Geotechnical and Geological Engineering

, Volume 37, Issue 5, pp 4435–4446 | Cite as

A method for selection of optimum distance between twin tunnels under static and pseudo-static conditions, case study: Pooneh tunnel

  • Hossein Ghorbani
  • Rassoul AjalloeianEmail author
Original Paper


Determination of optimum distance between twin tunnels is very important to reduce the construction’s costs in road or railway projects. When two tunnels are located close together, stress concentration in their space increases and it is possible that plastic zones would be merged. In mining engineering and especially underground mining applications, this zone (the distance between twin tunnels) is called pillar and there are some empirical models to estimate its width. However, these models are not completely suitable for all rock types and different tunnel geometries. In this study, an attempt was made to present a new criterion for the design of twin tunnels. It is based on ground reaction curve and takes width to height ratio (w/h) and shear strain of the pillar (obtained by numerical modeling) into consideration. Strain magnitude observed when normal stress (σ1) in the pillar reaches the value of compressive strength of the rock mass (σcm), denotes the allowable ratio of width to height (w/h) which shows the optimum distance between twin tunnels. Pooneh twin tunnels which located in Iran were selected as a case study. These are road twin tunnels excavated in layers of nine different zones (Arak–Khoramabad Expressway). Results of the suggested method show a good agreement between the pillar dimensions seen in the case study and the present method. Taking all aspects of geomechanical and geometrical characteristics of the tunnels into consideration, it is one of the main advantages of this method.


Ground reaction curve Pillar Iran 



This paper is the result of the first author’s PhD thesis, and was accomplished under the financial support of University of Isfahan. The authors are grateful to have the manuscript revised and edited by Dr. Sh. Arshadnejad and Dr. M. Kamani. Also, they acknowledge the great helps and suggestions of Mr. A. Sahebzamani and Mr. M. Mousavizadeh.


  1. Arshadnejad Sh, Poshtvan H, Parsaee H (2006) Determination of Optimum pillar size by empirical and numerical methods based on ground reaction curve—Case study, Soltan Abad’s underground salt mine. In: Proceedings of 7th tunneling conference in Tehran, Iran, pp 849–865 (in Persian)Google Scholar
  2. Aydan O, Dalgic S (1998) Prediction of deformation behavior of 3-lanes Bolu tunnels through squeezing rocks of North Anatolian fault zone (NAFZ). In: Proceedings of regional symposium on sedimentary rock engineering, pp 228–233Google Scholar
  3. Barton N (2002) Some new Q-value correlations to assist in site characterization and tunnel design. Int J Rock Mech Min Sci 39(2):185–216CrossRefGoogle Scholar
  4. Bieniawski ZT (1968) The effect of specimen size on the strength coal. Int J Rock Mech Min Sci 5:325–335CrossRefGoogle Scholar
  5. Bunting D (1911) Chamber pillars in deep anthracite mines. Trans AIME 42:236–245Google Scholar
  6. Chehade FH, Shahrour I (2008) Numerical analysis of the interaction between twin-tunnels: influence of the relative position and construction procedure. Tunn Undergr Space Technol 23(2):210–214CrossRefGoogle Scholar
  7. Daemen JJK (1975) Tunnel support loading caused by rock failure, Ph.D. thesis, University of Minnesota, Minneapolis, USA, p 234Google Scholar
  8. Daemen JJK (1977) Problems in tunnel support mechanics. Undergr Space 1(3):163–172Google Scholar
  9. Do NA, Dias D, Oreste P (2016) 3D numerical investigation of mechanized twin tunnels in soft ground–Influence of lagging distance between two tunnel faces. Eng Struct 109:117–125CrossRefGoogle Scholar
  10. Frith R, Reed G (2018) Coal pillar design when considered a reinforcement problem rather than a suspension problem. Int J Min Sci Technol 28(1):11–19CrossRefGoogle Scholar
  11. Ghazvinian A (1989) Prediction of stability of underground openings by equivalent material modelling (Doctoral dissertation)Google Scholar
  12. Ghazvinian AH, Gupta KK, Ramamurthy T (2000) Equivalent material modelling to predict the stability of underground openings. In: Proceeding of tunnelling Asia 2000, Central Board of Irrigation and Power, New Delhi, pp 1:58–69Google Scholar
  13. Goshtasbi K, Arshadnejad Sh (2008) Pillar design in underground mines by ground reaction curve. J Geol Environ 1:11–23 (in Persian) Google Scholar
  14. Greenwald HP, Howarth HC, Hartmann I (1939) Experiments on strength of small pillars of coal in the Pittsburgh bed (No. BM-TP-605). Bureau of Mines, Washington, DC (USA)Google Scholar
  15. Hardy MP, Agapito J (1977) Pillar design in underground oil shale mines. In: Proceedings of 16th US rock mechanics symposium, University of Minnesota, Minneapolis, pp 257–266Google Scholar
  16. Hasani H, Arshadnejad S, Khodadadi H, Goodarzi N (2008) 3D numerical modeling of a couple of power intake shafts and head race tunnels at vicinity of a rock slope in Siah Bishe pumped storage dam, north of Iran. J Appl Sci 8(23):4294–4302CrossRefGoogle Scholar
  17. Hazen G, Artler L (1976) Practical coal pillar design problem. Min Congr J 62(6):86–97Google Scholar
  18. Hedley DGF, Grant F (1972) Stope-and-pillar design for Elliot Lake uranium mines. Can Min Metall Bull 65(723):37–43Google Scholar
  19. Hedley DGF, Roxburgh JW, Muppalaneni SN (1984) A case history of rockbursts at Elliot Lake. In: Proceedings of 2nd international conference on stability in underground mining, Lexington. American Institute of Mining, Metallurgical and Petroleum Engineers, Inc, New York, pp 210–234Google Scholar
  20. Hoek E, Brown ET (1980) Underground excavations in rock. Institute of Mining and Metallurgy, London, p 156Google Scholar
  21. Hoek E, Brown ET (1982) Underground excavations in rock. The Institution of Mining and Metallurgy, Hertford, p 527Google Scholar
  22. Hoek E, Marinos (2007) A brief history of the development of the Hoek–Brown failure criterion. Soils and Rocks, No 2, NovemberGoogle Scholar
  23. Holland CT (1964) Strength of coal in mine pillars. In: Proceedings of 6th US symposium on rock mechanics. University of Missouri, Rolla, pp 450–466Google Scholar
  24. Holland CT, Gaddy FL (1957) Some aspects of permanent support of over burden on coal beds. In: Proceedings of West Virginia coal mining Institute, pp 43–66Google Scholar
  25. Kalamaras GS, Bieniawski ZT (1995) A rock mass strength concept for coal seams incorporating the effect of time. In: 8th ISRM Congress. International Society for Rock Mechanics and Rock EngineeringGoogle Scholar
  26. Krauland N, Soder PE (1987) Determining pillar strength-from pillar failure observation. E&MJ-Eng Min J 188(8):34–40Google Scholar
  27. Ladanyi B (1974) Use of the long-term strength concept in the determination of ground pressure on tunnel linings. In: Proceedings of 3rd congress, international society for rock mechanics, Denver, vol 2, pp 1150–1165Google Scholar
  28. Lombardi G (1970) The influence of rock characteristics on the stability of rock cavities. Parts 1 and 2. Tunnels & Tunnelling International, pp 104–109Google Scholar
  29. Lunder PJ, Pakalnis RC (1997) Determination of the strength of hard-rock mine pillars. CIM Bull 90(1013):51–55Google Scholar
  30. Madden BJ (1988) The performance of coal pillars designed to the squat pillar formula. In: The 29th US symposium on rock mechanics (USRMS). American Rock Mechanics AssociationGoogle Scholar
  31. Martin CD, Maybee WG (2000) The strength of hard-rock pillars. Int J Rock Mech Min Sci 37:1239–1246CrossRefGoogle Scholar
  32. Morrison RGK, Corlett AV, Rice HR (1956) Report of special committee on mining practices at Elliott lake. Ontario Department of Mines, Bulletin, p 155Google Scholar
  33. Nabavi MH (1976) An introduction to the geology of Iran. Geological survey of Iran, p 109 (in Persian)Google Scholar
  34. Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock. Wiley, New York, p 650Google Scholar
  35. Osman AS (2010) Stability of unlined twin tunnels in undrained clay. Tunn Undergr Space Technol 25(3):290–296CrossRefGoogle Scholar
  36. Potvin Y, Hudyma M, Miller H (1988) Design guidelines for open stope support. Paper presented at the CIM BulletinGoogle Scholar
  37. Sahoo JP, Kumar J (2013) Stability of long unsupported twin circular tunnels in soils. J Tunn Undergr Space Technol 38:326–335CrossRefGoogle Scholar
  38. Salamon MDG, Munro AH (1967) A study of the strength of coal pillars. J South Afr Inst Min Metall 68(2):55–67Google Scholar
  39. Sheory PR (1992) Pillar strength considering in situ stresses. In: Proceedings of work shop on coal pillar mechanics and design, Santa Fe, USBM IC 9315, pp 122–127Google Scholar
  40. Sojöberg JS (1992) Failure modes and pillar behaviour in the Zinkgruvan mine. In: The 33th US symposium on rock mechanics (USRMS). American Rock Mechanics AssociationGoogle Scholar
  41. Song G, Yang S (2018) Probability and reliability analysis of pillar stability in South Africa. Int J Min Sci Technol 28(4):715–719CrossRefGoogle Scholar
  42. Sorensen WK, Pariseau WG (1978) Statistical analysis of laboratory compressive strength and Young’s modulus data for the design of production pillars in coal mines. In: 19th US symposium on rock mechanics (USRMS). American Rock Mechanics AssociationGoogle Scholar
  43. Steart FA (1954) Strength and stability of pillars in coal mines. J South Afr Inst Min Metall 54(9):309–325Google Scholar
  44. Van der Merwe JN (2003) New pillar strength formula for South African coal. J South Afr Inst Min Metall 103(5):281–292Google Scholar
  45. Van der Merwe JN, Mathey M (2013) Update of coal pillar database for South African coal mining. J South Afr Inst Min Metall 113(11):825–840Google Scholar
  46. Van Heerden WL (1974) In-situ determination of complete stress-strain characteristics of 1.4 m square specimens with width to height ratio up to 3.4, C.S.I.R., South Africa, Research Report M.E., 1265Google Scholar
  47. Von Kimmelmann MR, Hyde B, Madgwick RJ (1984) The use of computer applications at BCL Limited in planning pillar extraction and design of mining layouts. In: Proceedings of ISRM symposium: design and performance of underground excavations. British Geotechnical Society, London, pp 53–63Google Scholar
  48. Wang FD, Skelly WA, Wolgamott J (1977) In-situ coal pillar strength study. In: Proceedings of 18th US rock mechanics symposium, University of Colorado School of Mines, Golden, pp 235–241Google Scholar
  49. Wang HN, Zeng GS, Utili S, Jiang MJ, Wu L (2017) Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock. Int J Rock Mech Min Sci 93:13–29CrossRefGoogle Scholar
  50. Wells DL, Coppersmith KJ (1994) New empirical relationships among magnitude, rupture length, rupture width, rupture area and surface displacement. Bull Seismol Soc Am 84(4):974–1002Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeologyUniversity of IsfahanIsfahanIran

Personalised recommendations