Abstract
Based on the unified strength theory and non-associated flow rule, with the consideration of the effects of intermediate principal stress and dilation characteristics, the analytical expressions of surrounding rock stress, displacement and plastic zone radius were obtained. Then the influences of the intermediate principal stresses and dilation angles on the surrounding rock stress, displacement and the plastic zone radius were analyzed by engineering example. The analysis shows that surrounding rock stress distribution and plastic zone radius have close relations with the intermediate principal stress. With the increase of the intermediate principal stress coefficient, the ultimate strength of surrounding rock increased, but the plastic zone radius shows a decreasing trend. The displacement of plastic zone is not only related to the intermediate principal stress coefficient, but also to the dilation angle. The displacement of plastic zone increased with the increase of dilation angle, and the displacement of plastic zone decreased with the increase of the intermediate principal stress coefficient.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bobet A (2009) Elastic solution for deep tunnels. Application to excavation damage zone and rockbolt support. Rock Mech Rock Eng 42(2):147–174. https://doi.org/10.1007/s00603-007-0140-0
Fraldi M, Guarracino F (2009) Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 46(4):665–673. https://doi.org/10.1016/S0020-7403(97)00058-1
Huang X, Zhang J, Yang L, Yang S, Wang X (2016) Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory. Int J Min Sci Technol 26(5):819–823. https://doi.org/10.1016/j.ijmst.2016.05.043
Lubliner J (2008) Plasticity theory. Courier Corporation, Chelmsford
Massinas SA, Sakellariou MG (2009) Closed-form solution for plastic zone formation around a circular tunnel in half-space obeying Mohr–Coulomb criterion. Geotechnique 59(8):691–701. https://doi.org/10.1680/geot.8.069
Ogawa T, Lo KY (1987) Effects of dilatancy and yield criteria on displacements around tunnels. Can Geotech J 24(1):100–113. https://doi.org/10.1139/t87-009
Park KH, Tontavanich B, Lee JG (2008) A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses. Tunn Undergr Space Technol 23(2):151–159. https://doi.org/10.1016/j.tust.2007.03.002
Serrano A, Olalla C, Reig I (2011) Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws. Int J Rock Mech Min Sci 48(6):878–887. https://doi.org/10.1016/j.ijrmms.2011.06.008
Sharan SK (2005) Exact and approximate solutions for displacements around circular openings in elastic–brittle–plastic Hoek–Brown rock. Int J Rock Mech Min Sci 42(4):542–549. https://doi.org/10.1016/j.ijrmms.2005.03.019
Wittke W (1990) Rock mechanics. Springer, Berlin
Yang XL, Huang F (2011) Collapse mechanism of shallow tunnel based on nonlinear Hoek–Brown failure criterion. Tunn Undergr Space Technol 26(6):686–691. https://doi.org/10.1016/j.tust.2011.05.008
Yang XL, Xu JS, Li YX, Yan RM (2016) Collapse mechanism of tunnel roof considering joined influences of nonlinearity and non-associated flow rule. Geomech Eng 10(1):21–35. https://doi.org/10.12989/gae.2016.10.1.021
Yu MH, Zan YW, Zhao J, Yoshimine M (2002) A unified strength criterion for rock material. Int J Rock Mech Min Sci 39(8):975–989. https://doi.org/10.1016/S1365-1609(02)00097-7
Zareifard MR, Fahimifar A (2014) Elastic–brittle–plastic analysis of circular deep underwater cavities in a Mohr–Coulomb rock mass considering seepage forces. Int J Geomech 15(5):04014077. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000400
Zhang C, Zhao J, Zhang Q, Hu X (2012) A new closed-form solution for circular openings modeled by the unified strength theory and radius-dependent Young’s modulus. Comput Geotech 42:118–128. https://doi.org/10.1016/j.compgeo.2012.01.005
Acknowledgements
The research described in this paper was financially supported by the Liaocheng University Research Fund (No. 318051703).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, W. Analysis of Deformation of Circular Roadway Considering Effects of Intermediate Principal Stress and Dilatancy. Geotech Geol Eng 38, 529–536 (2020). https://doi.org/10.1007/s10706-019-01043-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-019-01043-4