–394. https://doi.org/10.1016/0045-7825(92)90042-I
TM5-1300 (1969) Structures to resist the effects of accidental explosions. Department of Army technical manual TM 5-1300, USA
Larcher M, Casadei F (2010) Explosions in complex geometries: a comparison of several approaches. Int J Protect Struct 1:169–195. https://doi.org/10.1260/2041-4196.1.2.169
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. https://doi.org/10.1016/j.tafmec.2013.03.006
Banadaki MMD (2010) Stress-wave induced fracture in rock due to explosive action, Doctoral Dissertation, University of Toronto
Wang J, Yin Y, Esmaieli K (2018) Numerical simulations of rock blasting damage based on laboratory-scale experiments. J Geophys Eng 15:2399–2417. https://doi.org/10.1088/1742-2140/aacf17
Nicholls H (1971) Blasting vibrations and their effects on structures, U.S. Department of the Interior, Bureau of Mines
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. https://doi.org/10.12989/GAE.2020.23.3.245
Zaid M, Sadique MR (2020) Numerical modelling of internal blast loading on a rock tunnel. Adv Comput Des 5:417–443. https://doi.org/10.12989/acd.2020.5.4.417
Acknowledgements
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
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
About this article
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). https://doi.org/10.1007/s40098-021-00511-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40098-021-00511-0
Keywords
- Blast
- Rock
- Trinitrotoluene
- Finite element analysis
- Coupled Eulerian–Lagrangian