Abstract
Seepage force is simplified as seepage volumetric force in the stress field along the radial direction. Out-of-plane stress and seepage force are incorporated, and the theoretical solutions for stress, displacement, and plastic radius of a circular opening for the elastic-brittle-plastic and elastic-plastic rock mass are proposed based on the Mohr–Coulomb (MC) and generalized Hoek-Brown (HB) failure criteria. The presented solution and Wang’s solution (2012) are compared, and the corrected version of the proposed method is validated. Numerical examples of the proposed method based on the MC and generalized HB failure criteria reveal that the distributions of stress and displacement in the surrounding rock of the tunnel are significantly influenced by seepage force and out-ofplane stress. Displacement and plastic radius when seepage force and out-of-plane stress are considered are larger than those when the seepage force is not considered; the regulations of stress, however, run opposite. The results of displacement and plastic radius based on the generalized HB failure criterion are larger than those based on the MC failure criterion.
Similar content being viewed by others
References
Ahamad, F. and Mohammad, R. Z. (2009). “A theoretical solution for analysis of tunnels below groundwater considering the hydraulic–mechanical coupling.” Tunnelling and Underground Space Technology, vol. 24, no. 6, pp. 634–646, DOI: 10.1016/j.tust.2009.06.002.
Bear, J. (1988). Dynamics of fluids in porous media, Dover Publications Inc., New York, pp. 222–235.
Brown, E. T., Bray, J. W., Ladanyi, B., and Hoek, E. (1983). “Ground Response Curves for Rock Tunnels.” Journal of Geotechnical Engineer, vol. 109, no. 1, pp. 15–39.
Carranza-Torres, C. (2003). “Dimensionless graphical representation of the exact elasto-plastic solution of a circular tunnel in a mohr-coulomb material subject to uniform far-field stresses.” Rock Mechanics and Rock Engineering, vol. 36, no. 3, pp. 237–253.
Carranza-Torres, C. (2004). “Elasto-plastic solution of tunnel problems using the generalized form of the hoek-brown failure criterion.” International Journal of Rock Mechanics and Mining Science, vol. 41, no. 3, pp. 480–481, DOI: 10.1016/j.ijrmms.2003.12.014.
Carranza-Torres, C. and Fairhurst, C. (1999). “The elasto-plastic response of underground excavations in rock masses that satisfy the hoekbrown failure criterion.” International Journal of Rock Mechanics and Mining Science, vol. 36, no. 6, pp. 777–809, PII: S0148-9062(99)00047-9.
Lee, S. W., Jung, J. W., Nam, S. W., and Lee, I. M. (2006). “The influence of seepage forces on ground reaction curve of circular opening.” Tunnelling and Underground Space Technology, vol. 22, no. 1, pp. 28–38, DOI: 10.1016/j.tust.2006.03.004.
Lee, Y. K. and Pietruszczak, S. (2008). “A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strainsoftening rock mass.” Tunnelling and Underground Space Technology, vol. 23, no. 5, pp. 588–599, DOI: 10.1016/j.tust.2007.11.002.
Li, Z. L., Ren, Q.W., and Wang, Y. H. (2004). “Elasto-plastic analytical solution of deep-buried circle tunnel considering fluid flow field.” Chinese Journal of Rock Mechanics and Engineering, Vol. 23, No.8, pp. 1291–1295 (in Chinese).
Lu, A. Z., Xu, G. S., Sun, F., and Sun, W. Q. (2010). “Elasto-plastic analysis of a circular tunnel including the effects of the axial in situ stress.” International Journal of Rock Mechanics & Mining Sciences, vol. 47, no. 1, pp. 50–59, DOI: 10.1016/j.ijrmms.2009.07.003.
Nam, S. W. and Bobet, A. (2006). “Lining stresses in deep tunnels below the water table.” Tunneling and Underground Space Technology, vol. 21, no. 6, pp. 626–635, DOI: 10.1016/j.tust.2005.11.004.
Pan, X. D. and Brown, E. T. (1991). “Influence of axial stress and dilatancy on rock tunnel stability.” Journal of Geotechnical Engineering, vol. 122, no. 2, pp. 139–146.
Park, K. H. and Kim, Y. J. (2006). “Analytical solution for a circular opening in an elastic-brittle-plastic rock.” International Journal of Rock Mechanics and Mining Science, vol. 43, no. 4, pp. 616–622, DOI: 10.1016/j.ijrmms.2005.11.004.
Reed, M. B. (1988). “The influence of out-of-plane stress on a plane strain problem in rock mechanics.” International Journal for Numerical Analytical Methods in Geomechanics, vol. 12, no. 3, pp. 173–181.
Sharan, S. K. (2003). “Elastic-brittle-plastic analysis of circular openings in hoek-brown media.” International Journal of Rock Mechanics and Mining Science, vol. 40, no. 6, pp. 817–824, DOI: 10.1016/S1365-1609(03)00040-6.
Sharan, S. K. (2005). “Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic hoek-brown rock.” International Journal of Rock Mechanics and Mining Science, vol. 42, no. 4, pp. 542–549, DOI: 10.1016/j.ijrmms.2005.03.019.
Sharan, S. K. (2008). “Analytical Solutions for stresses and displacements around a circular opening in generalized hoek-brown rock.” International Journal of Rock Mechanics and Mining Science, vol. 45, no. 1, pp. 78–85, DOI: 10.1016/j.ijrmms.2007.03.002.
Wang, S. L., Wu, Z. J., Guo, M. W., and Ge, X. R. (2012). “Theoretical solutions of a circular tunnel with the influence of axial in situ stress in elastic-brittle-plastic rock.” Tunnelling Underground Space Technol., vol. 30, no. 7, pp. 155–168, DOI: 10.1016/j.tust.2012.02.016.
Wang, Y. (1994). “The Effect of a nonlinear mohr-coulomb criterion on borehole stresses and damage-zone estimate.” Canadian Geotechnique Journal, vol. 31, no. 1, pp. 104–109.
Wang, Y. (1996). “Ground response of circular tunnel in poorly consolidated rock.” Journal of Geotechnical Engineer, vol. 122, no. 9, pp. 703–708.
Zhou, X. P. and Li, J. L. (2011). “Hoek-Brown criterion applied to circular tunnel using elasto-plasticity and in situ axial stress.” Theoretical and Applied Fracture Mechanics, vol. 56, no. 1, pp. 92–103, DOI: 10.1016/j.tafmec.2011.10.005.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zou, Jf., Li, Ss., Xu, Y. et al. Theoretical solutions for a circular opening in an elastic–brittle–plastic rock mass incorporating the out-of-plane stress and seepage force. KSCE J Civ Eng 20, 687–701 (2016). https://doi.org/10.1007/s12205-015-0789-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-015-0789-y