Technical Papers
Jun 18, 2019

Effect of Gravity of the Plastic Zones on the Behavior of Supports in Very Deep Tunnels Excavated in Rock Masses

Publication: International Journal of Geomechanics
Volume 19, Issue 9

Abstract

The vertical load acting on a support structure is affected by the loss of self-bearing capacity of the rock inside the plastic zone. This load can then be accounted for by analytical calculation methods capable of evaluating the stresses in the tunnel support system to proceed with the tunnel design. Generally, the effect of the rock’s own weight in the plastic zone is considered in a simplistic way by evaluating an additional vertical load given by the weight of the rock due to the thickness of the plastic zone. This approach leads to a significant increase in the vertical load with the risk of overdesigning the support structure. In this work, the effect of the rock’s own weight in the plastic zone was considered by modifying the numerical solution of the convergence-confinement method for tunnels built in rock. In this way, through the intersection of the characteristic curve of the tunnel and the intersection line of the support structure, it is possible to determine both the vertical loads (with the effect of the weight of the rock) and the horizontal load (without the effect of weight of the rock). The application of the method to a project in the Alps allowed the detection of the magnitude of the percentage increase of the vertical load and a significant increase in the thickness of the plastic zone and determination of the consequences that this may have on the designing of the radial bolting length in that zone. Increasing the plastic radius led to an increase in the length of the bolts. This is interesting because, in the area of the crown where the weight of the plasticized rock is considered, the bolts are usually installed with a greater length. In the final part of the study, a new procedure was illustrated to define the vertical and horizontal loads acting on the support structures, starting from the convergence-confinement curves obtained for the crown and for the lateral areas (sides).

Get full access to this article

View all available purchase options and get full access to this article.

Disclaimer

BASF is not involved in any form with the research presented in this paper and is only the current affiliation of one of the authors.

References

Alonso, E., L. R. Alejano, F. Varas, G. Fdez-Manin, and C. Carranza-Torres. 2003. “Ground response curves for rock masses exhibiting strain-softening behaviour.” Int. J. Numer. Anal. Methods Geomech. 27 (13): 1153–1185. https://doi.org/10.1002/nag.315.
Brown, E., J. Bray, B. Ladanyi, and E. Hoek. 1983. “Ground response curves for rock tunnels.” J. Geotech. Eng. 109 (1): 15–39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15).
Carranza-Torres, C. 2004. “Elasto-plastic solution of tunnel problems using the generalized form of the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 41 (3): 480–481. https://doi.org/10.1016/j.ijrmms.2003.12.014.
Carranza-Torres, C., and C. Fairhurst. 1997. “On the stability of tunnels under gravity loading, with post-peak softening of the ground.” Int. J. Rock Mech. Min. Sci. 34 (3–4): 75.e1–75.e18. https://doi.org/10.1016/S1365-1609(97)00253-0.
Carranza-Torres, C., and C. Fairhurst. 1999. “The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 36 (6): 777–809. https://doi.org/10.1016/S0148-9062(99)00047-9.
Carranza-Torres, C., and C. Fairhurst. 2000. “Application of the convergence-confinement method of tunnel design to rock masses that satisfy the hoek-brown failure criterion.” Tunnelling Underground Space Technol. 15 (2): 187–213. https://doi.org/10.1016/S0886-7798(00)00046-8.
Detournay, E. 1984. “The effect of gravity on the stability of a deep tunnel.” Int. J. Rock Mech. Min. Sci. 21 (6): 349–351. https://doi.org/10.1016/0148-9062(84)90368-1.
Do, N. A., D. Dias, P. Oreste, and I. Djeran-Maigre. 2014a. “The behaviour of the segmental tunnel lining studied by the hyperstatic reaction method.” Eur. J. Environ. Civ. Eng. 18 (4): 489–510. https://doi.org/10.1080/19648189.2013.872583.
Do, N. A., D. Dias, P. Oreste, and I. Djeran-Maigre. 2014b. “A new numerical approach to the hyperstatic reaction method for segmental tunnel linings.” Int. J. Numer. Anal. Methods Geomech. 38 (15): 1617–1632. https://doi.org/10.1002/nag.2277.
Einstein, H. H., and C. W. Schwartz. 1979. “Simplified analysis for tunnel supports.” J. Geotech. Eng. Div. 105 (4): 499–518.
Fahimifar, A., and A. Hedayat. 2008. “Determination of ground response curve of the supported tunnel considering progressive hardening of shotcrete lining.” In Proc., 5th Asian Rock Mechanics Symp. Lisbon, Portugal: International Society for Rock Mechanics and Rock Engineering.
Fahimifar, A., and A. Hedayat. 2009. “The elasto-plastic analysis of a circular opening excavated in elastic-strain-softening Hoek-Brown rock.” In Proc., 8th Int. Congress on Civil Engineering. Shiraz, Iran: Department of Civil And Environmental Engineering.
Fahimifar, A., F. Monshizadeh, A. Hedayat, and A. Vakilzadeh. 2010. “Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field.” Tunnelling Underground Space Technol. 25 (4): 297–304. https://doi.org/10.1016/j.tust.2010.01.002.
Hedayat, A. 2016. “Stability of circular tunnels excavated in rock masses under gravity loading.” In Proc., 50th US Rock Mechanics Symp. Alexandria, VA: American Rock Mechanics Association.
Hoek, E., and E. T. Brown. 1980. Underground excavations in rock. London: Institute of Mining and Metallurgy.
Hoek, E., and E. T. Brown. 1988. “The Hoek-Brown failure criterion.” In Proc., 15th Canadian Rock Mechanics Symp., 31–38. Toronto: Univ. of Toronto.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek-Brown failure criterion—2002 edition.” In Proc., 5th North American Rock Mechanics Symp. and 17th Tunnelling Association of Canada Conf., 267–273. Richmond, BC, Canada: Tunnelling Association of Canada.
Lee, Y. K., and S. Pietruszczak. 2008. “A new numerical procedure for elasto-plastic analysis.” Tunnelling Undergound Space Technol. 23 (5): 588–599. https://doi.org/10.1016/j.tust.2007.11.002.
Marinos, P., and E. Hoek. 2000. “GSI: A geologically friendly tool for rock mass strength estimation.” In Proc., GeoEng2000, Melbourne. CD-ROM. Lancaster, PA: Technomic Publishing Company.
Marinos, V., P. Marinos, and E. Hoek. 2005. “The geological strength index: Applications and limitations.” Bull. Eng. Geol. Environ. 64 (1): 55–65. https://doi.org/10.1007/s10064-004-0270-5.
Oreste, P. 2007. “A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports.” Tunnelling Underground Space Technol. 22 (2): 185–205. https://doi.org/10.1016/j.tust.2006.05.002.
Oreste, P. 2009. “The convergence-confinement method: Roles and limits in modern geomechanical tunnel design.” Am. J. Appl. Sci. 6 (4): 757–771. https://doi.org/10.3844/ajassp.2009.757.771.
Oreste, P. 2014. “A numerical approach for evaluating the convergence-confinement curve of a rock tunnel considering Hoek-Brown strength criterion.” Am. J. Appl. Sci. 11 (12): 2021–2030. https://doi.org/10.3844/ajassp.2014.2021.2030.
Oreste, P., G. Spagnoli, and A. C. Luna Ramos. 2019. “The elastic modulus variation during the shotcrete curing jointly investigated by the convergence-confinement and the hyperstatic reaction methods.” Geotech. Geol. Eng. 37 (3): 1435–1452. https://doi.org/10.1007/s10706-018-0698-1.
Oreste, P., G. Spagnoli, A. C. Luna Ramos, and L. Sebille. 2018. “The hyperstatic reaction method for the analysis of the sprayed concrete linings behavior in tunneling.” Geotech. Geol. Eng. 36 (4): 2143–2169. https://doi.org/10.1007/s10706-018-0454-6.
Panet, M. 1995. Le calcul des tunnels par la méthode convergence-confinement. Paris: Press de I’ENPC.
Park, K. H., and Y. J. Kim. 2006. “Analytical solution for a circular opening in an elastic-plastic rock.” Int. J. Rock Mech. Min. Sci. 43 (4): 616–622. https://doi.org/10.1016/j.ijrmms.2005.11.004.
Peila, D., and P. P. Oreste. 1995. “Axisymmetric analysis of ground reinforcing in tunnelling design.” Comput. Geotech. 17 (2): 253–274. https://doi.org/10.1016/0266-352X(95)93871-F.
Spagnoli, G., P. Oreste, and L. Lo Bianco. 2016. “New equations for estimating radial loads on deep shaft linings in weak rocks.” Int. J. Geomech. 16 (6): 06016006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000657.
Spagnoli, G., P. Oreste, and L. Lo Bianco. 2017. “Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation.” Int. J. Geomech. 17 (9): 04017051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000949.
Wang, Y. 1996. “Ground response of circular tunnel in poorly consolidated rock.” J. Geotech. Eng. 122 (9): 703–708. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(703).
Zareifard, M. R., and A. Fahimifar. 2012. “A new solution for shallow and deep tunnels by considering the gravitational loads.” Acta Geotech. Slovenica 9 (2): 37–49.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 19Issue 9September 2019

History

Received: Jun 14, 2018
Accepted: Mar 28, 2019
Published online: Jun 18, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 18, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Pierpaolo Oreste, Ph.D. [email protected]
Full Professor, Dept. of Environmental, Land and Infrastructural Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, Torino 10129, Italy. Email: [email protected]
Ahmadreza Hedayat, Ph.D., A.M.ASCE [email protected]
Assistant Professor, Dept. of Civil and Environmental Engineering, Colorado School of Mines, 1500 Illinois St., Golden, CO 80401. Email: [email protected]
Global Project and Technology Manager Underground Construction, BASF Construction Solutions GmbH, Dr.-Albert-Frank-Straße 32, Trostberg 83308, Germany (corresponding author). ORCID: https://orcid.org/0000-0002-1866-4345. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share