Analytical Solution for a Lined Tunnel with Arbitrary Cross Sections Excavated in Orthogonal Anisotropic Rock Mass
Publication: International Journal of Geomechanics
Volume 17, Issue 9
Abstract
A complete and accurate method for determining the stresses and displacements of a lined arbitrary shaped tunnel excavated in orthogonal anisotropic rock mass is proposed. The method is based on an analytical method, the complex variable method, and the power series method. The basic equations can be obtained according to the stress boundary conditions along the inner boundary of the lining and the stress and displacement continuity conditions along the lining–rock interface. Based on the method, the tangential stresses along the excavation boundary, the inner and outer boundaries of the lining, and the normal and shear stresses along the lining–rock interface are given. Results show that, when the number of terms of the series is large enough, solutions with high accuracy can be obtained. The positions of the tangential stress concentration, the effect of the displacement release coefficient, and the angle of the rock layers on the tangential stresses along the excavation boundary and both boundaries of the lining are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The study is supported by the Natural Science Foundation of China (Grants 11172101 and 11572126).
References
Abaqus [Computer software]. SIMULIA, Providence, RI.
Amadei, B., and Goodman, R. E. (1981). “A 3D constitutive relation for fractured rock masses.” Proc., Int. Symp. on Mechanical Behavior of Structured Media.
ANSYS [Computer software]. ANSYS, Canonsburg, PA.
Bobet, A. (2011). “Lined circular tunnels in elastic transversely anisotropic rock at depth.” Rock Mech. Rock Eng., 44(2), 149–167.
Chen, Z. Y. (1994). Analytical method of rock mechanics analysis, China Coal Industry Publishing House, Beijing.
Fossum, A. F. (1985). “Effective elastic properties for a random jointed rock mass.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22(6), 467–470.
Gerrard, C. M. (1982a). “Elastic moduli of rock masses having one, two and three sets of joints.” Int. J. Rock. Mech. Min. Sci. Geomech. Abstr., 19, 15–23.
Gerrard, C. M. (1982b). “Equivalent elastic moduli of a rock mass consisting of orthohombic layers.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 19, 9–14.
Gerrard, C. M. (1982c). “Joint compliances as a basis for rock mass properties and the design of supports.” Int. J. Rock. Mech. Min. Sci. Geomech. Abstr., 19, 285–305.
Hefny, A. M., and Lo, K. Y. (1999). “Analytical solutions for stresses and displacements around tunnels driven in cross-anisotropic rocks.” Int. J. Numer. Anal. Methods Geomech., 23(2), 161–177.
Kargar, A. R., Rahmannejad, R., and Hajabasi, M. A. (2014). “A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method.” Int. J. Solids Struct., 51(6), 1475–1482.
Kolymbas, D., Wagner, P., and Blioumi, A. (2012). “Cavity expansion in cross-anisotropic rock.” Int. J. Numer. Anal. Methods Geomech., 36(2), 128–139.
Kulatilake, P. H. S. W., Wang, S., and Stephansson, O. (1993). “Effect of finite size joints on the deformability of jointed rock in three dimensions.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(5), 479–501.
Lekhnitskii, S. G. (1968). Anisotropic plates, Gordon and Breach, New York.
Lekhnitskii, S. G. (1981). Theory of elasticity of an anisotropic body, Mir Publishers, Moscow.
Lu, A. Z., Zhang, L. Q., and Zhang, N. (2011). “Analytic stress solutions for a circular pressure tunnel at pressure and great depth including support delay.” Int. J. Rock Mech. Min. Sci., 48, 514–519.
Lu, A. Z., Zhang, N., and Kuang, L. (2014). “Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay.” Int. J. Rock Mech. Min. Sci., 70, 69–81.
Lu, A. Z., Zhang, N., and Qin, Y. (2015a). “Analytical solutions for the stress of a lined non-circular tunnel under full-slip contact conditions.” Int. J. Rock Mech. Min. Sci., 79, 183–192.
Lu, A. Z., Zhang, N., Zhang, X. L., Lu, D. H., and Li, W. S. (2015b). “Analytic method of stress analysis for an orthotropic rock mass with an arbitrary shaped tunnel.” Int. J. Geomech., 04014068.
Manh, H. T., Sulem, J., and Subrin, D. (2013). “Semi-analytical solution for stresses and displacements in a tunnel excavated in transversely isotropic formation with non-linear behavior.” Rock Mech. Rock Eng., 46(2), 213–229.
Manh, H. T., Sulem, J., and Subrin, D. (2015). “A closed-form solution for tunnels with arbitrary cross section excavated in elastic anisotropic ground.” Rock Mech. Rock Eng., 48(1), 277–288.
Morland, L. W. (1976). “Elastic anisotropy of regularly jointed media.” Rock Mech., 8(1), 35–48.
Muskhelishvili, N. I. (1963). Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, Netherlands.
Salamon, M. D. G. (1968). “Elastic moduli of a stratified rock mass.” Int. J. Rock. Mech. Min. Sci., 5, 519–527.
Singh, B. (1973a). “Continuum characterization of jointed rock masses: Part I—The constitutive equations.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 10(4), 311–335.
Singh, B. (1973b). “Continuum characterization of jointed rock masses: Part II—Significance of low shear modulus.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 10(4), 337–349.
Zhang, Z., and Sun, Y. (2011). “Analytical solution for a deep tunnel with arbitrary cross section in a transversely isotropic rock mass.” Int. J. Rock Mech. Min. Sci., 48(8), 1359–1363.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 9 • September 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Sep 2, 2015
Accepted: Dec 20, 2016
Published online: Apr 12, 2017
Published in print: Sep 1, 2017
Discussion open until: Sep 12, 2017
Authors
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.