In this paper, two new analytical approaches are presented on the basis of convergence-confinement method to compute both the ultimate convergence of circular tunnel and its plastic zone having been reinforced by systematically pre-tensioned fully grouted rockbolts. The models have two basic assumptions: (1) the grouted rockbolts increase the radial internal pressure within a broken rock mass by both the pre-tensioned force and the probable following induced force due to rock mass movement (2) tunnel convergence (specially short-term) occurs only due to reducing and diminishing of the radial constrained stress on tunnel surface provided by the working face. Hence, the values of both the pre-tensioned pressure and the mentioned radial constrained stress are specially taken into consideration in this paper. That is, according to their magnitudes, two different conditions occur: the magnitude of pre-tensioned pressure is greater than that of the constrained stress at bolt installation time and vice versa. The solutions are extended to each of conditions, and illustrative examples are solved. The proposed approaches predicting almost identical results show that pre-tensioning of grouted rockbolts will increase the efficiency and effectiveness of rockbolts.
Alonso E., Alejano L.R., Varas F., Fdez.-Manin G., Carranza-Torres C., 2003. Ground reaction curves for rock masses exhibiting strain-softening behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 27, 13, 1153-1185.
Aydan Ö., 1989. The stabilisation of rock engineering structures by rockbolts. Ph.D. Thesis, Nagoya University.
Bernaud D., Maghous S., Buhan P., Couto E., 2009. A numerical approach for design of bolt-supported tunnels regarded as homogenized structures. Tunnelling and Underground Space Technology, 24, 5, 533-546.
Bobet A., 2006. A simple method for analysis of point anchored rockbolts in circular tunnels in elastic ground. Rock Mechanics and Rock Engineering, 39, 4, 315-338.
Bobet A., Einstein E., 2011. Tunnel reinforcement with rockbolts. Tunnelling and Underground Space Technology, 26, 1, 100-123.
Brown E.T., Bray J.W., Ladanyi B., Hoek E., 1983. Ground response curves for rock tunnels. Journal Geotechnical Engineering, 109, 1, 15-39.
Carranza-Torres C., 2009. Analytical and numerical study of the mechanics of rockbolt reinforcement around tunnels in rock masses. Rock Mechanics and Rock Engineering, 42, 2, 175-228.
Cai Y., Esaki T., Jiang Y., 2004a. An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling. Tunnelling and Underground Space Technology, 19, 6, 607-618.
Cai Y., Jiang Y., Esaki T., 2004b. A rock bolt and rock mass interaction model. International Journal of Rock Mechanics and Mining Science, 41, 7, 1055-1067.
Fahimifar A., Soroush H., 2005. A theoretical approach for analysis of the interaction between grouted rockbolts and rock masses. Tunnelling and Underground Space Technology, 20, 4, 333-343.
Fahimifar A., Ranjbarnia M., 2009. Analytical approach for the design of active grouted rockbolts in tunnel stability based on convergence-confinement method. Tunnelling and Underground Space Technology, 24, 4, 363-375.
Grasso P.G., Mahtab A., Pelizza S., 1989. Riqualificazione della massa roccoisa: un criterio per la atabilizzaazione della gallerie. Gallerie e Grandi Opere Sotterranee, 29, 35-41.
Guan Zh., Jiang Y., Tanabasi Y., Huang H., 2007. Reinforcement mechanics of passive bolts in conventional tunnelling. International Journal of Rock Mechanics and Mining Science, 44, 4, 625-636.
Huang Z., Broch E., Lu M., 2002. Cavern roof stability-mechanism of arching and stabilization by rockbolting. Tunnelling and Underground Space Technology, 17, 3, 249-261.
Hoek E., Brown E.T., 1980. Underground Excavations in Rock. The Institution of Mining and Metallurgy, London.
Hoek E., Brown E.T., 1997. Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Science, 34, 8, 1165-1187.
Indraratna B., Kaiser P.K., 1990a. Design of grouted rock bolts based on the convergence control method. International Journal of Rock Mechanics and Mining Science, 27, 4, 269-281.
Indraratna B., Kaiser P.K., 1990b. Analytical model for the design of grouted rock bolts. International Journal for Numerical and Analytical Methods in Geomechanics, 14, 4, 227-251.
Lee Y-K., Pietruszczak S., 2008. A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass. Tunnelling and Underground Space Technology, 23, 9, 588-599.
Li C., Stillborg B., 1999. Analytical models for rock bolts. International Journal of Rock Mechanics and Mining Science, 36, 8, 1013-1029.
Oreste P., 2003. Analysis of structural interaction in tunnels using the convergence-confinement approach. Tunnelling and Underground Space Technology, 18, 4, 347-363.
Oreste P., 2004. Designing of radial bolting in tunnels. Journal of Mining science, 40, 4, 384-394.
Oreste P., 2008. Distinct analysis of fully grouted bolts around a circular tunnel considering the congruence of displacements between the bar and the rock. International Journal of Rock Mechanics and Mining Science, 45, 7, 1052-1067.
Oreste P., 2009. The convergence-confinement method: Roles and limits in modern geomechanical tunnel design. American Journal of Applied Science, 6, 4, 757-771.
Osgoui R.R., Oreste P., 2007. Convergence-control approach for rock tunnels reinforced by grouted bolts, using the homogenization concept. Geotechnical and Geological Engineering, 25, 4, 431-440.
Osgoui R.R., Oreste P., 2010. Elasto-plastic analytical model for the design of grouted bolts in a Hoek-Brown medium. International Journal for Numerical and Analytical Methods in Geomechanics, 34, 16, 1651-1686.
Park K-H., Tontavanich B., Lee J.G., 2008. A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses. Tunnelling and Underground Space Technology, 23, 2, 151-159.
Peila D., Oreste P., 1995. Axisymmetric analysis of ground reinforcing in tunneling design. Computer and Geotechnics, 17, 2, 253-274.
Peila D., Oreste P., 1996. Radial passive rockbolting in tunneling design with a new convergence-confinement model. International Journal of Rock Mechanics and Mining Science, 33, 5, 443-454.
Ranjbarnia M., Fahimifar A., Oreste P., 2014a. A simplified model to study the behaviour of pre-tensioned fully grouted bolts around tunnels and to analyse the more important influencing parameters. Journal of Mining Science, 50, 3, 533-548.
Ranjbarnia M., Fahimifar A., Oreste P., 2014b. Analysis of non-linear strain softening behaviour around tunnels. Proceedings of the institution of civil engineers, 168, 1, 16-30.
Ranjbarnia M., Fahimifar A., Oreste P., 2015. Practical Method for the Design of Pretensioned Fully-Grouted Rockbolts in Tunnels. International Journal of geomechanics, 10.1061/(ASCE)GM.1943-5622.0000464.
Ranjbarnia M., Oreste P., Fahimifar A., 2016. Analytical-nimerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts. International Journal for Numerical and Analytical Methods in Geomechanics, 40, 13, 1844-1862.
Stille H., Holmberg M., Nord G., 1989. Support of weak rock with grouted bolts and shotcrete. International Journal of Rock Mechanics and Mining Science, 26, 1, 99-113.
Wang Sh., Yin X., Tang H., Ge X., 2010. A new approach for analyzing circular tunnel in strain-softening rock masses. International Journal of Rock Mechanics and Mining Science, 47, 1, 170-178.
Ward W.H., Coats D.J., Tedd P., 1976. Performance of support systems in the Four Fathom Mudstone. Proceedings of Tunnelling, London.